Mineral Physics Crystallography A Handbook of Physical Constants9780875908526
Mineral Physics Crystallography A Handbook of Physical Constants9780875908526
Mineral Physics Crystallography A Handbook of Physical Constants9780875908526
Reference
Shelf
AGU
Reference
Shelf
Mineral
Physics
&Crystallography
AHandbook
ofPhysical
Series.
QE366.8.M55
1995
549'. I--de20
95-3663
CIP
ISBN
0-87590-852-7
ISSN
1080-305X
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onacid-free
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Washington, DC 20009
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Published by
American Geophysical Union
Printed
in the United
States of
CONTENTS
Preface
Thomas
J. Ahrens
vii
and Donald
G. Isaak
64
Knittie
98
143
218
PlasticRheology
of Crystals
(2-10)
J.P.
Poirier
237
C. Presnall
CONTENTS
F. Stebbins
303
McCaramon
332
PREFACE
Severalgenerations
of solidEarthscientists
havefoundthesehandbooks'to
be themost
frequentlyuseditem in their personallibrary. The first versionof thisHandbookwas
editedby F. Birch, J. F. Schairer,and H. Cecil Spicerand publishedin 1942 by the
GeologicalSocietyof America(GSA) as SpecialPaper36. The secondedition,edited
by SydneyP. Clark, Jr., was alsopublishedby GSA as Memoir 92 in 1966. Since
1966, our scientificknowledgeof the Earth andplanetshasgrown enormously,spurred
by thediscoveryandverificationof platetectonics
andthesystematic
explorationof the
solar system.
The presentrevisionwas initiated,in part, by a 1989 chanceremarkby Alexandra
NavrotskyaskingwhattheMineral Physics(nowMineral andRockPhysics)Committee
of the American GeophysicalUnion could producethat would be a tangible useful
product. At the time I responded,"updatethe Handbookof PhysicalConstants."As
soon as thesewords were uttered, I realized that I could edit sucha revised Handbook.
Carl Agee
Thomas
Thomas
Thomas Herring
George Rossman
Joel Ira
John Sass
Andreas K. Kronenberg
Robert A. Langel
John Longhi
Guenter W. Lugmair
Stephen Mackwell
Surendra
Gerald
Maureen
J. Ahrens
Orson
Anderson
Don Anderson
George H. BrimhaH
John Brodhok
J. Michael
Brace
Buffett
Robert
Clement
Robert
Brown
Butler
Chase
Creaser
Heaton
M.
Mavko
Ricardo
Schwarz
Doug E. Smylie
Carol
Stein
Steiner
Herbert
Edward Stolper
Stuart Ross Taylor
JeannotTrampert
Palme
Alfred
Larry Finger
Michael Gaffey
Carey Gazis
RichardH. Rapp
JustinRcvcnaugh
Rich Reynolds
Robert Reynolds
Michael
Yanick
William W. Hay
K. Saxena
Schmucker
Lars Stixrude
Dean
Gumis
Ulrich
Walter D. Mooney
Veronique Dchant
G. D uba
Frank
Presnall
Ricard
Richter
oo
Marius
Richard
John M.
Yuk
Vassiliou
P. Von Herzen
Wahr
b,andcinngstrom
units(10-l m)andinter-axial
angles
ct,[3,indegrees,
unitcellvolume
in/k3,molarvolume
in
cm3, calculated
densityin Mg/m3, anda reference
to the
completecrystalstructuredata.
To facilitategeochemical
andgeophysical
modeling,data
for pure synthetic end members are presented when
available. Otherwise, data are for near end-member natural
samples.
For manyminerals,structure
data(or samples)for
pure end membersare not available,and in thesecases,
indicatedby an asteriskafter the mineralname,datafor an
impure, natural sample are presentedtogether with an
approximateidealformulaand formulaweightand density
calculated from the ideal formula.
studies.
composing
the crustof theEarthas well as highpressure
synthetic
phasesthatarebelievedto compose
thebulkof the
idealformulaweight,crystalsystem,spacegroup,structure
type,Z (numberof formulaunitspercell),unitcelledges,a,
naturalsamples.
Reference
Shelf 2
Copyright1995by theAmericanGeophysical
Union.
CRYSTALLOGRAPHIC
DATA
FOR MINERALS
oo
oo
SMYTH
AND
McCORMICI
'
oo
z
CRYSTALLOGRAPHIC
DATA
FOR
,o
r.q
,.-,
,.-.,
MINERALS
SMYTH
AND
(--,i
,,,-,
c5
o,
o,
'O
oo oo
'
McCORMICK
CRYSTALLOGRAPHIC
DATA
FOR MINERALS
oooo00,,("',10
SMYTH
'"'
'-'
oo f'-. oo
AND
McCORMICK
CRYSTALLOGRAPHIC
SMYTH
AND
McCORMICK
10
oo
SMYTH
Acknowledgements.
The authorsthankStephenJ. Guggenheim
(University of Illinois) and two anonymousreviewersfor con-
AND
McCORMICK
11
NationalScienceFoundation
GrantEAR 91-05391andU.S. Dept.
of EnergyOffice of BasicEnergySciences.
structivecriticismof themanuscript.
This workwassupported
by
REFERENCES
a structural
a detailed
refine-ment
HarvardUniversity,440p., 1985.
7. Angel, R.J., L.W. Finger,R.M. Hazen,
M. Kanzaki, D.J. Weidner, R.C.
Liebermann, and D.R. Veblen, Struc-
1989.
behavior
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structure
cristalline
du
cinabre
520 1956.
Edelamblygonits LiA1PO4(OH,F),
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17. Baur, W.H., Atomabstaende und Bil-
typecompounds
IV. SiO2,GeO2,anda
comparison with other rutile-type
compounds, Acta Cryst. B27,
2133-2139, 1971.
21. Beran, A. and J. Zemann, Refinement
and comparison of
1979.
the crystal
structures of a dolomite
and of an
1985.
1969.
1973.
microcline,
M. Stewart,On cooperitc,
braggitc,and
vysotskite,Am. Mineral., 63,832-839,
1978.
1984.
12
CRYSTALLOGRAPHIC
Randaccio, Cation-site
DATA
FOR
MINERALS
location in
1982.
of
whitlockite
from
the
An X-ray andneutrondiffractionstudy
of hydrouslow cordierite,Am. Mineral., 62, 67-78, 1977.
46. Cole, W.F., and C.J. Lancucki, A
refinement of the crystal structureof
with discussion
of someaspectsof the
stereochemistry of calcite type
oxide
1981.
Crystal
1976.
forsterire,
1970.
constants
1956.
stxucture refinement of
solutions: I. Lattice
Mineral.,
58,
833-841, 1971.
Galli, E., G.
Gottardi,
and D.
SMYTH
Ref'mement of the
transition of mo--
1977.
79. Gramlich-Meier,
of the zeolite
ferrierite.
Z.
cancrin-
of zinnwaldite-lM
in sub-
1980.
AND
McCORMICK
13
14, 334-345,
1976.
1973.
1979.
of
anatase
at
several
temperatures,
Z. Krist., 136, 273-281,
1989.
1987.
1972.
strukturdesmonoklinentief tridymits,
Acta Cryst.,B32, 2486-2491, 1976.
112. Kato, T., and Y. Miura, The crystal
structuresof jarosite and svanbergite,
Mineral. J., 8, 419--430, 1977.
B.C.
Frazer, and I.
Nukleonik, 5,
41-48,
1963.
14
CRYSTALLOGRAPHIC
DATA
FOR MINERALS
diffraction
measurements,
parametersfor thewurzitestructureof
ZnS and ZnO using powder neulxon
diffraction, Acta Cryst., C45, 18671870, 1989.
122.
Koto,
K.
and
N.
Morimoto,
Superstructure
investigationof bornitc, CusFeS4,by the modifiedpartial
pattersonfunction,Acta Cryst., B31,
2268, 1975.
123. Krstanovic, I., Redetermination of
oxygenparameters
in xenotime,YPO4,
Z. Kristal., 121, 315-316, 1965.
1959.
of
sodium
sulfate
3502-3510,
the structures
of potassiumsulfateand
1978.
1984.
in-
1973.
Struk-
turverfeinemngvon sodalith,NasSi6
AIaO2nC12,
Acta Cryst.,23, 434-436,
1967.
crystalstructureof a naturalgehlenite,
Ca2A1A1Si)2Ov,Cartad. Mineral., I0,
822-837
potassiumchromate:the effect of
1970.
polytypism,
587-598, 1982.
of alunite
and
syntheticjarosite,NeuesJ. Mineral.
Mortat., 406-417, 1976.
force
constants
of
barite
150.Mofimoto,N., D. E. ApplemanandH.
T. Evans, The crystal structuresof
clinoenstatiteandpigeonitc,Z. Krist.,
114, 120-147, 1960.
151. Morimoto, N., M. Tokonami, M.
1899-1903, 1972.
153. Mottier, L., J. J. Pluth, andJ. V. Smith,
382, 1984.
141. Mazzi, F., A.O. Larsen, G. Gottardi,
and E. Galli, Gonnardite has the
tetrahedral
framework
of
natrolite:
Refinementof thecrystalstructures
of
realgar,AsS and orpiment,As2S3,Z.
Krist., 136, 48-65, 1972.
SMYTH
1977.
1960.
diffraction
determination
of
potassium
nitrate
at25Cand100C,
J. of Phys.,C6, 201-211, 1973.
160. Noda, Y., K. Matsumoto, S. Ohba, Y.
Saito, K. Toriumi, Y. Iwata, and I.
Shibuya,Temperaturedependenceof
atomic thermal paramters of lead
chalcogenides,
PbS, PbSe and PbTe,
Acta Cryst.,C43, 1443-1445, 1987.
161. Novak, G. A., G. V. Gibbs,The crystal
chemistryof the silicate garnets,Am.
Mineral., 56, 791-825, 1971.
162. Nowack, E., D. Schwarzenbach, W.
Gonschorek, and Th. Hahn, Defor-
mationsdichten
in CoS2 und NiS2 mir
pyritstruktur,Z. Krist., 186, 213-215,
1989.
1973.
refinement
of the
176. Perflik, F., Verfeinerungder kristallstmktur yon claudetit (As203), Mortars. Chem., 106, 755-762, 1975.
549-557, 1974.
cation
distribution
in
1400Cand20GPa,Am.Mineral.,77,
681-684, 1992.
167. Papamantellos,
P. Verfeinerungder
T1203-strukturmittels neutronenbeu--
and
1969.
59,
170-176, 1978.
178. Perrotta, A. J., and J. V. Smith, The
try of calciumTschermak'spyroxene,
Mineral.,
1971.
structure
Am.
15
inversion,
McCORMICK
AND
16
CRYSTALLOGRAPHIC
DATA
FOR
MINERALS
Mg2Si206,Co2Si206,andFe2Si206,Z.
Krist., 156, 279-297, 1982.
198. Sass, R.L., R. Vidale, and J. Donohue,
Interatomic
distances
and
thermal
202.
1987.
1976.
1969.
Fischer,
I, Advancesin ChemistrySeries,101,
259-265, 1971.
203. Schutte, W. J., J. L. de Boer, and F.
Jellinek,Crystalstructures
of tungsten
disulphideand diselenide,J. Solid St.
Chem., 70, 207-209, 1987.
204. Shintani, H., S. Sato, and Y. Saito,
Electron-densitydistributionin futile
crystals,Acta Cryst.,B31, 1981-1982,
1975.
91,988-992,
1986.
K. Egorov-Tesmenko,
andN. V. Belov,
Crystal structure of willemite,
Zn2SiO4, Kristal., Dokl., Akad. Nauk
USSR, 237, 581-583, 1977.
208. Smith, D. K., and H. W. Newkirk, The
crystal structure of
badOeleyite
53, 1139-
03, ActaCryst.,B30,458--461,1974.
217. Svennson, C., Refinement of the
1975.
159-170, 1982.
220. Takeuchi, Y., T. Ozawa, T. Ito, T.
comments
on
the
of Si tetrahedra in sili-
minerals
from
the
and
their
occurrence
in
tallstrukturund magnetischenstruktur
des ferberits FeWO4, Z. Krist., 124,
192- 219 1967.
crystalchemistryof gismondines:
the
non-existenceof K-rich gismondines,
Bulletin de Mineralogie, 107, 805812, 1984.
232.Willis,
B.T.M.,Anomalous
behavi
ur
of the neutron reflexions of fluorite,
axinite
ungvonWolframitenundColumbiten.
deformation
expansionandhightemperature
crystal
chemistryof theA12SiO5polymorphs,
Am. Mineral., 64,573-586, 1979.
234. Winter, J. K., F. P. Okamura, and S.
Ghose,A high-temperaturestructural
studyof highalbite,monalbite,andthe
analbite-monalbitephase transition,
Am. Mineral., 64,409-423,
1979.
SMYTH
par processus
hydrothermal,Bull. Soc.
Fr. Mineral. Cristallogr., 94, 549-550,
1971.
thermal
vibration
in ZnX
characters,
Acta
system Ni-As,
1273-1296,
1961.
AND McCORMICK
17
1977.
ThermodynamicPropertiesof Minerals
AlexandraNavrotsky
1. INTRODUCTION
(}V/}P)T.
Forsolids,
Cp - Cvisontheorder
ofa few
percent of Cv, and increaseswith temperature. The
vibrationalheatcapacitycanbe calculated
usingstatistical
mechanicsfrom the densityof states,whichin turncanbe
modeledat variousdegreesof approximation[20]. The
magneticcontributions,importantfor transitionmetals,
play a major role in iron-bearing minerals [32].
Electronictransitionsare usuallyunimportantin silicates
but may become significant in iron oxides and iron
silicatesat high T and P. Order-disorder
is an important
complicationin framework silicates(A1-Si disorderon
thermochemical data [4, 5, 7, 9, 10, 13, 15, 16, 18, 19, 31]
tetrahedral
sites),
in spineIs
(M2+-M
3+ disorder
over
octahedral and tetrahedral sites) and in olivines,
CAPACITIES
The isobaricheatcapacity,
Cp, is the temperature
derivative
of theenthalpy,
Cp= (dH/}T)p.
Forsolids,
Cp
is virtually independentof pressurebut a strongfunction
pyroxenes,amphiboles,and micas(cationdisorderover
severalinequivalentoctahedralsites). Thesefactorsmust
be consideredfor specificmineralsbut detaileddiscussion
is beyondthe scopeof thisreview.
of temperature
(seeFig. 1). Contributions
to Cp arise
from latticevibrations,andfrom magnetic,electronic,and
positional order-disorder. The relation between heat
capacity
at constant
pressure,
Cp, andthatat constant
volume,
Cv = (}E/}T)v,
isgiven
byCp- Cv=TVo2/B,
where T = absolutetemperature,V = molar volume, o =
thermalexpansivity
= (l/V) (}V/}T)pand 13=
compressibility = inverse bulk modulus = -(l/V)
gasconstant,
n thenumber
ofatoms
performula
unit).Cp
is then 5-10% larger than 3nR and varies slowly and
roughlylinearlywith temperature
(seeFig. 1).
Table 1 lists heat capacities for some common
minerals. The values at high temperature may be
compared with the 3nR limit as follows: Mg2SiO4
(forsterite)
3nR= 175J/K.mol,Cp at 1500K = 188
J/K-mol;
MgAI204(spinel)
3nR= 188J/Komol,
Cpat
1500 K = 191 J/Komol. Thus the Dulong and Petit limit
givesa usefulfirst orderestimateof the hightemperature
heat capacityof a solid, namely 3R per gram atom,
irrespective
of structural
detail.
The entropy,
A. Navrotsky,PrincetonUniversity,Departmentof Geological
and GeophysicalSciencesand PrincetonMaterials Institute,
Guyot Hall, Princeton,NJ 08544
Reference
ST=IoT(Cp
/ T)dT
Shelf 2
18
(1)
NAVROTSKY
T(K)
0
400
19
800
1200
1600
200
160
Thesharpdependence
of Cp on T at intermediate
temperature
makesit difficultto fit Cp by algebraic
120
express.
ionof theMaier-Kelley
form,[31]
i
Cp=A+BT+CT-0-5
+DT-2
(2)
,40
Cp=3nR[
1+kI T-1+k2T'2+k3T-3]+
lOO
(3)
A + BT+ Cp (disordering)
200
'r(K)
Because
differentauthorsfit Cp datato a varietyof
Table 1. HeatCapacities
andEntropies
of Minerals(J/(K-mol))
298 K
Cp
1000K
1500 K
O
S
,
MgO (periclase)
A1203 (corundum)
"FeO" (wustite)
Fe203 (hematite)
Fe30 4 (magnetite)
TiO2 (ruffle)
FeTiO3 (ilmenite)
Fe2TIO4 (titanomagnetite)
MgA1204 (spinel)
Mg 2SIO4 (forsterire)
MgSiO3 (enstatite)
NaAISi308 (low albite)
KAISi 308 (microcline)
Mg 3AI2Si3012 (pyrope)
Ca3AI 2Si3012 (grossular)
CaSiO3 (wollastonite)
CaSiO3 (pseudowollastonite)
CaMgSi206 (diopside)
Mg 2AI2Si5018 (cordierite)
CaCO3 (calcite)
MgCO 3 (magnesite)
CaMg(CO3)2 (dolomite)
Dala from [5,311.
37.8
79.0
26.9
50.9
51.2
124.9
82.2
180.2
53.1
132.1
103.5
232.3
48.12
103.9
57.6
87.4
55.8
148.5
121.4
252.7
63.6
144.6
145.3
310.5
150.8
146.1
206.0
390.2
201.0
471.5
55.1
50.3
73.2
129.2
79.5
160.1
99.5
105.9
133.7
249.3
155.0
307.4
463.4
142.3
168.9
197.5
375.1
243.2
115.9
80.6
178.3
264.5
191.3
339.5
117.9
95.2
175.3
277.2
187.7
350.8
127.6
243.5
269.1
82.1
67.9
121.3
192.9
205.1
207.4
312.3
530.1
202.4
214.2
310.3
533.8
325.5
222.0
474.0
730.8
330.1
255.5
491.7
773.0
85.3
82.0
123.4
213.4
86.5
87.5
122.3
217.6
132.3
166.5
143.0
248.9
401.7
269.7
506.3
452.3
407.2
698.3
1126.6
753.6
1420.9
220.2
83.5
91.7
124.5
76.1
65.1
131.5
190.5
157.5
155.2
253.1
406.0
20
THERMODYNAMICS
600
I i . i . i
IJq
500
400-
liquid
Tg
300
.'
200
la
20O
'""''
100'
0
300
.-',,,
.- 600 9{0crystal
12'00
15'00
400
Temperature
1800
800
12'00 16'00
Temperature
(K)
(K)
Table
2.
HeatCapacities
of Glasses
andLiquidsandGlassTransition
Temperatures
,
Composition
SiO2
Cpglass
298K
Cpglass
(atTg)
J/mol-K
J/mol-K
38[311
74[28,291
Tg
(K)
Cpliquid
J/mol-K
1607128,291
81128,291
CaMgSi206
170a
256[28,291
1005[28,29]
335128,29]
NaAISi308
2101311
321128,291
1096128,291
347128,291
KAISi308
209[31!
316128,291
1221128,291 338128,291
CaAI2Si20
8
2111311
334128,29]
1160128,29!
Mg2SIO4
424128,29]
268/11,12l
Na2Si205
217128,291
703128,291
263128,29]
K2Si205
226128,29!
770128,29!
259128,29!
CaSiO
3
871301
131128,29,301
1065
167128,29]
Mg3AI2Si3012
330a
516128,291
1020
679128,29]
Mg2A14Si5018
460a
731128,291
1118
928128,29]
aEstimated
from highertemperature
dataandfrontcomparison
withc7stalline
phases.
2000
NAVROTSKY
16], Berman [5], JANAF [18], and Fei et al. [9] for such
equations.
In glass-formingsystems,seeFig. 2, the heatcapacity
of the glassfrom room temperatureto the glasstransition
is not very different from that of the crystallinephase.
oxide
components
in glasses
andmelts,
Cp,.,aregiven
in
Table 3.
ForCaMgSi206Cp, glass
= 170J/moloK
at298K, 256
J/moloK
at 1000K; Cp,crystal
= 167J/moloK
at298K,
249 J/moloKat 1000K [21]. At Tg, the viscosity
3. MOLAR
VOLUME,
ENTROPY,
ENTHALPY
minerals
from
the elements
aA + bB + cC + n/2 02 = A aBbCcOn
(5)
and
(6)
(4)
Glass
[291
298 K
OF
FORMATION
Cp=X
i 2p
i
21
Liquid122,2833!
400 K
1000 K
1500 K
SiO2
44.04
52.39
70.56
82.6
TiO2
44.92
58.76
84.40
109.2
A1203
79.22
96.24
124.98
170.3
Fe203
94.89
115.74
143.65
240.9
FeO
43.23
47.17
70.28
78.8
35.09
42.89
56.60
94.2
CaO
43.00
45.67
57.66
89.8
Na20
74.63
79.09
96.64
97.6
K20
75.20
79.43
84.22
98.5
B203
62.81
77.67
120.96
H20
46.45
62.04
78.43
22
THERMODYNAMICS
ii
i
i I
ii
i
i
NAVROTSKY
----_.,.
(i) .....---"'"'"
2)
A+ 02=AO
(7)
_.., 3)
-:too
..............
-,-,
.,.o.'.
..........
::5;
.........
s_.....-t16)
','.s'"" '"
and
23
...C."""
. .....
. ..........
.,,.,,
AOn+- 02=AOm+
n
(8)
-40O
e.g.QFM (quartz-fayalite-magnetite),
NNO (nickel-nickel
(andalusite)
AI-I,ox,
298=-1.1 kJ/mol;for MgSiO3
(enstatite)
AI-I,o,298
= -35.6kJ/mol,andfor CaSiO3
(wollastonite)
AI-f,
ox,
298= -89.4kJ/mol.Entropies
of
formationof ternaryoxidesfrom binarycomponentsare
generallysmall in magnitude(-10 to +10 J/moloK)unless
majororder-disorder
occurs.
4. ENTHALPY
AND
TRANSFORMATION
ENTROPY
OF PHASE
AND MELTING
AG,
=0=AH,
- TAS,
(9)
At constanttemperature,a thermodynamically
reversible
phasetransitionoccurs with increasingpressureif the
highpressurephaseis denserthanthelow pressure
phase
.O
:..-'
,-'
O?-
-looo
""
-. ......
%!-%'"'"_)4.o,
o_-__
...........
,_., _o..
o.o.ooo---"
..,,oO
........
_
(4)
2H2
* 02'2H20
(S) 6FeO * 02- 2Fe304
-1200 ".C,o
(6)
(7)
(:e) 2Fe
9)
300
8(0
,3)0
02 - FeO
C + 02
- C02
,8;0
Temperature (K)
At
constant
(atmospheric)
pressure, a
thermodynamically
reversiblefirst orderphasetransition
occurswith increasingtemperatureif both the enthalpy
andentropyof the hightemperature
polymorphare higher
than thoseof the low temperaturepolymorphand, at the
transformation
temperature
..........'::.,.,:::_
..............................
.............
ro' .............
flP AV(P,T)dP
(1o)
atm
An equilibriumphaseboundaryhasits slopedefined
by the Clausius- Clapeyronequation
(dP/dT)equi
I = AS/AV
(11)
24
THERMODYNAMICS
AS(J/mol
K)
AV(cm3/mol)
Mg2SIO4 (a =
_3.16a [21
39.1+ 2.6121
-15.0+ 2.4[2]
-4.14[2]
Fe2SIO4(or= [)
9.6+ 1.3121
-10.9+ 0.8[2]
-3.20[21
Fe2SiO4(or= h,)
3.8+ 2.4121
-14.0+ 1.9121
-4.24[21
MgSiO3(px= il)
59.1+ 4.3131
-15.5+ 2.0[31
-4.94131
MgSiO
3 (px= gt)
35.7+ 3.0191
-2.0+ 0.5[9!
-2.8319!
MgSiO3(il = pv)
51.1+ 6.6//7/
+5+ 4[/71
-1.89/17/
Mg2SiO40/)=MgSiO3(pv)+MgO
96.8 + 5.81/71
+4 + 41171
-3.791171
SiO2(q = co)
2.7+ 0.5l/1
-5.0+ 0.4l/1
-2.05lll
49.0+ 1.7lll
-4.2+ 1.7III
-6.63[11
a zll-IandASarevalues
at1 attonear1000K,AVisAV298,for
alllistings
intable,oc= olivine,
fi = spinelloid
orwadsleyite,
y=
spinel,px = pyroxene,il = ilmenite,gt = garnet,pv = perovskite,q = quartz,co = coesite,st = stishovite
Table6. Thermodynamic
Parameters
for OtherPhaseTransitions
Transition
AH o
(kJ/mol)
SiO2 ( a-quartz= [3-quartz)
SiO2 ( [3-quartz= cristobalite)
0.47a,b
2.94[5]
5.6[23]
5.0[311
3.88[5!
-8.13[5!
-0.37[5]
1.59151
-0.17[251
2
(mtile = quartz)
CaSiO3 (wollastonite= pseudowollastonite)
AI 2SiO 5 (andalusite= sillimanite)
AI 2SiO5 (sillimanite= kyanite)
MgSiO3 (ortho= clino)
MgSiO3 (ortho= proto)
FeSiO3 (ortho= clino)
0.25[251
MnSiO3 (rhodonite= pyroxmangite)
MnSiO3 (pyroxmangite= pyroxene)
13.5/311
NaAISi30 8 (low albite= highalbite)
14.0
11.1[5]
- 1.03
0.88125!
a Treatedasthougit
allfirstorder,though
a strong
higher
ordercomponent.
bAHandASarevalues
near
1000
K,AVisAV298
foralllistings
intable.
AS o
(J/K-mol)
0.35
1.93
4.0
3.6
4.50
-13.5
O.16
1.27
-0.03
AV o
(cm3/mol)
0.101
0.318
11.51
0.12
-0.164
-0.571
-0.002
0.109
-0.06
-0.39
-0.39
-2.66
-0.3
0.40
15.0
0.40
0.027
'Compound
Vitrification
Fusion
All (kJ/mol)
Melting Point
All(T)
(kJ/mol)
T(K)
MgO
CaO
107.5+ 5.4[28]
9.4 + 1.01281
8.9 + 1.01281
31.3 + 0.21281
2323
1700b
1999
1652
42 + 11281
2163
114+
1834a
77 + 5 [281
89 + 10[28]
62+ 41281
57+ 31281
138+ 2128]
63 + 201281
56 + 4128]
134+ 41281
20+ 4[ 28]
243 + 81281
346+ 101281
1490
25.5+ 0.41261
CaSiO3 (wollastonite)
CaSiO3 (pseudowollastonite)
CaMgSi206 (diopside)
NaAISi308 (highalbite)
KAISi308 (sanidine)
CaAI2Si208 (anorthite)
I(2SiO 3
Mg 3AI 2Si3012 (pyrope)
Mg2AI4Si.5018(cordierite)
1770b
1817
85.8+ 0.8[241
51.8+ 08[241
1665
1373
1473 a
77.8+ 0.8[241
9 + 1128!
1830
1249
1500 a
209+ 2161
1740
20 a
aEstimated
roetastable
congruem
melting.
bMelting
ofroetastable
phase.
I
ROCKSALT
PEROVSKITE
+ RUTILE
18
NTO3,22
Fe2SO4.23
MgTO3
22
C oaSO4.17
COT,O3.22
LITHIUMNIOBATE
N2SO4.15
'--'"'/-M
ZnTO3.22
CoGeO3.22
N2GeO4.20
ILMENITE
14
GARNET
CaGeO3.9
03
BaGeO3.9
NTERMEDIATE
z
uJ
STRUCTURES
o IsPINEL
+RUTILE
z
MgSO3,17ZnSO3,12
-[
uJ
FeSO3,8 MgGeO3.3
f-)
CoSO3.9
MgSO3.16
MnSO3.12
PYROXENE
FeSO3,1
MnSO3.7
COS,O3,2
PYROXENOID
OLlVINE
+QUARTZ
I
Fig. 4. Schematic diagram showing phase transitions
observedin analoguesystemsof silicates,germanates,
andtimnates. Numbersrefer to pressurein GPa.
- Fe
600
'-Ni2S104
1000
1400
T(K)
26
THERMODYNAMICS
o
o
o
o
o
(edg)
anssed
(ed9)
anssad
NAVROTSKY
VIII
Vl
200
LIQUID
-
300
27
400
TEMPERATURE (K)
REFERENCES
New calorimetric
and calculation
6.
of
phasediagrams,Phys.Earth Planet.
Inter.,36,
measurenents,
7.
Fei,
Y.
and S. K.
Saxena, A
calculation,
and geophysical
application,J. Geophys.Res., 94,
equilibriain thesystemFe-Mg-Si-O
15,671-15,686, 1989.
Ashida, T., S. Kume, E. Ito, and A.
Thermochemical properties of
inorganic substances, pp. 921,
Springer-Verlag,New York, 1973.
Berman,R. G., Internally-consistent
thermodynamicdata for mineralsin
the systemNa 20-K 20-CaO-MgOFeO-Fe2O3-A1203-SiO2-TIO2-
1986.
Fei, Y.
and S. K. Saxena, An
12.
Fei, Y.,
S. K. Saxena, and A.
1980.
9.
8.
Mao, and B. O.
1991.
11.
thermochemical
Mysen,Experinentaldetermination
of element partitioning and
calculationof phaserelationsin the
MgO-FeO-SiO2 system at high
pressureand high temperature,J.
Geophys. Res., 96, 2157-2169,
McConnell,
Enthalpy effects
associatedwith A1/Si ordering in
anhydrousMg-cordierite,Geochim.
124-134, 1984.
10.
1988.
14.
Mao,
New
transformations
betweencrystallineand amorphous
28
15.
THERMODYNAMICS
internallyconsistent
thermodynamic
dataset
912,1991.
with
uncertainties
and
22.
23.
the systemK20-Na20-CaO-MgO-
MnO-FeO-Fe2O3-A1203-TiO2-
SIO2-C-H2-O2,J. Metamorphic
24.
18.
JANAF,Thermochemical
Tables, 25.
Third Ed., edited by American
Chemical Society and American
19.
20.
Institute
ofPhysics,
1986.
65-126,1985.
21.
29.
30.
1986.
1987.
Hemingway, Thermodynamic
properties
of wollastonite,
pseudowollastonite and CaSiO3
glassandliquid,Europ.J. Mineral.,
3, 475-485, 1991.
31.
K and 1 bar
St.
26.
28.
consistentthermodynamicdataset
melts, Geochirn.Cosmochirn.Acta.,
48, 471-483, 1984.
Chern.,
17,
53-86,
1987.
32.
Oestrike,
and
P.
ManJar,
27. Richet,
P., Viscosity
and
configurationalentropy of silicate
33.
Thermal Expansion
Yingwei Fei
SinceSkinner[75] compiledthethermalexpansiondata
of substances of geological interest, many new
V(T)
=-[1+2.k(1-4kE/Q0)l/2
]
(l)
E=9nRT
I v/r
x3 dx
(2)
formulaandthegasconstant,respectively.
In this model, four parameters,0o, Qo,/, and Vo, are
required to describethe thermal expansionof a solid.
When the thermalexpansionis accuratelymeasuredover
a wide temperaturerange,the four parametersmay be
uniquelydefinedby fitting the experimentaldata to the
model.Furthermore,measurements
on heatcapacityand
bulk moduluscan provide additionalconstraintson the
model.A simultaneous
evaluationof thermalexpansion,
bulk modulus,andheatcapacitythrougha self-consistent
model suchas the Debye model [e.g., 81] is, therefore,
recommended,especiallywhen extrapolationof data is
involved.
MineralPhysicsand Crysta!!ography
A Handbookof PhysicalConstants
AGU
Reference
Shelf 2
29
30
THERMAL
EXPANSION
thermalexpansioncoefficientmay be used
(3)
a(r,r)/a(r)=[v(r,r)/v(r)]ar
V(T) = Vr,exp
a(T)d
(4)
(7)
(8)
and
(5)
2LV(P,T)
i.e.,
(6)
Viiq(T)
-- Xiii,n[1
+ (T- Tr)] +Vcx
(lO)
in Tables 3a-3d.
T range
0.o(10
'6)
ao(104)
a! (10'8)
a2
ref.
[2]
[2]
[2]
Oxides
293-2298
7.3
0.0758
0.1191
-0.0603
293-2298
8.3
0.0773
0.1743
0.0000
293-2298
23.0
0.2276
0.4198
-0.0897
FEI
TABLE 1. (continued)
Names
BeAI204, chrysoberyl
ao(10'6)
T range
ao(10-)
a1(10's)
a2
298-963
6.6
0.0250
1.3569
0.0000
298-963
8.7
0.0490
1.2777
0.0000
0.0000
298-963
7.6
0.0540
0.7315
298-963
23.8
0.1320
3.5227
0.0000
BeO
292-1272
17.8
0.1820
1.3933
-0.4122
CaO
293-2400
33.5
0.3032
1.0463
0.0000
3CaO-A!203
17CaO-7AI203
CaO-AI203
CO304,normalspinel
Cr203, eskolaite
FeA!204, hercynite
FeCr204, chromite
293-1473
19.5
0.2555
0.7564
-0.7490
298-1073
12.3
0.1230
0.0000
0.0000
10.5
0.2232
0.0259
-1.0687
14.8
0.0631
2.8160
0.0000
FeO, wiistite
Fe203, hematite
293-1473
301-995
293-1473
18.6
0.2146
0.1154
-0.2904
293-1273
15.6
0.0977
1.9392
0.0000
293-1273
9.9
0.0513
1.5936
0.0000
V
a
293-873
293-673
K
K
33.9
0.3203
0.0350
0.6293
0.0000
7.9
1.4836
0.0000
293-673
8.0
0.0559
0.7904
0.0000
293-673
23.8
3.8014
Fe304, magnetite
293-843
20.6
0.1238
-0.0353
8.0591
0.0000
0.0000
843-1273
FeTiO3, ilmenit
0.5013
0.1006
0.0000
297-1323
50.1
10.1
0.0000
0.0000
0.0000
7.6
0.0638
0.4031
0.0000
27.9
0.2689
0.3482
0.0000
c
V
297-1323
HfO2
MgAI204, normalspinel
MgA1204,disorderedspinel
MgCr204, picrochromite
MgFe204, magnesioferrite
MgGeO3, ilmenite
Mg2GeO4,olivine
Mg2GeO4,spinel
MgO, periclase
MnO, manganosite
ThO2, thorianite
297-1323
293-1273
293-873
993-1933
15.8
0.1264
1.0368
0.0000
24.9
0.2490
0.0000
0.0000
29.4
0.2940
0.0000
0.0000
293-1473
16.5
0.1430
1.1191
-0.1063
293-1473
20.5
0.3108
1.2118
-1.2773
299-1023
22.4
0.2244
0.0000
0.0000
298-1273
41.1
0.4110
0.0000
0.0000
298- 1273 K
32.1
0.3210
0.0000
0.0000
303-1273
31.6
0.3768
0.7404
-0.7446
V
V
293-1123
293-1273
K
K
34.5
28.5
0.3317
0.2853
1.2055
-0.2094
0.0000
0.0000
TiO
293-1073
22.3
0.1832
1.3236
0.0000
TiO2, rutile
298-1883
8.9
0.0890
0.0000
0.0000
298-1883
11.1
0.1110
0.0000
0.0000
298-1883
28.9
0.2890
0.0000
0.0000
293-1273
24.5
0.2180
1.2446
-0.0920
293-1273
21.2
0.2042
0.2639
0.0000
100-530
9.7
-0.0048
3.4000
0.0000
100-530
25.3
-0.0232
9.2000
0.0000
100-530
0.7
0.0005
0.2000
0.0000
100-530
35.7
-0.0275
12.8000
0.0000
U02.o3, uraninite
Zr02, baddeleyite
K
K
ref.
[30]
[30]
[30]
[30]
[93, cf. 29]
[93]
[75]a
[151
[75]
[49]
[751
[75]
[75]
[75]
[75]
[75]
[75]
[751
[75]
[951
[95]
[95]
[75]
[102]
[102]
[75]
[75]
[3]
[72]
[72]
[86]
[90]
[75, cf. 96]
[75]
[851
[851
[85]
[75, cf. 96]
[751
Hydrous minerals
AIOOH, boehmite
[71
[71
[7]
[71
31
32
THERMAL
EXPANSION
TABLE 1. (continued)
Names
Ca2MgSi802(OH)2
tremolite
KAI2(AISi30lo)(OH)2
muscovite
Mg(OH)2, brucite
T range
ao(10'6)
ao(10'4)
a(10-8)
a2
297-973
12.0
0.1202
0.0000
0.0000
b
c
297-973 K
297-973 K
11.7
5.8
0.1167
0.0583
0.0000
0.00
0.0000
0.00
/ 297-973 K
-2.7
-0.0266
0.0000
0.00
V
a
297-973 K
293-1073 K
31.3
9.9
0.3131
0.0994
0.0000
0.00
0.0000
0.00
b
c
293-1073 K
293-1073 K
11.1
13.8
0.1110
0.1379
0.0000
0.00
0.0000
0.0000
d001
293-1073 K
13.7
0.1367
0.0000
0.0000
V
a
293-1073 K
300-650 K
35.4
11.0
0.3537
0.1100
0.0000
0.0000
0.00
300-650 K
59.0
0.5900
0.0000
0.0000
300-650 K
80.0
0.8000
0.0000
0.00
0.0000
ref.
[83]
[83]
[83]
[83]
[83]
[25]
[25]
[25]
[25]
[25]
[191
[19]
[19]
Carbonates
BaCO3(hexagonal)
1093-1233
-102.0
-1.0200
0.0000
0.0000
1093-1233
297.0
2.9700
0.0000
0.0000
V
a
1093-1233 K
293-673 K
93.0
8.3
0.9300
0.0833
0.0000
0.0000
0.0000
0.0000
b
c
293-673 K
293-673 K'
18.6
35.2
0.1862
0.3520
V
a
293-673 K
297-1173 K
62.2
-3.2
0.6221
-0.0315
0.0000
0.0000
CaCO3, calcit
0.0000
0.0000
297-1173
13.3
0.1922
2.5183
-1.2140
297-1173 K
293-593 K
3.8
-5.6
0.0713
-0.0560
3.3941
CdCO3, otavite
V
a
-1.2140
0.0000
293-593 K
22.7
0.2270
0.0000
0.0OOO
293-593 K
297-973 K
11.5
3.2
0.1150
0.0271
0.0000
0.0000
CaMg(CO3)2,dolomite
V
a
0.6045
-0.1152
297-973
15.6
0.1233
2.2286
-0.3089
V
a
297-973
297-773
K
K
22.8
2.2
0.1928
0.0775
3.1703
-0.5393
MgCO3, magnesite
0.2934
-0.5809
297-773 K
297-773 K
297-773 K
13.2
18.2
1.8
0.0037
0.1686
0.0180
4.2711
0.0000
4.7429
MnCO3, rhodochrosite
c
V
a
0.0000
-1.1618
o.oooo
297-773 K
297-773 K
297-773 K
19.2
22.8
5.4
0.1920
0.2280
0.0540
0.0000
o.oooo
0.0000
o.oooo
FeCO3, siderite
c
V
a
0.0000
0.0000
297-773
16.1
0.1610
0.0000
0.0000
297-773 K
293-1073 K
26.9
7.1
0.2690
0.0508
0.0000
0.0000
SrCO3, strontianite
V
a
0.6630
0.0000
b
c
293-1073 K
293-1073 K
12.1
36.5
0.1107
0.2629
0.3362
0.0000
3.4137
0.0000
293-1073
59.2
0.4982
3.1111
0.0000
CaCO3, aragonite
0.0000
0.0000
0.0000
0.0000
0.0000
[43]
[43]
[43]
[7s]
[75]
[75]
[75]
[53]
[53]
[53]
[5]
[5]
[5]
[70]
[70]
[70]
[53]
[53]
[53]
[69]
[69]
[69]
[64]
[64]
[64]
[75]
[75]
[75]
[75]
FEI
TABLE 1. (continued)
Names
Su!fides
ao(10-6)
T range
ao(10'4)
a (10'8)
a2
ref.
and Sulfates
FeS2, pyrite
PbS, galena
ZnS, sphalerite
293-673
25.7
0.1256
4.3873
0.0000
293-873
58.1
0.5027
2.6125
0.0000
293-1273
17.8
0.2836
0.0000
-0.9537
ZnS, wurtzite
293-1273
6.7
0.0763
0.3815
-0.1885
-0.1274
BaSOn, barite
K2SO4
293-1273
6.5
0.0762
0.1134
293-1273
19.0
0.2136
1.0938
-0.5061
298-1158
20.7
0.2070
0.0000
0.0000
298-1158
25.5
0.2550
0.0000
0.0000
298-1158
17.2
0.1720
0.0000
0.0000
V
a
298-1158 K
293-673 K
63.7
0.6370
0.0000
0.0000
15.5
-0.1713
10.8705
0.0000
293-673
33.4
0.3337
0.0000
0.0000
293-673
42.6
0.1628
8.7701
0.0000
293-673
91.4
0.3252
19.6406
0.0000
293-693
10.7
0.1065
0.0000
0.0000
293-693
5.9
0.0346
0.8280
0.0000
V
a
293-693
27.1
0.2453
0.8700
0.0000
298-1273
12.5
0.1223
0.0963
0.0000
298-1273
8.1
0.0753
0.1918
0.0000
298-1273
2.3
0.0233
0.0000
0.0000
298-1273
22.8
0.2181
0.3261
0.0000
298-1073
2.6
0.0260
0.0000
0.0000
298-1073
-2.9
-0.0290
0.0000
0.0000
298-1073
2.3
0.0230
0.0000
0.0000
293-1473
33.1
0.2883
1.4106
0.0000
293-1473
31.4
0.4601
0.0158
-1.3157
[75]
[75]
[75]
[75]
[75]
[75]
[73]
[73]
[73]
[73]
[75]
[75]
[75]
[75]
Silicates
Akermanite,Ca2MgSi207
Andalusite,A!2SiO5
Beryl, Be3A!9_Si608
Calcium
[31]
[31]
[31]
[97]
[97]
[97]
[97]
[58]
[58]
[58]
silicates
Ca3Si207,rankinite
lS-Ca2SiOa
Ca3SiO5
Cancrinite
293-1273
25.7
0.1852
2.4073
0.0000
298-673
7.0
0.0034
2.2150
0.0000
298-673
16.1
0.0328
4.2629
0.0000
298-673
29.9
0.0364
8.7589
0.0000
[75]
[75]
[75]
[75]
[75]
[75]
Cordierite
Mg2A14Si5O18
(hexagonal)
[5-Eucryptite,LiAISiO4
Feldspars
Celsian,BaAI2Si208
High Albite, NaAISi308
298-873
2.2
0.0220
0.0000
0.0000
298-873
-1.8
-0.0180
0.0000
0.0000
[35]
[35]
298-873
2.6
0.0260
0.0000
0.0000
[35,cf.67]/'
296-920
8.6
0.0860
0.0000
0.0000
296-920
-18.4
-0.1840
0.0000
0.0000
296-920
-1.2
-0.0120
0.0000
0.0000
[66]
[66]
[66]
8.7
0.0605
0.8692
0.0000
9.6
0.0716
0.8114
0.0000
6.6
0.0656
0.0000
0.0000
5.2
0.0523
0.0000
0.0000
293-673
297-1378
297-1378
297-1378K
[75]
[68]
[68]
[68]
33
34
THERMAL
EXPANSION
TABLE 1. (continued)
Names
o0O)
T range
0.1603
-6.0284
0.0000
297-1378 K
297-1378 K
-2.3
-0.0197
-0.1120
0.0000
-2.6
-0.0252
-0.0252
0.0000
297-1378
26.8
0.7621
298-1243
11.7
0.2455
0.0882
0.0000
0.0000
0.9479
ref.
a2
-2.1
298-1243
4.7
0.0371
0.3400
0.0000
298-1243
0.3
-0.0113
0.4618
0.0000
298-1243
0.0000
-2.7
0.0263
-1.7927
298-1243 K
298-1243 K
-5.2
-0.0547
0.0987
0.00
-0.5
0.0061
-0.3641
0.00
298-1243 K
0.1737
22.6
11.2
0.1846
1.7276
0.5719
-0.80
293-1273
15.6
0.1297
0.8683
293-1273
9.7
-0.0097
3.5490
0.0000
293-1273
15.4
0.2199
1.0271
-0.8714
293-1273
8.9
0.1612
0.7683
-0.83
293-1273
10.6
0.1524
0.5038
-O.555O
293-1273
14.1
0.1394
0.0597
0.0000
293-1273
Adularia, Or88.3Ab9.3An2.
4
Microcline, Or83.sAb6.5
Orthoclase,Orr.6Ab32.sAno.6
Plagioclase,Ab99An
Plagioclase,Ab77An23
Plagioclase,Ab50,n
Plagioclase,AbsAn95
a (10's)
297-1378
ao(10'4)
0.0000
0.0000
[75,
24c]
Garnets
Almandite,Fe3A12Si3012
Andradite,Ca3Fe2Si3012
Cacium-richgarnet
Grossularite,Ca3A12Si3012
Pyrope,Mg3AI2Si302
Spessartite,Mn3AI2Si302
Natural garnet(pyrope-rich)
Gehlenite,Ca2AI2SiO7
294-1044
294-963
15.8
0.1776
1.2140
-0.5071
20.6
0.2103
0.6839
-0.2245
20.2
0.2647
0.3080
-0.6617
16.4
0.1951
0.8089
-0.4972
19.9
0.2311
O.5956
-0.4538
17.2
0.2927
0.2726
-1.1560
K
K
23.6
24.0
0.2880
0.2320
0.2787
0.2679
-0.5521
o.oooo
300-1000
292-980
283-1031
292-973
V
V
298-1000
293-1473
K
K
K
Hornblende
293-1273
23.8
0.0000
298-1073
7.5
0.2075
0.0749
1.0270
Kyanite, AI2SiO5
0.0000
o.oooo
298-1073
6.6
0.0661
0.0000
0.0000
298-1073
10.9
0.1095
0.0000
o.oooo
V
V
298-1073
293-1473
K
.
25.1
0.0000
29.8
0.2505
0.2521
1.5285
o.oooo
o.oooo
17tJK
3.9
0.0390
0.00
o.oooo
73K
7.0
0.0700
0.0000
o.oooo
o.oooo
Merwinite, Ca3Mg(SiO4)2
[75]
[75]
[381
[751
[751
[751
[87]
[75]
[75]
[97]
[97]
[97]
[97]
[75]
Mullite,
A!2O3(71.2%)SiO2(28.6%)
53
5--1'
A1203(.o%)SiO2(28.4%)Cr
Al 2O3(62.1%)Si02
(27.4%)Fe
73-[173
5.8
0.0580
0.00
573-1173
16.7
0.1670
0.00
o. oooo
573-1173
3.1
0.0310
0.0000
o.oooo
573-1173
6.2
0.0620
0.0000
o.oooo
573-1173
5.6
0.0560
0.0000
o.oooo
573-1173
573-1173
K
K
14.9
0.1490
0.0000
o.oooo
3.3
0.0330
0.0000
o.oooo
573-1173
7.0
0.0700
0.0000
o.oooo
573-1173
5.6
0.0560
0.0000
o.oooo
573-1173
15.9
0.1590
0.0000
o.oooo
[74]
[74]
[74]
[74]
[74]
[74]
[74]
[74]
[74]
[74]
[74]
[74]
FEI
TABLE 1. (continued)
Nephelines
(Nao.78.22)SiO4
(Nao.59Ko.41)AISiO4
ao(10'6)
T range
Names
ao(10-4)
a1(10'a)
a2
293-1073
11.1
0.0512
1.9931
0.0000
293-1073
8.3
0.0665
O.5544
0.0000
V
a
293-1073
293-1073
K
K
31.3
0.1889
0.1952
4.1498
0.0000
19.5
-0.0211
0.0000
293-1073
19.8
0.2627
-2.1428
0.0000
293-1073
58.5
0.6515
-2.2071
0.0000
CaMgo.97Feo.o7SiO4
298-1068
6.4
0.0855
0.1308
-0.2331
monticellite
298-1068
7.4
0.0965
0.1806
-0.2575
ref.
[75]
[75]
[75]
[75]
[75]
[75]
Olivines
CaMn(MgZn)SiO4
glaucochroite
Mg2SiO4, forsterite
Mg2SiO4, forsterite
Mg2SiO4, forsterite
Mg2SiO4, forsterite
Mn2SiO4, tephroite
Ni2SiO4, Ni-olivine
Fe2SiO4,fayalite
298-1068
10.3
0.1235
0.4236
-0.2891
V
a
298-1068
298-1073
K
K
24.2
0.6733
0.2233
-0.8133
6.5
0.3114
0.0976
298-1073
6.4
0.0953
0.2091
-0.3536
298-1073
7.2
0.1055
0.2783
-0.3852
V
a
298-1073
303-1173
K
K
20.3
0.3007
0.7192
6.6
0.0663
0.3898
-1.1080
-0.0918
303-1173
9.9
0.1201
0.2882
-0.2696
303-1173
9.8
0.1172
0.0649
-0.1929
V
V
303-1173
296-1293
K
K
26.4
30.6
0.3034
0.7422
0.2635
1.4036
-0.5381
0.0000
298-1273
28.2
0.3407
0.8674
-0.7545
-0.3842
-O.3605
300-1300
27.3
0.2854
1.0080
298-1123
5.8
0.0397
0.5249
0.0621
298-1123
8.8
0.1042
0.2744
-0.2188
298-1123
8.0
0.0807
0.3370
-0.0853
V
a
298-1123
K
K
22.6
9.5
0.2307
0.1049
1.0740
0.2093
-0.2898
298-1173
298-1173
8.9
0.0990
0.1746
-0.1387
298-1173
9.0
0.1004
0.1827
-0.1396
V
a
298-1173
298-1123
K
K
27.3
0.3036
0.5598
-0.4204
5.5
0.1050
0.0602
-0.4958
-0.1409
298-1123
7.9
0.0819
0.1629
-0.0694
298-1123
9.9
0.1526
-0.1217
-0.4594
V
a
298-1123 K
297-983 K
26.1
(Mgo.7Feo.3)2SiO4
6.1
0.2386
0.0610
1.1530
o.oooo
-0.0518
0.0000
hortonolite
297-983
9.6
0.0960
o.oooo
0.0000
297-983
9.7
0.0975
o.oooo
o.oooo
297-983
25.5
0.2557
o.oooo
o.oooo
Mgo.75Fel.loMno.15SiO4
296-1173
9.2
0.0916
0.0000
0.0000
hortnolite
296-1173
11.1
0.1109
0.0000
0.0000
296-1173
14.6
0.1456
o.oooo
0.0000
296-1173
35.0
0.3504
0.0000
o.oooo
77-298
8.4
0.0840
o.oooo
o.oooo
0.0000
o.oooo
o.oooo
[45]
[45]
[45]
[45]
[45]
[45]
[45]
[45]
[86]
[86]
[86]
[861
[541
[40]
[61]
[61]
[61]
[45]
[451
[45]
[45]
[911
[911
[91]
[91, 76, 27]
[13]
[13]
[13]
[13]
[27]
[27]
[27]
[27, cf. 79]
Perovskite
MgSiOa
77-298
0.0
[71]
[71]
35
36
THERMAL
EXPANSION
TABLE 1. (continued)
Names
(Mgo.9Feo.1)SiO3
(Mgo.9Feo.1)SiO3
Phenakite,Be2SiO4
Pseudowollastonite,
CaSiO3
Pyroxenes
CaAI2SiO6, CaTs
a1(10-s)
a2
77-298
5.9
0.0590
0.0000
0.0000
77-298
14.5
0.1450
0.0000
0.0000
22.0
298-381K
0.0000
100-250
5.8
0.2200
0.0580
0.0000
0.0000
0.0000
100-250
5.2
0.0520
0.0000
0.0000
100-250
4.5
0.0450
0.0000
0.0000
100-250
15.5
0.1550
0.0000
0.0000
250-373
8.1
0.0810
0.0000
0.0000
250-373
5.4
0.0540
0.0000
0.0000
250-373
5.4
0.0540
0.0000
0.0000
250-373
18.9
0.1890
0.0000
0.0000
V
V
150-373
298-840
K
K
19.0
0.1900
0.0000
0.0000
30.7
0.3156
0.9421
-0.3271
298-963
5.2
0.0520
0.0000
0.0000
298-963
6.4
0.0640
0.0000
0.0000
298-963
16.8
0.1680
0.0000
0.0000
293-1473
27.8
0.2474
1.0096
0.0000
298-1473
8.8
0.0882
0.0000
0.0000
298-1473
12.0
0.1204
0.0000
0.0000
298-1473
8.9
0.0888
0.0000
0.0000
298-1473
27.8
0.2780
0.0000
0.0000
297-1273
7.8
0.0779
0.0000
0.0000
297-1273
2O.5
0.2050
0.0000
0.0000
297-1273
6.5
0.0646
0.0000
0.0000
d100
297-1273
6.1
0.0606
0.0000
0.0000
V
a
297-1273
293-1123
K
K
33.3
0.3330
13.5
0.1350
0.0000
0.0000
0.0000
293-1123
14.5
0.1450
0.0000
0.0000
293-1123
15.4
0.1540
0.0000
0.0000
V
a
293-1123 K
293-973 K
43.8
0.4380
0.0000
0.0000
16.2
0.1620
0.0000
0.0000
Cao.o15Mgo.3osFeo.SiO3
ferrohypersthene
Cao.o15Mgo.3osFeo.SiO3
clinohypersthene
0.0000
293-973
10.4
0.1040
0.0000
0.0000
293-973
13.8
0.1380
0.0000
0.0000
d100
293-973
8.3
0.0830
0.0000
0.0000
293-973
32.7
0.3270
0.0000
0.0000
297-1273
7.2
0.0724
0.0000
-0.0000
297-1273
17.6
0.1760
0.0000
0.0000
297-1273
6.0
0.0597
0.0000
0.0000
297-1273
d100
Cao.15Feo.85SiO3,
FsWo
ao(10'4)
CaMgSi206,diopside
CaFeSi20,hedenbergite
aoO0)
T range
4.8
0.0483
0.0000
0.0000
V
a
297-1273 K
297-773 K
29.8
0.2980
0.0000
0.0000
18.9
0.1890
0.0000
0.0000
297-773
13.3
0.1330
0.0000
0.0000
297-773
15.2
0.1520
0.0000
0.0000
d100
297-773
8.9
0.0893
0.0000
0.0000
297-773
37.6
0.3760
0.0000
0.0000
ref.
[71]
[71]
[71]
[62]
[62]
[62]
[62]
[62]
[62]
[62]
[62]
[62]
[42]
[30]
[30]
[30]
[75]
[26]
[26]
[26]
[26]
[14]
[14]
[14]
[14]
[14, cf. 22]
[78]
[78]
[78]
[78]
[77]
[77]
[77]
[77]
[77]
[14]
[14]
[14]
[14]
[14]
[6o]
[6o]
[6o]
[6o]
[6o]
FEI
TABLE 1. (continued)
Names
FeSiO3, orthoferrosilite
LihlSi206, spodumene
Mgo.sFeo.2SiO3,
bronzite
MgSiO3, enstatite
MgSiO3, protoenstatite
MnSiO3, pyroxmangite
NaAISi206, jadeite
NaCrSi206, ureyite
NaFeSi206, acmite
Silicateilmenite,MgSiO3
Silicatespinel
-Mg2SiO,
-Ni2SiO,
-Fe2SiO
4
-Fe2SiO
4
Sillimanite,AI2SiO5
aoOO)
T range
ao(10'4)
a1(10's)
a2
297-1253
11.2
0.1120
0.0000
0.0000
297-1253
10.9
0.1090
0.0000
0.0000
0.0000
297-1253
16.8
0.1680
0.0000
297-1253
39.3
0.3930
0.0000
0.0000
297-1033K
3.8
0.0380
0.0000
0.0000
297-1033
11.1
0.1110
0.0000
0.0000
297-1033
4.8
0.0475
0.0000
0.0000
d100
297-1033
6.0
0.0600
0.0000
0.0000
297-1033
22.2
0.2220
0.0000
0.0000
298-1273
16.4
0.1640
0.0000
0.0000
298-1273
14.5
0.1450
0.0000
0.0000
298-1273
16.8
0.1680
0.0000
0.0000
298-1273
47.7
0.4770
0.0000
0.0000
293-1073
24.1
0.2947
0.2694
-0.5588
1353-1633
297-1073
16.7
0.1670
0.0000
0.0000
7.6
0.0760
0.0000
0.0000
297-1073
13.8
0.1380
0.0000
0.0000
297-1073
6.7
0.0670
0.0000
0.0000
297-1073
28.1
0.2810
0.0000
0.0000
297-1073
8.5
0.0850
0.0000
0.0000
297-1073
10.0
0.1000
0.0000
0.0000
297-1073
6.3
0.0631
0.0000
0.0000
all00
297-1073
8.2
0.0817
0.0000
0.0000
297-1073
24.7
0.2470
0.0000
0.0000
297-873
5.9
0.0585
0.0000
0.0000
297-873
9.5
0.0946
0.0000
0.0000
297-873
3.9
0.0390
0.0000
0.0000
d100
297-873
6.9
0.0691
0.0000
0.0000
297-873
20.4
0.2040
0.0000
0.0000
297-1073
7.3
0.0727
0.0000
0.0000
297-1073
12.0
0.1200
0.0000
0.0000
297-1073
4.5
0.0450
0.0000
0.0000
d100
297-1073
8.0
0.0804
0.0000
0.0000
297-1073
24.7
0.2470
0.0000
0.0000
298-876
7.1
0.0707
0.0000
0.0000
298-876
10.0
0.0996
0.0000
0.0000
298-876
24.4
0.2440
0.0000
0.0000
297-1023
18.9
0.2497
0.3639
-0.6531
298-973
26.8
0.2680
0.0000
0.0000
0.0000
K
K
298-673
27.0
0.2697
0.0000
298-673
23.0
0.2300
0.0000
0.0000
298-1273
1.0
0.0231
0.0092
-0.1185
298-1273
7.4
0.0727
0.0470
0.0000
298-1273
4.2
0.0386
0.1051
0.0000
298-1273
13.3
0.1260
0.2314
0.0000
ref.
[]
[]
[4]
[]
[141
[14]
[14]
[14]
[14]
[23]
[23]
[23]
[23]
[75]
[59]
[65]
[65]
[65]
[65]
[14]
[14]
[14]
[14]
[14]
[14]
[14]
[14]
[14]
[14]
[14]
[14]
[14]
[14]
[14]
[4]
[4]
[4]
[88]
[lOl]
[lOl]
[521
[971
[971
[971
[971
37
38
THERMAL
EXPANSION
TABLE 1. (continued)
T range
Names
ao(11Y
a)
ao(10.4)
a (10.8)
a2
ref.
SiO 2 group
Coesite
293-1273
6.9
0.0597
0.7697
-0.1231
Cristobalite, low
301-491
19.5
0.1950
0.0000
0.0000
301-491
52.7
0.5270
0.0000
0.0000
301-491
91.7
0.9170
0.0000
0.0000
[75]
[63]
[63]
[63]
Cristobalite,high
673-1473
6.0
0.0600
0.0000
0.0000
[75]a
a-Quartz
298-773
24.3
0.1417
9.6581
-1.6973
O-Quartz
848-1373
0.0
0.0000
0.0000
0.0000
1473-1673
-4.4
-0.0440
0.0000
0.0000
Stishovite
291-873
7.8
0.0758
0.0656
0.0000
291-873
0.9
0.0060
0.6553
-0.1500
[1]e
[1]
[1]
[39]
[39]
[39]
[181
[18]
Stishovite
Spodumene,t-LiAlSi206
Topaz, AI2SiOn(F,OH)2
Wadsleyite(O-phase)
Mg2SiO4
Zircon, ZrSi04
K
K
K
291-873
16.4
0.1574
0.7886
-0.1500
300-693
7.5
0.0750
0.0000
0.0000
300-693
3.8
0.0380
0.0000
0.0000
300-693
18.6
0.1860
0.0000
0.0000
0.0758
1.1542
0.0000
0.0000
293-1073
11.0
[75]
[75]
[75]
[75]
[75]
[89]
[89]
[89]
[89]
[6]
293-1273
4.6
0.0316
0.4698
293-1273
3.6
0.0245
0.3795
0.0000
293-1273
6.3
0.0485
0.4924
0.0000
293-1273
14.8
0.1098
1.2700
0.0000
293-1073
6.0
0.0851
0.1388
-0.2662
293-1073
5.6
0.0791
0.1165
-0.2487
293-1073
9.3
0.1196
0.3884
-0.3412
293-1073
20.9
0.2893
-0.8903
293-1293
3.4
0.0340
0.5772
0.0000
293-1293
5.6
0.0560
0.0000
0.0000
293-1293
12.3
0.1230
0.0000
0.0000
293-873
20.6
0.2060
0.00
0.0000
295-520
13.8
0.1380
0.00
0.0000
[104]
[50]
[50]
[50]
[50]
[50]
[50]
[50]
[50]
[105]
[105]
[105]
[105]
[105]
[32]
[32]
[32]
0.0000
Perovskites
BaZrO3, perovskite
CaGeO3, perovskite
NaMgO3, perovskite
NaMgO3, cubic
ScAIO3, perovskite
295-520
6.8
0.0680
0.0000
0.0000
295-520
10.5
0.1050
0.00
0.
295-520
31.1
0.3110
0.0000
0.0000
520-673
12.1
0.1210
0.00
0.0000
520-673
12.1
0.1210
0.0000
0.0000
520-673
10.5
0.1050
0.00
0.0000
0.0000
0.0000
520-673
35.0
0.3500
0.0000
298-873
40.4
0.4040
0.0000
298-873
15.3
0.15300
0.0000
0.0000
298-873
30.6
0.3060
0.00
0.0000
288-873
88.0
0.0000
1038-1173
94.9
0.8800
0.9490
0.0000
0.00
0.0000
293-973
10.0
0.1000
0.00
0.00
0'.0700
0.00
0.00
0.1000
0.00
0.
K
K
b 293-973 K
c
293-973
7.0
10.0
FEI
TABLE 1. (continued)
Names
SrZrO3, perovskite
V
a
T range
ao(10)
283-1373 K
293-973 K
27.0
12.4
ao(10'n)
0.2700
0.1240
a Offs)
a2
ref.
0.0000
0.0000
0.0000
0.0000
[32]
[]o4]
[104]
[104]
[104]
[104]
[104]
[104]
[104]
[104]
[lO41
[104]
293-973
7.5
0.0750
0.0000
0.0000
293-973
9.7
0.0970
0.0000
0.0000
293-973
973-1123
29.8
0.2980
0.0000
0.0000
7.6
0.0760
0.0000
0.0000
973-1123
16.1
0.1610
0.0000
0.0000
973-1123
8.2
0.0820
0.0000
0.0000
973-1123 K
1123-1443 K
32.4
14.9
0.3240
0.1490
0.0000
0.0000
0.0000
0.0000
a
c
1123-1443
6.8
0.0680
0.0000
0.0000
1123-1443
37.5
0.3750
0.0000
0.0000
bSee
[56]fororthorhombic
cordierite
and[33]forhydrous
Mg-andFe-cordierites.
CSee
[24]for plagioclases,
An100,
Ab9An9
, Ab7An93
, Ab75An22Or3,
Ab63An36Orl,
AbnAn57Or2,
andAb23An76Or
1.
dinversion
at491K.Alsosee[75]fordataontridymite.
ea-andO-quartz
transition
at846K; see[1]fordiscussion
onthermal
expansion
nearthetransition.
Fe(bcc)
Fe(hcp)
Fe(fcc)
NaCI
LiF
MgO, periclase
(Mgo.6Feo.4)O,
magnesiowiistite
Mg(OI-I)2
Mg2SiO4, olivine
[5-(Mgo.sFeo.16)2Si04
MgSiOn, spinel
(Mgo.9Feo.
1)Si03, perovskite
Kr, OPa
KT'
fit
165.0
212.0
167.0
24.0
65.3
160.3
157.0
54.3
129.0
174.0
183.0
261.0
5.30
4.00
4.00
5.01
5.10
4.13
4.00
4.70
5.37
4.00
4.30
4.00
6.5
6.5
6.5
5.8
5.4
4.7
4.3
4.5
5.5
5.1
5.8
6.5
references
[34]
[34]
[9]
[10{3]
[10]
[36]
[20]
[19]
[37]
[21]
[55]
[51]
39
40
THERMAL
TABLE
EXPANSION
TABLE
Viiq(r)
-- XiVii,Tr[
1+ i(T-Tr)]+XNa2OXTiO2
VNa20-TiO2
a = Yiai
64liquids
b
iron-freesilicateliquida
Oxides
Vi,1673
ai (x105)
,
Oxides
Vi,1773
K ai (x105) Vi,1573
K ai (x105)
SiO2
TiO2
AI203
FeO3
26.88
23.98
37.52
-
FeO
-1.2
36.5
2.0
-
26.92
22.43
36.80
41.44
0
32.3
7.1
21.9
13.35
21.9
MgO
11.85
: 0.7
11.24
23.3
CaO
16.84
25.1
16.27
17.9
NaeO
KeO
Li20
NaeO-TiOe
29.53
47.10
17.42
20.10
26.8
72.8
33.4
28.02
44.61
16.19
20.33
26.4
26.7
32.4
SiO2
TiO2
Fe203
26.75
22.45
44.40
0.1
37.1
32.1
FeO
13.94
34.7
MgO
12.32
12.2
CaO
16.59
16.7
Na20
K20
29.03
46.30
25.9
35.9
Li20
17.31
22.0
MnO
14.13
15.1
NiO
12.48
24.9
ZnO
13.64
43.0
SrO
20.45
15.4
BaO
26.20
17.4
PbO
25.71
16.1
54.22
68.33
61.3
71.4
b Datawerederivedfromdensity
measurements
of 64 meltsil
Rb20
the systemNa2C,-K20-CaO-MgO-FeO-Fe203-AI203-TiO2-SiO2 Cs20
[8, 46, 57, 801.
TABLE
Fiq(T)
= X,r[1+ i(r- T0]+Xs,oXo
Vs,o-cao
> 20 wt% silica a
Oxides Vi,1673
I
25.727
37.501
FeO
14.626
21.0
CaO
18.388
12.1
low silica
0
9.2
Yiiq(T)
= Xiii,r[1
+ i(TOxides
Vi,1573
26.60
41.39
ai (x105)
27.801
35.770
0
13.3
13.087
19.4
SiO2
F203
21.460
10.5
FeO
13.61
18.7
Na20
28.48
23.2
-11.042
a Datawerederivedfromdensitymeasurements
of 30 meltsin
the systemCaO-FeO-Fe203-SiO
2 [16, 57]. Unitsarein cc/mole
and 1/K.
Volume
SiOe
FeeO3
SiOe-CaO
ExpansionCoefficientof OxideComponents
in NaeO-FeO-Fe203-SiO2 Melts [47]
0.3
12.9
a Datawerederivedfromdensitymeasurements
of 12 meltsin
the system Na20-FeO-Fe203-SiO [17] and ferric-ferrous
relations[47]. Unitsarein cc/moleand1/K.
FEI
41
REFERENCES
1.
Traverse,
0A1203:A high-temperaturethermal
expansionstandard,High Temperature-High Pressure, 16, 127-135,
1984.
3.
cient of ilmcnitc-typcMgGcO3,
Phys. Chem. Minerals, 12, 129-131,
1985.
.
Navrotsky,
MgSiO ilmcnitc:heat
capacity, thermal cxpansivity,and
enthalpy of tramsformation,Phys.
Chem. Minerals, 16, 239-245, 1988.
.
7.
9.
S. Sueno, C. T.
densities
in
the
CaO-FeO-
Fe20-SiOsystem
and the compositional dependenceof the partial
molar volume of ferric iron in silicate
melts, Geochim.Cosmochim.
Acta,
52, 2815-2825, 1988a.
theNaO-FeO-FeO-SiOsystem
and
the partial molar volume of tetrahedrally-coordinated ferric iron in
silicate melts, Geochim. Cosmochim.
Acta, 52, 2467-2475, 1988b.
18. Endo, S., T. Akai, Y. Akahama, M.
1976.
high-temperature
X-ray studyof low
and high plagioclasefeldspars,in
The Feldspars, Proceedings of a
NATO Advanced Study Institute,
edited by W.S. MacKenzie and J.
Zussman,pp. 162-173,Universityof
Manchester Press,1974.
25. Guggenheim,
S.,Y-H. Chang,andA.
F. K. van Groos,Muscovitedehydroxylation: High-temperature
studies,
Amer. Mineral., 72, 537-550, 1987.
26. Haselton, Jr.,
H. T., B. S.
CaAI2SiO6glassand pyroxeneand
thermal expansion of CaAI2SiO,
pyroxene, Amer. Mineral., 69, 481489, 1984.
Akermanite:
capacityandthermalexpansion,
and
revised thermodynamicdata, Can.
diffraction
studyof 15-(Mg,Fe),SiO
4
42
THERMAL
EXPANSION
The lime-iron-silicatesystem:Redox
and volume systematics,Geochim.
Cosmochim. Acta, 53, 2883-2892,
1989.
single-crystalMgO up to 1800 K,
1989.
1989a.
1972.
Smith,Thermalexpansionof silicate
perovskiteand stratificationof the
Earth's mantle, Nature, 319, 214216, 1986.
8079, 1991.
52. Mao, H. K., T. Takahashi, W. A.
Bassett, J. S. Weaver,
and S.
T.
Vaughan,
Leinenweber,
Y.
Wang,
K.
R. E. Pacalo, A.
Yeganeh-Haeri,andY. Zhao,In-situ
highP-T X-ray diffractionstudieson
threepolymorphs
(a, , ) of Mg,SiOo
J. Geophys.
Res.,in press,1993
56. Mirwald, P. W., Thermalexpansion
of anhydrous
Mg-Cordieritebetween
25 and 950C, Phys. Chem.
Minerals, 7, 268-270, 1e.,1.
57. Mo, X. , I. S. E. Carmichael, M.
expansion
of beryl,Acta Cryst.,B28,
1899-1903, 1972
59. Murakami, T., Y. Takeuchi, and T.
FEI
crystalstructureof betaeucryptiteas
a function of temperature, Amer.
Mineral., 58, 681-690, 1973.
67. Predecki, P., J. Haas, J. Faber, Jr.,
and R. L. Hitterman, Structural
Papike,The crystalstructures
of high
albiteandmonalbiteat hightemperatures, Amer. MineraL, 61, 12131225, 1976.
69. Rao, K. V. K., and K. S. Murthy,
SinglecrystalX-ray diffractionstudy
of MgSiO3Perovskitefrom 77 to 400
K, Phys. hem. Mineral, 16, 415420, 1989.
59, 1069-
propertiesof synthetichigh-pressure
compoundsrelevant to the earths
mantle, in High-Pressure Research
in Geophysics,
editedby S. Akimoto
and M. H. Manghnani,pp. 411-464,
Cent. Acad. Pub. Janpan, Japan,
1982.
95
Crystalstructure
of ilmenite(FeTiO3)
at high temperature and high
pressure,Am. Miner., 69, 176-185,
1984.
1991.
Elasticityandthermalexpansionof a
naturalgarnetup to 1,000 K, J. Phys.
Earth, 31, 125-138, 1983.
88. Suzuki, I., E. Ohtani,
and M.
89. Suzuki,
43
I.,
E. Ohtani,
and M.
Okamura,A high-temperature
study
of the thermal expansion and the
anisotropy
of thesodiumatomin low
albite, Amer. MineraL, 62, 921-931,
1977.
Ghose,A high-temperature
structural
studyof high albite,monalbite,and
the analbite-monalbitephasetransition, Amer. MineraL, 64, 409-423,
44
THERMAL
EXPANSION
1979.
1986.
and Y. Takeuchi,
Order-disordertransitionin MgAI20n
spinel at high temperaturesup to
1700 C,Z. Kristallogr., 165, 65-78,
1983.
Jay D. Bass
INTRODUCTION
The main
content
trij = cij,e
(1)
Reference
Shelf 2
Hill averages
of the Voigt and Reussbounds[135]. In
conjunctionwith the density,the moduli can be used
to calculateacousticvelocitiesusing standard relations
[16].
This chapter is not meant to be either historically
completenor encyclopedicin scope. In caseswhere a
material hasbeen the subjectof severalstudies,we have
Sincethe earliercompilationby Birch[16],the quantity of data related to the equation of state of rocks
and minerals has grown considerably. For many materials, complimentary results on the equation of state
of minerals from static compressiondata are found in
the chapter by Knittle, with which there is a degreeof
overlap. Likewise, the chapter by Anderson and Isaak
present considerablymore detail on the high temperature elasticity of minerals.
The results in this chapter derive from a variety of
techniqueswhich have a broad range of precision. We
have not made any attempt to assessthe relative accuracy of results from different laboratories on a given
material.
46
ELASTICITY
The number of independent elastic constants appropriate to a materiM dependson the symmetry of that
GPa
Mg/ms
Units
Description
cij
GPa
Single-crystalelastic stiffness
GPa
Adiabatic
bulk modulus
Ks,o
GPa
Adiabatic
bulk modulus
GPa
Shear modulus
Vr
m/s
Kelvins
moduli
Ks
at zero
frequency
Density
Superscripts
Indicates
Symbol
Pressure
the framework
of this review
to summarize
the
p
Mg/ms
Ks
GPa
GPa
171.7
102.0
27.6
29.2
535.7
ences
Ag, Silver
C, Diamond
Cu, Copper
Fe, a-Iron
Feo.94Sio.06
Feo.94Sio.06
Fe0.91Sio.o9
BaO
CaO, Lime
CoO
re0.92O, Wutite
Fe0.9430
Fe0.9sO
MnO, Manganosite
MgO, Periclase
NiO, Bunsenire
19.283
10.500
3.512
8.932
7.874
7.684
7.675
7.601
191
122
1079
169
230
221.0
222.3
216.4
42.4
45.5
578
162
92
124
75.3
117
122.3
123
124.6
122
135
135.1
135.5
134
443.0
137.3
166.7
163.7
164.4
161.4
45
60
70.7
114.7
36.0
81.2
47, 126
46, 111
80.59
71.3
46.1
46.4
46.8
68.1
81
47
120
56
15
47
5.992
3.346
Binary Ozides
122
34.4
224
80.6
3.349
6.438
5.681
5.708
5.730
5.365
220.5
260
245.7
218.4
217
227
80.03
82.4
44.7
45.5
46
78
57.7
145
149.3
123.0
121
116
112.0
183.3
181.4
154.8
153.0
153.0
5.368
223.5
78.1
111.8
149.0
5.346
3.584
3.584
3.584
6.828
226.4
294
296.8
297.8
344.6
79.0
155
155.8
155.8
40
114.9
93
95.3
95.1
141
152.1
160.0
162.5
162.7
205
46.9
81.5
80.40
81.1
80.1
68.3
68.7
130.3
130.8
131.1
58.8
47
47
77
46
47
103
72
72
89
138
46
57
152
134
BASS
47
Table 1. (continued)
Material
Mg/ms
SrO
UO2, Uraninite
5.009
10.97
Subscript
ij in moduluscij (GPa)
11
44
12
Ks
GPa
GPa
ences
87.3
58.1
46, 116
170
55.6
46
389
59.7
119
209
83
35
104
161.0
91.4
47
162.0
91.2
47
203.3
104.9
47
46, 24
Magnetite
FeCr:O4, Chromite
MgAI204,
Spinel
MgO-2.6AI03
MgO.3.5AI03
5.206
275
95.5
270
5.09
98.7
322
117
144
3.578
282
154
154
196.7
108.3
3.578
282.9
154.8
155.4
197.9
108.5
152
153.7
202.0
115.3
106
153.7
202.6
116.4
126
168
216.0
114.8
46
158
206.3
114.7
46
97
130
3.619
3.63
298.6
157.6
300.5
158.6
312
157
303
M go.75Feo.36
AI .90O4,
108
156
3.826
269.5
143.5
163.3
198.7
4.280
266.0
327
366
300
133.5
126
106
126
182.5
112
155
118
210.3
184
226
179
84.5
119
106
110
33.6
-44
142.7
104.7
58.6
77.1
125.7
149.7
31.9
31.5
108
57.8
25.1
46
86.3
42.4
46
24.9
14.7
46
18.1
9.4
46
172.8
92.0
85
177
89
67
108.9
11
162
92
10
178.8
96.3
11
Pleonaste
FeAI204, Hercynite
-Mg2Si04, Pdngwoodite
3.559
Ni2SiO4
5.351
MgGeO4
4.389
FeS, Pyrite
5.016
PbS, Galena
ZnS, Sphalerite
7.597
4.088
BaF, Frankdicksonite
CaF2, Fluorite
NaCI, Halite
KC1, Sylvite
4.886
3.181
2.163
1.987
130
144
13
140
Sulphide.
s
361
402
127
102
105.2
114
23
44.6
24.4
64.6
47
47
47
Binaqt Halides
90.7
165
49.1
40.5
25.3
33.9
12.8
6.27
41.0
47
12.8
6.9
91.6
90
104.6
111.1
117
91.2
91
Garnels
Pyrope(Py),
MgaAISiaO
Grossular,(Gr99)
3.567
3.563
3.602
296.2
295
321.7
3.850
304
84
4.195
309.5
95.2
H ibschite
3.13
187
63.9
57
100
64.3
86
3.836
289
85
92
157
90
10
An7oGr2Alm4Pys
Gr4sPysAlmsSp
Alm4Py2GrSpAnda
AIm74PyoGrsSps
3.775
3.741
4.131
4.160
281.2
310.2
306.7
306.2
87.9
99.5
94.9
92.7
80.4
100.4
111.9
112.5
147.3
92.7
170.4
101.6
84
176.8
95.9
177.0
94.3
111
Py73Alm16And4Uv
Py6Alma6Gr
3.705
3.839
296.6
301.4
91.6
94.3
108.5
110.0
171.2
92.6
121
173.6
94.9
136
168.4
CasAl:SisOl:t
Uvarovite(Uv)
CaaCr2SiaO
Spessartite(Sp95)
113.5
MnsAISiaO
CasFe2+3Si3012
48
ELASTICITY
Table 1. (continued)
Material
p
Mg/ma
Sp54AIm46
Subscript
ij in modulus
cij (GPa)
11
44
12
Ks
Refer-
GPa
GPa
ences
177.7
96.1
3.555
164
89
12
3.545
3.527
3.606
170
172
174
92
92
115
150
150
90
4.249
308.5
94.8
112.3
132
Mgs(Mg,Si).s:AI1.18Sis01:
MjssPy6?
Mj6PY34
Nal.s7Mgl. 18Si4.94012
329
114
96
Abbreviations:
Py,pyrope;
Aim,almandite;
Gr,grossular;
Uv,uvarovite;
An,andradite;
Sp,spessartite;
Mj, majorite(Si-richandAl-poorgarnet).
Material
BeO, Bromellite
Beryl
BesAlSi018
C, Graphite
Ca,0(PO4)(OH),
Mg/ms
3.01
2.724
2.698
2.26
3.146
11
470
304.2
308.5
1060
140
Subscript
ij in modulus
cii (GPa)
Ks
GPa
GPa
119
114.5
118.5
15
251
176
181
161.0
162
78.8
79.2
109.3
69
80.4
45.6
47
46
56
212.3
101.8
47
38
21
48.9
30.7
46
33
494
277.6
283.4
36.5
180
44
153
65.3
66.1
.3
36.2
12
168
123.8
128.9
180
13
177
44.3
125
37.2
13
ences
14
153
153
18
Hydroxyapatite
Ca10(PO4)F2,
3.200
141
Fluorapatite
Cancrinite
2.6
79
(NaCa)4(AI,SiO4)aCOs.nH20
CdS, Greenockite
4.824
86.5
cD
cz
H20, Ice-I (257K)
Ice-I (270K)
NasKA14Si4016,
0.9175
2.571
94.4
15.0
54.0
47.3
62.7
16.9
47
83.8
83.1
96.5
94.8
15.8
15.3
51.1
50.4
45.0
46.2
60.7
60.7
17.5
61
13.5
13.70
79
14.9
14.70
125
3.09
2.96
37.2
6.5
6.97
38
5.9
5.63
21
8.72
8.73
48.9
117
209
110
218
36
44.1
16
120
33
104
207.0
209.6
209.5
221.0
44.8
46.1
117.7
120.4
106.1 142.6
101.3 142.9
122
138
28.7
17.1
3.48
3.40
61
46
37
30.7
47
41.4
47
Nepheline
-SiO2 (873K)
ZnO, Zincite
5.675
cz
cD
Wurtzite, ZnS
4.084
58
42
56.4
143.5
74.0
46.8
46
46.3
61
48.2
61
33.3
46
BASS
p
Mg/m3
A12Os,Sapphire,
Corundum
11
14
Ks
GPa
Refer-
GPa
ences
3.999
495
497
146
160
115
-23
251.7
162.5
46
3.982
497
501
146.8
162
116
-21.9
253.5
163.2
83
ALPO4, (cE)
Berlinire, (c)
2.620
64.0
69.8
85.8
87.1
CaCOs, Calcite
Cr2Os, Eskolaite
Fe2Os, Hematite
MgCOs, Magnesite
NaNOs, Nitratine
AgsAsSs,
2.712
5.21
5.254
3.009
2.260
5.59
144
374
259
54.6
59.5
156
34.9
39.8
54.8
11.3
9.97
75.6
18.9
31.7
58.8
19.3
29.6
73.3
234.0
206.6
-19.0
114.0
7.5
28.2
0.18 36.8
2.648
2.648
2.648
3.100
86.6
86.74
86.47
305.0
106.1
107.2
107.2
176.4
57.8
57.9
58.0
64.8
6.7
6.98
6.25
108
12.6
11.9
11.9
51
-17.8
-17.9
-18.1
-6
84.0
362
43.2
42.2
33.5
159
7.2
10.6
53.9
148
9.6
14.9
51.1
175
-12.4
13.4
29.3
33.9
-20.5
-19
33.0
25
32.7
32
32.0
46
123.2
1, 46
91.0
69
68.0
46, 50
12.0
46
11.0
47
44.3
46
44.4
46
44.5
46
81.5
87
Proustite
SiO2, c-Quartz
cz
cD
Tourmaline,
37.8
37.8
37.5
127.2
(Na)(Mg,Fe+2,Fe+,Al,Li) Al6(BO)s(Si6018)
(OH,F)4
Dolomite,
Mg/ms
11
33
3.795
205
113
2.960
341.9
391.0
3.795
472
382
44
12
13
39.8
71.0
57.4
91.4
148.0
136.0
14
-19.5
15
Ks
GPa
GPa
References
13.7
94.9
45.7
46, 50
3.5
212.8
98.9
148
CaMg(COs)
Phenacite
0.1
BeSiO4
MgSiOs
Ilmenite
structure
106
168
70
-27
24
212
132
141
49
50
ELASTICITY
p
Mg/ms
11
13
Ks
GPa
Refer-
GPa
ences
316
220
Si02,
4.290
453
776
252
302
211
203
143
Stishovite
Si02,
2.335
59.4
42.4
67.2
25.7
3.8
6.975
261.7
449.6
103.1
207.4
177.2
6.02
55.7
105.8
26.5
65.9
5.99
53.2
108.5
24.4
55.2
269
337.2
480
599.4
124
161.5
192
258.4
177
188.2
-4.4
16.4
39.1
151
155.5
212.3
101.8
22
51.2
21.8
45.0
20.4
93
48.6
21.2
43.7
19.0
122
a-Cristobalite
SnO2,
Cassiterite
TeO,
Paratellurite
TiO, Rutile
GeO
4.260
6.279
146
215.5
112.4
47
187.4
257.6
150.8
131
46
Other Minerals
Ba2Si2TiOs,
140
83
33
59
36
24
56.9
42.1
166
100
31.7
69.4
58
44
77.6
43.3
46
99
113
15.6
22.9
35.1
35.4
58.0
23.1
47
102
102
140
140
23.0
23.0
30.4
30.4
38.9
38.9
43.3
65.3
29.1
47
43.3
65.3
29.1
47
153
166
55.8
54.0
48
44
82.6
55.5
47
4.675
424.3
489.3
149
227.9
109.0
88
4.70
256
372
214
223.9
66.6
47
Fresnoite
(cr)
Scapolite,
(Na,Ca,K)4Als(AI,Si)s
Si6024(CI,SO4,COs)
Vesuvianite
Ca0Mg2A14(SiO4)5(Si2O7)2(OH)4
ZrSiO4 a,
Zircon
131.1
73.5
48.3
116
69.7
175
a nonmetamict.
CaMo04,
11
33
4.255
144
127
6.119
141
6.816
109
108
Mg/ms
44
Ks
GPa
GPa
Refer-
66
12
13
16
36.8
45.8
65
47
-13.5
81.0
39.9
46
125
33.7
40.7
61
41
-17
76.5
37.4
46
92
95
26.7
26.4
33.7
35.4
68
63
53
51
-13.6
-15.8
72.4
70.8
24.5
25.0
46
ences
Powellite
CAW04,
Scheelite
PbMo04,
Wulfenite
46
BASS
o o
51
52
ELASTICITY
BASS
o
o
I'--,
t.c'D
.,,.
C'4" C"'q
53
54
ELASTICITY
BASS
Composition
CaAISiOs (An)
kg/ms
2490
3950
1833
6.54
5.54
2.56
1893
An ,
Ans6Di4
AnsDi4 '
AnsoDiso
AnsoAbso
AbsoDiso
AbzsDis
AbssAnssDias
BaSiOs
CaSiOs
CaTiSiOs
CsSiOs
CaMgSi2Oa(Di)
Di
Fe.22Sio.s9Oa
Fe2SiO4
K2Si2Os
K9.SiOs
LiSi2Os
Li2SiOs
MgSiOs
NaCI
(SO)(^O)(SiO)
(SO)
Na2Si205
NaSiOs
O) (SiO)
Ks,co
Vp
GPa
m/s
94.8
52.4
20.6
3808
3075
2850
20.4
Refer enc es
48
48
3.529
3.0
100
107
1923
1677
1673
2.61
17.9
23.0
24.2
1673
1573
1753
1698
1598
1753
1648
1698
1583
1793
1693
1836
1753
1653
2.60
2.61
2.44
2.45
2.46
2.39
2.40
2.49
2.50
3.44
3.47
2.65
2.96
3.01
21.6
22.1
17.8
18.2
19.3
16.4
16.7
19.5
19.8
19.5
20.2
27.1
19.9
20.0
1693
3.14
6.4
1450
3.854
100
1208
3.34
8.8
2345
4.023
100
1773
2.61
22.4
1758
1698
1693
1598
1653
1503
1693
1408
1698
1498
1693
1411
1543
1913
1094
2.60
2.61
3.48
3.51
3.71
3.76
2.16
2.22
2.10
2.17
2.12
2.17
2.08
2.52
24.2
24.1
19.2
20.6
21.4
22.6
10.3
11.9
7.5
8.5
15.0
16.3
20.7
20.6
3040
3020
2345
2450
2400
2450
2190
2600
1890
1970
2670
2740
3160
2860
1727
3.842
3.83
3.665
3.680
7.65
8.67
3.955
3.951
4.909
5.242
4.100
3.852
3.712
4.040
8.61
100
1540
2653
2695
2835
2525
2680
2663
2752
8.61
3.707
3.764
5.558
3.934
3.990
10.1
8.4
1322
1684
1599
1690
1693
1408
1573
1458
2.55
Frequency
106s-
2.20
2.26
2.22
2.25
15.8 a
16.4 a
18.6
14.0
16.2
15.7
17.0
99
107
98
2885
2910
2850
2735
2830
2800
3400
2805
2880
2390
2410
3120
2590
2580
3.635
3.922
3.858
3.662
3.943
3.565
3.833
3.803
3.944
3.906
3.652
3.484
4.014
4.013
100
100
100
100
100
100
100
100
100
100
100
100
100
100
99
100
100
100
100
100
100
100
100
100
100
100
100
100
63
63
63
63
63
100
100
100
100
55
56
ELASTICITY
Table 9. (continued)
Composition
Or7sAn22
Or61Di39
Rb2Si205
SrSi205
Tholeitic
Basalt
Basalt-Andesite
Andesite
Ryolite
kg/ma
K,,oo
V,
GPa
m/s
Frequency
106s-1
References
1783
2.33
13.8
4300
3.836
lOO
1598
2.35
14.1
5200
3.923
lOO
1768
2.38
16.0
2795
3.656
lOO
1578
2.40
16.5
3470
3.673
lOO
1693
2.78
7.8
1678
3.945
lOO
1408
2.88
9.9
2130
3.974
lOO
1758
3.02
19.6
2550
3.690
lOO
1653
3.04
20.1
2570
3.833
lOO
1708
2.65
17.9
2600
3.839
lOO
1505
1803
2.68
2.55
18.3
18.6
2610
2700
3.909
3.790
lOO
1503
2.59
19.4
2980
3.863
lOO
1783
2.44
16.1
2775
3.827
lOO
1553
2.46
16.6
3850
3.889
lOO
1803
2.29
13.0
4350
3.664
lOO
1553
2.31
13.5
5280
3.723
lOO
lOO
Table
10. Elastic
Moduli
of Glasses
Refer enc es
Composition
kg/m3 GPa
GPa
MPa g -1
SiO2
2.204
36.5
31.2
MgSiO3
2.761
78.8
41.8
129
CaSiOs
2.880
69.2
36.3
129
CaMgSi206
2.863
76.9
39.7
129
2.847
74.1
38.8
113
CaA12Si2Os
Na2Si206
2.693
2.494
69.2
41.9
38.7
24.1
129
(Na20)as(Si02)s'
2.495
2.369
41.0
39.1
23.0
29.2
4.6
2.490
2.749
45.1
50.0
30.2
30.2
2.4
4.9
-0.35
0.5
-7
-8.1
-9
-7.1
2.42
30
21
to +4
- 1
- 2.4
- 3.4
Obsidian
2.331
37.8
30.1
Andesire
2.571
52.5
33.6
Basalt
2.777
62.9
36.5
NaA1SiaO8
Na2A128i208
(NaeO)ao(TiO2)20(SiO2)so
-6
-3.4
16
MPa g -1
4
38, 79
129
0.7
-12.2
-10.7
75
129
-4
-1.8
44
74
75, 36
-1.7
79
0.6
-0.8
79
2.1
-0.3
79
BASS
tKs/tip
5G/SP
5Ks/tit
MPa/K
tG/ST
MPa/K
AT
References
Elements,Metallic Compounds
Ag, Silver
6.09
1.68
-21.5
-12.7
79-
298
Au, Gold
C, Diamond
6.13
1.27
-31.0
-8.4
79-
298
4.0
2.3
-8.7
-5.7
223-
ct-Fe,(bcc)
323
17
17
77
5.29
1.82
-31
-27
25-
5.97
1.91
-43
-33
300-
5.13
2.16
-51
-47
500-
700
4.3
3.4
-43
-43
800-
900
-18
-14
77-
300
71
-19
-17
80-
298
103
-33
-30
298-
Feo.94Sio.o
300
500
900
29, 42
29, 102
29, 128
29, 49
103
Simple Oxides
A1203, Corundum
BaO
4.3
5.52
1.12
-15
-27
@296
-23
-24
@1ooo
40
-19
-24
@1825
40
-23.9
-12.0
-7
CaO, Lime
195-
293
5.23
1.64
-14.3
-13.8
283-
303
6.0
1.7
-I9.2
-15.0
195-
293
-14.1
-14.7
4.83
1.78
-12.8
-14.9
20
112
CoO
Feo.9O, Wiistite
Feo.9430, Wiistite
Fe203, Hematite
GeOa,
281 - 298
-20
5.1
0.71
4.5
0.73
6.2
1.2
12.4
300-
1200
281 - 298
293-
303
@298
39, 40
26
127
112
8, 114
81
26
120
120
56
69
-36
-12
293-
-20.3
-11
273-473
373
131
(futile structure)
MnO, Manganosite
5.28
1.55
4.7
1.2
138
-21
MgO, Periclase
SrO
3.85
-15.3
89
@298
120
300 - 800
115
4.5
2.5
4.13
2.5
-14.5
-24
@300K
4.27
2.5
-22.5
-26
@1200K
-21.3
-21
5.18
1.61
-17.8
-12.6
-7.1
-11.9
195-
293
5.50
0.61
-19
-6.7
298-
373
6.4
0.46
-8.5
-0.8
6.76
0.78
-48.7
-21.0
6.0
SnO:, Cassiterite
SiOn, Quartz
TiO., Rutlie
UO., Uraninite
14.6
4.69
52, 57
23, 52
@1800K
52
281 - 298
26
@293
298 - 583
1.42
8, 114
22
78, 110,118
34, 73, 76
35
fl-Mg9.Si04, Wadsleyite
MgAI9.O4, Spinel
MgAI9.O4
MgO-2.6AleO3
4.8
5.66
1.7
43
-15.7
-9.4
293 - 423
70,152
4.89
24
4.18
106
57
ELASTICITY
alf'
MateriM
Mg0.?5Feo.36
All.9o04,
4.92
a:slT
MPa/K
References
AT
K
MPa/K
130
0.29
Pleonaste
Sulphides
PbS, Galena
ZnS, Wurtzite
6.28
BaF2,
5.05
4.37
77-
-39.0
0.00
-9.56
0.00
300
91, 94
298-
373
21
195-
298
145
195-
298
145
195-
295
300-
800
116
147
Binary Halides
-14.5
Frankdicksonite
CaF2, Fluorite
NaCl, Halite
-17.5
4.92
5.27
-10.8
2.14
-11.13
5.256
KCI, Sylvite
5.0
-9.9
2.0
-10.5
-8.2
294-
338
-15.2
-9.5
745-
766
-7.2
-3.2
-8.7
-5.6
300-
1000
147
7, 28, 30
294-
865
146
298 -
1000
121
298-
338
Garnets
Py?aAlm16And4Uv6
Py62AIm36Gr2
Py61AIma6Gr2
Sp,4AIm46
Alm, Py Gr AndsSpa
-19.5
4.93
4.95
1.44
5.43
1.40
Other
MgSiO4
Olivine, Fo90
Fo93Fa7
Fo91Fa9
Fo9oFalo
Fo92Fas
(Mg.sFe0.2)SiOa
ALPO4, Berlinite
Beryl, BeaAISi60 s
Calcitea, CaCOa
Nepheline,
2O
132
288 -
313
111
-20.1
-10.6
-14.9
-12.5
300 -
1350
54
-14.7
-12.5
300 -
1250
54
41
Minerals
4.97
1.82
-17.6
-13.6
300 -
700
5.37
1.80
-15.0
-13.0
298 -
306
65
-16.0
-13.5
293 -
673
119
-15.7
-13.5
4.56
5.13
4.6
1.71
1.79
1.9
FayMite(Fa),
Fe2SiO4
Orthopyroxene
137
-18.8
4.74
Gr9sAnPyl
Gr?6An2Spl
Forsterite(Fo),
-10.2
1.56
10.8
2.06
9.6
2.38
300 -
1700
53
154
-15.6
-1.30
298- 306
65
136
-18.0
-16.9
-13.6
-13.8
300- 1500
300- 1500
51
-24
- 13
300- 500
55
51
137
-26.8
-7
- 11.9
-2
298- 623
33
180- 298
25
153
3.90
4.83
58
-3.7
1.6
298- 353
19
298- 573
88
NaaKAI4Si406
Zircon, ZrSiO4
6.5
0.78
-21
-9.4
Abbreviations: Py, Pyrope MgaAlaSi3012; Aim, Almandite Mg3A12Si302; Gr, GrossularCaaA12Si3012;Uv, Uvarovite
Ca3Cr2Si3012; And, Andradite Ca3Fe2Si3012; Sp, SpessartiteMn3A12Si3012;Fo, Forsterite Mg2SiO4; Fa, FayMite
Fe2SiO4.
a Pressurederivative of KT is given.
BASS
59
52K/SP2
GPa-1
SiOe Glass
Grossular
52G/Sp
52K/ST
52G/ST
GPa-1
kPa K -2
kPa K -
2.9
38
Garnet
CasA12SisO12
Pyrope Garnet
MgaAlSiaO
Forsterire,
T < 760
MgSiO4
T > 760
Olivine,
References
-0.28
-0.08
-1.8
-1.1
54
-1.8
-1.1
136
-5.2
-0.7
-2.6
53
53
-0.15
-0.11
136
(Mg,Fe)SiO4
-0.05
-0.06
154
MgO, Periclase
Fe0.s4sO,Wiistite
CaO, Lime
Orthopyroxene,
-0.03
-0.07
-0.10
57
56
-1.4
- 1.6
0.3
81
-0.12
137
(Mg,Fe)SiOs
MgAI204, Spinel
0.5
24
Acknowledgments:
Thisworkwassupported
in part by the NSF undergrantno. EAR-90-18676.
The review of O.L. Andersonis appreciated.
REFERENCES
3. Alexandrov, K. S., T. V. Ryzhova, and Belikov, The elastic properties of pyroxenes, Soy.
Phys. Crystallogr., 8, 589-591,
1964.
5. Babuka, V., J. Fiala, M. Kumazawa, I. Ohno, and Y. Sumino, Elastic properties of gat-
J. Am.
Ceramic
cal Constants,
(revised),pp. 97173, edited by S. P. Clark, Jr.,
Geological Soc. Am. Mem. no.
6O
17.
ELASTICITY
of noble metals
from -196
19.
20.
and
thermoelastic
con-
29.
dence
30.
22.
elastic
constants
of
31.
32.
33.
24.
constants
and thermal
ex-
36.
37.
38.
27.
28.
of c-iron
to
10
45.
46.
of al-
A.M. Hellwege,Springer-Verlag,
47.
49.
50.
9, 121-131, 1968.
40.
constants
1191, 1978.
39.
of
function
541-549, 1968.
43.
408, 1974.
135, 1976.
as a
1974.
of bronzite
as
constants
forsterite
1969.
42.
1973.
25.
in
6384, 1972.
34.
35.
tal
astic
constants
cassi-
1975.
of the elastic
1402, 1969.
1977.
21.
BASS
elasticity of iron-bearingolivines,
J. Geophys. Res., 97, 1871-1885,
1992.
ity of calcium-richgarnets,Phys.
19,
106-120,
52, 283-293,
64. Kumazawa, M., The elastic constants of single-crystal orthopyroxene, J. Geophys. Res., 7,
in Geophysics,
Advancesin Earth
and Planetary Sciences,vol. 12,
edited by S. Akimoto and M.
H. Manghnani, pp. 93-113, Center for Academic Publications,
Tokyo, 1982.
50, 251-260,
1988b.
62. Koptsik, V. A., and L. A. Ermakova, Electric and elastic parameters of cancrinite as a func-
5973-5980, 1969.
1992.
Planet.
Cosmochem. Acta,
1988.
Chem. Minerals,
61
erature dependenceof the elastic constantsof single-crystal rutlie between 40 and 583K, J.
Phys. Chem. Solids, 33, 21492159, 1972.
69. Liebermann, R. C., and E. Schreiber, Elastic constants of polycrystalline hematite as a function
of pressureto 3 kilobars, J. Geophys. Res., 73, 6585-6590, 1968.
70. Liu, H-P, R. N. Schock, and D.
L. Anderson, Temperature de-
pendenceof single-crystalspinel
from
293
to 423K
measured
constants
of iron-silicon
of elastic
constants
of
62
ELASTICITY
97.
98.
617-621, 1991.
99.
of nonmetamict
zir-
101.
215-224, 1978.
102.
1992.
17, 431-437,
A Handbook,
2nd Ed., M.I.T.
silicate:
results for
104.
inerals V. Additional
data on sil-
Chem.
Solids,
36,
and Bril-
1105-1122,
106.
115.
107.
118.
119.
108.
2508-2511, 1967.
1976.
114.
single-crystalspinelat 25 C and
95. Proctor, T. M., Jr., Low temperature speedof sound in singlecrystal ice, J. Acoustic.Soc.Am.,
1975.
1966.
105.
Soga,N., Elasticconstantsof garnet under pressure and temperature, J. Geophys.Res., 7, 42274234, 1967.
Soga, N., Elastic constants of
CaO under pressureand temperature, J. Geophys.Res., 73, 53855390, 1968.
113.
1ouinscatteringresults, J. Phys.
and raman
112.
dielectric
111.
1971.
1990.
paratellurite(TeO2): Ultrasonic,
110.
267-276, 1966.
103.
109.
Elastic constants of
sion of molten
20,031-20,037, 1993.
87. Okan, H., Elastic constants of
6006-6008, 1979.
1750, 1972.
Sumino, Y., The elastic constants
of Mn2Fe2SiO4 and Co2SiO4,
BASS
121.
122.
123.
124.
134.
126.
127.
137.
1978.
138.
Wang, Hong, Elasticity ot' Silicate Glasses, M.S. Thesis, University of Illinois at Urbana,
140.
141.
94pp., 1989.
130.
1. Pleonaste
142.
and her-
143.
147.
144.
of the
elastic
constants
of
148.
692, 1989.
364, 1989.
149.
Yeganeh-Haeri, A., D. J. Weldnet, and E. Ito, Single-crystalelastic moduli of magnesium metasilicate perovskite, in Perovskite: A Structure of Great Interest
to Geophysicsand Materials Science, Geophys. Monogr. Set., vol.
45, pp. 13-25, 1989.
150.
151.
1973.
132.
146.
of c-cristobalite:
A silicon
diox-
153.
tives
1977.
117-131, 1988.
139.
roxene(Mg0.$Fe0.2)SiO3,Europ.
145.
563, 1976.
136.
Vaughan, M. T., and D. J. Weldnet, The relationship of elasticity and crystal structure in andalusite and sillimanite, Phys.
Chern. Minerals, 3, 133-144,
Verma, R. K., Elasticity of some
high-density crystals, J. Geophys.
Res., 65, 757-766, 1960.
Vetter, V. H., and R. A. Barrels,
BaO single crystal elastic constants and their temperature dependence, J. Phys. Chem. Solids,
8, 153-156, 1991.
135.
4664, 1986.
125.
2607-2613, 1974.
133.
8, 475-495, 1980.
63
154.
155.
Orson L. Anderson
1.
and Donald
G. Isaak
ABSTRACT
The techniques
of RUS do not lendthemselves
to pressure measurement.
Data
A synopsisof quasiharmonic
theory in the high temperature limit shows that anharmonic corrections to
evaluated.
2.
INTRODUCTION
bulk modulusKT (computedfrom Ks) and the specificheat at constantV Cv (computedfromCr). The
densityp is computedfrom a, whichallowsthe respective isotropiclongitudinaland shearsoundvelocities,
vp and v, to be computedfrom Ks and G.
lemsin mantlegeophysics
and geochemistry
oftenrequire valuesof elasticconstantsat temperaturesfound
in the lowercrustandmantle(1000to 1900K).
Using the techniquesof resonantultrasoundspectroscopy(RUS) [6, 7], elasticconstantdatahavebeen
taken above the Debye temperature of mantle minerals, often as high as 1825 K, which is of the order
Reference
Shelf 2
64
ANDERSON
AND
ISAAK
elastic
moduli
(GPa)from300to 1800
K
crystal
elastic
moduli
(GPa)from300to
T (K)
300
Cxx
Cx
C44
C$
T (K)
Oil
Cl
C44
Cs
300
296.6
108.5
91.6
94.0
.+1.5
.+1.4
.+0.2
.+1.0
299.0
96.4
157.1
101.3
+0.7
.+0.6
.+0.3
.+0.2
400
292.9
97.0
155.8
98.0
350
294.6
107.6
91.2
93.5
500
296.9
97.6
154.3
94.6
400
292.7
106.9
90.8
92.9
600
280.6
98.0
152.8
91.3
450
291.0
106.5
90.4
92.3
700
274.5
98.4
151.3
88.0
500
289.2
105.9
90.0
91.7
800
268.2
98.5
149.7
84.8
550
287.3
105.2
89.6
91.1
900
261.9
98.6
148.1
81.7
600
285.5
104.6
89.1
90.5
1000
255.7
98.7
146.5
78.5
650
283.8
104.2
88.7
89.8
1100
249.5
98.6
144.8
75.5
700
282.1
103.7
88.3
89.2
1200
243.3
98.4
143.1
72.5
750
280.3
103.2
87.8
88.6
1300
237.2
98.1
141.3
69.6
800
278.5
102.6
87.4
88.0
1400
231.0
97.6
139.5
66.7
850
276.7
102.1
86.9
87.3
1500
224.9
97.1
137.9
63.9
900
274.8
101.5
86.5
86.7
1600
219.0
96.4
136.2
61.3
950
273.1
101.0
86.0
86.1
1700
213.4
95.7
134.7
58.9
1000
271.2
100.3
85.5
85.5
1800
208.2
95.0
133.1
56.6
.+2.0
+1.9
.+0.2
.+1.4
.+1.2
.+0.5
.+0.2
:::1:1.2
Cs - (1/2)(C
- C).
Cs - (1/2)(Cll - Cid).
AfterSuzuki
& Anderson
[65].
From
Isaak
etal.[34].
elastic
moduli
(GPa)from300to1200
K
crystal
elastic
moduli]
(GPa)from300to
T (K)
Cll
Cl
C44
Cs
300
220.5
57.67
80.03
81.43
.+0.1
.+0.08
.+0.02
.+0.04
400
215.7
57.96
79.35
78.85
500
210.7
58.23
78.70
76.25
600
205.9
58.44
77.94
700
201.2
58.66
77.18
800
196.6
58.81
900
192.0
58.98
1000
187.2
58.98
1100
182.7
1200
178.1
.+0.3
.+0.24
T (K)
Cll
300
318.9
92.2
102.9
113.4
.+0.8
9:0.7
.+0.2
400
500
315.2
311.7
91.8
91.5
101.4
100.4
.+0.3
111.7
110.1
73.72
600
307.8
91.1
99.8
108.4
71.28
700
303.8
90.5
98.7
106.6
76.46
68.88
800
97.6
104.9
66.52
74.92
64.13
58.96
74.17
61.89
900
1000
1100
300.2
296.5
292.7
289.1
90.4
75.72
90.2
89.9
89.8
96.5
95.3
94.2
103.2
101.4
99.7
58.99
73.48
59.56
.+0.09
.+0.09
1200
1300
1350
284.8
280.5
278.8
89.1
88.6
88.7
93.0
91.8
91.2
97.8
96.0
95.0
4-1.4
9:1.2
9:0.3
.+0.4
Cs - (1/2) (C - C).
From
Odaetal.[43].
C12
Cs - (1/2)(C - C).
After
Isaak
etal.[36].
C44
Cs
65
66
HIGH
7' ELASTICITY
OF MANTLE
MINERALS
elastic
moduli
(GPa)from300to1000K
elastic
moduli$
(GPa)from300to850K
(max. measured
valueof T/O: 4.42)
T (K)
Cll
300
400
292.2
4-5.2
290.1
288.6
168.7
4-5.2
167.2
166.3
156.5
4.1.0
155.0
155.3
450
500
286.2
284.4
164.8
163.7
154.4
153.6
60.7
60.3
550
600
282.8
281.1
162.8
161.9
152.9
152.2
60.0
59.6
650
297.1
160.8
151.5
59.1
700
277.2
159.8
150.7
58.7
750
800
850
275.3
273.3
271.1
158.8
157.7
156.5
149.9
149.2
148.5
58.2
57.8
57.3
350
C12
44
$
61.8
T (K)
300
4.0.3
61.5
61.1
900
269.2
155.5
147.7
56.9
950
267.3
154.4
146.9
56.4
1000
266.0
4.6.5
154.0
4.6.5
146.1
4-1.3
56.0
4-0.4
350
400
450
500
550
600
650
700
750
800
850
C'
C'
C44
Cs
40.1
6.6
6.35
16.7
4-0.4
4-0.5
4-0.02
4-0.3
38.4
36.9
35.4
33.8
32.3
31.1
29.7
28.2
26.6
25.2
23.5
4-0.5
6.8
7.0
7.1
7.2
7.3
7.5
7.7
6.28
6.21
6.15
6.11
6.05
5.96
5.87
7.7
7.7
7.8
7.7
4-0.5
5.79
5.69
5.57
5.57
+0.02
15.8
15.0
14.1
13.3
12.5
11.8
11.0
10.2
9.5
8.7
7.9
4.0.4
Cs = (1/2)(C'n - C').
AfterY,mamoto
& Anderson
[76].
Cs = (1/2)
AfterCynn
[19].
elastic
moduli
(GPa)from300to500K
elastic
moduli
(GPa)from300to750K
T (K)
300
T (K)
Cn
C44
223.5
111.8
78.1
55.9
4-4.5
4-3.1
4-0.9
4-2.7
300
C'
C'
C44
Cs
49.5
13.2
12.79
18.1
4-0.4
4-0.4
4-0.02
4-0.3
17.1
350
220.4
111.8
78.1
54.3
350
47.6
13.3
12.62
400
217.2
111.8
77.8
52.7
400
45.8
13.4
12.43
16.2
450
214.1
111.7
77.3
51.2
500
210.9
111.7
76.5
49.6
4-4.5
4-3.1
4-0.9
-/-2.7
450
500
550
44.1
42.4
40.5
13.5
13.6
13.5
12.26
12.09
11.90
15.3
14.4
13.5
600
650
38.7
37.0
13.2
13.1
11.71
11.52
12.7
11.9
700
35.4
13.1
11.31
11.2
750
33.7
12.9
11.10
10.4
:::i:0.3
Cs = (1/2)(Cn -- C'2).
AfterPacalo
& Graham
[47].
:::i:0.4
+0.4
AfterYamamoto
etal.[77].
:9:0.02
ANDERSON
AND
Table9. Mg2SiO4'
Measured
single-crystal
elastic
moduli
(GPa)from300to 1700K
(max. measuredvalueof T/O: 2.1)
300
400
500
600
700
800
900
1000
1100
1200
1300
1400
1500
1600
1700
330.0
4-0.7
326.3
322.4
318.6
314.5
310.3
306.3
302.0
297.4
292.8
288.3
283.8
279.1
274.4
269.8
4-1.1
200.0
4-0.4
197.2
194.2
191.2
188.0
184.8
181.5
178.3
175.1
171.8
168.7
165.1
162.2
159.0
155.6
+0.8
236.0
+0.6
233.1
230.1
226.8
223.6
220.3
216.9
213.5
209.8
206.1
202.7
199.2
195.5
192.0
188.2
+1.0
67.2
4-0.1
65.9
64.4
63.0
61.6
60.1
58.8
57.4
56.1
54.7
53.3
51.9
50.6
49.3
48.0
4-0.2
81.5
4-0.2
80.1
78.7
77.2
75.8
74.3
72.8
71.3
69.9
68.3
66.9
65.4
64.0
62.5
61.0
4-0.2
81.2
+0.2
79.6
78.0
76.3
74.6
73.0
71.3
69.6
67.9
66.2
64.6
62.9
61.4
59.9
58.4
4-0.3
72.1
+0.4
71.6
71.1
70.4
69.7
69.1
68.3
67.8
67.2
66.6
66.0
65.2
64.6
64.0
63.3
4-0.7
68.0
+0.5
67.0
66.1
65.1
64.3
63.3
62.5
61.5
60.5
59.4
58.5
57.6
56.7
55.8
54.9
4-0.9
66.2
+0.5
65.2
64.0
62.9
61.8
60.7
59.4
58.4
57.3
56.3
55.3
54.2
53.2
52.1
51.0
4-0.8
t Fzom
Isaak
etM.[35].
Table10. Olivine
Fo90Fam:
Measured
elastic
moduli
(GPa)from300to 1500K
(max. measuredvalueof T/O' 2.26)
T (K)
300
320.6
197.1
234.2
+0.4
+0.3
+0.5
400
316.8
194.1
231.0
62.37
76.3
76.61
74.4
70.3
68.6
500
313.0
190.9
227.6
61.05
74.9
74.97
73.7
69.3
67.4
600
309.0
187.7
224.1
59.73
73.6
73.33
73.0
68.3
66.2
700
305.0
184.6
220.6
58.45
72.3
71.73
72.3
67.2
65.0
800
300.7
181.5
217.2
57.23
71.0
70.17
71.6
66.1
63.6
900
297.0
178.3
214.3
55.91
69.9
68.59
71.2
66.0
62.8
1000
293.1
175.3
210.4
54.68
68.5
67.07
70.3
64.7
61.8
1100
289.0
172.3
206.6
53.47
67.1
65.53
69.4
63.4
60.5
1200
1300
1400
285.1
280.9
276.6
169.2
166.1
163.0
202.9
199.3
195.6
52.28
51.06
49.83
65.8
64.5
63.2
64.01
62.51
61.02
68.6
67.8
67.0
62.4
61.4
60.5
59.4
58.2
57.2
+0.5
4-0.4
4-0.7
1500
272.0
159.8
192.1
+0.07
48.57
4-0.2
62.2
+0.11
59.52
4-0.5
66.4
+0.5
59.8
+0.4
56.2
tFzom
Isaak
[32].
C:2
Caa
C44
63.72
+0.05
C55
77.6
+0.1
C6s
78.29
+0.08
Cs
74.8
4-0.3
Cs
71.2
+0.4
C2
69.8
+0.2
ISAAK
67
68
HIGH
T ELASTICITY
OF MANTLE
MINERALS
Table11. Fe2SiO4:
Measured
single-crystal
elastic
moduli
(GPa)from300to
700 K (max. measuredvalueof T/O' 1.41)
T (K)
C22
Css
C44
C55
C66
C23
C12
C31
300
266.9
173.5
239.1
32.4
46.7
57.3
97.9
98.7
95.1
350
400
J:1.9
264.5
262.2
J:1.1
171.8
170.1
J:1.4
237.0
234.7
J:0.1
31.9
31.7
+0.1
46.2
46.0
J:0.1
56.3
55.3
J:1.2
97.7
97.4
J:1.6
98.2
97.7
J:1.5
94.3
93.4
450
500
260.7
258.8
168.4
166.6
232.4
229.9
31.4
31.4
45.8
45.8
54.5
53.7
97.2
96.8
97.5
97.0
92.8
91.9
550
600
650
700
257.0
255.0
252.8
251.0
J:2.2
164.9
162.8
160.9
159.0
:]:1.3
227.5
225.1
222.7
220.5
J:l.6
31.4
31.5
31.5
31.6
:]:0.1
45.7
45.6
45.6
45.5
J:0.1
52.9
52.3
51.6
51.0
J:0.2
96.5
96.0
95.4
94.8
:]:1.3
96.6
96.1
95.5
94.9
4-1.8
91.0
90.0
88.9
87.7
:]:1.7
AfterSumino
[58].
Table12. Mn9.
Si04:Measured
single-crystal
elastic
moduli
(GPa)from300to
700 K (max. measuredvalueof T/O: 1.28)
T (K)
Cll
C44
C55
C66
C23
C31
12
300
258.3
165.5
206.7
45.3
55.6
57.8
91.7
95.2
87.1
400
J:l.9
254.8
+1.0
162.7
:]:1.3
203.9
:]:0.1
44.4
:]:0.2
54.4
:]:0.2
56.4
:t:l.0
90.6
:]:1.5
93.8
J:l.3
85.5
251.3
201.0
198.2
195.3
89.5
92.3
83.8
42.5
52.0
53.7
244.3
159.8
157.0
154.2
41.5
51.8
52.4
43.4
88.3
87.2
53.2
90.9
89.4
55.1
82.2
80.6
4-2.4
4-1.3
4-1.7
4-0.1
4-0.2
4-0.2
4-1.3
4-1.9
4-1.6
500
600
700
247.8
C22
33
AfterSumino
[58].
Table13. Co2SiO4:
Measured
single-crystal
elastic
moduli
(GPa)from300to
700 K (max. measuredvalueof T/O: 1.25)
T (K)
Cll
C22
C33
300
307.7
4-1.2
194.7
4-0.7
400
500
304.0
301.1
192.6
230.7
190.5
600
297.8
700
294.5
4-1.7
C55
C66
46.7
63.9
64.8
4-0.1
4-0.1
4-0.1
227.4
46.2
45.7
62.9
61.9
188.8
224.0
45.2
186.2
4-1.2
220.6
4-1.4
44.7
+0.1
AfterSumino
[58].
234.1
4-0.9
C44
C23
C31
C12
103.2
4-0.7
105.0
4-1.0
101.6
4-0.8
62.8
101.8
100.5
103.6
102.3
99.8
97.9
60.8
61.8
99.1
100.9
96.1
59.8
+0.1
60.8
4-0.2
97.8
4-1.1
99.6
4-1.3
4-1.3
63.8
94.3
ANDERSON
AND
ISAAK
Table14. AleOs'
Measured
single-crystal
elastic
moduli
(GPa)
from 300 to 1800K (max. measuredvalueof T/O' 1.95)
T (K)
300
400
500
600
Cxx
Caa
C44
C2
Cxa
497.2
500.8
146.7
162.8
116.0
+1.5
:!:1.8
+0.2
:!:1.7
+1.0
494.7
490.6
486.0
497.2
493.6
489.2
144.4
141.8
139.2
163.8
163.7
163.1
115.3
114.4
113.0
C14
-21.9
4- 0.2
-22.5
-23.0
-23.3
700
481.5
484.9
136.5
162.9
111.9
-23.4
800
476.8
480.4
133.9
162.4
110.6
-23.7
900
472.3
476.0
131.2
162.4
109.6
-23.9
1000
467.4
471.2
128.6
161.8
108.2
-24.1
1100
462.5
466.4
125.8
161.4
107.1
-24.2
1200
457.3
461.1
123.2
160.7
105.4
-24.3
1300
451.9
456.2
120.4
160.0
104.1
-24.4
1400
446.7
450.8
117.7
159.5
102.4
-24.5
1500
442.2
446.4
115.1
159.4
101.6
-24.5
+1.9
+2.1
4-0.2
+2.2
4-2.1
1600
437.2
441.3
112.5
159.0
100.5
-24.6
1700
432.3
436.5
110.0
158.4
99.4
-24.5
1800
427.2
432.5
107.4
158.0
99.1
-24.5
+ 0.2
t From
Goto
eta].[26].
Table15. MgO:Thermal
expansivity,
specific
heat,isotropic
elastic
constants
andvelocities$
Ks
Cp*
9/
J/(gK)
K.
vr
GPa
km/s
V$
g/cma
10-5/K
3.602
0.63
165.7
132.0
0.194
1.59
0.194
165.6
9.80
6.13
200
3.597
2.24
164.6
130.3
0.662
1.55
0.658
163.5
9.78
6.10
300
3.585
3.12
163.9
131.8
0.928
1.54
0.915
161.6
9.73
6.06
+0.6
+0.5
:t:0.6
4-0.01
4-0.01
+0.06
GPa J/(gK)
Cv
100
4-0.005
GPa
4-0.03
km/s
400
500
3.573
3.559
3.57
3.84
162.3
160.7
129.4
126.9
1.061
1.130
1.53
1.53
1.048
1.098
158.9
156.1
9.68
9.63
6.02
600
3.545
4.02
158.9
124.4
1.173
1.54
1.131
153.2
0.57
5.92
700
800
900
3.531
3.516
3.501
4.14
4.26
4.38
157.1
155.1
153.1
121.8
119.2
116.7
1.204
1.227
1.246
1.53
1.53
1.54
1.153
1.166
1.175
150.4
147.4
144.3
9.51
9.45
9.39
5.87
1000
3.486
4.47
151.1
114.1
1.262
1.54
1.181
141.4
9.33
5.72
1100
3.470
4.56
148.9
111.5
1.276
1.53
1.185
138.3
9.26
5.67
1200
3.454
4.65
146.7
109.0
1.289
1.53
1.188
135.1
9.19
5.62
1300
1400
1500
1600
1700
1800
3.438
3.422
3.405
3.388
3.371
3.354
4-0.007
4.71
4.80
4.89
4.98
5.04
5.13
4-0.10
144.4
106.4
103.8
101.3
99.0
96.7
94.5
+1.6
1.301
1.312
1.323
1.334
1.346
1.358
1.52
1.52
1.52
1.51
1.50
1.50
+0.03
1.190
1.191
1.191
1.191
1.193
1.193
132.1
9.13
9.05
8.98
8.92
8.85
8.78
4-0.04
5.56
142.0
139.7
137.3
134.9
132.7
4-1.1
$Computed
from
Table
1;t Suzuki
[64];
'Garvin
etal.[25].
128.1
125.7
122.5
119.6
116.6
4-1.1
5.97
5.82
5.77
5.51
5.46
5.41
5.36
5.31
4-0.05
69
70
HIGH
T ELASTICITY
OF MANTLE
MINERALS
Table16. A12Os'
Thermal
expansivity,
specific
heat,isotropic
moduli
andvelocities
T
300
Ks
1.62
4-0.03
1.99
2.23
2.40
2.51
253.6
4-1.7
252.6
250.9
248.6
246.6
163.0
4-2.8
161.1
158.8
156.6
154.2
0.779
700
3.982
+0.009
3.975
3.966
3.957
3.947
800
3.937
2.59
244.4
151.9
900
3.927
2.66
242.4
1000
3.916
2.73
1100
3.906
2.80
1200
3.894
1300
Cg
0.774
1.148
1.32
4.0.03
1.34
1.36
1.37
1.36
1.180
1.36
149.5
1.205
1.36
240.0
147.1
1.223
237.8
144.6
1.244
2.88
235.2
142.2
3.883
2.96
232.6
1400
3.872
3.03
1500
1600
3.860
3.848
1700
1800
400
500
600
Ka,vp
1.121
252.0
4-1.7
249.9
247.1
243.8
240.8
10.88
4.0.05
10.84
10.80
10.75
10.70
1.148
237.7
10.65
6.21
1.167
234.8
10.61
6.17
1.37
1.179
231.4
10.55
6.13
1.37
1.194
228.2
10.50
6.09
1.257
1.38
1.199
224.5
10.44
6.04
139.7
1.267
1.40
1.203
220.8
10.39
6.00
230.0
137.2
1.277
1.41
1.205
217.1
10.33
5.95
3.09
3.15
228.1
225.9
134.8
133.5
1.286
1.296
1.42
1.43
1.207
1.209
214.0
210.7
10.28
10.23
5.91
5.86
3.835
3.20
224.8
131.2
1.306
1.43
1.212
207.5
10.17
5.82
3.823
3.25
221.8
127.5
1.318
1.43
1.216
204.7
10.12
5.78
4-0.009
4-0.06
4-2.3
4-4.8
4-2.2
4-0.009
4-0.11
0.943
1.040
1.103
0.933
1.024
1.082
4-0.03
6.40
4-0.06
6.37
6.33
6.29
6.25
Computed
from
Table
14;White
& Roberts
[75];
*Furukawa
etal.[24];
Dimensions
asinTable
15.
Table17. MgA1204'
Thermal
expansivity,
specific
heat,isotropic
moduli$
andvelocities$
T
300
350
400
450
500
550
600
650
700
750
at
Ks
C'p*
0.819
3.576
4-0.005
3.572
3.568
3.564
3.560
3.555
2.11
+0.04
2.18
2.25
2.32
2.38
2.45
209.9
108.2
+5.2
208.2
207.1
205.3
203.9
202.8
4-2.5
107.7
107.2
106.6
106.0
105.5
3.551
2.51
201.6
104.9
1.088
1.115
3.547
3.542
2.57
2.63
200.3
199.0
104.3
103.6
1.139
1.160
1.28
1.27
0.899
0.963
1.014
1.055
1.51
4.0.05
1.41
1.36
1.32
1.30
1.28
Cg
0.811
0.889
0.952
1.001
1.039
Ka.
207.9
vp
4-5.2
205.9
204.6
202.5
200.8
199.4
9.95
4.0.09
9.92
9.91
9.87
9.85
9.83
5.50
4.0.06
5.49
5.48
5.47
5.46
5.45
197.8
9.81
196.1
194.4
9.78
9.76
5.45
5.42
5.41
3.537
2.69
197.7
103.0
1.179
1.27
1.069
1.094
1.115
1.133
1.149
192.7
9.73
5.40
800
3.532
2.74
196.2
102.4
1.180
1.27
1.164
190.9
9.71
5.38
850
900
3.528
3.523
2.80
2.85
194.7
193.4
101.8
101.1
1.213
1.229
1.27
1.27
1.178
1.190
189.0
187.3
9.68
9.65
5.37
5.36
950
3.518
2.90
192.0
100.5
1.243
1.27
1.201
185.5
9.63
5.34
1000
3.512
2.94
191.3
99.8
1.253
1.28
1.208
184.4
9.61
5.33
4.0.005
4-0.06
4-6.5
4-2.7
4-6.3
4-0.11
4-0.07
1.28
4-0.05
$Computed
from
Table
5;tTouloukian
etal.[69];
*Robie
etal.[48];
Dimensions
asinTable
15.
ANDERSON
AND
ISAAK
Table18. Mg2SiO4'
Thermal
expansivity,
specific
heat,isotropic
moduli
andvelocities
T
300
400
500
600
700
800
900
1000
1100
1200
1300
1400
1500
1600
1700
p
3.222
-4-0.007
3.213
3.203
3.192
3.181
3.170
3.159
3.147
3.135
3.122
3.109
3.096
3.083
3.069
3.055
4.0.008
at
2.72
-4-0.05
3.03
3.22
3.36
3.48
3.59
3.70
3.81
3.92
4.05
4.16
4.27
4.39
4.50
4.62
4.0.08
Ks
128.6
-4-0.4
127.1
125.4
123.7
121.9
120.2
118.3
116.6
114.8
112.9
111.1
109.2
107.5
105.6
103.7
4.0.5
81.6
-4-0.3
80.3
78.9
77.4
76.0
74.5
73.1
71.6
70.1
68.6
67.1
65.6
64.1
62.7
61.2
4-0.3
C*
0.840
0.990
1.068
1.119
1.156
1.186
1.211
1.235
1.256
1.277
1.296
1.315
1.334
1.352
1.370
7
1.29
-4-0.02
1.21
1.18
1.17
1.16
1.15
1.15
1.14
1.14
1.15
1.15
1.15
1.15
1.15
1.14
4-0.02
Cv
0.831
0.976
1.048
1.093
1.124
1.148
1.167
1.183
1.197
1.210
1.220
1.231
1.240
1.249
1.257
KT
127.3
4-0.4
125.2
123.1
120.8
118.6
116.3
114.0
111.7
109.4
106.9
104.6
102.2
99.9
97.6
95.2
4-0.5
v,
8.58
4-0.01
$.54
8.48
8.43
8.38
8.32
8.27
8.21
8.15
8.09
8.03
7.97
7.91
7.85
7.79
4-0.02
V$
5.03
4-0.01
5.00
4.96
4.93
4.89
4.85
4.81
4.77
4.73
4.69
4.65
4.60
4.56
4.52
4.48
4-0.01
[Computed
from
Table
9;tKajiyoshi
[38];
*Barin
& Knacke
[15];
Dimensions
asinTable
15.
Table19. Olivine
Fo9oFalo'
Thermal
expansivity,
specific
heat,isotropic
moduliandvelocities
T
300
400
500
600
700
800
900
1000
1100
1200
1300
1400
1500
at
Ks
3.353
4-0.004
3.343
3.333
3.322
2.66
4-0.05
2.99
3.21
3.35
129.3
4-0.3
127.7
125.9
124.1
78.1
4-0.2
76.8
75.3
73.9
0.816
3.311
3.299
3.287
3.275
3.263
3.251
3.238
3.225
3.212
4-0.004
3.46
3.55
3.64
3.71
3.79
3.86
3.93
4.00
4.07
4-0.08
122.2
120.3
118.9
117.0
115.1
113.2
111.4
109.6
107.8
4-0.5
72.5
71.2
69.8
68.5
67.1
65.8
64.4
63.1
61.7
4-0.3
0.957
1.032
1.080
1.112
1.145
1.171
1.194
1.216
1.236
1.256
1.275
1.294
7
1.25
4-0.02
1.19
1.17
1.16
1.14
1.13
1.12
1.11
1.10
1.09
1.08
1.07
1.06
4-0.02
Cv
KT
0.808
128.0
4-0.3
125.9
123.6
121.2
8.34
4-0.01
8.29
8.24
8.19
4.83
4-0.01
4.79
4.75
4.72
118.2
116.6
114.7
112.1
110.0
107.8
105.6
103.4
101.3
4-0.5
8.13
8.07
8.03
7.97
7.92
7.86
7.81
7.75
7.69
4-0.01
4.68
4.65
4.61
4.57
4.54
4.50
4.60
4.22
4.38
4-0.01
0.944
1.013
1.055
1.086
1.109
1.129
1.147
1.163
1.177
1.191
1.203
1.216
Computed
from
Table
10;tSuzuki
[64];
*Barin
&Knacke
[15];
Dimensions
asinTable
15.
V$
71
Table20. Fe2SiO4'
Thermal
expansivity,
specific
heat,isotropic
moduliandvelocities:
T
300
400
500
600
700
'
Ks
Cr*
4.400
4.0.009
4.388
2.61
4.0.05
2.74
138.0
4.0.8
135.9
51.0
4.0.5
49.7
0.673
4.375
4.362
4.348
4-0.009
3.00
3.12
3.22
4-0.06
134.0
131.8
129.3
4-0.9
48.8
48.0
47.4
4-0.4
0.793
0.830
0.863
0.746
C,
1.21
4-0.03
1.18
0.667
1.16
1.13
1.11
4-0.03
0.779
0.813
0.842
0.736
K.
vp
V$
136.7
4-0.8
134.1
6.84
4-0.02
6.79
3.40
4-0.02
3.37
131.7
129.0
126.1
4-0.8
6.74
6.70
6.65
4-0.02
3.34
3.32
3.30
4-0.02
Computed
from
Table
11;Suzuki
etal.[67];
*Watanabe
[72];
Dimensions
asinTable
15.
Table21. Mn2SiO4:
Thermal
expansivity,
specific
heat,isotropic
moduli:
andvelocities
T
300
at
Ks
Cr*
0.666
4.129
2.27
128.9
54.5
4-0.005
4-0.05
4-0.6
4-0.3
1.06
400
4.119
2.57
127.0
53.5
0.736
1.08
500
600
700
4.108
4.096
4.084
4-0.005
2.77
2.91
3.03
4-0.06
125.0
123.0
121.1
4-0.8
52.5
51.4
50.4
4-0.3
0.781
0.818
0.850
1.08
1.07
1.06
4-0.03
Cg
0.661
KT
vp
V$
128.0
6.99
3.634
4-0.6
4-0.01
-90.009
0.728
125.6
6.94
3.604
0.770
0.803
0.831
123.1
120.8
118.4
4-0.8
6.89
6.84
6.79
4-0.02
4-0.03
3.573
3.543
3.512
4-0.011
Comruted
from
Table
12;Okajima
etal.[46];
*Barin
& Knacke
[15];
Dimensions
asinTable
15.
Table22. Co2SiO4'
Thermal
expansivity,
specific
heat,isotropic
moduliandvelocities;
af
300
4.706
4-0.009
2.27
4-0.05
148.2
+0.5
62.0
4.0.3
0.640
1.12
4-0.03
0.636
147.1
4-0.5
7.00
4-0.01
3.621
4-0.009
400
500
600
700
4.695
4.682
4.669
4.655
4-0.009
2.57
2.77
146.2
144.3
142.3
140.4
4-0.7
61.4
60.7
59.9
59.1
4.0.3
0.747
0.803
1.07
1.06
0.739
0.791
144.6
142.2
6.97
6.93
3.611
3.594
0.840
0.868
1.06
1.05
4.0.02
0.825
0.849
139.8
137.3
4.0.6
6.89
6.86
4-0.01
3.557
4-0.010
2.91
3.03
4-0.06
Ks
C*
Cg
KT
vp
Us
3.575
Computed
from
Table
13; (assume
Mn2SiO4);
*Watanabe
[72];
Dimensions
asinTable
15.
Table23. MnO'Thermal
expansivity,
specific
heat,isotropic
moduli:
andvelocitiesJ:
T
300
Ks
(7
C*
3.46
4-0.07
3.58
149.0
350
5.378
4-0.001
5.369
4-2.6
148.0
68.3
4-1.5
67.6
0.632
400
5.359
3.68
146.9
66.7
0.653
0.669
450
500
5.349
5.339
3.77
3.85
145.8
144.8
65.6
64.4
0.682
0.692
4-0.001
4-0.08
4-2.6
4-1.6
?
1.51
4-0.04
1.51
Cg
0.623
1.51
0.641
0.655
1.51
1.51
0.665
0.673
4-0.04
K.
146.7
vp
Us
+2.5
145.2
6.68
4.0.05
6.66
143.7
6.63
3.53
142.2
140.7
6.60
6.57
3.50
3.47
4-2.5
4-0.05
4-0.04
Computed
from
Table
6;Suzuki
etal.[66];
*Barin
& Knacke
[15];
Dimensions
asinTable
15.
3.57
4.0.04
3.55
Table24. CaO'Thermal
expansivity,
specific
heat,isotropic
moduli$
andvelocities
300
Ks
C
0.752
3.349
3.04
112.0
80.59
4-0.001
4-0.06
4-0.1
4-0.02
7
1.35
Cv
0.743
4-0.03
K,
vr
V$
110.6
8.094
4.905
4-0.1
4-0.002
4-0.001
400
3.338
3.47
110.5
79.15
0.834
1.36
0.819
108.5
8.045
4.869
500
3.327
3.67
109.1
77.71
0.880
1.37
0.858
106.4
7.996
4.834
600
3.314
3.81
107.6
76.22
0.904
1.37
0.877
104.3
7.946
4.796
700
3.301
3.92
106.2
74.76
0.921
1.37
0.888
102.3
7.897
4.759
800
3.288
3.275
4.01
104.7
103.3
73.33
71.90
0.933
0.943
1.37
0.894
0.898
100.3
900
98.4
7.848
7.799
4.723
4.686
1000
3.262
4.14
101.7
70.40
0.952
1.36
0.901
96.3
7.745
4.646
1100
3.248
4.20
100.2
68.99
0.959
1.35
0.903
94.3
7.693
4.609
1200
3.234
4.26
98.7
67.56
0.965
1.35
0.903
92.3
7.640
4.571
4-0.002
4-0.09
4-0.2
4-0.08
4-0.3
4-0.006
4-0.003
4.08
1.36
4-0.03
Computed
fromTable
2; Odaetal.[43];
'Garyin
etal.[25];
Dimensions
asinTable
15.
_
Table25. Grossular
garnet:
Thermal
expansivity,
specific
heat,isotropic
moduli
andvelocities
T
300
400
500
600
700
800
900
1000
1100
1200
1300
al
3.597
1.92
167.8
106.9
0.736
1.22
4-0.006
4-0.05
4-0.7
4-0.2
3.589
3.532
3.522
2.28
2.49
2.61
2.71
2.78
2.83
2.88
2.92
166.2
164.9
163.3
161.6
160.3
158.9
157.5
156.2
105.7
104.5
103.1
101.8
100.5
99.1
97.7
96.4
.0.865
0.945
0.995
1.028
1.052
1.072
1.092
1.113
1.22
1.21
1.20
1.19
1.19
1.19
1.18
1.16
0.855
0.931
0.977
1.006
1.025
1.041
1.056
1.073
3.512
3.501
4-0.006
2.97
3.00
4-0.07
154.4
94.9
1.139
1.14
1.095
148.3
152.6
4-1.2
93.4
4-0.2
1.170
1.12
4-0.03
1.121
146.2
4-1.2
3.581
3.571
3.562
3.552
3.542
Ks
Cu
0.730
4-0.03
K,
vr
166.6
9.29
5.453
4-0.7
4-0.01
4-0.006
164.4
9.25
9.22
9.18
9.14
9.10
9.06
9.03
8.99
5.427
5.401
5.373
5.346
5.318
5.289
5.259
5.230
8.94
8.90
4-0.02
5.198
5.165
4-0.008
162.5
160.3
158.1
156.2
154.3
152.3
150.6
J;Computed
from
Table
4;Isaak
etal.[36];
*Krupka
etal.[39];
Dimensions
asinTable
15.
Table26. Pyrope-rich
garnet:
Thermal
expansivity,
specific
heat,isotropic
moduli;
andvelocities:
T
300
400
500
600
700
800
900
1000
p
3.705
at
2.36
171.2
Ks
92.6
0.726
1.50
4-0.005
4-0.04
4-0.8
4-0.4
3.696
3.686
3.675
3.664
3.653
3.642
3.631
4-0.005
2.64
2.80
2.90
2.97
3.03
3.07
3.11
4-0.06
168.9
167.0
164.9
163.2
161.3
159.3
157.3
4-1.1
91.6
90.6
89.7
88.7
87.6
86.5
85.5
4-0.6
Cg
1.34
1.29
1.26
1.24
1.23
1.22
1.21
4-0.02
vr
169.4
4-0.8
0.02
4-0.01
0.889
0.964
1.010
1.040
1.057
1.068
1.076
166.5
164.0
161.4
159.1
156.6
154.1
151.6
4-1.1
8.87
8.84
8.80
8.76
8.72
8.68
8.64
4-0.03
4.98
4.96
4.94
4.92
4.90
4.87
4.85
4-0.02
4-0.03
0.902
0.981
1.032
1.067
1.088
1.104
1.116
K,
0.718
Computed
from
Table
3;t Suzuki
&Anderson
[65];
*idare;
Dimensions
asinTable
15.
8.92
5.00
74
HIGH
T ELASTICITY
OF MANTLE
MINERALS
Table27. NaCI:Thermal
expansivity,
specific
heat,isotropic
elastic
moduliandvelocities
T
300
350
400
450
500
550
600
650
700
750
p
2.159
4-0.005
2.146
2.132
2.118
2.104
2.089
2.074
2.059
2.043
2.026
4-0.006
at
Ks
11.8
4-0.2
12.2
12.7
13.2
13.7
14.3
14.8
15.4
16.0
16.6
4-0.3
25.3
4-0.3
24.8
24.2
23.7
23.2
22.5
21.7
21.1
20.5
19.8
4-0.3
14.71
4-0.08
14.27
13.81
13.39
12.96
12.53
12.11
11.68
11.25
10.80
4-0.11
C'*
0.868
0.883
0.897
0.910
0.923
0.937
0.950
0.964
0.979
0.997
7
1.59
4-0.04
1.60
1.61
1.62
1.64
1.64
1.63
1.63
1.63
1.63
4-0.04
C'v
0.822
0.826
0.829
0.830
0.830
0.830
0.830
0.829
0.828
0.829
Ka.vp
24.0
4-0.3
23.2
22.4
21.6
20.8
19.9
19.0
18.1
17.3
16.5
4-0.3
4.56
4-0.02
4.52
4.47
4.43
4.39
4.33
4.27
4.22
4.17
4.11
4-0.02
2.610
4-0.008
2.579
2.545
2.514
2.482
2.449
2.416
2.382
2.346
2.309
4-0.012
Computed
from
Table
8;tEnck
&Dommel
[22];
*Stull
&Prophet
[57];
Dimensions
asinTable
15.
Table28. KCI:Thermal
expansivity,
specific
heat,isotropic
elastic
moduli;andvelocities;
T
300
350
400
450
500
550
600
650
700
750
800
850
at
Ks
1.982
4-0.005
1.971
1.959
11.0
4-0.2
11.3
11.7
17.8
4-0.4
17.3
17.0
9.47
4-1.03
9.18
8.91
1.948
1.935
1.923
1.910
1.897
1.883
1.869
1.855
1.840
4-0.005
12.1
12.6
13.2
13.7
14.2
14.7
15.2
15.7
16.2
4-0.2
16.6
16.1
15.7
15.4
15.0
14.5
14.0
13.6
12.0
4-0.4
8.64
8.39
8.13
7.85
7.57
7.29
6.98
6.67
6.41
4-0.13
C*
0.689
0.701
0.713
0.724
0.735
0.745
0.756
0.767
0.778
0.791
0.806
0.823
7
1.44
4-0.04
1.42
1.42
1.42
1.43
1.44
1.45
1.46
1.46
1.44
1.43
1.39
4-0.04
C'v
0.657
0.664
0.669
0.672
0.674
0.675
0.676
0.676
0.677
0.679
0.683
0.691
Ka.vp
17.0
4-0.3
16.4
15.9
3.92
4-0.09
3.88
3.84
2.19
4-0.12
2.16
2.13
15.4
14.7
14.2
13.7
13.2
12.6
12.0
11.5
10.9
4-0.3
3.80
3.75
3.71
3.68
3.64
3.59
3.53
3.48
3.42
4-0.03
2.11
2.08
2.06
2.03
2.00
1.97
1.93
1.90
1.87
4-0.02
Computed
from
Table
7;tEnck
etal.[23];
*Stull
&Prophet
[57];
Dimensions
asinTable
15.
ANDERSON
AND
300
400
1034
1029
r
0.235
0.237
$
3.30
3.16
$T
(ZT-Zs) v
5.71
5.16
5.71
5.16
1.82
1.49
1.60
1.52
aKT
MPa/K
GPa
4.08
4.98
0.00
0.45
0.98
500
1022
0.239
3.20
5.03
6.27
1.35
1.46
5.53
600
1015
0.240
3.31
5.08
6.09
1.29
1.42
5.85
1.55
700
1008
0.241
3.43
5.17
6.05
1.28
1.40
6.03
2.15
800
1001
0.243
3.55
5.29
6.06
1.28
1.38
6.15
2.76
900
1000
1100
1200
1300
1400
1500
1600
1700
1800
994
986
979
971
963
955
947
939
932
924
0.244
0.246
0.247
0.248
0.250
0.251
0.253
0.255
0.257
0.259
3.62
3.66
3.65
3.60
3.51
3.39
3.24
3.06
2.85
2.60
5.37
5.42
5.42
5.39
5.32
5.22
5.08
4.92
4.73
4.50
6.08
6.09
6.07
6.03
5.98
5.93
5.87
5.80
5.74
5.66
1.28
1.29
1.29
1.30
1.29
1.30
1.30
1.30
1.32
1.32
1.36
1.36
1.36
1.37
1.38
1.40
1.43
1.47
1.52
1.58
6.24
6.30
6.40
6.45
6.52
6.57
6.62
6.64
6.64
6.66
1.43
4.01
Calculated
from Tables
4.64
5.93
5.93
6.59
7.24
7.91
8.57
9.24
14 & 16.
300
800
900
945
937
928
920
911
902
894
0.183
0.185
0.188
0.190
0.192
0.194
0.196
2.83
2.79
2.81
2.86
2.92
2.98
3.04
1000
1100
1200
1300
1400
1500
1600
1700
1800
885
875
806
857
847
838
828
820
811
0.198
0.200
0.202
0.204
0.206
0.208
0.209
0.211
0.212
3.12
3.21
3.30
3.41
3.47
3.50
3.46
3.36
3.12
400
500
600
700
Calculated/tom
5.26
1.57
1.33
1.23
1.18
1.16
1.15
1.13
1.40
1.40
1.38
1.37
1.35
1.34
1.32
5.04
5.67
6.00
6.16
6.23
6.28
6.32
0.00
4.74
4.78
5.73
5.34
5.17
5.08
5.05
5.03
5.02
4.84
4.92
4.99
5.08
5.12
5.13
5.07
4.95
4.66
5.05
5.08
5.09
5.10
5.04
4.92
4.75
4.56
4.34
1.12
1.12
1.11
1.10
1.09
1.07
1.07
1.06
1.03
1.31
1.30
1.28
1.26
1.24
1.22
1.21
1.20
1.23
6.32
6.31
6.28
6.22
6.19
6.16
6.13
6.03
6.00
4.24
4.83
4.69
4.67
4.70
(ZT--ZS) v
0.54
1.12
1.73
2.35
2.98
3.61
4.87
5.50
6.12
6.74
7.36
7.97
8.58
9.20
ISAAK
75
(9
6s
6T
300
400
500
600
700
800
900
1000
1100
1200
671
666
660
654
649
643
637
631
625
619
0.210
0.211
0.212
0.213
0.215
0.216
0.218
0.219
0.220
0.221
4.15
3.75
3.60
3.54
3.52
3.53
3.55
3.58
3.62
3.65
6.19
5.54
5.27
5.14
5.07
5.03
5.01
5.00
5.01
5.01
6.00
5.38
5.13
5.01
4.99
4.95
4.93
4.94
4.96
4.99
(zT-zs) v
1.51
1.31
1.22
1.17
1.13
1.10
1.07
1.05
1.03
1.01
1.24
1.24
1.23
1.23
1.23
1.23
1.22
1.22
1.22
1.22
cKT
3.36
3.73
3.90
3.98
4.01
4.02
4.01
3.99
3.96
3.93
0.00
0.36
0.74
1.13
1.53
2.34
2.34
2.54
3.13
3.53
(9
I'
300
400
500
600
700
800
900
1000
1100
1200
1300
824
820
816
811
806
801
796
791
786
780
715
0.237
0.238
0.239
0.239
0.240
0.241
0.242
0.243
0.244
0.245
0.246
4.64
3.93
3.64
3.49
3.41
3.35
3.31
3.29
3.27
3.26
3.25
6.30
5.36
4.98
4.80
4.70
4.64
4.60
4.58
4.57
4.57
4.58
6.09
5.27
4.97
4.87
4.84
4.86
4.90
4.96
5.03
5.11
5.20
(z'-zs)
1.36
1.17
1.11
1.08
1.08
1.08
1.08
1.09
1.11
1.15
1.18
trKT
APTIt
1.22
1.23
1.24
1.25
1.26
1.27
1.28
1.29
1.30
1.31
1.32
3.21
3.74
4.03
4.18
4.28
4.34
4.36
4.38
4.41
4.40
4.38
0.00
0.36
0.75
1.16
1.57
1.98
2.40
2.83
3.25
3.69
5.40
300
350
400
450
500
550
600
650
700
750
800
850
900
950
1000
779
777
775
773
771
769
767
765
764
761
759
757
755
753
751
0.271
0.271
0.270
0.270
0.270
0.270
0.270
0.270
0.270
0.270
0.270
0.270
0.270
0.270
0.270
4.81
4.52
4.36
4.24
4.16
4.11
4.07
4.05
4.01
4.00
3.98
3.98
3.98
3.97
3.97
6.27
5.90
5.70
5.55
5.46
5.41
5.35
5.34
5.30
5.29
5.28
5.29
5.30
5.30
5.32
4.29
4.07
3.96
3.90
3.86
3.86
3.86
3.88
3.89
3.92
3.94
3.98
4.02
4.06
4.10
0.97
1.00
1.00
1.00
1.00
1.02
1.04
1.04
1.04
1.05
1.06
1.07
1.09
1.10
1.11
0.88
0.89
0.90
0.92
0.93
0.94
0.96
0.97
0.98
1.00
1.01
1.02
1.04
1.05
1.06
4.00
4.25
4.40
4.51
4.59
4.64
4.68
4.69
4.72
4.74
4.74
4.74
4.73
4.73
4.71
0.00
0.21
0.42
0.65
0.87
1.10
1.34
1.57
1.81
2.04
2.28
2.52
2.75
2.99
3.23
ANDERSON
AND
300
0.238
0.239
0.240
0.241
0.242
4.45
5.94
6.07
1.16
1.20
3.46
4.20
5.58
5.66
1.14
1.21
3.80
0.36
500
600
700
763
757
751
744
738
4.15
4.15
4.16
5.49
5.48
5.49
5.54
5.50
5.46
1.14
1.14
1.15
1.20
1.20
1.20
3.97
4.07
4.13
0.75
800
900
1000
1100
731
724
718
711
0.243
0.244
0.245
0.246
4.13
4.08
4.05
4.00
5.47
5.46
5.47
5.46
5.45
5.44
5.45
5.43
1.17
1.20
1.25
1.28
1.18
1.20
1.22
1.20
4.18
4.22
4.26
4.31
1200
1300
1400
1500
1600
1700
704
697
689
682
674
668
0.248
0.249
0.250
0.251
0.252
0.254
4.02
3.97
3.90
3.92
3.93
3.96
5.49
5.44
5.37
5.38
5.40
5.42
5.38
5.32
5.24
5.22
5.19
5.16
1.28
1.28
1.28
1.27
1.28
1.28
1.21
1.20
1.21
1.23
1.19
1.20
4.33
4.36
4.37
4.39
4.40
4.39
400
Calculated
tr
a"F
(r-s)
as in Table
aKr
0.00
1.16
1.57
1.98
2.40
2.83
3.25
3.69
4.13
4.5O
5.07
5.43
5.87
29.
300
400
731
725
0.249
0.250
5.24
4.70
6.59
5.95
500
600
700
800
719
713
706
700
0.251
0.252
0.252
0.253
4.46
4.33
4.25
4.21
900
1000
699
688
0.255
0.255
1100
681
1200
1300
1400
1500
675
669
662
665
Calculated
a"F
(r-s)
6.56
5.92
1.07
1.03
1.17
1.17
3.37
3.76
0.00
5.65
5.51
5.44
5.40
5.63
5.50
5.42
5.38
1.02
1.02
1.04
1.06
1.17
1.18
1.18
1.18
3.97
4.05
4.11
4.14
0.75
4.16
4.14
5.36
5.36
5.36
5.35
1.07
1.10
1.18
1.18
4.18
4.17
2.38
0.256
4.13
5.37
5.35
1.13
1.18
4.17
3.22
0.257
0.258
0.259
0.260
4.12
4.07
4.10
4.10
5.38
5.35
5.41
5.43
5.36
5.32
5.39
5.41
1.16
1.18
1.23
1.26
1.18
1.18
1.19
1.19
4.16
4.15
4.14
4.13
3.63
as in Table
29.
aKr
0.36
1.15
1.56
1.97
2.80
4.05
4.46
4.88
ISAAK
77
78
HIGH
7' ELASTICITY
OF MANTLE
MINERALS
300
400
500
600
700
511
506
501
497
494
0.336
0.337
0.338
0.338
0.338
5.99
5.56
5.35
5.24
5.18
7.34
6.85
6.62
6.50
6.45
9.34
7.49
6.02
4.69
3.43
Calculated
from Tables
as in Table
(zT-ss) v
1.12
1.09
1.09
1.11
1.14
1.54
1.33
1.09
0.85
0.60
aKT
3.56
3.82
3.95
4.02
4.06
0.00
0.37
0.76
1.16
1.56
29.
300
400
500
600
700
535
530
525
520
0.315
0.315
0.316
0.317
515
0.317
6.66
5.95
5.61
5.43
5.31
8.19
7.35
6.96
6.76
6.63
8.43
7.57
7.17
6.97
6.84
Calculated
from Tables
as in Table
(sT-Zs) ,
1.44
1.30
1.25
1.24
1.25
1.19
1.19
1.19
1.19
1.20
aKT
2.90
3.23
3.41
3.52
0.00
3.59
1.34
0.31
0.64
0.99
29.
I'
300
400
500
600
700
551
548
545
541
538
0.317
0.316
0.316
0.316
0.316
5.81
5.19
4.88
4.71
4.60
7.32
6.56
6.19
6.01
5.88
5.51
4.91
4.62
4.46
4.35
Calculated
from Tables
as in Table
(Sr-Ss)
1.35
1.27
1.23
1.22
1.21
0.96
0.96
0.96
0.96
0.96
aKT
3.34
3.72
3.94
4.07
4.16
APTH
0.00
0.35
0.74
1.14
1.55
29.
300
350
400
450
500
534
531
527
523
519
0.301
0.302
0.303
0.305
0.307
4.14
4.03
3.94
3.88
3.83
5.96
5.82
5.71
5.64
5.58
8.33
8.14
8.01
7.95
7.94
Calculated
from Tables
az in Table
(z,-Ss)
1.20
1.18
1.17
1.16
1.16
29.
1.56
1.57
1.57
1.57
1.58
aKT
5.07
5.20
5.29
5.36
5.41
APTH
0.00
0.26
0.52
0.79
1.05
ANDERSON
AND
(r
6s
(zT-zs)
aKT
APTH
300
862
0.280
6.03
7.73
5.30
1.12
0.90
4.38
0.00
400
858
0.279
5.72
7.36
5.01
1.20
0.90
4.60
0.45
500
600
854
850
0.279
0.278
5.49
5.27
7.07
6.82
4.78
4.59
1.22
1.21
0.90
0.90
4.79
4.97
0.92
1.41
700
845
0.278
5.10
6.62
4.43
1.20
0.90
5.11
1.91
800
840
0.278
4.96
6.47
4.30
1.19
0.90
5.24
2.43
900
835
0.277
4.85
6.35
4.20
1.18
0.90
5.33
2.96
1000
830
0.278
4.74
6.24
4.11
1.17
0.90
5.43
3.49
Calculated
from
Tables
as in Table
29.
6s
(8-s)
rKT APTH
300
304
0.256
3.47
5.56
5.05
1.32
1.29
2.82
0.00
350
400
300
296
0.258
0.260
3.56
3.65
5.62
5.69
5.00
4.95
1.29
1.27
1.26
1.23
2.83
2.84
0.14
0.28
450
500
550
600
650
291
287
283
278
274
0.262
0.266
3.72
3.80
3.91
4.03
4.14
5.74
5.82
5.95
6.10
6.24
4.90
4.86
4.83
4.79
4.77
1.25
1.24
1.25
1.27
1.29
1.20
1.18
1.16
1.13
1.11
2.86
2.86
2.84
2.81
2.78
700
750
269
264
0.268
0.270
4.23
4.34
6.37
6.53
4.76
4.76
1.31
1.35
1.10
1.08
2.77
2.73
Calculated
0.264
0.265
0.265
from Tables
as in Table
0.43
0.57
0.71
0.85
0.99
1.13
1.27
29.
(9
er
300
350
400
450
500
550
600
650
700
750
800
850
230
227
224
221
218
214
211
208
204
200
196
192
0.274
0.275
0.277
0.278
0.278
0.279
0.282
0.284
0.285
0.286
0.289
0.288
3.77
3.86
3.92
3.97
4.02
4.05
4.06
4.09
4.18
4.27
4.34
4.50
Calculated
5.84
5.88
5.88
5.88
5.88
5.87
5.84
5.83
5.90
5.98
6.04
6.19
(r-s)
4.66
4.77
4.86
4.93
4.97
5.02
5.10
5.19
5.30
5.44
5.61
5.76
1.34
1.34
1.32
1.30
1.28
1.26
1.23
1.21
1.23
1.25
1.27
1.33
1.17
1.17
1.17
1.17
1.17
1.17
1.18
1.18
1.18
1.18
1.19
1.19
as in Table 29.
cKT APH
1.87
1.86
1.86
1.86
1.86
1.87
1.88
1.88
1.86
1.83
1.81
1.77
0.00
0.09
0.19
0.28
0.37
0.47
0.56
0.65
0.75
0.84
0.93
1.02
ISAAK
79
80
HIGH
T ELASTICITY
OF MANTLE
MINERALS
The appropriateequationsusedin preparingthe tables are presented in Section 2. The various correlations between the thermoelastic constants are pre-
Mie-Griineisenequationof state).
tion 3.
so that
The
mineral
data
4.
3. EQUATIONS
OF
PHYSICAL
Once
the elastic
in Section
- v
6.
USED IN TABLED
VALUES
PROPERTIES
constants
OT v
where//is
the thermal pressure.Thus alCT is the
slope for the PT/versus T curve at constant V.
-f
tiT,
(7)
a KT
(1)
- - ( ) (Ks
OT
) --(OlnKs
6T
----(o
f,'
) (O
KT
)r _(O
OT
0n
inK,
p )r
r- - (a--J-)
(-)p
OG
Ptl-/(OT)v
dT.
If alCT is independentof T at constant V and also
independent of volume, then aKT comes out of the
O).
(s)
APTH -- aKt(T-
300).
(9)
Cv =
1 -F a7T
(10a)
(9-
Ks
4rM (vS
+2v-S)-/s' (5) KT-- 1+a7T'
(lOb)
ANDERSON
AND
ISAAK
81
/0n
v/
v-- /9n
vp p'
sure.
3Ks - 2G
a - 6Ks+ 2G'
4. SOME
CORRELATIONS
PROPERTIES
IN THE
(12)
FOUND
TABLES
FOR
showingthe relationship
between/a,/s and-r is [10]'
tionscalculated
by (5) is 1094K. The valuesvp- 10.94
kin/s, vs - 6.69 km/s, and p0 - 4.108g/cma usedin
the calculationare givenby Yeganeh-Iiaeriet al. [78].
Oac for corundumis 1033 K, and p0 - 3.981. This
similarity in valuesof Oac and p0 suggeststhat the
OnT
p OnTP1}
{1+ [(o')na)(On-r)
(1+
. (13)
- -
If the relative increasein a with T nearly compensatesfor the relative decreaseof -r with T taking into
accountthe changein the denominatorof (13), then
we may expect that /T- /s is closein value to 'rSince the rate of changeof 7 with T is seldom the
same as the rate of changeof a with T, we see that
tT--S = -r may be an approximationvalid onlyovera
limited range of temperatures,usuallynear and above
1100
O.
In somethermodynamics
manipulations,the approximation/a,-s = -r is useful.In Tables29-42, we show
_.perovskite
.
lOOO
900
is
8OO
/a,-/s - -r.
a-Mg SiO
4
(14)
7OO
600
cause
thecorrection
involves
- f a-rq
dT,and
allval-
I
200
,
600
1000
I
1400
1800
Temperature (K)
data for O (acoustic)for perovskiteat roomtemperature. The dashedline showsthe expected variation
of O (acoustic)with T, yielding a value near 900 at
1900 K.
82
HIGH
T ELASTICITY
OF MANTLE
MINERALS
which allows one to calculate G for KT in high temperature ranges where G is not known. It immediately followsfrom (15) that, becauseG is lessthan
mus
5.
PRESENTATION
I.
OF
MINERAL
DATA
ences.The (7ij data for thirteenof the fourteenminerals in Tables 1-14 were retrieved by the already defined
minerals
deviations
of each measured
errors in-
these thirteen
These
de-
2% (unlessspecified
otherwisein the originalreference
from whichthe a data are obtained)and rigorously
propagateerrorsto p, Cv, K., %, and v, at highand
low temperaturesin Tables 15-28. The uncertainty in
the dimensionless
quantities5s, gT, I', and v shouldbe
taken as5% or more,sincethe valuesof theseparameters can dependsomewhat on the order of polynomial
modal
5a. MgO
echo method
reflect how consistentthe frequencydata are in providare not from RUS mea-
to obtain
ambient
Graham[47]from a weightedlinearregression
analyses
togetherwith the PacaloandGraham[47]temperature
derivatives.
VRH schemeto determinethe isotropicG for KC1 becauseof difficultiesin interpreting the HS upper and
spectively.
an alternative
source for
ditch [80]. In their Table 2, Zouboulisand Grimsditch [80]report Cu(T), C44(T), and the combined
moduli(Cll --C12--2C44)/2and (Cll -C12)/2 versusT. However,there is more scatter(especiallyin
the C44modulus)in the data of ZouboulisandGrim,sditch[80]thanin the dataof Isaaket al. [34].We find
excellentareement
in (oCij/c?T)p
valueswhencomparingthe resultsof Spetzler[55],Suminoet al. [63],
and Isaaket M. [34]in their T rangeof overlap.The
high T (i.e., T > 1400K) Zouboulisand Grimsditch
[80] data haveT dependence
nearlyidenticalto that
of the Isak et al. [34]data up to 1800K.
The valuesof the dimensionless
parameters,s, T,
F, and v, in Table 30 are foundusingsixth orderpoly-
ANDERSON
AND
ISAAK
83
5b.
CaO
Garnet
the T derivatives
MnO
valsof50Kwherethenonzero
valueof (O:Cij/OT:)r
recommendedfirst temperature derivatives are based
on both ultrasonicpulse-echo
[47] and resonant[62]
a value of 0.97 over the 300-1000 K range in T. Thermal expansion a data on pyrope-rich garnet are also
Grossular
Garnet
84
HIGH
T ELASTICITY
OF MANTLE
MINERALS
(149.0:t:2.6 GPa) and that givenby Pacaloand Graham [47](150.64-2.5GPa). The valuesat 500 K in our
Table 6 require an extrapolation of 27K beyond the
39.
5g. KCI
Table 7 showsCij for KCI wherewe use the Yamamotoand Anderson[76]data to interpolateat even
intervalsof 100K. The C, C2, and C44 [76] are
Yamamoto
et al. [77]is assumed
to be 0.005gm/cms
the VRH
used to calculate
of measurement
to a polynomial;Yamamotoet al. [77]
find T derivativesby taking a finite differencebetween
two adjacent data points.
5i. MgaSiO4
5h.
NaCI
to T near ambient
[27,40].Thereis general
agreement
between
thedata
requires a large volume to be heated when increasing temperature. For these reasonswe prefer the data
data.
the
values
in the li,terature).Isaaket al. [35]usedth
HS averagingscheme.There is only a smalldifference
(< 0.1 GPa) betweenthe two approaches.Isaak et
al. [35] showthat fits of the Ks, K., G, v, and vs
data with T imply that third order polynomialsare
appropriateto describethe data. Thus we use third
ANDERSON
werelimitedto temperatures
nearambient[40]. We includethe Cij for Fo90.sFa9.5
(referredto hereasolivine
Fo90Fax0)in Table 10. There are somedifferences
betweenthe Cij of the twoolivinesreportedby Isaak[32]
AND
ISAAK
85
at a muchlowertemperature(65 K).
Sumino[58] alsoreportselasticitydata on single-
in chemistry.The uncertainties
in Ks and G (and in
all propertiesthat dependon Ks and G) aresomewhat
smallerin Table 19 than foundin Isaak [32]for these
quantities. Isaak [32] estimatedthe uncertaintyby
simply adding the uncertaintywith whichthe HS averagevalueis known to the distancebetweenthe average
value and the HS high value. Here we squareboth the
uncertainty of the HS averageand the distance from
the HS averageto the HS high value, add the squares,
and take the root. We use linear fits in T to the Ks,
Sumino[58]presents
T datafrom25-400C(398673 K) on the elasticityof single-crystal
Fe2SiO4(fayMite). We interpolatethe Sumino[58] fayMite data
(seehis Table 3, specimen
TA) so as to provideCij
from 300-700 K in regular 50K intervals in Table 11.
A small extrapolation over 27K is required to extend
the values represented in Table 3 to 700 K. It should
be noted that there are questionsregardingthe values
Co2SiO4are linearly dependenton T with the exception of (744 for Co2SiO4. We construct Tables 12 and
T measured in order to
rametersall T derivatives
areassumed
linearin T (see
Figure2 in Sumino[58]).
51. Corundum (AI2Oa)
The C'ij(Table14), Ks, and(7 (Table16) for AlaO3
are thosefound in Goto et al. [26]. The Ks and G
givenby Goto et al. [26] are foundby the the VoigtReuss-Hill averaging scheme. Full account is made of
the differencebetweenthe Hill (averagedVRH) valuesfor Ks and G and the Voigt (upperbound)values
when assigningerrors to Ks, (7, and other isotropic
quantitiesderivedfrom them. This accountsfor larger
errors being assignedto the G valuesin our Table 14
86
HIGH
T ELASTICITY
OF MANTLE
MINERALS
14 and 16 at 300 K.
tisticalconsideration,
i.e., an Fx test [18]. Thus,the
Ezv-
(17)
j=l
Yi= hwJ
kT'
(18)
(19)
where
29.
8pN
6.
THEORETICAL
PROPERTIES
BASIS
AT
HIGH
FOR
OBSERVED
8pN
AT,-- kT n
(1- e-yj)-- kT .ATIt.
i.
TEMPERATURE
j=l
sulatoris [41]
4TH the energy arising from temperature excitation, called the thermal energy. Ezv is not affected
by T, as shownin (17). Thus 4TH --* 0 as T --. 0.
However, Avlr --* Ezv as T .- O, and Ezv is a nonzero number. Ezv is sufficiently small that for most
numerical evaluations it could be dropped, but it is
useful to keep this term in Av.r for algebraicmanipulations
is thus
to vibrate
.A = ET=o + .ATH,
statistical
mechanical
definition
(21)
around a lattice
point.
The
(20)
j=l
of the vibra-
(16)
(22)
where
(23)
A = EsT + Aver,
(24)
ANDERSON
AND
ISAAK
Cv
-k (e,Yse';),
= Cvs.
not dependentupon T, the sum n(1- e-ys) dependsuponT. When wj are different,then Yi are also
different, and the sum above becomesT-dependent,
especially at low T.'
The internal energy/g is found by applying the for-
87
(31)
$-kyi(ey' _1)-k n
(1-e-")
(32)
The expression
for aKw isfoundby applying02/OTOV
to (22), yielding
aKw
- -.
y (e',1)]'
(33)
Yi --Ew=0
+ kTZ Ewts.
/g--ET=0
+kTj=lZeY,_l
j=l
To get a we divideaKw (givenby (33)) by Kw, defining Kw =-V(OP/OV)w, and usingP givenby (26).
Using(30), wefind that oKw= 7Cv IV, and equating this to (33), we find that [16]
kT
p__(OEs
+- . 7jeS- 1,
OV )+- Z 7jYj
Y-
Cv '
(34)
where
n
wI
7.= 0
OtnV
(27)
(2s)
Y'
Pw,- kF 7ieys
- 1'
(29)
energy.
tain seriesexpansions.
The argumentin (16) becomes
small sincehwj << kT, that is, Yi is small. At high
temperatures,wetake advantageof the expansion[79],
n
(1-e
-y')--n
yj-(-y]
+...)
n
(1-1
---nyj+
vs).
(35)
PT,--F .Aws.
(30)
that
1
(36)
HIGH
T ELASTICITY
OF MANTLE
at
MINERALS
.A.ar
- kT (n
y,- yj).
(37)
Aht-Es+Ez+kT(n-Ej). (38)
J
Yht
- (T-oo)
= 3pN
y"7j,
(44)
(39)
j=l
In- 3pN
Inj,
(40)
- 3pNT ( in h-
in kT).
(41)
6d. Thermodynic
Properties in the High T
Lit
of the Quasiharmonic Approximation
At high T, A includesonly the static potential and
the thermal energy in the quiharmonic approxima-
Tables 15-28.
thedeparture
from(07/OT)p: 0 is slight,however.
Applyingthe operator-(O/OV)a. to (38), we find
thehighT pressure,
pat, whichbyusing(44)becomes
" v) - r(0, v) +
(45)
P't -
3pR
V
7at T.
(42)
Chw
t -- 3pR.
V 7atT.
3pR
(43)
3R7ht
p0(1
--aT)T.
PT.- (M/p)
(46)
is given by
APa-. -Pa"
(47)
interestto geophysicists
(OCv/OT)r = 0 at high T.
This is true for MgO, CaO, and A12Oaand NaCI, but
not for olivine, garnets, spinel, or KCI. We must con-
ANDERSON
10
/ /
//
CaO
' 6.0 67FeSiO,
/// /
4.0
v) =
8NaCL
<:1
0'00
v)
3Rp
qht
(M/p)7a,(1)T,
(49)
6 8
2.0
(OK
3Rp
aTt)v-_- (MIr--
7t(1
- qh,)
.
T/o
(OAPTH
--(M/r)
3R7ht
aT )r - aKT
po(1-aT)- const.,
(48)
for silicates
of constant
M/p, !3 = const
p4/S[2],we
seethat (OP.f/OT)rshould
increase
ass/4: In general,the mineralwith the highestvalueof po/(M/p)
will havethe highestslope,according
to (48), andthat
is borneout by the experimentalresultsshownin Figure 2.
89
3 Spinel
4 Grossular
5Mg2SiO4
'
ISAAK
AI203
8.0
AND
(50)
(OKT)
(O'T)
(51)
OT p _(OKT)
OT v --aKT
OP T '
Thus at high T, alongan isobar,
OTp-- (M/p)
7ht
(1--qht)
_aK.
,OP.'
The term on thefar right of (49) is the thermalbulk
modulus,KTH. Using(48) in (52), we have
OKT
(qta_
1)--aKT
k,aPT'
OT p --aKT
Letting aKT:
(53)
(01)
OT r __aKT(K,+qt_i).
qht= 1.4 [8]. Thuswefindfrom(53) that a predictedvalueof (OKT/OT)p = 0.031 GPa/K. This
result agreeswell with the measurementsfound in Ta-
ble 16 showing
(OKs/OT)pto be 0.03GPa/K in the
high T range.
90
HIGH
T ELASTICITY
6f. Entropy
OF MANTLE
MINERALS
and
Sat- -3pR(n
kT- n
h + 1).
(54)
Applyingtheoperator(0/c9T)gto thepressure
given
sentially
independent
of anharmonicity.
If (OP/OT)v
is independent
of T, then a is controlled
by (57), a
strictly quasiharmonicequation.
5T=(qat_
1)+(OKT
k,Op)
(aKw)at
= 3pRyat
V -_ Ctyat
(M/r)p0(1-aT)
(55)
(OKT/OP)T -- K is virtuallyindependent
of T, and
theexperimental
evidence
isin favorofthis,5T at high
T shouldbe slightlyhigherthan K, providingq > 1.
We deriveda relationshipbetweenthreeimportant
dimensionless
thermoelastic
constants
at highT. The
Tables
aboveequationcan be expressedas
Equation(55)is to be compared
to (48). The actual
measuredaKT will have more structure than aKT
29-42
show.
Usingtheexpression
forK t versus
T, (49),andthe
expression
for aKT givenby (48), we have
aKT
a-KTo+ (OK"t
OT)r T'
(58)
Equation(58)isappropriate
forhighT only,arisingas
it doesfrom the high temperaturelimit of the quasiharmonicapproximation. For the low temperature
equationcorresponding
to (59), we takethe logarithmic derivativeof 7, as definedby (1), yielding
(56)
q-- (On)
0tn T_&r_K,+l_(OnCv)
'0n
V T. (59)
(57)
fortheP - 0 isobar
andwhere
a - (OKt/OT)p,
a-- KTo
--aT
is independent
of V abovethe Debyetemperature.
quasiharmonic
approximation.This steadyincreaseof
a with T at high T doesnot necessarily
requirethe
fourproperties.They alsosuggest
that the quasiharmonicapproximation
may or may not be validfor Cg
yondthe quasiharmonic
highT approximation,
(41).
It arisesbecause
the denominator
in (57) hasa term
that decreases
withT evenin the quasiharmonic
approximation.
Wesawsomeevidence
of anharmonicity
for anharmonic
effectsfor pressures
andtemperatures
corresponding
to mantleconditions.For an explana-
ANDERSON
AND
ISAAK
91
tion of why P, KT, aKT and a do not require anharmonic correction, while at the same time Cv and S
may require anharmoniccorrection,see Andersonet
tion of T. Anderson[3] used (61) in a more convenient form, which followswhen 5s is independentof
al. [13].
T. Along isobars,
7.
HIGH
TION
TEMPERATURE
EXTRAPOLA-
[v(:r)]
FORMULAS
7a. Introductory
Comments
Ks--Kso
L Vo
L Po J
Using(62)heestimated
Ks forMgOupto 2000C(see
Figurei andEquation(21) of Anderson[3]). Sumino
et al. [61] used(62) to extrapolatevaluesof Ks for
forsterite
act)- ao
Knowledgeof Co(T) is not requiredfor (62) and
(63), but someknowledge
of a(T) at highT isrequired
to get p(T) at high T. The appropriateequationrelating p and a is
If 7 is independent
of T, asin the caseof MgO, CaO,
andMg2SiO4at highT, andif a(T) andCp(T) data
p(T) - 0exr -
a(T) d
(64)
determined
from (1), is useful.Using(1)
[c"]
Cro J
(6o)
Ks(T)-[a(T)V(T)]
aoo
that minimizes
the
dependence
of Ks upona(T) and p(T).
Combining(1) and (2), wehave
(MgO). We emphasize
that reliableextrapolations
using (60) requirethat a be knownat high T and the
OKs
aKs
- .
s.Cr(65)
OT )p - -s
Integrating(65) with respectto T
Ks(T)- Ks(To)
- -
V dT.
f Ss7CP
(66)
assumptionthat 7 is constant.
With
(61)
tCs() -
78s
oo
[H(T)-H(To)]
[1_a(TTo)]
2
'
(67)
92
HIGH
T ELASTICITY
OF MANTLE
MINERALS
whereH(T) - f Cp dT is theenthalpy.
Equation(67) showsthat Ks(T) shouldbe linear in
H(T). This wasprovenexperimentallyfor three mineralsfor 300 < T < 1200 K by Sogaet al. [54], and
for the same three minerals for 300 < T < 1800 K by
0)P To(T-To).
o'(T)
--o'o
+ ('
sequencein the calculation and can be ignored. Anderson[5] used (67) to extrapolatethe velocitiesof
soundfrom O to the melting point. Equation (67) is
_----
130
(69)
Surmno
elal.[1977]
z:x,,.
......... Extrapolation
(Eq.
60)
--
Extrapolation
(Eq62)
_,.'.-.....
-....
'--_......Extrapolatio
(Eq
67)
.. 120
110
-.
100
II
400
Fig. 3.
150
140
120
11o
(68)
.".J
2000
Sumino
et
al.
[1983]
MgO
,
500
1000
1500
2000
2500
3000
T (K)
1600
100
To
&&&,.
(a.- a")
170
130
160
1200
T (K)
800
Fig. 4.
ANDERSON
AND
ISAAK
93
9O
The equation of G is
Extrapolation(Eq. 68)
Extrapolation(Eq. 70)
8O
Ks(T).
G(T)
- 3(1
(1-+2r(T))
r(T))
70-
(70)
andvpareextrapolated.
Sumino
et al. [61]gavevalues
for the extrapolatedvaluesof v, andv for forsteritcup
Mg2Si04
50
'
0
400
800
1200
1600
2000
T (K)
Fig. 5.
actualmeasurements
of v, andv by Isaaket al. [35]
and presentedin Table 15 are alsoplotted. It is clear
that the extrapolations
by Suminoet al. [61]werequite
successful.
170
,i
Cossular
(GGD)
",'.
8.8
8.6
TS1
160 -
8.4
8.2
k'%
,,.//6,
at
high
T
' A
7.8
'.
150
7.6
- -- - Extralat
(Sumino
elal.[1977])
5
6s at lowT
140
4.8
4.6
4.4
130
4.2 -
200
500
1000
15oo
20oo
T (K)
Fig. 6. Observedand extrapolatedvaluesof vp and
v, versusT for forsteritc.Experimental(plottedsymbols):Suminoet al. [61]up to 700 K; Isaak et al. [35]
up to 1700K. Extrapolationsby Suminoet al. [61]are
from 700 to 2200 K and are confirmed to within
1.5%
600
1000
1400
1800
Temperature
(K)
Fig. 7. Observedand extrapolated valuesof Ks vs. T
for grossulargarnet. Experimental points shown with
94
HIGH
T ELASTICITY
OF MANTLE
MINERALS
110
8s and I
Grossulor(GGD)
105 -
100 \
95TS1
F af low T
90-
F at highT
85-
Acknowledoements. The authors thank former members of the mineral physicslaboratory who contributedto
the dt bnk published here, including M. Kumazwa,
I. Ohno, Y. Sumino, I. Suzuki, S. Yamanoto, T. Goto,
tt. Oda, S. Ota, and H. Cynn. We acknowledgewith
thnks the works of E. K. Graham, N. Sog, R. Liebermnn, H. Spetzler, D. L. Weidner, J. Bass,I. Jckson,and
M. Mnghnni that affectedour researchprograms.Sung
Kim of Azusa Pacific University provided much help in the
statistical analysisrequired to arrive at valuesfor the variousdimensionless
parameters.The salary of one of us was
providedby grantsfrom the LLNL-IGPP branchunderthe
auspicesof the Department of Energy under contractW7405-ENG 48. Support for Mr. Kim w provided by the
Office of Naval Research through Grant no. N00014-93-
75
200
600
1000
1400
1800
Temperalure
(K)
Fig. 8. Observedand extrapolatedvaluesof G (GPa)
versus T for grossular garnet. Experimental points
10544.
IGPP
contribution
no. 3849.
REFERENCES
1.
2.
5.
1965.
between
4963-4971, 1966.
the
Grfineisen
constant
of
the
bulk
modulus
1989.
6.
axliabatic
resonant
ultrasound
and
its
ANDERSON
Measurement
of elastic constants
minerals
at tem-
77-89, 1957.
The dependence
of the Anderson- 17. Barron,T. H. K., A note on the
Grfineisen parameter T
upon
tions,jr. Phys.Chem.Solids,54,
221-227,
1993.
Robinson, Data
bulk
modulus-volume
relatedgeophysical
problems,jr.
Geophys. Res.,
70, 3951-3963,
1965.
constant
data
Lateral
21.
to geophysics,Rev. Ceophys.,30,
57-90, 1992.
14.
Anderson,
O. L., H. Oda, A.
15.
1993.
als and the mineralogy of the upper mantle, jr. Geophys.Res., 94,
Mixtures:
and Related
22.
Calcium
1895-1912, 1989.
in lower mantle
Research:Applicationto Earth
on minerals
constant
variations
13.
1992.
Reduction and
rela-
11.
9S
10.
AND ISAAK
Barin,
I., andO.Knacke,
Thering- 25.Garvin,
96
HIGH
T ELASTICITY
OF MANTLE
MINERALS
calcium-richgarnets,Phys. Chem.
115, 1978.
47. Pacalo, R. E., and E. K. Graham,
Pressure and temperature depen-
(105 Pascals)pressureand at
higher temperatures, Geol. Surv.
Bull., 15, 1-456, 1978.
49. Shankland, T. J., and J. D. Bass,
Calculated AggregateProperties,
310 pp., MIT Press, Cambridge,
MA, 1971.
51. Skinner, B. J., Physical properties of end-members of the garnet
group, Am. Mineral, il, 428-436,
1956.
1966.
Anderson,
Estimation
of bulk
of NaCl:
Ultrasonic
mea-
and H. Prophet
The
elastic con-
stants of Mn2SiO4,
Fe2SiO4,
Elasticconstantsof minerals,in
Handbook
of PhysicalProperties
of Rocks,VIII, edited by R. S.
Carmichael, pp. 39-137, CRC,
BocaRaton, Fl., 1984.
60. Sumino,Y., I. Ohno, T. Goto, M.
Kumazawa, Measurement of elastic constants
and internal
friction
392, 1977.
ANDERSON
63.
8, 475-495,
1977.
1980.
65.
66.
67.
60-63, 981.
68.
single-crystalforsterite Mg2SiO4
69.
70. Wachtman, J. B., Jr., T. G. Scuderi, and G. W. Cleek, Linear thermal expansion of aluminum oxide
and thorium
77.
1983.
78.
79.
97
319-323, 1962.
bounds
ISAAK
AND
the
effective
elastic
80.
Elise Knittle
1.
INTRODUCTION
98
KHE
99
Optic Access
satisfied:
g = 2dsin0
S_ple
lcm
on
Cylinder
Sample
2 cm
Lever
Arm
(1)
100
STATIC
COMPRESSION
Alignment
Sample
et
Screw
Chamber
i
I_
Plate
AlignmentPin
uniaxiallycompress
a samplecontainedwithina large
retainingring whichactsas a gasket. If all or a portionof
theretainingring is madeof a materialtransparent
to x-rays
(suchas B or Be), diffractionmeasurements
canbe madeon
a sampleheld at high pressures.The pressurelimit of the
Bridgman-anvil press is about 10-12 GPa at room
temperature,and the limit of the Drickamerpressis about
BackingPlate
30-35 GPa.
andOpticAccess
Application
to
and cubic-anvil
KNITTLE
III
Upper Diamon(
RubyGrains
Gasket
Sample
Culet Face
ure Medium
Lower
101
Dia
commonmethodfor estimatingthe pressurein all largevolume devices,the oil pressureof the pressis calibrated
against a series of materials or fixed points, with wellcharacterized
phasetransformations,
suchasthoseoccuring
in Bi (the I-II transition at 2.5 GPa and V-VI transitionat
7.7 GPa). Specific disadvantagesof x-ray diffraction
measurements
in large volumepressesinclude: 1) indirect
pressure calibration; 2) an inability to accurately
characterizepressuregradients;and 3) the small volumeof
the sample relative to the containing material, which
necessitates
both careful experimentaldesignand a high
intensityx-ray source. Furthermore,the diffractionangles
availablethroughthe apparatusmay be limited, producing
few redundancies
in the measurement
of latticeparameters.
3.
ANALYSIS
OF
THE
DATA
P = KOT/KOT'{
(Vo/V)KoT
' -1}
(2)
102
STATIC
COMPRESSION
P = 3f(l+2f)5/2KOT(1
+ xlf + x2f2 + ...)
<--40-->
((
Film
,r Solid
State Detector
(3)
X-rays
Sam
wheref is theEulerianstrainvariabledefinedas
Diamond
Anvil Cell
f: 12[(V/Vo)2/3
-]
and the coefficientsin (3) are:
irect X-ray
Xl = 3/2(KOT' - 4)
Beam
The
maximum
distance
between
the
corresponding
x-ray line on eithersideof the transmittedxray beam is 40, which is used in the Bragg equation to
determine the set of d-spacingsof the crystal at each
pressure.
P = 3 KOT(VoIV)2/311-(VIVo)
/3
exp{3/2(KOT'1) [1-(V/Vo)13]}.
(4)
KNrFrLE
lOB
Feedthrough
ressure Medium
X-Rays
Sample
!
5cm
I
pie
Assembly
2cm
Fig. 4a. A piston-cylinder apparatus shown in crosssection. Here, a uniaxialforce is usedto advancea piston
into a cylinder, compressinga pressuremediumand thus
applying hydrostatic or quasi-hydrostaticpressureto a
sample contained within the medium. The piston and
cylinder are usually made of tungstencarbide and the
maximum routine pressurelimit of this deviceis 5 GPa at
room temperature.The feedthroughinto the cylindergives
a way of monitoringthe sampleenvironment.For example,
electricalleadscanbe introducedinto thesampleto measure
temperatureor as a pressuregauge. Another use of the
feedthrough is to provide current to a resistanceheater
surroundingthe sample (not shown). Equation of state
measurementscan be made in this device by determining
the piston displacementas a functionof pressure.(From
[215]).
"ChainSilicates"category.
104
STATIC
COMPRESSION
Chemical
Formula
1 Density Isothermal
Bulk
(Mg/m
3)
Modulus
(GPa)
2
Framework
dKOT/dP
3
Technique
andNotes
4
Ref.
Silicates-
SiO2
2.65
Quartz
37.1 + 0.2
6.2+
115
6.3 + 0.4
98
(fixedfrom
ultrasonicdata)
SiO2
Quartz
2.65
36.4 + 0.5
SiO2
2.65
38.0
5.4
157
2.92
96 + 3
8.4 + 1.9
113
4.29
313 + 4
1.7 + 0.6
176
2.8 + 0.2
M EOS
Quartz
SiO2
Coesite
SiO2
Stishovite
SiO2
4.29
300 + 30
21
4.29
288 + 13
158
4.29
281
179
2.62
70
14
KAISi30 8
High Sanidine
2.56
67
14
CaA12Si208
2.76
94
14
2.76
106
14
3.12
159 + 3
4 (assmed)
77
2.61
70 + 3
5.3 __+1.5
63
Stishovite
SiO2
Stishovite
SiO2
Stishovite
NaA1Si308
Low Albite
Anorthite
(low-pressure
phase)
CaAI2Si208
Anorthite
(high-pressure
phase)
BeAISiO4OH
Euclase
Be4Si2(O2
Betrandite
KNITE
Chemical
Formulal Density Isothermal
Bulk
(Mg/m
3)
Modulus
12NaAISiO4
2.44
-27H20
Zeolite
ReL
dIT/dp3
Technique
andNotes
4
4 (asstuned)
73
69
76
4A
2.24
40 + 1
2.30
52 + 8
0.17(Ca4AI6Si6024
CO3) 0.83(Na4AI3
Si9024C1)
Scapolite
2.54
60
33
0.68(Ca4AI6Si6024
CO3) 0.32(Na4AI3
Si9024C1)
Scapolite
2.66
86
33
0.88(Ca4AI6Si6024
CO3) 0.12(Na4AI3
Si9024C1)
Scapolite
2.71
90 + 12
76
CaMgSi206
Diopside
3.22
114 + 4
4.5 + 1.8
112
CaMgSi206
Diopside
3.22
113 + 2
4.8 + 0.7
116
CaMgSi206
Diopside
3.22
122 + 2
4 (asstuned)
142
CaFeSi206
Hedenbergite
3.56
119 + 2
4 (asstuned)
228
Ca(Mg0.4F.6)
Si206
Hedenbergite
3.42
(Caa)(Mg,Fe,Al)
Si206
Omphacite
(vacancy-rich)
3.26
NaAISi206'H20
Analcite
Na4AI3Si3012CI
4 (asstuned)
Sodalite
Chain
4 (asstuned)
silicates'
82.7 + 1
4 (assumed)
228
129 + 3
4 (assumed)
142
105
106
STATIC
COMPRESSION
Table1. BulkModulifromStaticCompression
Data(continued)
Ref.
Chemical
Formula
1 Density Isothermal
Bulk
(Mg/m
3)
Modulus
andNotes
4
dKOT/dp3 Technique
(Ca,Na)(Mg,Fe,AI)
Si206
Omphacite
(vacancy-txr)
3.29
139 + 4
4 (assumed)
142
MgSiO3
3.22
125
5 (assumed)
159
3.52
161
4 (assumed)
223
{GPa)
2
Enstatite
MgSiO3
B-M EOS
(high-pressure
tetragonal-garnct
structure)
(Mg4Si4012)0.6
(Mg3AI2Si3012)0.4
Majorite
3.55
159.8 + 0.6
4 (assumed)
224
(Fe4Si4012)0.2
(Fe3AI2Si3012)0.8
4.41
164.6 + 1.1
4 (assumed)
224
Mg0.79Fe0.21SiO3
Majorite
3.74
221 + 15
90
MgSiO3
(high-pressure
perovskitestructure)
4.10
247
106
MgSiO3
(high-pressure
perovskitestructure)
4.10
254 + 4
173
MgSiO3
(high-pressure
perovskitestructure)
4.10
Mg0.88Fe0.12SiO3
(high-pressure
perovskitestructure)
4.26
M g 1.0-0.8Fe0-0.2
SiO3
(high-pressure
perovskitestructure)
4.10 -
CaSiO3
(high-pressure
perovskitestructure)
4.25
Majorite
4.4 + 4.8
4 (assumed)
258 + 20
4 (assumed)
220
266 + 6
3.9 + 0.4
102
261 + 4
4.33
4 (assumed)
138
x 10-2 GPa/K
281 + 4
133
KNITFLE
Chemical
Formulal Density Isothermal
Bulk
(Mg/m
3)
Modulus
CaSiO3
(high-pressure
4.25
325 + 10
andNotes
4
dKoT/dp3 Technique
4 (assumed)
Ref.
199
perovskitestructure)
CaSiO3
(high-pressure
perovskitestructure)
4.25
275 + 15
ZnSiO3
(ilmenitestructure)
2.96
216 + 2
2.99
Na2Mg3A12Si8022
(OH)2
Glaucophane
4 (assumed)
200
184
85
35
3.10
96
35
NaCa2Mg4AlSi6A12
O22(OH)2
Pargasite
3.10
97
35
(Na,K,Fe,Mg,A1)7
(Si,A1)8022
(OH,F,CI)2
3.50
50 + 1
13 + 1
229
135.7 + 1.0
3.98 + 0.1
214
Ca2Mg5Si8022
(OH)2
4 (assumed)
Tremolite
Grunerite
Mg2SiO4
3.22
G Pa, M EOS
Forsterite
3.22
120
5.6
159
3.22
122.6
4.3
105
Fe2SiO4
Fayalite
4.39
123.9 + 4.6
5.0 + 0.8
216
Fe2SiO4
Fayalite
4.39
Mg2SiO4
Forsterite
Mg2SiO4
Forsterite
124+2
7+4
5 (assumed)
222
107
108
STATIC
COMPRESSION
Table1. BulkModulifromStaticCompression
Data(continued)
Chemical
Formula
1 Density Isothermal
Bulk
(Mg/m
3)
Modulus
(GPa)
2
Fe2SiO4
Fayalite
4.39
Fe2SiO4
Fayalite
4.39
Fe2SiO4
4.39
124 + 2
diT/dp3
Technique
andNotes
4
Ref.
4 (assumed)
131
Fayalite
134
4 (assumed)
104
168
103.8
7.1
(at 400 C)
(at400 C)
3.05
113 + 3
ZrSiO4
4.65
227 + 2
3.53
174 + 3
Zircon
(Mg0.84Fe0.16)2
SO4
186
Monticellite
4 (assumed)
67
52
Wadsleyite
or[J-Phase
168+ 4
3.53
164 + 2
4 (assumed)
78
(MgFe)2SiO4
3.47 -
171 + 0.6
4 (assumed)
Re-analysisof [78]
92
1.00>Mg/(Mg+Fe)>
3.78
(Mg0.84Fe0.16)2
SiOn
Wadsleyite
or Phase
0.75
Wadsleyite
or fl-Phase
3.47
166 + 40
151
Mg2SiO4
Ringwoodite
or ?Phase
(spinelstructure)
3.55
213 + 10
151
(Mg0.6Fe0.4)2SiO4
Ringwoodite
or ?Phase
(spinelstructure)
4.09
183 + 2
227
Mg2SiO4
Wadsleyite
or -Phase
Fe2SiO4
(spinelstructure)
5.38 + 0.24
4.85
196 + 6
56
Chemical
Formula
1 Density Isothermal
Bulk
0Vlg/m
3)
Modulus
diT/dp3
Technique
andNotes
4
ReL
(OPa)
2
Fe2SiO4
(spinelstructure)
4.85
197 + 2
4 (assumed)
178
Fe2SiO4
(spinelstructure)
4.85
212
4 (asstuned)
131
Ni2SiO4
(spinelstructure)
5.35
227 + 4
Ni2SiO4
(spinelstructure)
5.35
227 + 4
Ni2SiO4
(spinelstructure)
5.35
214
Co2SiO4
(spinelstructure)
5.17
Co2SiO4
(spinelstructure)
5.17
206 + 2
Ca3AI2(O4H4)3
2.52
66 + 4
Katoite
56
4 (asstuned)
178
4 (asstuned)
127
210 + 6
4.0 + 0.6
123
4 (assumed)
4.1 + 0.5
178
156
or
Hydrogrossular
Ca3A12Si3012
3.59
168 + 25
6.2 + 4
Ca3A12Si3012
Mg3AI2Si3012
3.59
139 + 5
4.19
171.8
Pyrope
108
174.2 (fLXedfrom
ultrasonicdam)
7.0 + 1.0
3.58
175 + 1
4.5 + 0.5
114
3.58
171 + 3
1.8 + 0.7
183
3.58
212 + 8
3.5 + 0.6
195
Pyrope
Mg3AI2Si3012
Pyrope
Mg3AI2Si3012
156
6.1 __ 1.5
Grossular
Mn3AI2Si3012
Spessartine
Grossular
110
STATIC
COMPRESSION
Table1. BulkModulifromStaticCompression
D,ata(.ontinu.,.ed)
Chemical
FormulalDensity Isothermal
Bulk
(Mg/m
3)
Modulus
(GPa)
2
Mg3A12Si3012
3.58
179+ 3
dKOT/dp3 Technique
andNotes
4
4 (assumed) DAC, scXRD, P < 6
Pyrope
Mg3A12Si3O12
Pyrope
Fe3AI2Si3Oi2
3.58
175 + 0.3
3.3 + 1
3.8 + 1
4.32
175 + 7
1.5 + 1.6
183
4.32
190 + 5
3 + 0.5
195
3.83
162
4.7 + 0.7
3.86
159 + 2
4 (assumed)
3.15
135+ 10
3.68
Be3AI2Si6018
Beryl
(Mg,Fe)2A14Si5018
108
75
169
Andalusite
Mg 1.3Fe0.7Al2Si2
OI0(OH)4
Magnesiochloritoid
Andrad/te
AI2SiO5
108
Uvarovite
Ca3Fe2Si3O12
Almandine
Ca3Cr2Si3O12
75
Almandine
Fe3AI2Si3Oi2
Ref.
148 + 5 GPa
170 + 5
2.63
4 (assumed)
110
34
77
150
linPVfit
Cordierite
Be2SiO4
2.96
201 + 8
2.75
58.5 + 2
Phenakite
Sheet
2+
63
65
silicates:
KlVlg3AISi3010
(F,OH)2
Phlogopite
111
Table 1. BulkModulifromStaticCompression
Data(continued)
Chemical
Formulal Density Isothermal
Bulk
(Mg/m
3)
Modulus
(Mg,Fe,AI)6(Si,AI)4
Oo (F,OH)2
2.65
55.0 + 10
2.80
61.4 + 4.0
dKOTMP3 Technique
andNotes
4
Ref.
65
49
Chlorite
KAI3Si3010(OH)2
6.9 + 1.4
Muscouite
BaFeSi4010
GillespiteI
(low-pressure
tetmgonalsn'ucture)
3.72
62 + 3
4 (assumed)
71
BaFeSi4010
GillespiteII
(high-pressure
3.76
66 + 3
4 (assumed)
DAC, scXRD,
1.9<P<4.6 GPa,
71
M EOS
orthorhombic
smctt)
3.01
212+3
MgO
3.56
156 + 9
4 (assumed)
4.7+2
3.56
178
4.54
157
4.0
Periclase
(Mg0.6Fe0.4)O
Magnesiowastite
74
126
GPa, M EOS
Periclase
MgO
4 (assumed)
41
51
800 K, dKT/dT)p =-
4.2 + 0.2
CaO
Lime
3.38
CaO
3.38
112
3.9
3.79
130 + 20
3.5 _+ 0.5
41
DAC, pXRD,
170
55<P<135 GPa,
(high-pressure
B2 slxucttm:)
SrO
170
Lime
CaO
B-M EOS
4.70
90.6 + 2.4
4.4 + 0.3
120
112
STATIC
COMPRESSION
Table1. BulkModulifromStaticCompression
Data(continued)
Chemical
FormulalDensity Isothermal
Bulk
(Mg/m
3)
Modulus
SiO
6.14
160 + 19
diT/dp3 Technique
andNotes
4
4 (assumed)
(high-pressure
B2 structure)
B-M EOS
6.09
66.2 + 0.8
33.2 + 1.9
5.7 (fixedfrom
ultrasonics)
6.02 + 0.3
DAC, pXRD,
(high-pressure
PH4I
structure)
EOS
MnO
5.46
162 + 17
4.8 + 1.1
Manganosite
MnO
211
211
93
144
3.3
41
6.67
199
4.1
32
5.0
Manganosite
NiO
Bunsenite
182
36<P<59 GPa,
5.72
BaO
DAC, pXRD,
Ref.
CoO
6.45
190.5
3.9
41
CdO
8.15
108.0
9.0
41
9.63
22.7 + 6.2
17.8 + 1.6
Monteponite
PbO
Massicot
Law
EuO
8.25
97.0
231
Cu20
Cuprite
5.91
GeO2
4.23
131
5.7
208
GPa, M EOS
63.9 + 0.7
(quartzslxucture)
225
GeO2
(quartzslxucture)
4.23
GeO2
(quartzsu'ucture)
4.23
39.1 + 0.4
2.2 + 0.5
98
M EOS
26.5
34.3
16.8
86
KNITTLE
Table1. BulkModulifromStaticCompression
Data(continued)
Chemical
Formula
1 Density Isothermal
Bulk
(Mg/m
3)
Modulus
...
diT/dp3
Technique
andNotes
4
Ref.
4 (assumed)
225
(GPa)
2
GeO2
Argutite
(rutile smcmre)
6.24
GeO2
Argutite
(rutile structure)
6.24
TiO2
394.9 + 0.2
258 + 5
7 (assumed)
265 + 5
4 (assumed)
216 + 5
7 (assumed)
222 + 5
4 (assumed)
203
4 (assumed)
197
4.24
187
7.00
4.24
70
70
178
4 (assumed)
104
218 + 2
7 (assumed)
70
224 + 2
4 (assumed)
DAC, pXRD, P < 25
119
Rutde
TiO2
4.24
Rutile
TiO2
Rutile
SnO2
Cassiterite
6.26
44.4 + 1.6
5.8 + 0.5
Paratellurite
(tetragonalsxucture)
10.96
207
7.13
230 + 10
7.2
Uraninite
CeO2
4 (assumed)
7.84
304 + 25 GPa
4 (assumed)
270 + 6
ZrO2
Baddeleyite
5.81
95 + 8
ZrO2
(high-pressure
6.17
phase)
45
DAC, pXRD,
45
B-M EOS
6.97
orthorhombic-I
3 l<P<70 GPa,
(high-pressure
ot-PbCl2-type
stmcture)
RuO2
24
Cerianite
CeO:
4 (assumed)
70
110
220
110
113
114
STATIC
COMPRESSION
Chemical
Formulal Density Isothermal
Bulk
(Mg/m
3)
Modulus
HfO2
9.68
145
andNotes
4
dKoT/dp3 Technique
ReL
109
HfO2
(high-pressure
10.14
210
109
orthorhombic-II
phase)
10.98
475
109
(high-pressure
orthorhombic-HI
phase)
HfO2
(high-pressure
tetragonal
phase)
11.88
550
269 + 3
V305
(highpressure
phase)
5.39
175 + 11
ALPO4
2.57
36
MgAI204
Spinel
3.55
3o4
Magnetite
5.20
DAC, scXRD,0<P<
5.5 GPa, linPVfit
DAC, scXRD,6.3<P<
7.5 GPa, linPVfit
16
4 (assumed)
190
194 + 6
4 (assumed)
55
186 + 3
4 (assumed)
55
183 + 5
5.6 (from
ultrasonics)
DAC, scXRD, P < 4.5
GPa, B-M EOS
154
212
Berlinite
Fe304
5.20
181 + 2
5.20
155 + 12
5.5 +__15
Magnetite
Fe304
4 (assumed)
5.20
183 +_10
4 (assumed)
4.83
137.0 + 3.8
4 (assumed)
slxucture)
130
163
Hausmannite
Mn304
(high-pressure
marokite-type
Magnetite
Mn304
16
Magnetite
Fe304
109
4.73
V305
5.33
166.6 + 2.7
4 (assumed)
163
KNeE
Table1. BulkModulifromStaticCompression
Data(continued)
Chemical
FormulalDensity Isothermal
Bulk
(Mg/m
3)
Modulus
diT/dp3
Technique
andNotes
4
4 (assumed)
62
23
Ref.
(pa)2
AI2BeO4
Chrysoberyl
ReO3
3.70
242 + 5
6.9
200 + 4
linPVfit
LiNbO3
4.63
134 + 3
CaTiO3
3.98
210 + 7
2.9 + 0.5
5.6 (assumed)
5.12
Tausonite
SrTiO3
174.2
5.3
(fixed from
ultrasonicvalue)
5.12
176
4.4
218
57
47
GPa, M EOS
4.72
170 + 7
8+ 4
llmenite
177 + 3
(Fe,Mg)TiO3
Tausonite
FeTiO3
37
Perovskite
SrTiO3
4.44
168 + 13
207
123
4 (assumed)
5+ 1
llmenite
MnTiO3-I
Pyrophanite
4.54
70 + 9
4 (assumed)
175
MnTiO3-II
(LiNbO3 structure)
4.68
158 + 9
4 (assumed)
175
4.88
227 + 4
4 (assumed)
175
MnSnO3
(perovskitestructure)
6.12
196 + 20
MgGeO3
4.97
187 + 2
4.97
195
MnTiO3-III
(perovskitestructure)
4 (assumed)
(ilmenite structure)
MgGeO3
3.6
184
17
(ilmenite structure)
CuGeO3
111
5.11
67.8
11
116
STATIC
COMPRESSION
Chemical
Formulal Density Isothermal
Bulk
(Mg/m
3)
Modulus
...
(GPa)
2
diT/dp3
Technique
andNotes
4
Ref.
Na0.55WO3
(perovskitestructure)
7.23
105
72
Na0.62WO3
(perovskitestructure)
7.44
119
72
Na0.70WO3
(perovskitestructure)
7.61
91
72
5.25
225
4 (assumed)
54
5.25
199 + 6
4 (assumed)
212
Fe203
Hematite
Fe203
Hematite
5.25
228 + 15
4 (assumed)
22
5.25
178 + 4
4 (assumed)
181
A1203
Ruby
3.98
253 + 1
171
A1203
3.98
Fe203
Hematite
Fe203
Hematite
5.0 + 0.4
226 + 2
4 (assumed)
Corundum
239 + 4
A1203
Ruby
3.98
257 + 6
A1203
3.98
254.4 + 2.0
4.87
171 + 1
4 (assumed)
4.275 + 0.006
4 (assumed)
Karelianite
175 + 3
V203
40
181
195 + 6
4 (assumed)
54
5.21
222 + 2
4 (assumed)
181
54
231+5
Cr203
53
4.87
Eskolaite
Eskolaite
3.1 + 0.7
Karelianite
Cr203
181
0.9 + 0.8
Corundum
V203
5.21
238 + 4
2.0+
1.1
4 (assumed)
KNeE
Table1. BulkModulifromStaticCompression
Data{continued)
Chemical
FormulalDensity Isothermal
Bulk
(Mg/m
3)
Modulus
(GPa)
2
diT/dp3
Technique
andNotes
4
Ref.
KVO3
84.7
RbVO3
42.9
CsVO3
62.9
NaNO2
2.17
21.9 + 0.2
4.3 + 0.8
68
NaNO3
2.26
25.8 + 0.6
6.6 + 1.5
68
2.39
54.3 + 1.5
4.7 + 0.2
50
Nitratine
Mg(OH)2
Brucite
dKT/dP= -0.018_+0.003
GPa/K
Ca(OH)2
2.24
37.8 + 1.8
5.2 + 0.7
Carbon-Bearing
SiC
Moissonite
CaMg(CO3)2
144
Minerals:
3.22
227 + 3
4.1 + 0.1
2.86
94
174
Dolomite
CaMg0.3Fe0.7
(CO3)2
Portlandite
3.05
91
174
Ankerite
BaCO3
4.30
50 + 3
4 (assumed)
139
3.73
58 + 5
4 (assumed)
139
3.67
95 + 9
4 (assumed)
139
2.71
71.1
189
Witherite
SIC03
Strontianite
MnCO3
Rhodocrosite
CaCO3
Calcite
4.15
polyPVfit
117
118
STATIC
COMPRESSION
Table1. BulkModulifromStaticCompression
Dam{continued)
Chemical
Formula
1 Density Isothermal
Bulk
(Mg/m
3)
Modulus
(OPa)
2
CaCO3
CalciteII
2.71
CaCO3
CalciteIII
2.85
CaCO3
2.85
diT/dp3
and
Ref.
189
32.7
(at 1.4 GPa)
4.4
(at 1.4 GPa)
75.2
(at 1.7 GPa)
84.0+ 8
GPa, polyPVfit
189
GPa, polyPVfit
Calcite III
Sulfides
Technique
andNotes
4
139
Te!!urides-
HgS
8.13
19.4 + 0.5
11.1
Cinnabar
HgTe
8.09
16.0 + 0.5
7.3
56.7
4.9
41
4.82
86.7
4.36
192
4.82
94.0
7.6
41
3.99
81.0
3.3
41
3.99
72 + 2
4.2 + 1.3
140
Greenocla'te
MnS
Alabandite
MnS
210
2.50
Greenocla'te
CdS
Oldhamite
CdS
210
Coloradoite
CaS
Alabandite
NiS
(NiAs-typestructure)
5.50
BaS
4.25
156 + 10
4.4 + 0.1
27
55.1+ 1.4
211
4.67
21.4 + 0.3
7.8 + 0.1
(highpressureB2structure)
ZnS
DAC, pXRD,
EOS
4.02
76.5
4.49
Sphalerite
ZnS
(high-pressure
phase)
211
230
4.72
85.0 + 3.8
230
KNFI'rLE
Table1. BulkModuiifromStaticCompression
Data(continued)
Chemical
Formulal Density Isothermal
Bulk
(Mg/m
3)
Modulus
YbS
7.38
60 + 3
dKOT/dp3 Technique
andNotes
4
4 (assumed)
Ref.
194
5.93
82
2.2
204
8.38
101.5 + 1.0
5.4 + 0.2
89
lsqPV fit
ThS
9.56
145 + 6
5 A + 0.1
160
GPa, M EOS
US
10.87
92 + 9
9.1 + 0.2
160
G Pa, M EOS
NiS2
4.45
109 + 6
NiS2
(high-pressure
metallicphase)
MnS2
4.91
141 + 11
3.46
76.0
5.4
Hauer/te
MnS2
(high-pressure
48
linPVfit
Vaesite
48
30
213.8
5.0
DAC, pXRD, 10
30
orthorhombic
marcasite-type
structure)
4.27
118.3
4.50
29
As4S3
Dimorphite
3.58
17.0
CuFe2S3
4.11
55.3 + 1.7
4.36
96 + 10
4.70
60 + 8
CoS2
'Cattierite
SnS2
Berndtite
Cubanite
CuGaS2
Gallite
AgGaS2
5.5
58
31
141
209
209
119
120
STATIC
COMPRESSION
Chemical
Formulal Density Isothermal
Bulk
(Mg/m
3)
Modulus
diT/dp3
Technique
andNotes
4
Ref.
(GPa)
2
La6CoSi2S14
4.37
79.2 + 0.4
145
La6NiSi2S14
4.37
75.5 + 0.5
145
Halides-
LiF
2.64
66.5
3.5
219
LiF
2.64
62.7
6.8
202
M EOS
LiF
2.64
65.0
4.7
41
LiCl
2.07
31.9
3.4
202
M EOS
LiBr
3.46
24.3
3.5
202
M EOS
LiI
4.08
16.8
4.3
202
M EOS
NaF
Villiaumite
2.56
45.9
4.4
219
NaF
Villiaumite
2.56
46.4 + 6.2
4.9 + 1.2
180
NaF
Villiaumite
2.56
NaF
Villiaumite
2.56
NaF
3.16
5.2
202
M EOS
45.6
103 _+19
5.7
4 (assumed)
41
DAC, pXRD,
180
(high-pressure,
B2
structure)
EOS
NaCI
Halite
2.17
26.4
3.9
DP, XRD, P _ 30
GPa, M EOS
41
NaCI
Halite
2.17
23.2
4.9
202
NaCI
Halite
2.17
M EOS
23.8 + 7.5
4.0 + 3.9
180
KNI'FFLE
Table1. BulkModulifromStaticCompression
Data(continued)
Chemical
Formula
1 Density Isothermal
Bulk
(Mg/m
3)
Modulus
dKOT/dp3 Technique
andNotes
4
Ref.
(GPa)
2
NaCI
2.34
36.2 + 4.2
4 (assumed)
DAC, pXRD,
(high-pressure
B2
structure)
EOS
NaBr
3.20
20.3
4.2
80
202
M EOS
NaBr
3.20
18.5 + 3.4
5.8 + 1.1
180
3.67
15.0
4.1
41
NaI
3.67
14.7 + 1.1
5.7 + 0.5
180
3.67
15.1
4.2
202
M EOS
KF
Carobbiite
2.48
29.3
5.4
219
KF
2.87
37.0
5.4
219
1.98
37.0
5.0
41
2.34
28.7 + 0.6
(high-pressure,
B2
structure)
KC1
Sylvite
KCI
(high-pressure
B2
structure)
CsCl
3.99
18.0
4.8
41
CsCl
3.99
18.2
5.1
219
CsCI
3.99
17.1
5.1
202
M EOS
CsBr
4.44
14.4
5.3
202
M EOS
CsBr
4.44
19.1 + 0.9
5.0 + 0.1
103
4.51
13.3 + 2.3
5.9 + 0.9
101
121
122
STATIC
COMPRESSION
Table 1. BulkModulifromStaticCompression
Data(continued).
Chemical
Formulal Density Isothermal
Bulk
(Mg/m
3)
Modulus
diT/dp3
Technique
and
Notes4Ref.
(GPa)
2
CsI
4.51
12.5
4.5
202
M EOS
CsI
4.51
13.5 +_ 0.2
5.45 +_ 0.06
137
GPa, V EOS
AgCl
Cerargyrite
5.56
AgBr
Bromyrite
6.47
CuBr
41.5
6.0
202
M EOS
38.2
5.9
202
M EOS
4.98
36.2
2.9
202
M EOS
MnF2
3.98
94 +_3
4 (assumed)
70
CaF2
3.18
81.0 +_1.2
5.22 + 0.35
13
4.24
69.1
5.2
149
Fluorite
SrF2
M EOS
BaCI2
3.87
69.8 +_0.5
1.40 +_0.05
107
BaCI2
(highpressure
hexagonalphase)
4.73
69.3 + 2
8.6 +_ 0.1
107
0.362 + 0.003
4.71 +_ 0.03
(4K)
(4K)
DAC, scXRD,
5.4<P<26.5 GPa, B-M
83
136
Group I Elements:
H2
0.088
EOS
H2
D2
0.172 +__
0.004
7.19 +__0.04
(4K)
(4K)
0.088
0.166
7.3
(4K)
(4K)
(4K)
lsqPVfit
0.20
0.46 + 0.05
5.2 +__0.2
DAC, scXRD,
6.5<P<14.2 GPa, B-M
V EOS
EOS
83
KNITrLE
Table 1. BulkModulifromStaticCompression
Data{continued)
Chemical
Formulal Density Isothermal
Bulk
(Mg/m
3)
Modulus
diT/dp3
Technique
andNotes
4
Ref.
(GPa)
2
0.35 + 0.03
6.6 + 0.2
v EOS
Li
0.53
11.556 + 0.033
3.51 + 0.06
11
lsqPVfit
Na
0.97
6.06 + 0.02
4.13 + 0.04
10
lsqPVfit
K
0.86
2.99 + 0.02
4.15 + 0.10
118
0.86
2.963 + 0.001
4.208 + 0.003
10
lsqPVfit
K
0.86
3.10 + 0.01
3.91 + 0.01
99
M EOS
Rb
1.53
2.301 + 0.003
4.15 + 0.1
10
lsqPVfit
Rb
1.53
2.61
3.62
197
1.90
1.698 + 0.006
3.79 + 0.02
11
lsqPVfit
Group II
Mg
Elements:
1.74
33.6
4.8
203
M EOS
Ca
1.54
18.7
2.5
201
M EOS
Ca
1.54
17.4 + 0.1
3.7 + 0.1
12
lsqPVfit
Sr
2.60
12.1
2.5
203
M EOS
Sr
2.60
11.83 + 0.07
2.47 + 0.07
12
lsqPVfit
Ba
3.50
9.4
2.1
201
M EOS
Ba
3.50
8.93 + 0.6
2.76 + 0.05
lsqPVfit
12
123
124
STATIC
COMPRESSION
Table1. BulkModulifromStaticCompression
Data(continued
Chemical
Formula
1 Density Isothermal
Bulk
(Mg/m
3)
Transition
Modulus
diT/dp3 Technique
andNotes
4
Ref.
Metals:
Ti
4.51
109.4
3.4
203
M EOS
6.10
154 + 5
4.27 (fixed
from
147
19
203
ultrasonics)
V
6.10
6.10
176.4
+ 3.0
139.4
18.2
M EOS
Cr
7.19
253.0 + 11.0
8.9
19
Cr
7.19
193 + 6
4.89 (fixed
147
198
203
from
ultrasonics)
Mn
7.43
131 + 6
Co
8.90
167.1
6.6+7
17.3
M EOS
Ni
8.92
190.5
4.0
201
M EOS
Cu
8.96
162.5
4.24
201
GPa, M EOS
Cu
8.96
137.4
5.52
124
Zn
7.14
59.8
4.4
201
M EOS
4.46
44.9
2.2
203
M EOS
Zr
4.46
104
2.05
217
Zr
6.49
102.8
3.1
203
M EOS
KNITLE
Table 1. BulkModulifromStaticCompression
Data(continued)
.,
Chemical
Formulal Density Isothermal
Bulk
(Mg/m
3)
Modulus
Nb
diT/dp3
Technique
andNotes
4
Ref.
203
(GPa)
2
8.41
144.2
14.5
M EOS
Nb
8.40
171 + 7
4.03
147
Nb
8.40
175.7 + 2.7
19
Mo
10.20
266.0
3.5
201
M EOS
Mo
10.20
267 + 11
4.46 (fixed
from
147
19
ultrasonics)
Pd
12.00
128.0 + 5.0
Ag
10.50
103 + 5
5.6 + 0.8
Ag
10.50
116.7 + 0.7
3.4
124
Ag
10.50
120.9
5.2
201
M EOS
Ag
10.50
106.1
4.7
193
Cd
8.65
44.8
4.9
201
M EOS
La
6.17
24.5
1.6
201
M EOS
Ta
16.60
205.7
3.7
201
M EOS
Ta
16.60
194 + 7
3.80 (fixed
from
147
203
ultrasonics)
W
19.30
300.1
19.1
M EOS
W
19.30
307 + 11
4.32 (fixed
from
ulxasonics)
147
125
126
STATIC
COMPRESSION
Table1. BulkModulifromStaticCompression
Data(continued)
Chemical
FormulalDensity Isothermal
Bulk
(Mg/m
3)
Modulus
(GPa)
2
Au
19.30
Au
19.30
166.4 + 2.6
163.5
8.3
dKOT/dP3 Technique
andNotes
4
7.3
124
148
5.5 _+ 0.8
81
5.31-6.43
148
201
4.42-5.16
(fixed from
ultrasonics)
Au
Group III
19.30
166.6 _+ 10.8
2.70
71.7 _+3.6
Ref.
Elements:
AI
(fixed from
ultrasonics)
Al
2.70
77.9
4.6
M EOS
AI
2.70
72.7
4.3
193
In
7.31
39.1
5.2
201
M EOS
In
7.31
38 + 2
5.5 + 0.3
185
TI
11.85
36.6
3.0
201
M EOS
Group IV Elements:
3.51
444 + 3
1.9 + 0.3
2.25
33.8 + 3
8.9 + 1.0
61
2.25
30.8
226
44
Diamond
Graphite
C
4 (assumed)
Graphite
C60
Fullerite
1.67
18.1 _+1.8
5.7 _+ 0.6
KNI'I.,E
Table 1. BulkModulifromStaticCompressio
n Data(continued)
Chemical
Formulal Density Isothermal
Bulk
0Vlg/m
3)
Modulus
diT/dp3
Technique
andNotes
4
4.7
Ref.
(GPa)
2
Si
2.33
100.8
203
M EOS
Si
2.33
97.9
4.16
191
3.09
72 + 2
3.91 + 0.07
43
3.25
82 + 2
4.22 + 0.05
DAC, XRD,
79<P<248 GPa,
43
(high-pressure
hcpphase)
Si
(high-pressure
fccphase)
Sn
B-M EOS
7.30
54.9
4.8
201
M EOS
an
7.30
50.2 + 0.5
4.9
121
Sn
7.30
56.82 + 2.19
2.3 + 0.8
28
=-1.38(+_
0.13)x 10'2
GPa/K
Sn
7.49
(high-pressure,
!xxly
tetragonalstructure)
Sn
7.49
82.0 + 1.2
5.5
56.65 + 9.04
4.53 + 0.81
(high-pressure,
body-ctexed
tetragonalstructure)
121
167
B-M EOS
x 10-2 GPa/K
an
7.49
76.4
4.04
(high-pressure,
body-centered
cubic
structure)
Pb
DAC, XRD,
45<P<120 GPa, B-M
39
EOS
11.40
40.0
5.8
201
M EOS
Pb
11.40
43.2
4.87
206
127
125
STATIC
COMPRESSION
Chemical
Formulal Density Isothermal
Bulk
(Mg/m
3)
Modulus
diT/dp3
Technique
andNotes
4
Ref.
(GPa)
2
Pb
11.62
39.9+
0.2
6.13 +_ 0.10
134
(combinedhcpand
bcc high pressure
phases)
Pb
11.57
46.63
5.23
206
11.66
29.02
7.16
206
1.03
2.69
3.93
155
1.21
2.98
3.78
155
2.70
36 + 2
4.5 + 0.5
DAC, pXRD,
98a
(high-pressure
hcp
phase)
Pb
(high-pressure
bcc
phase)
Group V Elements:
N2
(cubic8-phase)
N2
(hexagonale-phase)
P
(orthorhombic)
P
46 _+4
3.0 + 0.6
98a
(high-pressure
rhombohedml
structure)
P
3.08
95 + 5
2.1 + 0.8
(high-pressure
simple
DAC, pXRD, 10
98a
cubic structure)
P
3.08
114
6.62
40.4
(high-pressure
simple
187
203
cubic structure)
Sb
4.3
M EOS
Bi
9.80
29.7
2.4
201
M EOS
Group VI Elements:
02
(high-pressure
phaseindexedas
monoclinic)
1.32
37.5
3.31
177
KNITLE
Table 1. BulkModulifromS,tatic.Compression
Data(continued)
Chemical
Formula
1 Density Isothermal
Bulk
(Mg/m
3)
Modulus
diT/dp3
Technique
andNotes
4
Ref.
(GPa)
2
02
(high-pressure
ephaseindexedas
orthorhombic)
1.32
16.7
4.09
177
2.07
8.8
6.5
203
M EOS
2.07
14.5
125
2.72
17.3
125
Se
4.79
48.1 + 0.2
(at 7.7 GPa)
4.33 + 0.04
(at 7.7 GPa)
165
Se
4.79
7.9
5.8
203
(high-pressure
phase)
M EOS
Te
6.24
18.2
8.4
203
M EOS
6.24
Group VII
24 + 2
2.3 + 0.2
(at 2 GPa)
(at 2 GPa)
164
46
Elements:
C12
2.09
11.7 + 0.9
5.2 (assumed)
Br2
4.10
13.3 + 0.7
5.2 (assumed)
46
I2
4.94
8.4
6.0
203
M EOS
I2
4.94
13.6 + 0.2
5.2 (assumed)
46
GasesHe
(solid)
0-0.43
GPa:
0.23
0.085
>0.18
GPa:
0.21
0.082
see reference
42
129
130
STATIC
COMPRESSION
Chemical
Formulal Density Isothermal
Bulk
(Mg/m
3)
Modulus
andNotes
4
dKoT/dp3 Technique
ReL
(GPa)
2
He
(solid)
Ne
(solid)
0.23
(0 K)
only
GPa
1.51
1.097
9.23 _+ 0.03
DAC,XRD,4.7<P<
110 G Pa, B-M EOS
(4 K)
Ar
1.73
2.86
7.2
(solid)
(4 K)
(at 4 K)
(at 4 K)
lsqPVfit
1.65
1.41
8.4
(77 K)
(at 77 K)
(at 77 K)
1.73
(solid)
Ar
(0 K)
only
GPa
Kr
2.317
1.41
4.3 + 0.1
(solid)
Kr
3.09
3.34
7.2
(solid)
(4 K)
(at 4 K)
(at 4 K)
lsqPVfit
Xe
(solid)
Xe
(solid)
2.82
1.58
7.6
(110 K)
(at 110 K)
(at 110 K)
3.78
5.48 + 0.24
(0 K)
(0 K)
(0 K)
3.78
3.63
7.2
(4 K)
(at 4 K)
(at 4 K)
lsqPVfit
3.41
1.48
8.8
(159 K)
(at 159 K)
(at 159 K)
6.77
30.2
1.6
135
172
166
15
Lanthanides:
Pr
203
M EOS
Nd
7.00
32.6
3.0
203
M EOS
Gd
8.23
35.5
4.8
203
M EOS
Gd
8.23
22.71 + 2.07
4.31 + 0.29
Dy
8.78
40.3
5.1
203
KNFI'rLE
Table 1. BulkModulifromStaticCompression
Data{continued
)
Chemical
Formula
1 Density Isothermal
Bulk
(Mg/m
3)
Modulus
Er
9.37
44.9
dKOT/dp3 Technique
andNotes
4
3.5
ReL
203
M EOS
Actinides'
Th
11.70
54.0
4.9
203
M EOS
Pa
15.40
157
1.5
Fe
a (bcc)phase
Fe
7.86
164 + 7
7.86
175.8
4 (assumed)
3.7
212
201
M EOS
a (bcc)phase
Fe
7.86
162.5 + 5
5.5 + 0.8
196
7.88
156 +7
4.2 + 0.8
196
7.88
153 + 7
5.7 + 0.8
196
7.39
175 + 8
4.3 + 1.0
188
7.35
174.0
4.6
41
6.77
214 + 9
3.5 + 0.8
188
6.58
250.0
-2.0
41
Fe
e (hcp)phase
8.30
208 + 10
196
Fe
8.30
192.7 + 9.0
4.29 + 0.36
96
8.30
164.8 + 3.6
5.33 + 0.09
132
a (bcc)phase
Fe-5.2 wt. % Ni
R (bcc)phase
Fe-10.3 wt. % Ni
a Cocc)phase
Fe-7.2 wt. % Si
a (bcc)phase
Fe-8 wt. % Si
R (bcc)phase
Fe-25 wt. % Si
a Cocc)phase
Fe3Si
Suessite
4 (assumed)
e (hcp) phase
Fe
e (hcp) phase
131
132
STATIC
COMPRESSION
Table1. BulkModulifromStaticCompression
Data(continued)
Chemical
FormulalDensity Isothermal
Bulk
(Mg/m
3)
Modulus
diT/dp3
Technique
andNotes
4
Ref.
(GPa)
2
Fe0.8Ni0.2
e (hcp) phase
8.37
171.8 + 2.2
Fe-5.2 wt. % Ni
8.41
212 + 15
8.42
4.95 + 0.09
132
4 (assumed)
196
215 + 25
4 (assumed)
196
7.76
188 + 14
4 (assumed)
188
Fe-10 wt. % Co
7.93
171+ 6
4 (assumed)
162
Fe-20wt. % Co
7.98
169+ 6
162
e (hcp) phase
Fe-10.3 wt. % Ni
(hcp)phase
Fe-7.2 wt. % Si
(hcp) phase
Fe-40 wt. % Co
8.08
166+ 6
4 (assumed)
162
Fe0.980
5.87
169 + 10
4 (assumed)
(ideal)
221
Wiistite
157 + 10
4 (assumed)
94
142 + 10
131
Fe0.9450
5.87
Wtistite
(ideal)
FeO
5.87
Wiistite
(ideal)
FeO
W 'astite
5.87
(ideal)
Fel_xO
x = 0.055, 0.07,
5.87
150 + 3
3.8
155 + 5
(ideal)
122
91
41
213
87
100
0.10
W 'tistite
FeO
W 'tistite
5.87
154.0
Fe0.9410
Wastite
5.87
(ideal)
154 + 5
Fe2U
13.19
239
FeS
Troilite
3.4
(ideal)
4.74
82 + 7
4 (assumed)
-5 + 4
KNrrlE
Table1. BulkModulifromStaticCompression
Data(continued)
Chemical
Formulal Density Isothermal
Bulk
(Mg/m
3)
Modulus
dKOT/dp3 Technique
andNotes
4
Ref.
(GPa)
2
FeS
4.77
35 + 4
5 + 2
(high-pressureMnPtype structure)
DAC, scXRD,
3.6<P<6.4 GPa, B-M
100
EOS
95
41
58
5.5
29
146.5 + 0.6
4.9
29
3.21
121 + 19
5.31 + 0.9
18
CO2
1.40
2.93 + 0.1
7.8
117
NH3
0.86
7.56 + 0.06
5.29 + 0.03
161
H20
(cubicphaseVII)
1.46
22.3 + 1.0
4.9+0.7
DAC, XRD,
152
FeS2
Pyrite
4.95
143
FeS2
Pyrite
4.95
148
FeS2
Pyrite
4.95
157
FeS2
Pyrite
4.95
215.4 + 0.2
FeS2
4.87
Fell
4 (assumed)
5.5
Marcasite
Ices:
D20
(cubicphaseVII)
1.48
30.0 + 1.5
4.1+0.5
DAC, XRD,
152
H20
(cubicphaseVII)
1.46
23.7 + 0.9
4.15 + 0.07
DAC, XRD
2.3<P<128, B-M EOS
82
VH0.5
---5.73
193.5 + 4.0
19
NbH0.75
6.60
202.3 + 3.0
19
Hydrides'
133
134
STATIC
COMPRESSION
Table1. BulkModulifromStaticCompression
Data(continued)
Chemical
Formula
1 Density Isothermal
Bulk
0Vlg/m
3)
Modulus
diT/dp3
Technique
andNotes
4
Ref.
(pa)2
PdH
-10.2
130.0 + 5.0
4.8
19
PdD
-10.2
135.0 + 5.0
4.7
19
CrH
-6.23
248.0 + 9.3
11.0
19
AIH 3
-1.50
47.9 + 1
3.3 + 0.2
19
H(AIH3)
-1.28
30.9 + 2
3.2 + 0.4
19
Cull
6.38
72.5 + 2
2.7 + 0.3
19
-5.42
22.2 + 2
3.6 + 0.3
19
H(CuH)
Amorphous
Materials:
Fe2SiO4
liquid
3.747
24.4
10.1
PC, sink/float
(1773K)
( 1773K)
(1773K)
measurements,
SiO2 glass
2.21
37.0 + 5.5
-5.6 + 6.2
DAC, length-change
143
measurements, P <10
GPa, B-M EOS
Ca-Mg-Na glass
35.5 + 3.7
-2.9 + 4.1
DAC, length-change
measurements, P <_10
GPa, B-M EOS
Mineralnames
aregivenin italicswhereapplicable.
All values
areatambient
pressure
androomtemperature
except
where
noted.
A dash
implies
a linear
fit tothepressure-volume
data(implies
thatKOT'=
0) oranunstated
KOT'.
Thetemperature
derivative
of thebulkmodulus
(dKot/dT)
isgivenwhereavailable.
Key: DAC = diamond-anvil
cell. BA = Bridgrnan
anvilpress.DP = Drickamerpress.
CAP = cubic-anvil
press.TAP = tetrahedral-anvil
press.MAP = mulianvilpress.
TCOA = tungstencarbideopposedanvils,BCAC = boroncarbideanvil cell.
ND = neutrondiffraction.EXAFS = extended
x-rayabsorption
f'mestructure.
P = pressurein GPa.
143
KNI'I'IE
Acknowledgements.
This work was supportedby NSF andthe
W34. Keck Foundation.I thankT.J. Ahrensandan anonymous
reviewer for helpful comments. I'm sure references were
missed,for whichI apologizein advance.This papercouldnot
135
208.
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1. INTRODUCTION
[193,194].
andmegabar
(Mbar).These
areequal
to109,1010,
and
1012dyne/cm
2, respectively,
or 108,109,and1011
pascalsin SI units.
91125
2.
PresentAddress:M. L. Johnson,GemologicalInstituteof
Reference
Shelf 2
143
144
c:Sd
oo
AHRENS
dddd
ddd
o
o
ooc
o
,---
AND
JOHNSON
145
146
'.-1
..=
AHRENS
ot,'
0,
AND
JOHNSON
147
148
SHOCK
WAVE
DATA
FOR
MINERALS
AHRENS
.,
AND
JOHNSON
149
lS0
SHOCK
WAVE
DATA
FOR MINERALS
AHRENS
AND
JOHNSON
151
152
SHOCK
WAVE
DATA
FOR MINERALS
('",1 Oh 0
AHRENS
AND
JOHNSON
153
154
o. o o. o.
oc5ooc5c5
,, c5
o c',!.
'.
AHRENS
AND
JOHNSON
155
156
SHOCK WAVE
DATA
FOR MINERALS
AHINS
'"'4' 0
AND $OHNSON
17
158
AHRENS
AND JOHNSON
159
160
SHOCK
WAVE
DATA
FOR
MINERALS
oo
c5o
c5
c5
c5 ,,o
AHRENS
AND
JOHNSON
C',I
("',1
0
!
C',I
.
161
162
SHOCK
WAVE
DATA
FOR MINERALS
AHRENS
AND
JOHNSON
163
164
SHOCK
WAVE
DATA
FOR
MINERALS
AHRENS
AND
OHNSON
165
0,'
166
SHOCK
WAVE
DATA
FOR MINERALS
AHRENS
oO
ocTc
,--
AND
JOHNSON
167
168
'I
'{::
AHRENS
AND
JOHNSON
169
1'70
SHOCK WAVE
DATA
FOR MINERALS
AHRENS
AND JOHNSON
171
172
SHOCK
WAVE
DATA
FOR
MINERALS
Ts
US
A
Po
Up canempirically
be described
in regionswherea
P = Po (Us-uo)/(Us-u)
P1 - Po = Po(Ul-Uo)(Us-uo)
()
(2)
Us= Co+ S Up
(3)
(4)
Isentrope
Hugoniot
designated
asUsandUl. Thusfora single
shock
Up= Ul.
In thecaseof multiple
shocks,
thevalues
of Up andUs
given in the Table are for the final (highestpressure)
shock state. Equations (1)-(3) are often called the
Rankine-Hugoniotequations.It shouldbe understoodthat
in this sectionpressureis usedin place of stressin the
indicatedwavepropagation
direction. In actuality,stress
in the wavepropagation
directionis specifiedby Eq. (2).
A derailedderivationof Eqs. (1), (2), and (3) is given in
Duvall and Fowles[70]. Equation(3) alsoindicatesthat
the matehalachievesan increasein internalenergy(per
unitmass)whichis exactlyequalto thekineticenergyper
unit mass.
Isot
Vo
equations
involvesixvariables
(Us,u1, Po,P1, E1 - Eo,
shock, the
AHRENS
KH = -V (3P/3V)H.
(5)
173
(11)
KS
(12)
Co= x/ICs/po,
JOHNSON
The analogous
bulkmodulusalongtheHugoniotis:
AND
7= V (3P/3E)v= 70(V/Vo)q,
(13)
where
= poUp(o+ s Up)
(6)
PH= PoCo2q/(1-Sq)
2
(7)
where
rI = 1 - V/Vo= Up/Us.
(14)
Tois theGriineisenparameterunderstandard
pressure
andtemperatures
and is givenby
(15)
the isothermal
bulkmodulus
andCp and Cv are the
specificheat at constantpressureand volume. We note
thatthe Ps and PH can be relatedby assumingthe MieGriineisen relation
PH-Ps
=V(EH-Es)'
(16)
(8)
if is independent
of temperature,
whereEH = El-E0 is
givenby Eq. 3 andE s is givenby
V
Es=-- I PsdV.
Vo
series
(17)
(9)
(10)
174
impact
of a flyerplateat velocity
Ufpona stationary
targetmaybe calculatedfrom thesolutionof theequation
equating
theshockpressures
in theflyeranddriverplate:
HEL
(18)
That is;
u1=(-b- qb2-4ac)/2a,
(19)
where
ParticleVelocity
a = SA PoA- PoBSB,
(20)
(21)
and
c=Ufp(CoAPoA+ SAPoAUfp).
3. SHOCK-INDUCED
PHASE
DYNAMIC
YIELDING
(22)
3
2
AND
HEL
TRANSITIONS
Bothdynamicyieldingandphasetransitions
giverise
to multipleshockwaveprofileswhenpressure
or particle
velocityversustimeis recorded.Virtuallyall nonporous
mineralsand rocksin whichdynamiccompression
has
beenstudieddemonstrate
phenomenon
relatedto dynamic
yielding,in which materialstransformfrom finite elastic
strainstatesto statesin which irreversibledeformationhas
occurred.Moreover,mostminerals
anda largenumberof
compounds,
elements,
andorganicmaterialsdemonstrate
shock-induced
phasechanges.
The dynamicyieldpointundershockcompression,
the Hugoniot elastic limit, or HEL, is defined as the
maximum
shockpressure
a materialmaybe subjected
to
withoutpermanent,
massive,
microscopic
rearrangement
takingplaceat theshockfront. As shownin Fig. 3a, the
shockvelocityof theHEL stateremainsnearlyconstant
and for non-porousmedia is usually equal to the
longitudinal
elasticwavevelocity.Viscoelasfic
polymeric
mediagenerallydo not displaythe HEL phenomenon.
Wedenotefiveregimes
in Fig. 3 for thecaseof dynamic
yielding and phasetransitionand the available shock
wave data are separatelyfit to linear relationsin these
regimesin Table 1. For some minerals there are more
than four regimes indicated, for reasons such as
crystallographic
controlof compression
at low pressures
Volume
FIG.3. Sketch
of shockvelocity-particle
relation
(a)and
corresponding
pressure-volume
Hugoniotcurves(b) for a
mineralwhichundergoes
dynamic
yieldinganda phase
change.
0: compression
upto theHugoniot
ElasticLimit
(HEL)
1: transition
viadynamic
yieldingtoa quasihydrostaticstate
2: low pressurestate
3: mixedregion
4: highpressurestate
(suchasOa,Obforquartz),andformorethanonehighpressure
state(suchas4a, 4b, and4c for halite).
The crystallographicor atomisticlevel natureof
shock-induced
phase
changes
variesfromsimpleaverage
coordinationchangesobservedin variousliquids,
ionization and debondingin non-metallic fluids,
electronic
transitions
in metalandnon-metals,
changes
in
crystalstructurein solidmaterials,and transitionfrom the
solid to the fluid state.
AHNS
Vo
TH
V
Ps)
= ICvdT
(PH-
(25)
Ts
complementary
informationfor the thermalequationof
state,that is, ,as well as Cv. Minerals for which shock
temperatures
havebeenmeasured(usuallyvia radiative
techniques)are soindicatedin Table 1.
In the case of molecular fluids such as water, a
formulation
basedonthenearconstancy
of Cp at constant
volume.
4. SHOCK
175
P1(VooV1)=- V1
J'PdV
+V1(P1Ps)
+ETR (23)
2
3dqD .{OHNSON
TEMPERATURES
(24)
Acknowledgments.
Researchsupportedunder NSF,
NASA,andDoD. We appreciate
comments
onthismanuscript
fromWilliamW. Anderson,
Kathleen
Gallagher,
WenboYang,
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and in [42].
JT = oE + e3Fi}t
(1)
(2)
OT=IJT + ioT = O+ io
(3)
= '- it"
Mineral Physicsand Crystallography
A Handbook of Physical Constants
AGU
Reference
Shelf 2
(4)
defined as
185
186
ELECTRICAL
PROPERTIES
OF MINERALS
(5)
p'-ip"=(oT+ioT)-1
(6)
where
(7)
lowerthanabout10'13S/matroomtemperature.
Many
earthmaterials,e.g., halides,are insulators.
Effects of temperature and pressure. The NemstEinsteinrelation links the electrical conductivityto the
diffusioncoefficientof the charge-carrying
species
conductivities
of 106S/mormore.Evenattemperatures
approaching0 K metallic conductivityis very high. In
addition to metals, materials such as graphite exhibit
metallic
conduction.
Semiconductors.
Semiconductors
to the conduction
band can
Semiconductors
(8)
theconducting
species,e is thechargeof theelectron,n is
the concentration of the conducting species, k is
Boltzmann'sconstant,and T is temperature.Diffusionis
a thermallyactivatedprocessso that D = Do exp(-E/kT),
thereforethe temperaturedependenceof the conductivity
will be of the form
!30
13=- exp(-E/kT)
(9a)
or
a relativelysmalldifference
in energyEg between
the
electrons
o = Dz2e2n/(kT)
have conductivities
oT = A exp(-E/k
(9b)
in which13oandA arepre-exponential
constants
andE is
the activationenergy. E is often expressedin electron
voltseV; Boltzmann's
constant
k isequalto8.618x 10'5
eV/deg. In practice,the 1/T factorin the pre exponential
termon the fight handsideof equation(9a) is notalways
used,andexpressions
of the form
o = Ooexp(-FT)
(10)
in
of expressions
areused,andthereadershouldbe careful
to employ the proper form of the equationfor the
constantsgiven. Plots of the logarithm of electrical
conductivity
versus1/T thatcoveran extendedrangeof
temperature
frequentlyshowtwo or morelinearregions.
The variationsin slopecanbe causedby transitionfrom
one dominant conductingspeciesto anotheror by a
TYBURCZY
(11)
AND
FISLER
187
(13)
m2 V'1 sec
'1). In general,
alldefects
arepresent
in some
In the data tablesthat follow, experimentaldata that have
been fit simultaneouslyto multiple linear segmentsare
indicatedby braces.
The effect of pressure on conductivity can be
characterizedby the inclusionof an activationvolume
term V o so that
U+ PVo.
O=ooexp(-
(12)
notation,
each
defect
isgiven
asymbol
oftheformAB,in
AA = VA + AI
(14)
IVA
(15)
(16)
00 = 1/202(g)+
V0 +2e'
(17)
1/202=VMg+ 2h'+OO
(18)
188
ELECTRICAL
PROPERTIES
OF MINERALS
Symbol
form
Meaning
Subscript
Site
Atomic symbol
to normallattice
site
V (vacancy)
inwhichFeM_isthefraction
ofFeonMgsites
andn and
x (zero)
!
(negative)
' lpositive)
oi= Ooexp(-E/kT)
(Fvlg)fo2n
I (Interstitial)
Chargerelative
e (electron)
h (hole)
(Atomic symbol)
Superscript
(19)
m areconstants
arising
fromthedefect
reaction
oi=Ooexp(-E/kT)
(FeMg)fo2nasio2
p
(20)
Species
Normal
Symbols
Lattice
Substitutional
Sites
Defects
Lattice Vacancies
Interstitial
Ions
Electronic
Defects
Defect Dimers
MgMgFeMg00
Fehg
FeMg
VMgVO
MgI O FeI
ii
ii
(FeMi-VMs-FeMi
?
TYBURCZY
AND
FISLER
189
190
ELECTRICAL
PROPERTIES OF MINERALS
TYBURCZY
II
II
ee
II -
II
AND
FISLER
191
TYBURCZY
AND
FISLER
193
194
ELECTRICAL
PROPERTIES OF MINERALS
II
II
000
--0
""0
TYBURCZY
II
II
II
II
II
000000000
UUUUUUUUU
AND
II
II
II
FISLER
II
II
oo
195
II
oo
II
II
II
II
II II II II
< .=..=..=..=.
00000
===
TYBURCZY
AND
'!:3
0
'..q
zo
FISLER
197
TYBURCZY
'
AND
FISLER
199
200
N
0
oL 0
II
II II II
TYBURCZY
AND
FISLER
Table 8. Electricalconductivity
of anhydrous
naturally-occurring
silicatemeltsat temperatures
between
1200 and 1550C. Expressedaslog o, whereo is in S/m. Data from [45, 64, 65, 67].
Temperature,C
Melt type
1200
1250
1300
1350
1400
1450
1500
Nephelinite(C- 195)
0.59
0.91
1.15
1.27
1.35
1.43
1.48
Basanite (C-90)
Tholeiitic olivine basalt(C-50)
Olivine tholeiite (C-214)
Tholeiite (C-8)
Tholeiite (70-15)
Tholeiite (PG-16)
Quartz tholeiite (HT- 1)
Hawaiite (C-42)
Alkali olivine basalt (C-222)
Alkali olivine basalt (C-70)
Alkali olivine basalt (BCR-2)
Mugearite(C-210)
Andesite (HA)
Andesite (VC-4W)
Latite (V-31)
Trachyte(C-128)
Rhyodacite(HR- 1)
Rhyoliteobsidian(YRO)
0.41
042
0.48
0.36
0.41
0.39
0.16
0.62
0.48
0.53
0.30
0.49
0.39
0.34
0.48
0.75
0.46
0.41
0.73
0.76
0.67
0.56
0.65
0.58
0.40
0.77
0.66
0.69
0.46
0.59
0.48
0.42
0.57
0.81
0.52
0.47
1.03
0.93
0.82
0.71
0.84
0.75
0.59
0.88
0.81
0.82
0.60
0.69
0.56
0.50
0.64
0.87
0.60
0.53
1.27
1.06
0.96
0.85
1.00
0.91
0.76
1.00
0.95
0.95
0.73
0.78
0.64
0.58
0.71
0.93
0.66
0.58
1.36
1.16
1.06
0.95
1.11
1.02
0.90
1.11
1.05
1.04
0.83
0.85
0.71
0.65
0.77
0.97
0.72
0.62
1.45
1.25
1.17
1.07
1.20
1.12
1.01
1.21
1.15
1.16
0.92
0.96
0.79
0.71
0.83
1.02
0.76
0.67
1.49
1550
1.25
1.15
1.27
1.20
1.26
1.27
1.23
1.22
1.00
1.07
1.00
0.86
0.92
0.88
1.04
0.81
0.71
0.91
0.74
Melt Type
kb
P range
oCt
inS/m eV
log Oo
Ea
AV
YellowstoneRhyolite Obsidian,YRO
0 - 12.8
17 - 25.5
2.19
2.77
0.50
0.76
7.9
3.2
Hawaiian Rhyodacite,HR-1
0 - 8.5
12.8- 25.5
2.36
2.75
0.55
0.74
11.1
5.3
0 - 8.5
12.8 - 25.5
3.00
3.82
0.78
1.17
17.9
3.3
Hawaiin Tholeiite
0 - 4.3
8.5 - 25.5
5.05
5.33
1.30
1.53
4.6
-0.1
cm/mol
201
zz
.
FeMg _.~
[ FeMg
._. , .-
'
18
...- .-
.----'. , _.->('Y,?.
... -') ....
II
-.. o o o o
e / o o oo;oo o o o
14
Fet
z0
-6
-1;!
-8
Log(fOz,
MPa)
Fi&re
t.Caicutat
int
cfcct
met,
lott
as
to
of
c
c[t
concentur
versus
[o
o[
oxcn
[uS
acity
Fo
olivinc
at
14'13
K
[lII.
VcC
dott
lines
prent
sbili
rc
o[
olivine.
-2
MgO:
40ppm
N
-5'
'3c
-
-9 -7 -5 -3 -
-3 - Log
P02'
P02
inMPa
Figu
2.
Log
conductivity
versus
log
f02
for
MgO
containing
40
ppm
kl.
Solid
lines
are
total
cond
das
....
'
'
'
IVlgO:
400ppm
AI fOz=
10-'3-1
)-Pa
-3
"
-3 5
-4.5
-5
-6
, , , I , , , I , , , I , , , I , , I , , , I , , , I . , ,
5.2:
5.4
5.6
5.8
6.2:
6.4
6.6
6.8
104/T (K-1)
Figure
3. Logconductivity
versus
T'l forfo2~ l0'3 to 10-4barforMgOcontaining
400ppmAI. Solidlineistotal
conductivity,whichis the sumof ionicconductivity(dashed-dotline) andthe electronicconductivity(dashedline) [54,
55].
-2.5
San Carlos
Olivine
El
T = 1473 K
]
.
-3
-4
-8
-7
-6
-5
-4
-3
-2
-1
Logfoz (Pa)
Figure4. Log conductivity
versuslog fo2 for SanCarlosolivine(1=o90)
illustratingthattotalconductivityis givenby the
sumof thetwo mechanisms
(dashed
lines)with differingoxygenfugacitydependences
[68].
'
'
'
'
'
''
'
'
'
'
60. -0,
')_
o (QFM) Fo (QFI)
._
bar,
F)'....
-''.... ..
'-...
-.
FOso(IW)
F9o(FM)
' FO9o(IW)
-6
10
12
14
16
18
104/T(K-)
Figure5. Logconductivity
versus
T-1 at 1 GPaforolivines
of different
compositions.
Solidbufferassemblages
controllingfo2 are given in parentheses;
solidlines are QFM, dashedlines at IW. Data are from [7, 69]. SanCarlos
olivineat 1 bar(self-buffered
at QFM) is shownfor comparison.
[68].
I
NaBr
-2
LiCI
KCI, RbCI
CI
-4
NaCI
-6
TICI
-8
o.s
.5
z.5
3.s
103/T(K-)
Figure
6. Logconductivity
versus
T'1forsome
halides.
Datafrom[28,33].Thelowtemperature
conductivity
ofNaCI
andNaBr is impuritycontrolled.Conductivities
for KCI andRbCl coincide.
-1
Felds'par
aridFelcspathid'
'
'
'
Electrical
Conductivity
at.)
-2
-;
NaAISiO
4
NaAISi30
a
NaAISi308
(nat.)
CaAIzSi
z 08
-3
Adularia (nat.)
10
12
3S
104/T (K )
Figure
7. Logconductivity
versus
T'1forfeldspars
andfeldpathoids.
Alllinesrefertointrinsic
regime.
Lines
labeled
by
formulaonly aresyntheticsamples;thoselabeled'nat'arenaturalsamples.Datafrom [34, 35].
10
8
....
I ....
I ....
I ....
I ' ' ' ' I ....
Conductivity of Some Binary Oxides
-
-Fe
0.95
I ....
Mgo.a3Feo.70
(Q.FM)
CaO
cr
-4
__1 -6
-8
[' , , , , I ....
5
I ....
I [ , a , I , , , I , , , , I , , , ,
10
11
1;>
104/T (K )
Figure
8. Logconductivity
versus
T'1forsome
binary
oxides.
Datafrom[6,61,63,70]. Oxygen
buffers
areshown
in
parentheses
whereappropriate.
206
ELECTRICAL
PROPERTIES OF MINERALS
10)kba
'
30 kbar
lOO
10 kbar
10'2
10-4
EquilibriumLine
Solid-Liquid
' kba
Saturation
Line
10-6
0.5
1.0
Density(g cm-3)
Figure9. Highpressure
electrical
conductivity
of supercritical
H20 versus
density
[13].
Shankland,
andAI Dubafor helpfulreviews.Theresponsibility
the National
Science Foundation.
REFERENCES
of
the
electrical
G. Duba,The electricalconductivity
of an isotropicolivinemantle,Journal
of GeophysicalResearch,97, 33973404, 1992.
Ringwood,The electricalconductivity
of pyroxene,Journalof Geology,81,
727-735, 1973.
5. Duba, A., H. C. Heard and R. N.
resultingselenotherm,
Proceedings
of
the 7th Lunar ScienceConference,
3173-3181, 1976.
6. (}artstein, E. and T. O. Mason,
Electricalconductivitymeasurements
on syntheticolivines and on olivine,
enstatite,and diopsidefrom Dreiser
ofCo2SiO
4,Physics
andChemistry
of
Minerals, 17, 187-190, 1990.
9. Hirsch, L. M. and T. J. Shankland,
Determinationof defectequilibriain
minerals, Journal of Geophysical
Research,96, 377-384, 1991.
10. Hirsch, L. M. and T. J. Shankland,
Equilibrium
point
defect
concentrations
in
MgO'
Understandingthe mechanismsof
conduction and diffusion and the role
of Fe impurities, Journal
of
GeophysicalResearch,96, 385-403,
1991.
Fe impurities, GeophysicalJournal
International, 114, 21-35, 1993.
12. Hirsch, L. M., T. J. Shankland and
A. G. Duba, Electrical conductionand
TYBURCZY
1983.
conductivity
ofFe-rich
(Mg,Fe)2SiO
4
olivines and spineIs, Physics and
Chemistry of Minerals, 12, 23-28,
1985.
5078, 1990.
30. Li, X. and R. Jeanloz, Effect of iron
Uhlmann,
Introduction
to
olivinen,
mobilityin cubicZr0.ssCa0.15Ol.ss,
Journal of the American Ceramic
Soc/ety,42, 393-398, 1959.
22. Kittel, C., Introduction to Solid State
Physics,JohnWiley andSons,Inc.,
New York, 1976.
of imperfections
in crystallinesolids,
in
Prot.
Elektrom.
Tiefenforsch,
editedby V. HaakandJ.
Homilius, pp. Berlin-Lichtenrade,
Berlin, 1980.
1231-1236, 1950.
I.
Methode
et
resultatsexperimentaux,Bulletin de la
SocieteFrancaise de Mineralogie et
Cristailographie,91,267-278, 1968.
35. Maury, R., Conductibiliteelectrique
des tectosilicates.
resultats,
II.
Bulletin
Discussion
de ia
des
Societe
Francaise de Mineralogie
et
Cristailographie,91,355-366, 1968.
36. Mirwald,
P. W.,
The
electrical
Fe304-FeCr204-MgCr204-FeA1204
spineIs, American Mineralogist, 76,
1933.
207
des
Amsterdam, 1974.
York, 1966.
FISLER
1956.
AND
405-426, 1991.
39. Nell, J., B. J. Wood and T. O.
distributionsin Fe304-MgFe204FeAI204-MgAI20
4 spineIs from
thermopower
and conductivity
m e a s u r e m e n t s,
American
Mg2GeO
4 asdetermined
byfrequency
dependent complex electrical
resistivitymeasurements,
Physicsand
Chemistryof Minerals, 19, 133-139,
1992.
electrolyte
behaviorof NaMgF3:
Geophysical implications, Science,
206, 599-600, 1979.
W. R. Judd and R. F.
208
ELECTRICAL
PROPERTIES
OF MINERALS
Pollock,
Conduction
D.
in
D.,
An
crystalCaWO
n, Journal of the
American Ceramic Society,56, 475478, 1973.
M.,
The
temperatures
under
defined
thermodynamicconditions,in HighPressure researches in Geoscience,
Electrical
Solids:
FeSiO
3 at high pressuresand
electrical
on syntheticpyroxenesMgSiO3-
Schweizerbart'sche
Verlagsbuchhandlung,
Stuttgart,1982.
54. Sempolinski, D. R. and W. D.
Kingcry, Ionic conductivity and
magnesium vacancy mobility in
magnesium oxide, Journal of the
American Ceramic Society,63, 664-
H.
nickel-nickel
oxide mixtures
and at
the nickel-nickel
oxide phase
boundary,Journalof AppliedPhysics,
54, 6459 - 6462, 1983.
64. Tyburczy, J. A. and H. S. Waff,
pressure: Geophysicalimplications
and significancefor chargetransport,
Journalof GeophysicalResearch,88,
2413-2430, 1983.
669, 1980.
L.
Tuller,
Electronic
Defects
in
Minerals,
Geophysical
Monograph31, editedby
R. N. Schock, pp. 78-87, American
GeophysicalUnion, Washington,D.
C., 1985.
67. Waft,
H. S. and D. F. Weill,
Donald B. Dingwell
1.
DEFINITIONS
A Newtonian
This ratio
(4)
(1)
(2)
q= v + 4 qs
3
(3)
AGU
additional
Reference
contributed
Shelf 2
209
at distinct
relaxation
timescales
of deformation
via
210
>'
VISCOSITY
AND ANELASTICITY
OF MELTS
3.0
2.0
z
o 1.0
best fit
o
o
I,
i
1.2
0.4
LOG
I
2.0
10 SHEARVISCOSITY
In contrast
Redrawn
CLASSES
OF
nonlinear
measurements
can deal
with
the
of deformation
rate
to the relaxation
rate
of
measurements
EXPERIMENTS
I RECOVER^BLE
...............
.STRAIN
t=0
TIME
DINGWELL
211
qL' rl
100-105
ias.Another
formof theCouette
viscometer
is
REAL
M o, K o0,
IMA
Shearviscosities
in the range109-1014Pas canbe
Mo,Ko,Go
A'
0
LOG
UJT
'determined
usingfiber elongationtechniques(seeFigure5).
Glassfibers with a diameter0.1-0.3 mm and lengths10-18
mm are commonly used. In a vertically mounted silica
glassdilatometerthe silica glassholder of the dilatometer
supportsthe beadedglass fiber in a fork. A secondsilica
glassrod holdsthe lower beadof the fiber in tension.The
strain-rate
rangeis machinelimitedto 10'7-10'4 s. A
tensilestress
(-107Pa)is applied
tothemeltfiberandthe
viscosityis determinedas the ratio of the applied stressto
the observed strain-rate. In this geometry the observed
Belongfrom102to 106s.Eachstructural
orphysical
component
of the system relaxes as a distinct relaxation mode at a
distinct timescale of frequency which is a function of
pressureand temperature.Frequency-dependent
or nonNewtonian effectsare seenin frequencydomaintheological
experimentswhen the measurement
timescaleapproaches
a
relaxation
{:
(5)
mode timescale.
T1elong=
3 rl,
3.
3rlv+ rls
(6)
GEOMETRIES
[11, 25] for times greater than the relaxation time of the
melt. Equation6 is known as Trouton'srule.
Absolute
shearviscosities
in therange109- 1011pa
s
can be determinedusingmicropenetration
techniques(see
Figure 5). This involves determiningthe rate at which an
VOLUME
RELAXATION
//
voltage
displacement
transducer.
Fora cylindrical
specimen
of anythickness
theshear
viscosity
canbedetermined
by
CONCENTRIC
CYLINDER
q4t'
(DENSlFIED
SIO
2)
/ )FIBER
ELONGAT;N
VISCOMETRY
SCANN,N
.lC
CAtO.,METRY rl.(Pa s) =
NORMAL
TORQUE
2mgh 5
3V 15h/St
(2rh3+ V)
(8)
TORSION
_ -2
gravity,
g (m2/s),
thevolume,
V (m3)ofthematerial,
the
'
-4,
andtheparallelplatesremainsconstant
andthecylinder
bulgeswithincreasing
deformation.
Thisis the"no-slip"
(. -6
UL'rRASONICS-..
thecylinderandtheplateincreases
with deformation
andthe
cylinderdoesnotbulgetheviscosityis
WAVE
AN36DI64
qs (Pa s) =
mgh2
3V 15h/St
10,000/T(K)
(9)
rangeof experimental
measurements
areperformed.The
describeda counterbalanced
sphereviscometerwhichhe
relaxationtimesrelatingto the variousexperimental subsequently
used
inviscosity
determinations
intheB203techniques
arediscussed
in DingwellandWebb(1989).
SiO2 [31]andNa20-A1203-SiO
2 [32] systems.
Falling
RedrawnfromDingwellandWebb(1989).
sphere
viscometry
hasbeenemployed
at 1 atmandathigh
viscosity.
Alternatively
thefallingsphere
method
maybe
usedwith inputvaluesof densityprovided
thedensity
contrastbetweenmelt and sphereis relativelylarge.
Maximizing the densitycontrastreduceserrorsassociated
theothervariables
affecting
viscosity
determination.
Very
highpressure
measurements
of viscosity
havebeenmade
qs(Pas)= 0.1875P t
r0.51] .5
pressures
[13, 34, 36]. The fallingsphere
method
maybe
usedfor the simultaneous
determination
of densityand
(7)
Theshearviscosity
of largecylinders
of meltor partially
moltenmaterialcan be determinedby deformingthe
cylinderbetweenparallelplatesmovingperpendicular
to
theirplanes.
Absolute
viscosities
in therange104- 108Pa
viscosity
usingthefallingsphere
method
at highpressure
to 10-3 Pa s.
determined
fromthevelocity,
c(m),andattenuation,
of a shearor longitudinal
wavetravelling
through
themelt;
wherethe amplitudeof thewaveis
(10)
DINGWELL
213
shearwave propagation
hasbeenobserved(B20 3 [43],
Na20-B203-SiO2 [23], Na2Si205 [46]).
4.
TEMPERATURE
DEPENDENCE
OF
VISCOSITY
The temperature-dependence
of silicateliquidviscosityhas
been describedusing a numberof different equations.The
simplest form, often valid for restricted temperature
intervals, is a linear dependence of the logarithm of
viscosity on reciprocal temperature, i.e. the Arrhenius
equation
l'og10q
= log0q0+ 2.303 E
RT
(14)
component
of the modulus,M'(to) = pc2, and the
imaginary component of the modulus, M'(co)=
M'(co)ccz/f (where the quality factor Q = M'(co)iM"(to) =
f/ct [27]. Viscosities are calculated for time, t and
distance,x [27]. The shearviscositycan be calculatedfrom
the velocity and attenuation data in that q*(co)= M
*(re)lira, or
(11)
andthereal component
of thefrequencydependent
viscosity
is
q'(co)
- 2pc3t
to2
SiO2,however,sufficientdatanowexistto demonstrate
that, in general, silicate liquids exhibit non-Ahrrenian
viscosity temperature relationships. The degree of
"curvature"of the viscositytemperaturerelationshipplotted
as log viscosity versus reciprocal absolute temperature
varies greatly with chemical composition(see [29] for a
summary). The temperature-dependence
of non-Arrhenian
datacanbereproduced
by addinga parameterto Equation14
to yield
(12)
R(T-To)
( 15)
the
(13)
214
VISCOSITY
AND
ANELASTICITY
OF MELTS
Kushiro[21] investigated
liquidsalongtheSiO2-CaAI204
changed
froma negativevalueat molefractionCaAI204=
0.15 and 0.2 throughpressureinvarianceat CaA1204 =
0.33 to a positivepressuredependence
at CaAI204.
NOAI$308
_O
0 MgO55,0 (1300C)
_o
Andesle
CaMgSi206-NaA1Si308.
Volatile-bearing
silicateliquids
have also been studied at high pressure [4, 7, 38, 49].
Figure7 summarizes
theeffectsof H20 andF20.1 on the
viscosity
of NaA1Si308liquid.
(1350*C)
livine
Tholeile
6.
(1400'C)
lO
2o
Pressure
(kbor)
SCHEMES
{1300*C)
CALCULATION
8o
4o
Albite-H20-F20-
7.Skbar
PRESSURE
DEPENDENCE
OF
VISCOSITY
to 2 GPa.
The
viscosities
of
silicate
and
1
6
10 4/T (K)
Figure 7. Viscositiesof melts in the systemNaA1Si308H20-F20_l with (X/X+O) = 0.1 and 0.2 plotted versus
reciprocal temperature(X = F,OH).
Redrawn from
Dingwell (1987).
DINGWELL
calculation
model
and
with
that
allowed
for
T(C)
N-zSi40,
z
the
NON-NEWTONIAN
MELT
4?4
tJ
4Z9
482
493
504
506
--
0.0
--
-0.5
--
RHEOLOGY
--:-1.5
-1.0
NaAISiO.
CaMgSIO.
-1.5
in silicate
1.0
:.-y.
of the relaxation
215
-4
-3
-2
-1
12.0
"1
LGM
I 1.6
12.0
CLA
11.8
HTB
11.4
Newtonian
viscosity
is seenbelowstrainratesof 10-4
12.0
+++-Vvvw
--
v.
NEP
I 1.6
_
%
_
11.2
-5
-4
-3
-2
-1
(s-')
andDingwell (1990b).
the relaxation
indicates
216
VISCOSITY
AND
ANELASTICITY
OF MELTS
REFERENCES
2.
1992.
3.
1989.
8.
339-355,
1, 423-433,
1987.
1925a.
with
different
structural
Webb,
1-6, 1989.
and M.
Pichavant,
The
1992.
Manghnani and S. Syono , American Geophysical Union, Washington, DC, 195-200, 1987.
Katahara
and
G.R.
Olhoeft,
1978.
30.
Cosmochim.
Acta,
48,
1984.
1963.
DINGWELL
38.
1964.
33. Rivers,
M.L.
and I.S.E.
Carmi-
melts,
J.
9247-9270,
(105Pa) pressure
and at higher
pressures,
U.S.Geol.Surv.Bull.,
17864, 563pp., 1987.
35. Sato, H. and M.H. Manghnani,
Ultrasonicmeasurements
of Vp and
Qp: relaxation spectrum of
complexmodulusof basaltmelt,
Phys. Earth Planet. lnt., 41, 1833, 1985.
36. Scarfe,C.M., B.O. MysenandD.
Shaw,
H.R.,
Obsidian-H20
6337-6343, 1963.
39. Shaw, H.R., Viscosities of magmatic silicate liquids: an empirical
and
E.
Matsubara,
2439-2442, 1963.
Vogel, H., Das Temperaturabhingigkeitsgesetzder Viskositit
yon F!ussigkeiten, Physik Z., 22,
645-646, 1921.
46. Webb,S.L., Shear and volume
relaxation in Na2Si205, Am. Mineral., 76, 451-456, 1991.
47. Webb, S.L. and D.B.
Dingwell,
Chem. Mineral.,
17,
125-132,
41. Simmons,
J.H.,R. OchoaandK.D.
1990a.
Simmons,
Non-Newtonian
viscous 48. Webb,S.L. and D.B. Dingwell,
flow in soda-lime-silicaglass at
forming and annealing temperatures,J. Non-Cryst. Solid., 105,
313-322, 1988.
Geochemical
SocietySpecialPub-
lication,1, 159-167,1987.
non-Arrhenius
behavior
in B203,
Springer,Berlin, 1988.
45.
Chem.,156, 245-257,1926.
43. Tauke,J., T.A. LitovitzandP.B.
und Eigenschaften.
407pp.
Virgo,Pressure
dependence
of the
viscosity of silicate melts,
37.Scholze,
H.,Glas:Natur,Struktur
Viscoelasticpropertiesof a simple
217
viscosity
of sanidine
liquidat high
pressures,
J. Geophy.Res.,95,
15683-15693,1990.
J. Am.Cer.Soc.,51, 158-163,
vitreous
state,Cambridge
Uni-
1968.
versity
Press,
Cambridge,
505pp.,
1991.
R. A. Secco
from
the various
observational
thesemeasurements,
rangingfrom 10- to 10poises,
suffer from long observationtimes which can introduce
largeuncertainties
from additionalenergysourcesand/or
sinks affecting the observedphenomenon. It must be
and theoretical
Confirmation
of
flow in a 3-dimensi-
field observations
at Earth's surface.
confinedrangeof 108-109
poises. While long period
method
or measurement
is also
R. A. Sccco,Departmentof Geophysics,
Universityof Western
Reference
Shelf 2
218
SECCO
219
Reference
DynamicViscosity
Methodt{
(Poises)
0.35 - 4.7 x 10
"Torsional
free oscillations
Verhoogen(1974)
2.6 x 10-!
Chandler
wobble
5X 109
"Chandler
wobble
Anderson (1980)
5 x 102
Molodenskiy (1981 )
_<107
Molodenskiy (1981)
< lO s
Molodenskiy(1981 )
2 x 10 I
"Chandler
Gwinn et al (1986)
<5.4 x 104
Neuberget al (1990)
<3.3 x 105
Smylie (1992)
7.7 x l0 s
<1012
'Theoretically
requiredfor seculardeceleration
of
of whole Earth
wobble
VLBI
core by viscouscoupling
Stewartson and Roberts (1963)
<10 9
tTheoryof rotatingfluids
Toomre (1966)
>6 x 105
'Theoreticallyrequiredfor steadyprecession
by
core/mantleviscouscoupling
> 10-
Toomre ( 1974)
<10 6
theory
observation
2.9 x 107
220
VISCOSITY
OF THE OUTER
CORE
Reference
Dynamic Viscosity
Method
(Poises)
5 x 108
Jeffreys (1959)
Attenuationof p-waves
8.6 x 10 2
Multiplyreflecteds-wavesat mantle/core
boundary.
108
Sacks (1970)
Attenuationof p-waves
3-7 x 10
Attenuation
of s-waves
Buchbinder (1971)
2x
108
Attenuationof p-waves
Adams (1972)
4x
108
Attenuationof p-waves
1-2 x 108
Attenuationof p-waves
<<10
Attenuationof p-waves
1.4 x 109
Reference
Dynamic Viscosity
Method
(Poises)
Bullard (1949)
10-2
Hide (1971 )
107
Magnetohydrodynamicinteractionsbetweenfluid motions
and bumps on MCB
2x 105
Officer (1986)
2x 108
drift
SECCO
221
TABLE 4. Dynamic Viscosity Estimatesof Outer Core from Theories of Liquid Metals
Reference
Dynamic Viscosity
Method
(Poises)
Bullard (1949)
Miki (1952)
l0 -2
10-2_ 10'j
Quantumstatistical
thermodynamics
of liquidmetals
5X 102
Backus (1968)
3.7-18.5 x 10-2
Gans (1972)
1-5 x 10-I
Leppaluoto (1972)
>10
3.4 x 102
Anderson (1980)
10 - 104
3x
Pokier (1988)
10-2
Thermodynamicscalingrelationbetweenmelting
temperature and viscosity and diffusivity of
metals
2.5 x 10-2
Svendsen et al (1989)
18
OUTER
CORE
VISCOSITY
12
.m
.-
SEISMOLOGY
E
>,
GEODESY
GEOMAGNETISMTHEORY
-6
Method
222
VISCOSITY
OF THE
OUTER
CORE
Reference
1536
1550
1600
1650
1700
1750
1800
1850
Kitchener(1955)
7.60e
6.79i
6.41
5.89i
5.70
5.48i
5.31
5.22
Thiele (1958)
4.7
4.6
4.2
3.9
3.7
3.4
Hoffman (1962)
5.42
5.30
4.90
4.55
3.98
Cavalier (1963)
4.95
4.87
4.54
4.30
4.10
3.92
Lucas (1964)
5.03
4.93
4.58
4.28
4.00
3.76
5.44 i
5.01 i
4.69 i
4.44
5.60
5.01
Barfield
T(C)
and
5.91
Vostryakov et al (1964)
5.54
Nakanishi et al (1967)
Kaplun et al (1974)
Arkharov et al (1978)
5.96
5.03
Steinberg et al (1981)
interpolated
extrapolated
Reference
Adachi
(1973)
Composition
wt% Ni
Temperature
(C)
Viscosity
Kinematic
Dynamic
(centipoises)
(millistokes)
et al
4.9
9.7
1516
6.11
1550
5.91
1604
5.69
1633
5.54
1665
5.36
1502
6.02
1513
5.95
1550
5.72
1596
5.43
1652
5.04
1693
4.81
SECCO
TABLE 6 (continued)
Composition
Reference
wt%
Ni
CC)
Viscosity
Kinematic
Dynamic
(millistokes)
(centipoises)
1471
28.6
Arkharov
Temperature
6.15
1519
5.62
1545
5.37
1581
5.11
1615
4.91
et al
0.52
(1978)
1600
8.48
1.04
8.28
1.49
8.15
1.99
8.13
2.46
7.98
Reference
Barfield
Composition
wt% S
Temperature
, (C)
Viscosity
Dynamic
Kinematic
(centipoises)
(millistokes)
and
Kitchener (1955)
1.16
(+0.02 wt%C)
Vostryakov et al
(1964)
0.39
1529
7.00
1600
6.45
1700
5.84
1800
5.41
1600
6.00
4.70
6.61
8.51
6.41
18.56
3.43
223
224
VISCOSITY
OF THE
OUTER
CORE
Reference
Composition
wt% O
Nakanishi
Temperature
(C)
Dynamic Viscosity
(centipoises)
et al
(1967)
0.012
1600
5.02
0.046
5.43
0.071
5.40
0.072
5.39
Reference
Romanov
and
Composition
wt% Si
0.1
Kochegarov (1964)
0.6
2.0
5.0
Temperature
(C)
1540
Viscosity
Dynamic
Kinematic
(centipoises)
(millistokes)
9.62
1580
8.72
1621
7.78
1668
7.55
1743
7.04
1782
6.66
1806
6.61
1549
7.70
1605
6.92
1642
6.83
1707
6.36
1756
6.15
1508
7.39
1553
6.90
1592
6.46
1654
5.85
1712
5.69
1758
5.49
1454
8.14
1508
6.78
1575
6.02
1627
5.61
1677
5.40
1716
5.37
SECCO
225
TABLE 9 (continued)
'Viscosity
Temperature
CC)
Conposition
Reference
wt% Si
Dynamic
(centipoises)
Nakanishi et al (1967)
0.9
2.9
1615
4.13
3.54
Kaplunet al (1979)
1.0
1550
5.41
2.0
1550
5.29
1600
4.89
1500
5.74
3.0
4.5
6.0
1550
5.18
1600
4.84
1500
5.51
1550
1600
4.72
Kinematic
(millistokes)
5.05
1500
5.04
1550
4.65
1600
4.35
Acknowledgements.
I gratefully
acknowledge
helpful
discussions
withH.H.Schloessin
andL. Mansinha,
comments
in reviews
byD.L.Anderson
andananonymous
reviewer,
aswellasfinancial
support
by theNatural
Sciences
and
Engineering
Research
Councilof Canada.
REFERENCES
pp.561-566,ed. S. Takeuchi,Taylorand
Francis, 1973.
7.
SecularVariation in a PerfectlyConducting
Core, Phil. Trans.Roy.Soc.Lond., A-263,
239-266,
4.
8.
1968.
429-456, 1971.
and Knopoff, L.
1955.
The
On the
226
1S(OSITY
OF THE
OUTER
(ORE
of the
Earth 2. Interpretation.J.Geophys.Res.
91,
4755-4765,
1986.
24. Lumb, L.I. and Aidridge, K.D. On ViscosityEstimatesfor the Earth'sFluid Outer
Core and Core-MantleCoupling, J.Geomag.Geoelectr. 43, 93-110, 1991.
25. Miki, H. Physical State of the Earth's
Core, J.Phys.Earth 1, 67, 1952.
Upper Viscosity
Phys.17, 903-909,1981.
27. Nakanishi, K., Saito, T. and Shiraishi, Y.
On the Viscosity of Molten Iron and Its
Dilute Binary Alloys of Aluminum, Silicon
and Oxygen, Jap.lnst.Metals.J. 37(7),
881-887, 1967, (in Japanese).
28. Neuberg,J., Hinderer,J. and Zurn, W. On
the Complex Eigen-frequency of the
"Nearly Diurnal Free Wobble" and Its
Geophysical
Interpretation,
in: Variationsin
Viscosity
42. Thiele, M.
O.A. ViscosityandElectricalResistivityof
MoltenAlloysof Iron with Phosphorus
and
Sulphur, Fiz.Metal. Metalloved. 18(3),
476-477, 1964.
72-89, 1980.
TripletandtheDensityNearEarth'sCenter,
Science, 255, 1678-1682, 1992.
by
W.B.
Hubbard, Pachart
Pub.House,
Tucson,388 pp., 1978.
Scott D. King
1. INTRODUCTION
q = 2'"
geochemical
mixingtime scalesare all stronglyaffected
by the pattern of convectiveflow which, in turn, is
stronglyinfluencedby the viscositystructureof the
mantle. There are two approachesto understanding
the
viscositystructure
of theEarth: usingobservations
suchas
the geoid and post-glacialuplift, combinedwith flow
models;or studyingthe physicaldeformationpropertiesof
mantle mineralsin the laboratory. Both approacheshave
advantages
anddrawbacks.
Laboratorymeasurements
of deformationindicatethat
the rheology of upper mantle mineralssuch as olivine
((Mg,Fe)2SiO4)
is a strongfunction
of temperature,
grain
size and stress[e.g., 3, 24, 43, 45, 46, 61, 65]. The
deformationof mineralsundermantleconditionsgenerally
(2)
mantle
(~ 10-14s'1). Whilethelaboratory
measurements
S. D. King, Purdue University, Departmentof Earth and
AtmosphericSciences,West Lafayette,IN 47907-1397
Mineral Physicsand Crysta!lography
A Handbook of PhysicalConstants
AGU
Reference
Shelf 2
smallgrain size.
The deformationof the major high pressuremantle
and
spinel
228
MODELS
OF MANTLE
VISCOSITY
is assumed.
modeled
asa halfspace
witha uniform
viscosity
of 1021
10-,
10-6
l
o
Fig. 1. ((r-z)-deformation
map for polycrystallineolivine
with grain size 0.1 mm. Thick lines are creep field
boundaries;
thin lines,constantstrainrate contours(given
as powers of t0). C and NH denoteCoble and NabarroHerring creep,respectively[3].
channel,
with1.3x 1019Pas viscosity,
overlying
an
effectively rigid mantle. Haskell also showed that the
viscositydid not changeover the interval of time of the
analysis,supportingthe notation of a NewIonian, rather
thanstress-dependent
mantle.
The effectsof an elasticlithospherewere first discussed
by Daly [7], who appealed to the strength of the
lithosphereto avoid the formationof a bulge of material
squeezed
out of the low viscositychannelperipheralto the
ice load in his model. McConnell [28] and Cathies[4, 5]
showedthe strengthof the elasticlithosphereas important
only in consideringthe short wavelength harmonics.
O'Connell [33] determinedthe viscosityof the lower
mantleby lookingat changesin the ice loadandrelating
themto longwavelength
rebound.He alsousedspherical
harmoniccorrelationto look for the reboundsignalin the
geoid. The effect of phase changesin the mantle on
reboundwas consideredby O'Connell [34]. O'Connell
concludedthat the effectof boththe olivine-spinelandthe
basalt-eclogite
phasechangeon post-glacialare rebound
negligible. Peltier [37] solved for the responseof a
viscoelastic (Maxwell) spherical Earth using the
correspondence
principle, later adding the effects of
varying sea level [42]. The correspondence
principle
assertsthat onecanconstructthe Laplacetransformof the
solutionby solvinga seriesof elasticproblemsover a
rangeof complexfrequencies
andtheninvertingto getthe
time domain responsefor the viscoelasticproblem.
Cathles [4, 5] presented an alternative viscoelasfic
formulationwhichavoidsthecomplexities
of theboundary
conditionsfor long time periods when using the
correspondence
principle. Cathiesarguesfor an increase
in viscosityin thelowermanfie,whilePelfierarguesfor a
KING
and co-workers
between Nakada
and Lambeck's
models based
229
surface,
c is theradiusat thecore,8plmis thedensity
contrastat a depth r of sphericalharmonicdegree I and
order
m,andGl(rjl(r))isthegeoid
response
kernel.
Thedensity
perturbations
(Spiro)
aredetermined
by
seismic velocity perturbation models from seismic
tomographicinversionsand/or tectonic plate and slab
modelsfrom boundarylayer theory and deep earthquake
locations
in subduction
zones.
To
transform
seismic
forresponse
functions
(kernels)
whichdepend
onlyonthe
viscositystructure. The geoid (V m) can then be
calculatedby convolvingthe responsefunctionswith a
disu'ibutionof densitycontrastsas follows
V = 4nTa G1
21+1[y (r,l(r))p
(r)dr
(3)
interior.
230
MODELS
OF MANTLE
VISCOSITY
Model
'flum
11
m
(Inn)
(Pa s)
(Pa s)
llm/lnm
PTa
MPb
LJN2c
LJN3d
LNAe
NI t'
120
120
100
150
75
50
1021
1021
3.5x 1020
3.8x 1020
2 x 1020
1020
2 x 1021
4.5 x 1021
4.7 x 1021
3.4 x 1021
7.5 x 1021
1022
2
4
15
8
40
100
RVGP
g
HGPA
h
HSi
(100)
(100)
(100)
2.6x 1020
2 x 1019
2 x 1020
1.3x 1022
6 x 1021
6 x l021
50
300
30
apeltierandTushingham
[41] model,basedon globalsealevel variations,with emphasis
on near-field
sites.
bMitrovica
andPelder
[29]model,
based
ontheassumption
thatthegravity
anomaly
overHudson
Bayis
totally due to delayedrebound.
CLambeck,
Johnston
andNakada[26] model2, basedon European
sealevelvariations
with emphasis
on
relativevariationsin sitesaway from the ice margins.
dLambeck,
Johnston
andNakada
[26]model
3,analternative
tomodel
2.
eLambexk
andNakada[25] modelfor Australia,
basedon sealevelvariations
withemphasis
onrelative
variationsin sitesspanning
thecontinental
margin.
fNakada
andLambeck
[32]model
forOceanic
response,
based
onsealevelvariations,
withemphasis
on
relative variations as a function of island size.
hHager
andRichards
[16]model
forrelative
manfie
viscosity
fromtheGeoid,
calibrated
forPlate
velocitiesand Advectedheat flux [14]. An additionallayer, from 400 km to 670 km depth has a
viscosity
of6 x 1020
Pas.
iAmodification
ofmodel
HRGP
that
hasanasthenospheric
viscosity
higher
byafactor
of10,asmight
be
expectedfor Shieldregions.
KING
2. RECENT
Ci
INRSION
231
RESULTS
oneshould
multiply
thehorizontal
axisscale
by1021
Pas.
static only
dynamiconly
dynamic only
SH425.2[62]asthedriving
force
(i.e.,$vslm
inequation
4) and Greens functions (kernels) for viscous flow
developedin Forte and Peltier [ 10], they parameterizeAthe
232
MODELS OF MANTLE
VISCOSITY
670- 1800km),withveryweaksensitivity
tochanges
in
viscosity
of uptoanorder
of magnitude
below
thisdepth
or in theuppermantle.Therefore,
models
withlarge
increases
inviscosity
withdepth
cannot
beruled
outbythe
RSLdataaslongastheaverage
viscosity
in the670-1800
1000
kmdepth
range
is1021
Pas. It should
bepointed
outthat
1500
Ricard
etal.[51]considered
a three
layermantle.
They
usedL02.56[8] for thedensities
in thelowermantle,
and
2500
10-
100
101
102
RelativeViscosity
Fig. 3. 1-D viscosity
modelsfrom Forteet al. [12]
determined
by inverting
observed
platevelocities
for the
bestfitting5 layerviscosity
model.Thedashed
line is the
mantle,
thedensity
coefficient
fortheslabmodel
(Pslab),
layers,
givingthemsixunknowns.
Theyused
theresponse
kernelsfor Newtonianviscousflow [50], andchosethe
viscosity
valuein the0-100km layerto be 1022Pas,
because
thegeoidis sensitive
onlyto relative
viscosity
preferred
model,
thesolidlineisalsoanacceptable
model. change.Theyperformeda MonteCarloinversionfor the
Theviscosities
in thisplotarescaled
by a characteristicviscosity
modelwhichbestfit boththegeoidandplate
mantle
viscosity
(q= 1021Pas).
velocities.Two classes
of modelsemerged
fromtheir
study;
onewithanincre.
asingviscosity
withdepth
(Figure
4 - solidline)andanother
withthehighest
viscosity
in the
transition
region
and
lower
viscosity
in
the
upper
100-300
flowdriven
bytheplates.Theresulting
viscosity
model
hasa continuous
increase
in viscosity
withdepth
to the
mid-lower
mantle,
thenadecrease
inviscosity
inthelower
discontinuities
orlowviscosity
zones.There
is a peak
change
inviscosity
ofabout
twoorders
ofmagnitude
from
However,
thismodelprovides
poorfits to the data;
variancereductions
are 44% for geoid,58% for
topography,
and19%forpoliodal
component
oftheplate
5O0
1000
I
I
I
I
I
I
I
velocities.
1500
2000
250O
Therehavebeenseveral
attempts
to formandsolvean
inverse
problem
fortheviscosity
ofthemantle
using
post-
glacialupliftdata[35,38]. Ananalysis
of therelative
sea
level,
oruplift
history,
over
Hudson
Baywas
performed
by
Mitrovica
andPeltier[30,31]. Thehorizontal
extentof
theLaurentide
icesheetsuggests
thatthissubset
of the
relativesealevel(RSL)datashould
be sensitive
to the
10-2
10-1
10o
101
102
RelativeViscosity
viscosity
at greater
depths
thanother
datasubsets
[30].
Theyconclude
thatthepreference
ofa uniform
viscosityFig.4. Threerepresentative
1-Dviscosity
models
from
inthelower
manfie
of1021
Pasfrom
other
studies
[e.g., Ricard
etal.[51]fromMonte
Carlo
inversion
using
geoid
2, 4, 5, 42] is moreappropriately
interpreted
as a andplatevelocities.
Theviscosities
in thisplotarescaled
constraint
ontheuppermost
partofthelower
mantle
(i.e., byacharacteristic
mantle
viscosity
(q= 1021Pa
s).
KING
233
1000
1500
2500
500
lOOO
1500
200O
10
15
Relative Viscosity
Fig. 6. 1-D viscositymodel from Forte tal. [13]. This
forward model provides good fits to geoid and plate
velocities. It compareswell with Figures3, 4 and 5. The
viscositiesin this plot are scaledby a characteristicmantle
viscosity
(q= 1021
Pas).
wild oscillations.All threeof the seismicvelocity models
predicta low viscositybetween400-670 km depth(Figure
5). The pattern of viscositywith depth for the three
modelsis strikinglysimilar:a high viscosityfrom 0 to 400
km depth,a low viscositybetween400 and 670 km, and
increasingviscositybelow 670 km. The largestdifference
betweenthe viscositymodelsis a factor of two difference
in the viscosityof the 400-670 km layer. It is interesting
to note that the viscosityin the lower mantle increasesby
a factor of five below 1022 km in addition to an increase
= 1021Va
s).
234
MODELS
OF MANTLE
VISCOSITY
viscositymodelis consistent
withrecentpost-glacial
uplift
analysesand mineralphysics.
3. COMPARISON
observations.
Uponconsidering
boththeuncertainty
in the
internal densitiesand surfaceloads and the uncertaintiesin
theobserved
globalrotationof thelithosphere
withrespect
to thehot spotreferenceframe(i.e., the degree1 toroidal
the viscositymodelsthemselves,
it appearsthat the results component of plate velocities).
A number of
from the differentobservations
are compatible.However, investigations
addressing
lateral viscosityvariationsare
ff the transition
zoneis Ca rich,assuggested
by some[ 1], currentlyunderway.
Karato's [21] results on the strengthof garnet are
incompatiblewith this new model. Mantle modelswith a
hard transitionzone appearcompatiblewith observations
[60].
Acknowledgments.
The authoracknowledges
support
from
NSF grantEAR-9117406.Thanksto R. O'Connell,A. Forte,and
4. LATERAL
VISCOSITY
VARIATIONS
Y. Ricardfor providing
theses,
reprts, andpreprints.Thanks
also to the numerousanonymousreviewerswhosecomments
REFERENCES
1.
pp.
1975.
57-62,
Blackwell
Scientific
Publications,Boston, 1989.
2.
6.
Andrews,J.T., A Geomorphological
Study of Postglacial Uplift with
Particular
Reference to
Arctic
Geographers,
London,1970.
Ashby, M.F., and R.A. Verrall,
of
flow
and
fracture, and their relevance to the
7.
Micromechanisms
5.
8.
4.
mantle:
determination
of
Inferences of mantic
1978.
lateralheterogeneity
in P velocityup
to degreeand order 6., J. Geophys.
1747-1750, 1991.
Earth's mantle.
Ph.D. thesis, 9.
PrincetonUniversity,1971.
KING
235
heat
flux,
in
Glacial
Pleistocene
and
Holocene
sea-level
on the structure
of mantle
Comer,
and A.M.
geneity,dynamictopogrpahyand the
geoid,Nature,313, 541-545,1985.
19. Haskell, N.A., The motion of a
viscous fluid under a surface load, I,
Peltier,
in the inference
of
mantleviscosityfrom observations
of
glacialisosaticadjustment,in Glacial
Isostasy, Sea-Level and Mantle
Rheology,edited by R. Sabadini,K.
Lambeck, and E. Boschi, pp. 63-78,
Kluwer
Academic
Publishers,
London, 1991.
30. Mitrovica, J.X. and W.R. Pelticr, A
Resolvingpower analysis,Geophys.
J. lnt., 104, 267-288, 1991.
31. Mitrovica, ].X., and W.R. Peltier, A
comparison of
inversion
of
viscoelastic
relaxation
creepin perovskitcs:Implicationsfor
the theology of the lower mantle,
Pleistocene
and J.T.
Andrews,
sea
level
rise
and
the
236
MODELS
OF MANTLE
VISCOSITY
K.
I.,ambeck,
Boschi,
pp.,
343-378,
and
E.
Kluwer
Y.,
and
instabilities
R.
Sabadini,
press,1993.
L.
Fleiotout,
and C.
1984.
51. Ricard, Y., C. Vigny, and C. 59. Sabadini, R., K. Larnbeck, and E.
Boschi (Eds.), Glacial lsostacy,SeaFroidevaux, Mantle heterogeneities,
Level, and Mantle Rheology,708 pp.,
geoid and plate motion: A Monte
Kluwer
Academic
Publishers,
Carlo inversion,J. Geophys.Res.,94,
London, 1991.
13,739-13.,754, 1989.
Differential
rotation
Dziewonski,
10,299-10,313, 1989.
56.
Ritzlet,
M., and W.R. Jacobi, Geoid
inducedby mantledensityanomalies,
and A.M.
Predominance of long-wavelength
heterogeneityin the mantle,Nature,
1984.
of the earth
J.H.,
and
A.M.
Dziew,
Mapping the upper
mantle: Three-dimensionalmodeling
of earth structureby inversion of
seismicwaveforms,J. Geophys.Res.,
89, 5953-5986, 1984.
67. Wu, P., and W.R. Peltier, Pleistocene
426, 1973.
J.P.
Poirier
1. PHENOMENOLOGY
DEFORMATION
OF
PLASTIC
; theyieldstress
usuallyincreases
with.Theconstitutive
equation
cantherefore
bewrittenc= f( ,T).
Plastic deformation of materials in the Earth, however,
theapplied
stress
is lowerthantheelasticlimit GEL,or
yieldstress; if c= EL' theplasticstraincantakeany
value.Any increasein appliedstresswould immediatelybe
relaxed by strain, so that the applied stresscannot be
greater than the yield stress. The yield stress usually
decreases with increasing grain size and increasing
temperature; in single crystals, it depends on the
orientationof the stressaxis with respect to the crystal
lattice. In actuality, the applied stress necessary for
continuing deformation usually increases with strain
(hardening). At high temperatures,however, many
crystallinematerialsexhibit negligiblehardeningand can
reasonablybe considered
asperfectlyplasticsolids.
For perfectly plastic solids, the stress-strain curve,
on temperature:
=f(cLT).In creeptests,thecrystals
are
o=f(e),isa straight
line,= EL' paralleltothestrainaxis
(Figure la). Time does not explicitly appear in the
constitutive equation. Standard stress-straincurves for
materialsare obtainedby straininga samplein a testing
France
Reference
Shelf 2
depends
onstress
bya power-lawd ocn, with1<n < 5.
237
238
PLASTIC
RHEOLOGY
OF CRYSTALS
const.
AH0(o)+PAV*
d=0fo2
TM
exp
(-
RT )
(1)
where
0 isa constant
thatoftendepends
ontheorientation
of thestressaxis with respectto the crystallattice.
const.
variable
(o, l/T, P, fo2--.),all theothervariables
being
kept constant.More reliable resultsare obtainedby global
inversion of the experimental results, which
simultaneously
yieldsbestvaluesof all the parameters[51,
48].
Fig. la
Stress-strain
curveof an elastic-perfectly
plasticsolidat constantstrainrate.
Abovetheelasticlimit CEL,stress
remains
constant.
activein theexperimental
rangeof o, T, fo2etc.Several
processes,
withrates i' mayact concurrently
or
sequentially.The resultingcreep-ratecan be expressedas:
d=I;idi'forconcurrent
processes,
and
as:
d=[I;i di-1]-1,
The temperaturedependenceof the creep-rateusually
followsanArrhenius
law, i.e.: 0 exp(-Q/RT),whereR
is the gasconstant,T is the absolutetemperature,
andQ is
the apparentactivationenergy, determinedfrom theslope
for sequential
processes.
TheArrhenius
plotIn d vs 1/Tis
then usually curved and the fit of a single straightline,
when it is possible, gives only an apparentenergy Q,
which doesnot correspondto any physicalprocess,[e.g.,
2].
If, for some reason, it becomes easier to deform an
alreadydeformedzonefurtherthanto initiatedeformation
elsewhere,plastic instability occurs,and strainbecomes
written:
Q = AH0(c
0 + PAV*,whereAH0 andAV* arethe
localized
in deformation
bands
or shear zones.
This
const.
- const.
oxygen
fugacityfo2.Inaddition,
thecreep-rate
of silicates
is also sensitive to the amount of water presentas an
impurity,expressed
astheratioH+/Si.
The constitutiveequation(rheologicalequation)of pure
singlecrystaloxideminerals,if creepis controlled
by only
oneprocess,is usuallyexpressed
as:
Fig. lb
Constantstresscreepcurve.Strainrate is
approximately
constantduringquasi steadystate creep.
POIRIER
PHYSICAL
MECHANISMS
239
thenproportional
to 2. The difference
between
the
motionof dislocations,
the shearstrain-rate obeys
rheological equation for glide-controlled and climbcontrolled creep essentially comes from the physics
underlyingthe expression
of the velocity.
i) In glide-controlledcreep (Figure2a), to moveby one
Burgersvector,a dislocationmustlocally nucleatepairsof
kinks over the potential hill; sidewaysmigration of the
kinks then brings the dislocationto the next low-energy
trough. Nucleation and migration of the kinks are
thermally activatedprocesses;the applied stresshelpsin
overcomingthe energy barrier and the activationenergy
decreasesby an amount equal to the work done by the
stress.In most cases, the dependenceof the activation
energy on stresscan be assumedto be linear: AH () =
Orowan equation'
AH0- B.
= plv
(2)
therelevant
physical
parameters:
T, c,P,fo2,etc.[45].
Glide of dislocations
is drivenby theappliedshearstress;
to movealongtheir slip planedislocations
have to go over
the potentialhills betweendenserowsof atoms;they also
have to overcome localized obstacles,due for instance to
Fig. 2a
Glide-controlledcreep.Dislocationstendto
lie in the potentialtroughs, overcoming of
the potentialhills is achievedby nucleation
andsidewaysspreading
of kink pairs(K).
240
PLASTIC
RIIEOLOGY
OF CRYSTALS
_L
121
121
Fig. 2b
Climb-controlledcreep.Edgedislocations
emittedby a source(S) glide on their
glideplane(G) untiltheyarestopped
in front
of an obstacle(0), they have to climb (C) to
clearthe obstacleandresumegliding(G).
alwaysthecase,andfor manycrystals3<n<5.
iii) In diffusion-creep (Figure 2c), diffusionof point
defectsnot only controlsthe creeprate, but alsocausesthe
creep strain: vacanciestravel down the stress-induced
chemicalpotentialgradientbetweencrystalfacesin tension
and in compression,
thusdeformingthe crystalin response
to the appliedstress.The creeprate is proportionalto the
applied stressand to the self-diffusioncoefficient;it is
inversely proportionalto the squareof the grain size if
diffusionoccursin thebulk (Herring-Nabarrocreep), and
inversely proportional to the cube of the grain size if
diffusionoccursalongthegrainboundaries
(Coblecreep).
Diffusion creep is a mechanismeffective only at high
temperaturesand in polycrystalsof small grain sizes. As
the creep rate is linear in stress(Newtonian viscosity),
diffusion creep can successfullycompete with climbcontrolledcreep only at low stresses.Deformation of the
grains of a polycrystal by diffusion creep creates
incompatibilitiesthat mustbe relievedby grain-boundary
sliding. Diffusion creep and grain-boundarysliding are
mutuallyaccommodating
processes.
Harper-Dorncreep,like diffusioncreep,is characterized
by a stressexponent n =1, but exhibits no grain-size
&
dislocation
density(proportional
to c2),andsincethe
activationenergyis stress-independent,
it follows that the
creep-rate at constanttemperatureand pressurecan be
theoretically
expressed
bya power
law: o,:03.Although
in manyinstancesthe stressexponentn of climb-controlled
power-law creep is indeed n = 3, this is by no means
Fig. 2c
Diffusioncreep.Vacancies(V) diffusefrom
regionsof high equilibrium concentration,
at surfacesnormal to the extensive stress,to
POIRIER
TEMPERATURE
-200
10-!
(C)
200
200
I )00
I'
'
'
--.L-LASTICITY
1400
1800
OLIVINE
d=I mm
10-3
,,, 10-2
10'2
(/) lO-3
POWER-LAW
o-
lO
(/) lO-4
nZ
PLASTICITY
OF
IMPORTANT
MINERALS
10-1
1o -6
02
04
06
10
08
found in [8].
,Fig. 3
of
the
active
mechanism
of
experimentalrheologicalequation(e.g., by comparingthe
stressexponent to that of the various models and the
activationenergyto thosefor diffusionof differentspecies).
It is essential,wheneverpossible,to examinethe deformed
samplesby transmission
electronmicroscopy[40] in order
to
3.
DIFFUSION
AL
FLO
W
,__
The
constructed
(Figure3), displayingin 2-dimensionalspace
(e.g., c/t and T/Tm) the domains where various
mechanisms are dominant (e.g., power-law climbcontrolled creep, diffusion creep, etc.). The boundaries
betweendomainsare obtainedby equatingthe theological
equationsfor the mechanismsdominantin each domain.
Deformation-mechanismmaps are useful to predict the
behavior of a material only in the intervals in which the
parameters
havebeenconstrained
by experiments.
iii
: lO
241
characterize
the
dislocations
and
observe
their
configurations,
lookingfor diagnosticfeatures[e.g.,5, 22].
The parametersof rheologicalequationssuchas (1) can
be constrained by experiments for various possible
deformation
3.1. Quartz
of water-related
defects contained
in the
defectsmightconsist
of 4 protons
(H+) substituted
for a
Si4+ ionor oneOH2 groupsubstituted
for an oxygen;
however,recentelectronmicroscopywork identifieswaterrelated defectswith high-pressureclustersof molecular
water [41].
(H+/106Si
> 500),oftensynthetic,
quartz
crystals.
Below a critical temperature,which decreasesas water
content increases,wet syntheticquartz is very strongand
TABLE1.High-temperature
compression
creep
ofwetsingle-crystal
quartz
OH-/Si SlipSystem
(ppm)
4300
....
370
....
370
....
T
(C)
{2110}c
{2110}C
{ 1010}a
cr
(MPa)
( inbars)
40 - 162
"
80 - 200
570- 800(]3)
400- 570(o0
570- 800([)
"
80 - 200
"
10-8-9
10-8-9
10-9-5
10-9'7
Ref.
(kJ/mol)
3.7
3.7
3.0
109
3.0
5.3
3.4
9:2
[28]
:3:3
92
[35]
213
"
117
"
ii) At higher
temperatures,
during
theincubation
period,
clusters
of watermolecules
precipitate
intowaterbubbles;
Observations
of experimentally
deformed
crystals
using theelastic
strain
around
thebubbles
isrelieved
bypunchedtransmission
electron
microscopy
[11,36, 9, 18] support outdislocation
loops,whichexpandby climbandactas
the followingmechanisms:
sources,
thusincreasing
thedislocation
density;
plastic
i) At low temperatures,
low waterfugacity,andhigh yieldoccurs
suddenly
witha stress
drop(yieldpoin0foran
strainrate,deformation
is controlled
by latticefriction,the
applied
stress
highenough
tomakemassive
multiplication
densityof grown-indislocationsis very small, the
of dislocations
possible.
FitzGerald
et al. [18]alsopoint
dislocations
arestraight
andtheirmobility
islow;quartz
is
thenvery strong.
TABLE2.High-temperature
compression
creep
ofsingle-crystal
olivines
Crystal
Orientation
of stress
axis
(C)
Atm.
Q
(kJ/mol)
(MPa)
(pseudo-cubic)
Ref.
Fo92
Various
1430- 1650
5- 150
CO2/H2 = 0.1
fro)
525
[31]
Fo92
<111>
1500 - 1600
10 - 40
CO2/H2 = 0.43
3.5
523
[13]
Fo92
<110>
1400- 1600
10 - 60
CO2/H2 = 0.43
3.7
523
[13]
Fo100
[101]
1550 -1650
8 - 60
CO2/H2 = 0.33
3.5
564
[14]
Fo100
[111]
1500- 1680
3- 30
H2/A
2.9
667
[16]
Fo90
[101]
1250 - 1400
100
CO22 = 2.3
536
[32]
Fo90
[101]
1250- 1400
100
C022 = 0.25
536
[32]
Fo90
[101]
1250- 1400
100
fo2= 10-6Pa
448
[32]
Fo100
[ 110]
1400-1650
2.6
460
[10]
Fo100
[101]
1400- 1600
3.6
573
[10]
Fo100
[011]
1500- 1600
30- 100
2.7
598
[10]
H2/CO2
POIRIER
243
TABLE 3. High-temperature
creeplawsfor bufferedsingle-crystal
Fo91 olivine
Orientation Buffer
of stressaxis
(pseudo-cubic)
[101]
[011]
[110]
dO
(o inMPa)
(kJ/mol)
opx
0.65
mw
5.3x1011 3.5
1.0x1014 3.5
0.06 690
0.40 700
2
1
0.16
3.5
0.05
2.1x 104
3.5
0.02 540
5.2x 105
3.5
0.23
mw
1.0x 10TM
3.5
0.40 750
opx
0.2
0.02
3.5
3.5
0.0
0.36
370
230
2
1
0.10
1000
g2
1.2
0.15
290
1.0x1022 3.5
0.2
1000
25
0.2
330
d2
opx
mw
3.5
3.5
3.5
0.33
250
300
540
After
[2].1200C
<T<1525
C'10
-12
< fo2< 10-3atm.,buffer:
opx(Mg0.9Fe0.1
$iO3)
or mw(Mg0.7Fe0.
3 O)
= 0o fo2 exp
(-Q/RT)-1
-1
-1
-1
n
in
Flow
law:[1011opx:
-1= 1 +2 ; [101]mw:
-1=1
. +2
.
-[0111opx:
= 1+2
-1=1
. -1+2
. -1 [1101opx:
.-1=1
. -1+2
. -1
[011]row:
= 1+[2 -1
+ 3-1]-1
-[110]mw:
3.2.
O!ivine
ratioisnotentirely
determined
whenT, P andfo2arefixed,
the activity of one component (orthopyroxene or
magnesiowtistite)
must also be specified.Bai et al [2]
performed systematic experiments on olivine buffered
against orthopyroxeneor magnesiowiistitefor various
orientations as a function of temperature, stress, and
oxygen fugacity. The results (Table 3) show wide
variations
in activationenergyand fo2 dependence
according to the experimental conditions:two or three
power law equations are needed to
describe
244
PLASTIC
RHEOLOGY
OF CRYSTALS
TABLE 4. High-temperature
compression
creepof single-crystal
pyroxenes
Crystal
d0
T
(C)
(( inMPa)
Ref
Q
Od/mol)
Enstatite(En99)
1350-
1450
4.6 x 10TM
3.8
750
Enstatite(En96)
1350-
1450
2.1 x 1015
3.9
880
Diopside
1000-
1050
Bufferedby olivine
....
[37]
[37]
4.3
284
[1]
[49]
Diopside
Slip on (100)
Slip on { 110}
Hedenbergite
1020 - 1137
4.9 x 103
8.1
742
1137- 1321
7.1 x 10-23
8.8
85
....
[49]
1020- 1130
4.1 x 10-4
6.5
442
....
[49]
1130- 1321
7.0 x 10-18
6.0
48
....
[49]
900 - 1100
1.2 x 108
3.6
526
sameconditions
at a constant
strainrateof 10-5s
-1, the
flow stressis reducedby a factorof 1.5 to 2.5, with respect
to that of crystals treated in a dry environment [38].
Samples deformed under wet conditionsand examined in
transmissionelectron microscopyexhibited evidence of
enhancedclimbof dislocations
(dislocation
walls,etc.).
3.3.
Pyroxenes
P = 10 kbar
[33]
POIRIER
245
TABLE 5. High-temperature
compression
creepof single-crystal
oxideswithperovskite
structure
Orientation
Crystal
T/Tm
Atm
of stressaxis
(pseudo-cubic)
In0
(( in Pa)
Ref.
(kJ/mol)
BaTiO3
<110>
0.75 - 0.92
Argon
-38
3.6
469
30
[4]
KNbO3
<110>
0.84 - 0.99
Argon
-43
3.7
415
38
[5]
KTaO3
< 110>
0.87 - 0.99
Argon
- 11
292
21
[5]
CaTiO3
< 110>
0.67 - 0.78
Air
-39
2.5
274
15
[53]
CaTiO3
< 100>
0.67 - 0.78
Air
-37
3.3
444
24
[53]
NaNbO3
<100>
0.70 - 0.98
Air
-92
5.3
192
14
[53]
theobservedhardening.
ilicatehigh-pressure
phases
comesfromexperiments
that
3.4. High-Pressure Mantle Minerals
Despite their importance for the rheology of the
transition
mantle,
there is no
of dislocation structures of
conditions;experiments
at about0.5Tm, in air or vacuum
are compatiblewith climb-controlleddislocationcreep,
with n = 4 and Q = 400 kJ/mol [8]. Wiistite Fel-x O, the
other end-member,is always non-stoichiometric
and Fedeficient; recent high-temperaturecreep experiments
performed
at variouscontrolled
oxygenfugacities
[24] give
results (n = 4.8, -0.02 < m < 0.11, Q = 290 kJ/mol)
compatible with dislocation creep controlled by the
diffusion of oxygen-relatedpoint defects whose nature
varieswith temperature.
Therearegoodreasons
to believe
that deformation of magnesiowiistiteat lower mantle
conditions is not very difficult: crystals formed by
decomposition
of olivine at high pressurein a diamondanvil cell containa highdensityof dislocations
[47].
All phasesotherthanmagnesiowiistite
arestableonly at
temperature
perovskite
wasstrongerthanspinelor olivine.
However,it shouldbe emphasized
thattheyield strengthof
crystals
depends
onthecriticalresolved
shearstress
(CRSS)
of the available slip systems; the dependence on
temperature
of theCRSSmay differ considerably
for the
variousslipsystems
of onemineral(let alonefor the slip
systems
of differentminerals),so thatthedominantslip
systemat roomtemperature
maynot be the sameat high
temperature,
andtherankingof minerals
according
to their
yield strengths
at roomtemperature
cannotbe assumed
to
remainthe sameat high temperature.
Althoughtransmission
electronmicroscopyof phases
deformedat hightemperature,
in theirstabilityfield, does
not providequantitative
informationon their strength,
it
doesat leastprovidereliablequalitative
information
on the
246
PLASTIC
RHEOLOGY
OF CRYSTALS
REFERENCES
1.
27, 1978.
Bai, Q., S.J. Mackwell and D.L.
Kohlstedt, High-temperature creep
of olivine single crystals, 1.
Mechanical
results
for
buffered
1991.
Creep
of baryum titanate
perovskite: a contribution to a
systematic approach to the
viscosity of the lower mantle,
Phys. Earth planet. Interiors, 55,
5.
187-189, 1989.
Beauchesne, S. and J.P. Pokier, In
182-198, 1990.
Blacic, J.D. and J.M.
Christie,
7.
9.
1989.
86, 6219-6234,
1981.
19.
123, 1985.
12. Duclos, R., N. Doukhan and B.
1. Mechanical
data, J..
and C. Goetze, A
dislocation
structure,
J.
la
forst6rite
1982.
2.Transmission
electron
micros-
14,287-14,297,
1991.
1990.
of microhardness
tests
1979.
in water-weakened
dans
1977.
263-274.
dislocations
POIRIER
1984.
4241-4255,
38.
deep-earthquake faulting in
subducting lithosphere, Science,
pyroxenes:1. Mechanicaltwinning
in diopside and hedenbergite,J.
Geophys. Res., 87, 4019-4034,
11319-11333,
39.
Revcolevschi,
35. Linker,
M.F.
and S.H.
Kirby,
Christie,
Effects
of
phase
and
1986.
66-68, 1980.
40. McLaren, A.C., Transmission elect-
temperature
deformationof diopside
single-crystal. 1.Mechanical data,
J. Geophys. Res., 96, 14,27714,286, 1991.
50. Ricoult, D.L. and D.L. Kohlstedt,
water-
weakening,Phys. Chem.Minerals,
1989.
51.
1983.
olivine
relevance
of
high-pressure polymorphs of
quartz:
Eutectoid
transformation
1985.
I6, 465-482,
1982.
and
1984.
24?
52.
Doukhan,
Transmission
PhaseDiagramsof Earth-FormingMinerals
Dean C. Presnall
Feldspars
Pyroxenes
2-7
8-13
Olivine
14-16
Garnet
17-20
Iron-titanium
oxides
Pargasite
Serpentine
Phlogopite
Iron
21-23
24
25
25
26-27
The compilationhasbeencompressed
in threeways. (1)
Reference
Shelf 2
248
PRESNALL
3000:
249
dodeite + I_quid
1500
1400
2000
Liquid
--
Jadeire
+
o 1300
Coesite
/I
Stishovite
1200
e +Quartz
I000
I100
Pressure, GPa
5
I0
Pressure, GPa
1600
Cor+
Liquid_
-
1400
Anorthite
1200
G+r _
- Liquid/
Ky
+
Oz
IOOO
o
Pressure,
GPo
i
4
2S0
PHASE DIAGRAMS
IGO0
I
--
1500
Liquid
o.,
'-
1400
--
E 1300
1200
ilOO
--
--
I
I
I
2
Pressure,
I
3
I
4
GPa
Fig.4. Isopleth
forthecomposition,
KAISi308[93,149]. At 12GPa,900C,
Ringwood
et al. [144]
synthesized
KA1Si308
in thehollandite
structure.
In experiments
from8-10GPaand700-1000C,
Kinomura
etal. [88]synthesized
theassemblage
K2Si409
(wadeite-type
structure)
+ kyanite
(A123iOs)
+ coesite
(SiO2)
fromthecomposition
KA1Si308;
andtheysynthesized
thehollandite
structure
ofKA1Si308
at900C,
12GPa,
and at 700C, 11 and 11.5 GPa.
An
CaAI2Si20e
0.1 GPa
Ab
NaAISi308
Or
Molepercent
KAISi30e
Fig.5. Compositions
of coexisting
alkalifeldspar
andplagioclase
at0.1GPaandtemperatures
from800to
900C,
asindicated
[49].Notethatthephase
boundary
isessentially
isothermal
except
intheAb-rich
portion
ofthediagram.
Manyothers
havediscussed
ternary
feldspar
geothermometry
[10,39,54,58,63,66,75,80,
139,142,151-153,
165]andternary
feldspar
phase
relationships
[68,121,156,
164,175].An,anorthite;
Ab,
albite; Or, orthoclase.
PRESNALL
1800
1700
Liquid
Liquid + Corundum
1600
1500
Liquid + Plagiocla
+
2GPa
Corundum
1400
Plagioclase
1300
1700
Liquid,+
Corunaum
? 16oo
Liquid
.--1500
Liq + Plag
+Corundum
E 1400
1300
Plagioclase
1200
I Atm
Liquid + H2!
I100
IOOO
H20-saturated,
0.5
GPa
9OO
Plagioclase+ H20
8OO
7OO
I0
NaAISi308
Albite
20
30
40
50
60
Mole Percent
70
80
90
CaAI2Si208
Anorthite
Fig. 6. Temperature-composition
sections
for thejoin NaAISi308(albite)- CaAI2Si208(anorthite)under
anhydrous
conditions
at 1 arm[26, 117], 1 GPa,2 GPa [33, 94], andunderH20-saturated
conditions
at 0.5
GPa [79, 175].
251
252
PHASE
DIAGRAMS
1300
Liquid
1200
Leucite + Liquid
Leucite
Feldspar
+Liquid
I Atm,
I100
hydrous
Feldspar
+Liquid
'
I000
Feldspar
900
Liquid
+ Vapor
0.2 GPa,
,O-saturated
8oo
0.5
GPa,
H20-saturated
Ab+
Liq + V
7OO
Albite
Orthoclase +Vapor
2 Feldspars
600
+ Vapor
5OO
I0
NaAISi08
20
30
40
50
60
70
Weightpercent
80
90
KAISi308
Fig. 7. Temperature-composition
sectionsfor thejoin NaA1Si308(albite)- KA1Si308(orthoclase)
under
anhydrous
conditions
at 1 atm[148],andunderH20-saturated
conditions
at 0.2 GPa [29] and0.5 GPa [119,
175]. Ab, albite;Liq, liquid;V, vapor. Locationsof dashedlinesareinferred.
PRESNALL
253
2500
Liquid
Majorire
2000
Perovskite
h
inoenstatite
Orthoenstatite
1500
Ilmenite
Protoenstatite
High-P
Modified Spinel
Clinoenstatite
Stishovite
IOOO
Spinel + Stishovite
Low
Clinoenstatite
5O0
IO
Pressure,
15
G Pa
20
25
Fig.8. Isopleth
forthecomposition
MgSiO
3 [7,9, 35,45,56,57,65,76,92, 127,140,169].Foradditional
dataatpressures
above15GPa,seealsoSawamoto
[147]. Notshown
is a singular
pointatabout0.13GPa
belowwhichenstatite
meltsincongruently
to forsterite
+ liquid[45]. Positionof dashedcurveis inferred.For
additionaldataon meltingtemperatures
up to 58 GPa,seeZerr andBoehler[177].
I
1900
-
,,oo
1400
I
13001
Pressure, GPa
254
PHASE
DIAGRAMS
1600
L
1650 C
l atm
20
,,Fo+
Liq
--
II+Gt
1,500
Liq
II + CoSiO3Pv
Gt + CoSi03Pv
18
,,
Gt
Di+
16
14oo
+ Fo+Liq
Gt+CM
+
,
CaSiOsPv
Cp Cpx
+C
x+Gt
Pig + Di
1300
Cpx+ Di
Di
12
-I-
CaSiO3 Pv
Cpx
2oo
Di
I0
Pen
+ Di
_
IlOO
Opx+ Cpx
IOOO
MgSiO3
Oen + Di
Mg2Si206 20
40
60
80 CoMgSi206
Mole percent
1800
20
30
40
50
Molepercent
CaSiO
3 Di
60CaSi03
----,,-
Oen + Di
1600['J
5_2 ''-/53 4 5
'.10GPo _l
?Cen
I 1.5
Di
Di
Oen+Pig
Mg2Si206 20
40
Mole
60
percent
80 CaMgSi206
PRESNALL
Di
255
Hd
I atm
-500-
ooo---,
--
,o
, -_
--
--Polythermal
, boundary
of
"Forbidden
'
Zone"
,,oo '"'-C
,
25
en
zoo oO5oo
50
75
Es
Mole percent
Fi[.]3.Ortboyroxee
+u[ite,
ortboproxee
+[ite+pi[eoite,
d i[oit
+[iteeqilibri
armad500-]
3C [95].Pberelationships
totefi[btofthe[orbidde
zone
boudr
e roetastable
mltiv
to[ite+olivi+silicm
LiJsl[] bspeseted
teeotbe
similar
di[rms
t0.5,],
P. LiJslJ AJs [9?]sbolJ
bconsulted
forcoffectio
pocedres
equimd
before
pyroxees
othese
di[ms
for8eotbermometry.
[, estatite
(8SiO3);
Fs,[rrosilit
(FSiO);
Di,
JiosiJ
(C[Si]Of); BJ,bedebersite
(CeSiO6).
I I JI+Liquid
I I %,,
I JI I I I I
2500
I I I I JI I I I JI I Periclase
Anhydrous B + Liquid
Liquid
Modified
Spinel
Forsterite
Spinel
IOOO
50O
I0
Presse,
15
20
25
G Pa
Fig.14.Isopleth
forthe
composition
Mg2SiO4
[48,
57,141].
Additional
studies
ofthe
melting
relationships
areOhtani
and
Kumazawa
[126]
and
Kato
and
Kumazawa
[84-86].
Locations
ofdashed
lines
areinferred.
2000
1800
Lquld
_
1700
1800
%
LIQUID
1600
1600
t500
14oo
-Spinel
+Lqud
/.z'-
Enstatlte
..--'"'/
+?+L)qu)d
Pyrope
Enst+at,te
/
Sapp+h,r,ne
/
1200
S11rncimt
1400
OLIVlNE
I000e/
1300
1200
Pressure, GPo
'o o Jo ooOFS,O
Mg2SO 'o 'oWeight
percent
Fig. 15. Phase relationshipsfor the systemMg2SiO4
(forsterite)- Fe2SiO4(fayalite) in equilibriumwith Fe at 1
atm [27]. Locationsof dashedlines are inferred.
i'
".1
_ bp
20
i '".//ooc
Sp + Mw + St
28
1600
O
,-,
Pv+Gt
[- 'v
..- Pv
+Ale0
3,
-
II
Sp
15
Mod Sp + Sp
o,oA
18
2oo c
'XNXX
x+Sp
NNN
I-
io
Mg2siO 20
40
60
/
Sp+St+Gf / /
16 .....
80 Fe2s04
Mole percent
I0
MgSiO 5
IO
15
20
25
50 A zO
Molepercent
AI20
Fig. 18.Pressure-composition
sectionfor thejoin MgSiO3A1203 at 1000 and 1650C [57, 82]. For additional data
PRESNALL
257
AI203
Corundum
(CaAI2SiO6
AI2SiOl
Ca3AI2Si
Pyrope
Grossu
Mg-Gt
Ca-Gt
Di + En
Wo+Di
CaSiO
3
CaMgSi
206
Wollastonite
Diopside
Weight
MgSi03
Enstatite
percent
Fig.19.Thesystem
CaSiO3-MgSiO3-AI203
at1200C,
3GPa[30].Co,corundum;
Di,diopside'
Ca-Gt,
Cagarnet;
Mg-Gt,Mg-garnet;
Wo,wollastonite;
En,enstatite;
CaA12SiO6,
Ca-Tschermak's
molecule.
Pyrope
Gt
9, 2000-
r, Mole
i/
io,2o35-
8, 195o-
II,20651
12,21oo
1
Cpx[
50
40
:30
20
,x
IO
Enstatite
MgSiO
Diopside
Mole5/oCaSiO3
Fig.20.Compositions
(unsmoothed)
of coexisting
garnet
(Gt),Ca-rich
pyroxene
(Cpx),andCa-poor
pyroxene
(OpxorCpx)atvarious
pressures
andtemperatures
[69].Labels
ofthetype,
9, 2000,indicate
pressure
(GPa)
followed
bytemperature
(C).Pyrope,
Mg3A12Si3012;
Grossular,
Ca3A12Si3012.
258
PHASE
DIAGRAMS
LIQUID
2 LIQUI
1600
'%,
-IRON
LIQUID
OXIDE
%-6
0
HEMATITE
I 2 '%10
xo
+
'X '%
LIQUID
MAGNETITE+LIQUID
. /I
I0%
HEMATIT
+ LIQUID
AIR
1400
)"-IRON
MAGNETITE
1200
10
..
7'
-i-
HEMATITE
WUSTITE
__ i( 12
I000
.o
WUSTITE
800
Q-IRON+ WOSTITE
10
TI4
+ MAGNETITE
iC'--.
600
Q-IRON
+ MAGNETITE
1(20
--I( I'0
id22___.__
I(24
ld,4___._
I 26
-28
1
3o
I0-
i( '2
iL
_.
18
400
Fe 0.1 0.3
FeO 23
24
25
26
27 Fe304
29
Fe203
Weight % Oxygen
Fig.21.Temperature-composition
section
forthesystem
Fe-Oat 1 atm[46,47,64, 120,138].Lightdash-dot
lines are oxygenisobarsin atm.
PRESNALL
259
Rutile
TiO 2
80 ,/
Rutile
-8
1300C
I '+
Fpb-Psb
Fpb
One
atm
t
-3.43
I
/
/
I
i
TIrn
/IIm-Hem
I
I
-8
/
4O
Ilrn-
Us
Fpb-Psb
Hern
C02
/
/
/
/
/
-I0
Usp-Mt
/
/
-8
/
FeO
Air
-I-
Usp- Mt
+
WEs
\
-0.68
IIm-Hem
Psb
20
40
60 Mt
Mole
percent
80
I
Fe203
Hem
Fig.22.The
system
TiO2-FeO-Fe203
at1300C,
1atm
[161
]. Light
dashed
lines
areoxygen
isobars
labeled
inlogoxygen
fugacity
units
(atm).
Psb,
pseudobrookite
(Fe2TiO5);
Fpb,
ferropseudobrookite
(FeTi20$);
Ilm,
ilmenite
(FeTiO3)'
Hem,
hematite
(Fe203)
' Usp,
ulvospinel
(Fe2TiO4);
Mt,magnetite
(Fe304)'
Was,
wiistite
(Fel_xO).
-IO
-2o
MT-USP
-25
500
Miscibility gap
900
Temperoture, C
Fig.
23.Temperature-oxygen
fugacity
(f02)
grid
forcoexisting
magnetite-ulvospinel
solid
solution
and
ilmenite-hematite
solid
solution
pairs
[155].
Lines
with
labels
ofthe
type,
1-70,
indicate
mole
%ilmenite
in
the
ilmenite
(FeTiO3)
-hematite
(Fe203)
solid
solution.
Lines
with
labels
ofthe
type,
U-70,
indicate
mole
%
ulvospinel
inthe
ulvospinel
(Fe2TiO4)
_magnetite
(Fe304)
solid
solution.
Mt,
magnetiteulvospinel' Usp,
PRESNALL
'
'
261
'
I-
3114
IOOO
15
12oo
14 o
Temperature *C
Pa-out (
Pc]
Pa-out
(0.3.)
---Pa-out
(0.5)
800
I000
II
1200
1300
1500
Temperature,C
6 r ,ot u,ivb,t
I114]. S
pressureis
262
PHASE
DIAGRAMS
8000[ I
2000
'
,,S,
I/
I
6000k
'/'
///
40001-
ooo
100
0
0
I00
?
Pressure,
Fi. ]?. ib
(bcc)
200
500
J
,oc
,
GPa
pressure melti
Mirwald
adKennedy
[i ]]], Budy[40],adBoebler
[17]
e usedCotthe -s-? phaserelmiosbips. Numbersbeside
50
o0o
IO
ti
2o
Pressure,
$o
which
brings
thedataof Bass
etal. [11]andBrown
and
4o
GPa
Acknowledgements.
Preparationof this compilation was
supported
byTexasAdvanced
Research
Program
Grants009741007 and 009741-066,andby NationalScienceFoundationGrants
EAR-8816044
and EAR-9219159.
Geosciences
Program,
Universityof Texasat Dallas.
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thermo-
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Kato, T., and M. Kumazawa, Sta-
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534-535, 1985b.
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Geophys. Res., 96, 16,26316,274, 1991.
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uncertainties
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termination
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Johannes,W., D. W. Chipman, J.
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Kushiro, I., Determination of liquidus relations in synthetic silicate systems with electron probe
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91.
Chem.
Petrol.,
R. C. Newton, A. L. Boettcher,
Phys.
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Kitahara, S., and G. C. Kennedy,
The quartz-coesite transition, J.
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68, 221-230,19'9.
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15,663-15,670,
1989.
Kinomura, N., S. Kume, and M.
211-214,
295-303,
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stabilities
of
1989.
12,
Post-
1990.
mental
results
to 8 kbar,
Geochim. Cosmochim. Acta, 37,
651-666,
1973.
r6actions
10,646,
77.
des
and
h l'aide
data
73.
75.
72.
84.
Environ.
71.
Experimental
70.
83.
for
1983.
An-Ab-Or,
69.
1987.
Pub.,
398-413,
68.
Scientific
Mg4Si4012-Mg3A12Si3O12,Phys.
Earth Planet. Inter., 49, 168-175,
1987.
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Terra
265
Mineral.,
57,
1260-1271,
1972.
92.
266
PHASE
DIAGRAMS
kbar
1966.
Lindsley,
D. H., Melting
relations of plagioclase at high
pressures, in New York State
and
Science
106.
Service
Mineral.,
107.
oxide
minerals,
in
A887-A906,
1983.
109.
195,
990-991,
110.
1977.
102.
103.
1978.
117.
3782, 1975.
Liu, L.-G., and W. A. Bassett,
Elements,
Oxides,
Silicates.
Mirwald,
120.
121.
P.
W.,
and G.
C.
the
common
rock-
1964.
Mori, T., and D. H. Green,Pyroxenes in the system Mg2Si20 6CaMgSi20 6 at high pressure,
Earth Planet. Sci. Lett., 26, 277286, 1975.
112.
of
L, L1-L158,
119.
2, 79-82,
74, 1-4,
135-138,
Core Earth,
Central
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1989.
A.
Bell, and C.
and
1987.
J.,
7990, 1980.
Modreski,
P.
Boettcher,Phaserelationshipsof
phlogopitein the system K20MgO-CaO-A1203-SiO2-H20to 35
101.
115.
1600C
data on
Pub.,
cates, Science,
Scientific
1987.
108.
1976.
100.
Terra
between
114.
600 and
1978.
99.
H.-J.
51, 1793-1799,
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113.
York, 1986.
Liu, L.-G., W. A. Bassett, and J.
493, 1983.
96.
Lindsley,
D. H.,
Melting
relations of KA1Si308: Effect of
pressuresup to 40 kilobars, Am.
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95.
1685-1692,
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94.
79,
1968.
122.
Minerals, Fluids,
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M'ineral.,
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Carmichael
and
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Ohtani,
E., T. Irifune,
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15,858, 1990.
Perkins,
D., III,
138.
orthoenstatite-
and
R.
64, 1451-1453,
139.
C.
129.
137.
Melting of forsterireMg2SiO4 up
136.
to
16.5
GPa
and
21,716, 1990.
Saxena, S. K., G. Shen, and P.
148.
149.
Research
in
Mineral
150.
the
1955.
151.
1982.
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1985.
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696-701,
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1990.
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70,
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1971a.
Mineral.,
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305.
147.
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The systemK20-AI203-SiO2,Am.
1969.
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1977.
Petrol.,
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1960.
Powell, M, and R. Powell, Plagioclase-alkali feldspar geothermometry revisited, Min. Mag., 41,
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140.
130.
of
145.
1983.
Reversals
with
1984.
125.
KAISi30 8, an aluminosilicate
1981.
267
153.
268
PHASE
DIAGRAMS
Petrol.,
101,
149-164,
1989.
66,
1189-1201,
1981.
156.
Stewart,
D.
B.,
and
E.
H.
terminations
of
the
three-
Bukowinski,
(Mg,Fe)SiO3
and
M.
S.
T.
Stability
of
perovskite and the
1992.
Mineral.,
60,
667-674,
1975.
1973.
Manghnani
and
S.
post-stishovite high-pressure
polymorph of silica, Nature, 340,
217-220,
1989.
49, 1O16-
1973.
57, 1232-1241,
1972.
62, 687-691,
1977.
1969.
M.
of
coesite-
1977.
1993.
Bell, and H. K.
1981.
John B. Brady
1.
INTRODUCTION
2. FORCES
AND
)G
II)P,T,
AG
+AG
ll-Ani[.ni
P,T,nj
Ani
hni
nj
-
AGTtal
_ Ani g _ [[i < 0 .
(1)
(2)
On a macroscopic
scale,linear equationsappearto
be adequatefor relating eachdiffusive flux to the set
of operative forces [137, p.45]. The instantaneous,
FLUXES
one-dimensional,
isothermal
diffusive
flux Ji (moles
of i/m2s) of componenti in a single-phase,
n-
(3)
where
x (m)isdistance
andthen2termsLi(moles
ampton, MA 01063
Reference
Shelf 2
269
270
DIFFUSION
DATA
rapidly with the numberof components.Two important resultshelp limit this complexity. First, the isothermal, isobaric Gibbs-Duhemequation [139, p.
134]
3. FICK'S
LAWS
Ji =
-Lij
(4)
Lj = Lj,
(5)
Ji--Di(
dCi
,dxJ
(7)
relatesthe instantaneous
flux Ji (moles of i/m2s) of
componenti to the one-dimensionalgradientof the
concentrationof i, dCi/dx (moles of i/m4), and
definesthediffusioncoefficientD i (m2/s). However,
unlessthe experimentattainsa steadystate,time (t) is
also a variable and a continuity equation (Fick's
SecondLaw)
(8)
--tJx- Dix2t'
(9)
involvemeasurable
compositions
Cj (molesofj/m3)
(6)
j=l
unfortunately
DiDi so that (n-l)2 diffusion
samplevolumedoeschange[10]. Similaranalytical
solutionsexistfor relatedboundaryconditionsand/or
other geometries,notably sphericaland cylindrical
cases. More complicatedboundaryconditionsand
geometries
may requirenumericalapproximation[32,
Chap. 8].
e (m2/s)areneeded
for (6).
coefficients
Dij
parameter
x/-t maybeused
tocharacterize
theextent
of diffusion. In semi-infinite casessuchas (10) and
(11), the distancex that hasattaineda particularvalue
BRADY
271
Table I. Commonly-used
solutionsto equation(9)
Solution
BoundaryConditions
Thin-film
Solution
Ci-->CO
for
Ixl>0
as
t->0
/
Ci-->oo for x=0 as t-->0 J
-CO=
c
exp
2x/Dt
where
c--I)(Ci-C0)dx
4Dt
(10)
(11)
CI-C0=erfc
2Dit
ICi=Cl
for
0<x<h
att=0/
Ci=C0tbrh<x<Latt=0?
(aci/ax),
=0 forx=O&L J
]-CO
L
=n
(Ci-CO)
h ;21
sin
exp L2
cos(-)
(12)
('.
=CO
for
-L<x
<Latt=0}
C=CI for x=0&L
at t>0
=1---
completion
of homogenization
by diffusion
ispropor-
tional
to x/-it.These
x/-itrelations
provide
importantteststhatexperimental
datamustpassif diffusion
is assertedas the rate-controllingprocess.They also
providesimpleapproximations
to the limits of
diffusion when applying measured diffusion
coefficients
to specificproblems[147].
4. DIFFUSION
COEFFICIENTS
In general,
onemustassume
thatDi isa function
of
Ci. Therefore,equations
(9)-(13) maybe usedwith
confidence
only if Ci doesnot changeappreciably
duringtheexperiment.Thisis accomplished
either
(a) by usinga measurement
technique
(typically
involvingradioactivetracers)that candetectvery
smallchangesin Ci, or (b) by usingdiffusional
exchange
of stableisotopes
of the sameelement
that
leave
Approach
(a)yieldsa "tracer
diffusion
coefficient"
for
the elementthat is specificto the bulk composition
studied.Approach
(b) yieldsa "self-diffusion
coeffi-
4L
cos 2L
-Di(2n
+21)22t)((2n
+1)x)
(13)
exp
assilicateminerals,glasses,
andliquids.
If Ci doeschangesignificantlyin the experiment
profiles
mightnotmatchtheshape
ofthose
predicted
by (9)-(13). In suchcasesthe Di calculated
with
these equationswill be at best a compositional
"average"andequation(8) shouldbe considered.
Experimentsin which compositiondoes change
significantlyare often termed "interdiffusion"
or
"chemicaldiffusion"experiments.A commonly-used
lcCi=C2
Di(C2)t 'i
i=C0
XClLi
.
(14)
C i =C2
Equation
(14)canbeevaluated
numerically
orgraphically from a plot of (Ci - C0)/(CI - CO) versusx,
wherethe point x = 0 (the Matano interface)is
selected such that
IC
Ci=Cl
xdC
i- 0
i=CO
(15)
272
DIFFUSION
DATA
0.0
1.0
(A)
(B)
0.8
-0.5
0.6
0.6
0.8
0.4
0.8
1.0
0.2
0.2
0.0
-2.0
0.2
0.4
0.6
0.8
1.0
0.0
0.2
0.4
x2
0.6
0.8
1.0
x/L
Figure
1. Graphical
solutions
toequation
(9).(A)The"thin
film"solution
ofequation
(10)is
shown
with(z=lforvarious
values
ofi t (labels
onlines).
Plotting
ln(Ci- CO)asafunction
of
x2atany
time
yields
astraight
line
ofslope
-1/(4Dit).
(B)The"finite
pair"
solution
ofequation
(12)isshown
forh/L=0.4
and
various
values
ofDt/L
2(labels
oncurves).
Plotting
(Ci-C0)/(C1
CO)
asafunction
ofx/Lnormalizes
allcases
toasingle
dimen
sionless
graph.
Theinitial
boundary
between
thetwophases
ismarked
bya dashed
vertical
line.
[32, p.230-234]. For binary,cationexchange
originalboundary
between
thetwocrystals.Diffusionexperimentsthat follow theBoltzmann-Matano
approach
havetheadvantage
of determining
Di asa
function
of Ci andthedisadvantage
of riskingthe
complicationsof multicomponent
diffusion, for
whichneither(8) nor(14) is correct.
independent
fluxes and, therefore,the "tracer"
diffusion
coefficients
of Cu andZn canbedetermined
inaddition
totheinterdiffusion
coefficient
Dczn_,.
A similaranalysis
for binarycationinterdiffusion
thatforelectrically
neutral
species,
thebinary
(A<--B)
interdiffusion
coefficients
(DAB_,)
obtained
in a
Boltzmann-Matano
typeexperiment
andthetracerdif-
fusion
coefficients
(D andD) fortheinterdiffusing
species
arerelatedby
DAB_
-- NBDA+ NADB 1+
(Dkz)(D3z)(a
+bNBz)
2[
DAUB_,
= (a2NAzD
Z+b2
NBzDBz)
. 1
[)lnNaz
)In
AZ
)P,T]'
()lnYA
) ],(16)
c]lnNAP,T
whereNA isthemolefraction
andAthemolaractiv-
itycoefficient
ofcomponent
A. Darken
developed
his
analysis
inresponse
totheexperiments
of Smigelskas
and Kirkendall [148], who studiedthe interdiffusion
of CuandZn between
Cu metalandCu?0Zn
3obrass.
Smigelskasand Kirkendall observedthat Mo wires
(inertmarkers)
placedat theboundary
between
theCu
andbrass
moved
in thedirection
of thebrass
during
theirexperiments,
indicatingthatmoreZn atomsthan
Cuatomscrossed
theboundary.Darken's
analysis
showedthat in the presenceof inert markersthe
(17)
whichrequires
vacancy
diffusion
if a;e:b.
If a=b,then
(17) simplifiesto
DAZ DBZ
DAB_,
DAZ
= (NAZ
, +NBzDBz
, 1
[)In
AZ
)]
)InNAZP,T
(18)
[121]. Thisexpression
permitsinterdiffusion
coeffi-
cientsto becalculated
frommore-easily-measured
tracerdiffusioncoefficients.
For mineralsthatarenot
BRADY
2'73
coefficients
D to calculatemulticomponent
interdif-
5. MULTICOMPONENT
DIFFUSION
6. EXPERIMENTAL
few
additional
DESIGN
considerations
should
be
mentioned
regarding
thecollectionandapplication
of
response
to factorsnotincludedin (7)-(!8), suchas
gradients
in thechemicalpotentials
of othercomponents,couplingof diffusingspecies,etc. In these
cases,equation(6) or (3) mustbe used. The off-
diffusion
diagonal
(i-j)diffusion
coefficients,
Di or Li!,are
diagonaldiffusivities
areavailable[19, 20] andthey
data.
mayhaveprofoundeffectson diffusionrates[e.g.,
121, 164]. Therefore,it is essentialthat the mineral
werefoundto be relativelysmall.
Oneapproach
usedby manyistotreatdiffusion
that
is one-dimensionalin real spaceas if it were onedimensionalin compositionspace. This approach
was formalized by Cooper and Varshneya[28, 30]
beingstudiedis we!l-characterized.
If the mineral,
liquid,or glasscontains
a multivalent
element
likeFe,
then an equilibriumoxygenfugacity shouldbe
controlled or measured because of its effect on the
vacancyconcentration.
Diffusion in rocks or other polycrystalline
materialsmay occurrapidly alonggrainboundaries,
experiments. In general,diffusioncoefficients
11, 47, 49, 95, 154, 13, 158] are beyond the scope
of this summary. If polycrystallinematerialsare
usedin experimentsto measure"intrinsic"or "vol-
eigenvector
analysis.Althoughsomesimplification
in datapresentation
is achievedin thisway, a matrix
theanalysiscanproceed.
to be negligible.
Water can have a major effect on diffusion in
Dij- Difiij- n
Dj- Dn
(19)
"extrinsic"grain-boundary
diffusionmustbe shown
experimentaldataset.
Because many kinetic experimentscannot be
"reversed," every effort should be made to
demonstrate that diffusion is the rate-controlling
process.
Important
testsinclude
the x/-itrelations
noted in equations (10)-(13) and the "zero time
experiment."
Thei t testcanbeusedif dataare
(19)zi isthecharge
oncationi, 15i.i-I if i=j, andij
2?4
DIFFUSION
DATA
TABLE
converted
totheunits(kJ,m2/s)andform(logDo) of
thiscompilation.Logarithmsare listedto 3 decimal
places for accurate conversion, even though the
original data may not warrant such precision. No
attemptwasmadeto reevaluatethedata,the fit, or the
uncertainties
given(or omitted)in the originalpapers.
Also listedare the conditionsof the experimentas
appropriate
includingthetemperature
range,pressure
range, oxygen fugacity, and sample geometry.
Extrapolation of the data using (20) to conditions
outsideof the experimentalrange is not advisable.
However, for easeof comparisonlog D is listedfor a
uniformtemperature
of 800C(1200Cfor the glasses
and liquids), even thoughthis temperaturemay be
outside of the experimental range. Use these
tabulatedlog D numberswith caution.
Finally, a sample "closuretemperature"(Tc) has
been calculated for the silicate mineral diffusion data.
to
(21)
(Soret)diffusiondata[see108]. Diffusiondatalisted
for silicate glassesand liquids have been further
restrictedto bulk compositions
thatmaybe classified
as eitherbasaltor rhyolite.
Because diffusion is thermally activated,
coefficientsfor diffusion by a singlemechanismat
different temperatures may be described by an
Arrheniusequation
D- DOexp-AH)
RT
(2O)
BRADY
2'75
BRADY
277
278
DIFFUSION DATA
BRADY
279
280
DIFFUSION
DATA
BRADY
281
282
DIFFUSION
DATA
BRADY
283
284
DIFFUSION
DATA
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Fe+2-Mginterdiffusion
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Rb
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Hayashi,T., andMuehlenbachs,
K., Rapid oxygen diffusion in
its relevance
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granitic melts, J.
water contents,
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diffusion
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petrology and mineral physics,
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186-201, 1988.
Petrol.,
99,
characteristics,
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98.
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Kinetics
mineral
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329-340,
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silicates,
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dolomite,
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Joesten, R., and Fisher, G.,
Sci., 3, 206-222,
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New
revisited.
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287
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4O5, 1969.
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Cosmo-
1979.
of
diffusion:
minerals,
in
defects
Kinetics
self-
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im
the
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coeffi-
concentrations
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and
NaSi-CaAi
Yund,
R.
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1933.
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T. M.,
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of cation diffusiv-
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19'74.
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Solid
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114. Liu,
1986.
!!3.
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118. Mackwe!l,
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121. Manning,
J. R., Diffusion
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--
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1573-
1580, 1981.
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197, Springer-Verlag,
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Experimental measurementof
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1313-1324,
1993.
152. Watson,
E.
B.,
Calcium
1994.
in
Shimizu,
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1989.
130-142, 1947.
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using
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27Al(p,)28Si
nuclearreaction:
preliminary
results, Earth
of tritiated
148. Smigelskas,
A.
D.,
and
Kirkendall,
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fluid-bearingand slightly-melted
rocks: experimental and numerical approaches illustrated by
iron transport in dunite,
Contrib. Mineral. Petrol., 107,
417-434, 1991a.
155. Watson, E. B., Diffusion of
dissolved
CO2 andCI in hydrous
silicic to intermediate magmas,
Geochim.
Cosmochim.
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55, 1897-1902, 1991 b.
156. Watson, E. B., and Baker, D.
R., Chemical
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magmas: an overview of
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L., and Kushiro, I., pp. 120151, Springer-Verlag, New
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157. Watson, E. B., Harrison, T. M.,
Cosmochim.
,/9, 1813-1823,
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1985.
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Mineral. Petrol., 108, 463-471,
1991.
1965.
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1969.
163. Yund,
dissolvedcarbonatein magmas:
experimentalresultsand appli-
160. Wendlandt,
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R.
F.,
Oxygen
Tullis,
R.
J.,
dislocations
A.,
Diffusion
The
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M.,
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55,
44 1-
103, 228-
Q. Williams
sciencesareexamined:1) infraredtroscopy;
distortions.
1.
INTRODUCTION
presence
andstrength
of theseinteractions
areprincipally
dependenton bondingproperties,the configurations
of
electronicstates,and local symmetryof ions, molecules
2) Raman
spectroscopy;
and3) opticalabsorption
spectroscopy.
Each of these techniquesprovides complementary
informationon the vibrationaland electronicpropertiesof
Earth materials.The bondingpropertieswhich produce
infrared and Raman-activevibrationalbandsprovide not
2.
VIBRATIONAL
INFRARED
AND
SPECTROSCOPY:
RAMAN
TECHNIQUES
only a usefulfingerprinting
techniquefor determiningthe
presence
or abundance
of differentfunctional
groups,such
as hydroxylor carbonateunits,but also(in a bulk sense)
fundamentallycontrol a variety of thermochemical
propertiesof materials,includingtheir heat capacity.
Moreover, the vibrational spectrum provides basic
information on the bond strengths present within a
material.Electronictransitionsmay occurin the infrared,
within
a material.
unit utilized
to
centimeters,
orwavenumbers
(cm-1):
these
maybereadily
convertedto Hertz by multiplyingby the speedof light, c
(2.998x 1010cm/sec),
tothewavelength
of light(incm)
by taking its inverse,and to energyby multiplyingby c
andPlanck's
constant,
h (6.626x 10-34J-sec).
Here, we focus on infrared and Raman spectroscopic
characterization of vibrational states: in this discussion,
Reference Shelf 2
291
292
INFRARED,
RAMAN
below~14000cm-1 (andmostoftenbelow5000cm-1) is
either absorbed or reflected from a material through
interaction with interatomic vibrations. The primary
measurementis thus of the intensity of transmittedor
reflected infrared light as a function of frequency.With
Raman spectroscopy, a photon of light interacts
inelasticallywith an optic vibrationalmodeand is either
red-shiftedtowardslower frequency(Stokeslines) or blueshifted to higher frequency (anti-Stokes lines) by an
amount correspondingto the energy of the vibrational
mode. When such an interaction
frequencyfromwhichtheoffsetvibrationalmodesmaybe
measured. Furthermore, the Raman effect is rather weak:
The vibrational
spectroscopy
may be describedas a functionof the force
constant of the vibration
or deformation
v,a,=
(0
interatomic
interactions
included in
thesecalculations.Suchcomputationsof latticedynamics
WILLIAMS
v 1-symmetric
stretch
800-950cm-1
Raman(often strong)
v2-symmetric
bend
300-500cm-1
Present in Raman
293
bend
v3-asymmetric
stretch v4-asymrnetric
400-600cm'1
850-1200cm-1
Infrared (strong),Raman
Infrared, Raman
Fig.1.Thenormal
modes
of vibration
of anSiO4-tetrahedra.
Withinisolated
tetrahedra,
allvibrations
are
Raman-active,
whileonlythev3 andv4 vibrations
areactivein theinfrared.
However,
environments
with
non-tetrahedral
symmetries
frequently
produce
infraredactivityof theVl andv2 vibrations
in silicate
minerals[modifiedfrom [ 12] and [ 1811.
havecontributed
majorinsightinto thecharacterization
of
differenttypesof vibrationalmodesin complexcrystals:
the precise equationsand means by which such
calculations are carried out have been reviewed elsewhere
[3, 91.
Whether
given
vibrational
motion
is
crystallographic
directions.
Thus,bothRamanandinfrared
activitiesare govemedby interactions
of theelectricfield
of theincominglightwith vibrationally
producedchanges
in the chargedistributionof the moleculeor unit cell.
Yet, despite Raman active vibrationsdependingon
changesin the polarizabilitytensorandinfraredactive
vibrationsbeing generatedby changesin the dipole
mutuallyexclusive:for non-centrosymmetric
molecules
(or unit cells), somevibrationscan be both Ramanand
infrared-active. Finally, the intensities of different
be relatedto themagnitude
of thechanges
producedin the
dipole moment or polarizability tensor in a given
with possiblecrystallographic
directionalityfor the
spectroscopically
activeunderinfrared
orRamanexcitation
is governedby selectionrulesassociated
with a given
crystal structure.These selectionrules are primarily
governedby the symmetryof the unit cell, and the
differingproperties
of Ramanandinfrared
activity.Infrared
activityis produced
whena changein thedipolemoment
vibration.
conducted
is throughan application
of grouptheorycalled
294
INFRARED,
SPECTROSCOPY
differentsymmetries
aregivenin manytexts(for example,
5), andcorrelationtablesaregivenin [7] and[8]: thelatter
text providesa numberof workedexamplesof factor
groupanalysis
appliedto mineralsandinorganic
crystals.
Infraredspectramay be presentedfrom two different
experimental
configurations:
absorption
(or transmission),
or reflection.Sampleabsorbanceis dimensionless,
and is
defined as
A = -1og(I/1o),
(2)
motion
would
constitute
an external
motion
of the
WILLIES
295
Figure3 showsrepresentative
vibrationalfrequencies
of different functional, or molecular-like groupings,in
functional
groupsmayoccur,andthesearenotincludedin
Figure3. As expected
fromEquation1, thereis a general
decrease
in frequencywith decreases
in bondstrength
for
differentisoelectronicand isostructuralgroupings,suchas
occursin the PO4-SiO4-AIO4 sequenceof tetrahedral
anions.
usefultechniques
for characterizing
bondingenvironments,
vibrationalmodefrequenciesand the molecularspecies
presentwithinminerals,infraredspectroscopy
hasbeen
extensively utilized as a quantitative techniquefor
determining
the concentration
and speciation
of volatile
components
within samples.Specificexamplesinclude
the determination of the dissolved molecular water and
dissolved
CO2relative
toCO32- groups,
andtheamount
of impurities
withincrystalssuchasdiamondanda range
of semiconductors.Such determinationsdepend on an
Raman
active
vibrations
(1Algandfourdoubly
degenerate
Egsymmetry
modes)
andeight,infrared-active
vibrations
1410and870cm-1, whilethestrongest
highfrequency
vibrations
in quartz
lienear1100cm-1 (theasymmetric
stretches
of the silicatetrahedra)
and 680-820cm-1
(corresponding
to Si-O-Si bendingvibrations).Moreover,
the LO-TO splitting of the asymmetric stretching
vibration of the carbonategroupis clearly visible in the
reflectancespectrum.Within the Raman spectrum,the
most intense vibration of calcite is the symmetric
stretching
vibration
ofthecarbonate
group
at~1080
cm-1,
while that within quartz is predominantlya displacement
of thebridging
oxygens
between
tetrahedra
at464cm-1.
Atlowerfrequency
(below
400cm-1),thespectrmn
ofthe
carbonate
has Raman
groupsanddisplacements
of thecarbonategroupsandthe
calcium ions both against and parallel to one another
c = (M.A)/(p.
d. e),
(3)
quantitative
application
of Equation3 depends:
typically,a
non-vibrationalmeansof analysisis usedto quantifythe
amountof dissolvedspecieswithina sequence
of samples
in order to calibratethe value of e. Severalcomplications
exist in the straightforwardapplicationof Equation 3:
fu'st,theextinctioncoefficientcanbe frequency-dependent,
in that the amount of absorption can depend on the
structuralenvironmentin which a given speciesoccurs.
Second,for someapplicationsa moreappropriatemeasure
of the numberof speciespresentis not the amplitudeof
absorption,but ratherthe integratedintensityunderneath
an absorption
band(see[21] for a mineralogically-odented
discussion
of eachof theseeffectsin hydratedspecies).
WILLIAMS
297
Cation-Oxygen
I<I I I I I
IStretches
I I I IA1I4A106
I'r[
i
ig(6[
CO
I
I III(K,Na)O1
lFe3+O6 Fe2+O6
IH-O-HI [2800-3700
]O-H
stretch
=1] I
cm-
In-Plane
Out-of-Plane
I
O-H Bends
bends
AsymmetricStretches
Bends
Bends
',
Stretches
Bends/Stretches SiO6-octahedra
I
Silica Networks
Carbonates
Polymerized
Hydroxides
O-H Bends
s:o'-si:
v3
Inosilicates
tridgin
OIv3&Iv1 I Si-O_SI
Io_si_o
I
& Non-Bridging O
bends bends
Orthosilicates
v 3 Vl
Sulfates
v3
Orthophosphates
I
1600
'
1400
Vl
v3
1200
v4
v4
v2
V , I ,
II , , , I 'I V4, , 2/
1000
8 O0
600
400
200
Frequency
(cm-1)
Fig. 3. Approximate
frequency
rangeof commonvibrations
of silicates,
oxidesandotherfunctionalgroups
withinminerals.For tetrahedral
species,
the modedesignations
are identicalto thoseshownin Figure1.
Most of the spectralrangesare derivedfrom [3]; thatfor octahedralsiliconis from [24].
3.
OPTICAL
SPECTROSCOPY
d-orbitals
areoctahedrally
coordinated
byanions,
thedx2_
y2anddz2orbitals,
which
have
lobes
ofelectron
density
0-5
/10
Y
dx2y
2 '-t
,0' x --
'
eg
dz2
10Dq
IZ
9 dxy
Energy
Iz
o'
dyz
.oG
-:
t2g
dxz
Fig.
4.The
effect
ofoctahedml
coordination
onthedifferent
d-orbitals
ofatransition
metal
cation
(labelled
M).Thesurfaces
ofthed-orbitals
represent
contours
ofconstant
probability
that
anelectron
lieswithin
the
boundaries.
Therepulsive
effect
produced
byclose
proximity
ofthenegatively
charged
oxygen
cations
to
the
dx2_y
2and
dz
zorbitals
separates
these
inenergy
from
the
dxy,
dyz
and
dxz
orbitals
byanamount
referred
toasthecrystal
fieldsplitting
energy
(also
as10DqorAo).
oriented
towards
theanions,
lieathigher
energy
thanthe
remaining
threeorbitals
because
of thelarger
repulsive
interactions
between
thedx2_y
2and
dz2orbitals
andtheir
neighboring
anions.
Thus,optical
absorption
maybe
produced
byexcitation
of electrons
intoandbetween
these
separated,
orcrystal-field
split,
energy
levels,
theenergetic
separation
between
which
isoften
referred
toas10Dqor
compounds
containing
suchtransition
metalionsasFe2+,
Fe3+,Mn2+,Ti3+,Cr3+,andisassociated
withboth
the
colors
andfluorescent
properties
ofa range
of minerals,
gemsand lasercrystals,includingforsteriticolivines
(peridot:
Mg2SiO4
withFe2+),
ruby
(A1203
withCr3+)
andbothsilicate
andaluminate
garnets
(whichmay
contain
a range
of transition
elements).
Thepreferential
occupation
of thelowerenergylevelsproduces
a net
crystal field stabilizationenergy(CFSE) which
contributes
tothethermochemical
energetics
of transition
metal-bearing
crystals.
Thecharacteristic
magnitude
ofthe
coordinated
cations,
thusproducing
a netpreference
of
many transitionmetal ions for octahedralsites.For
comparison,
characteristic
cohesive
energies
of divalent
transition
metal
ionsoctahedrally
coordinated
byoxygen
areontheorderof 3000-4000
kJ/mole
[4, 15,16].
Furthermore,
aseachorbitalcancontain
twoelectrons
of opposite
spins,two possible
configurations
are
possible
foroctahedrally
coordinated
cations
containing
between
threeand eightd-electronshighspin
configurations,
in which
theenergy
required
topairtwo
electrons
within
anorbital
isgreater
thanthecrystal
field
splitting
energy,
andelectrons
enter
intothehigher
energy
unoccupied
dx2_y
2and
dz2orbitals
(egstates)
rather
than
pairing
inthelower
energy
three-fold
t2gstates.
For
comparison,
electrons
in lowspinconfigurations
fully
occupy
thet2gstates
before
entering
theeglevels.
Among
major
transition
elements,
ironessentially
always
occurs
in thehighspinconfiguration
in minerals:
thisis
simply
aconsequence
oftheenergy
required
topairspins
CFSEfor Fe2+ (d6 configuration)
in octahedral in divalentironbeinglargerthanthe crystalfield
coordination
in mineralsis betweenabout40 and 60
stabilization
energy.
Estimates
ofthespin-pairing
energy
ld/mole;
that
foroctahedral
Cr3+(d3)isgenerally
between in iron-bearing
minerals
arepoorlyconstrained,
but
200 and275 kJ/mole.Characteristic
octahedral
CFSE
values
forother
transition
metal
cations
withunpaired
delectrons
generally
lie in between
theseextremes;
tetrahedrally
coordinated
cationstypicallyhaveCFS
energies
between
-30 and-70%thatof octahedrally
representative
values
forthisquantity
aregenerally
greater
than100kJ/mole
atambient
pressure.
Historically,
the
highspinto lowspintransition
of ironin crystalline
silicates
hasbeen
frequently
invoked
asa possible
high
pressure
phenomena.
Essentially
noexperimental
evidence
WILLIAMS
299
tetrahedral
sites:
intetrahedral
sites,
thedx2_y
2 anddz2
orbitals lie at lower energy than the threeremainingdorbitals.In more complex environments,suchas distorted
octahedraor dodecahedral
sites,a largernumberof crystal
field bandsmaybe observedbecause
of furthersplittingof
the d-levels.An exampleof spectraproducedby different
polarizations of light incident on Fe2SiO4-fayalite, a
materialwith distortedoctahedralsites,is shownin Figure
5, combinedwith an interpretationof the differentcrystal
field transitionspresent in this material [4]. The lower
than octahedral symmetry of the M1 and M2 sites
producesmore extensive splitting of the energy levels
thanoccursin sitesof idealoctahedralsymmetry.
The intensitiesof crystal-field absorptionbands can
vary over four orders of magnitude:theseare governed
both by the abundanceof the absorbingcation, in a
manner directly analogous to Equation 3, and by a
combinationof the symmetry of the cation environment
and quantummechanicalselectionrules. For example,
non-centrosymmetricenvironments(e.g. tetrahedrally
coordinated cations) generally produce more intense
absorptions.
The primary selectionrulesare relatedto spin
multiplicity (involving conservationof the number of
unpairedelectronsbetweenthe groundand excitedstate)
and to conservationof parity (or, transitionsbeing only
allowedbetweenorbitalswhich differ in the symmetryof
their wavefunction: the Laporte selection rule). These
selectionrules may be relaxed througha rangeof effects
which include orbital
interactions, vibrational
and
magneticperturbations,
and lack of a centrosymmetric
ion
site, producingboth weak spin-forbiddenand Laporteforbiddentransitions.Indeed, suchcrystalfield bandsare
frequently orders of magnitude less intense than the
vibrational bands discussed above.
Inter-valence,
chargetransfer,andvalenceto conduction
band transitionsare all termsusedto describeabsorption
mechanismsof similar origins:the transferof electrons
betweenions in non-metalsvia an inputof energyin the
Frequency
25 000 15,000
J
l,
I'l=l
J I
10,000
I
1.0
Octahedrai
Splitting
M1 Site
Splitting
Octahedrai
Splitting
M2 Site
Splitting
0.5
500
Wavelength (nm)
Fig. 5. Polarized crystal field absorption spectra of
Fe2SiO4-fayalite in three different crystallographic
orientations, combined with an interpretation of the
observed transitions in terms of the M1 and M2 cation
insets
represent
electrons
occupying
eachd-orbital
(Fe2+
hassixd-electrons).
Thesharp
bands
above20,000cm-1
are generatedby spin-forbidden
transitions.
300
INFRARED,
RAMAN
frequentlysmall),and represents
the interceptof a plot of
thelog of theconductivityandtheinverseof temperature.
Absorptionsgeneratedby such cation-anioncharge
delocalization
processes
are commonin ore mineralssuch
as sulfidesandarsenides,
andproducetheopacityor deep
red color in the visible of many such minerals.
Furthermore,they also induceeffective opacityof most
and
Band-Gap rystm-em
Absorptio,ns bsorptons
1.0
'
I'
4000"-",,,_
Biack-l)d--
oxygen-to-metal
chargetransfer
absorption
bandstypically
occurat highenergies
in theultraviolet,
andareextremely
intense:often three to four ordersof magnitudemore
intensethan crystalfield transitions.Effectively,such
Vibrational
, Absorptions
rmal
Radiation
O.OLO
associated
with delocalization
of an electron,or photoexcitation of an electron into the conduction band of a
material:the separation
in energybetweenthe valenceand
conductionband of materialsis commonlyreferredto as
thebandgap.Withinmanymaterials,
suchchargetransfer
bandsappearas an absorptionedge,ratherthana discrete
band:thisedgeis simplygenerated
becauseall photons
with an energy above that of the edge will produce
electrondelocalization.
Thisedgemaybeaccompanied
by
discretebandsat slightlylowerenergythantheedge:such
bandsare often associated
with a binding,or attractive
force between the photo-excitedelectronand its ion of
origin. These bound electron states are referred to as
excitons,and are discussedin greaterdetail in solid state
physics texts [e.g., 1]. There is an intimate association
betweensuchprocesses
of electrondelocalizationand the
high-andmoderate-temperature
electrical
conductivity
of
insulators and semiconductors:in materials in which the
lO-,
1
10
Wavelength ( lam)
22]. Thepre-exponential
factor,or0,isgenerallytreatedas
a constant(althoughbothit and thebandgap may be
temperature
dependent:
thesedependences
are, however,
temperatureconditions.
conduction
bandrepresents
the primarymeansby which
charge
carriers
aregenerated.
Thisrelationship
isexpressed
through
o'= o'0exp(-Eg/2kT),
(4)
constant
(1.381
x 10-23J/K),andT istemperature
[e.g.,
WILLIAMS
301
delocalize
electrons
as the
distance
between
ions
l(v) = 2ffehc2v5(exp[hv/kT]
- 1)-1
(5)
REFERENCES
1.
2.
6.
F.A.,
Chemical
Vibrations:
Method,
The
222
Correlation
pp.,
Wiley-
9.
York, 1977.
7.
8.
4.
Cotton,
3.
1970.
1974.
Introduction
to
Lattice
302
INFRARED,
Molecular
Structure:
H.
and
Radiation
Spectroscopy,
Rev.Mineral., 18,
99-159, 1988.
quantitative
laser
Raman
spectroscopy
for thestudyof fluid
inclusions, Geochim. Cosmo-
of hydroxylby infrared
absorption
in quartz, silicate glassesand
similarmaterials,Bull. Mindral.,
105, 20-29, 1982.
on
the
Electrical
Thermal
Radiation
HeatTransfer,
3rd Ed., 1072 pp., Hemisphere,
Washington,D.C., 1992.
24. Williams, Q., R. Jeanlozand P.
McMillan, Vibrationalspectrum
of MgSiO3-perovskite: Zero
pressure Raman and infrared
NuclearMagneticResonance
Spectroscopy
of SilicatesandOxides
in Geochemistryand Geophysics
Jonathan F. Stebbins
I.
INTRODUCTION
data.More extensivereviewshavebeenpublishedrecently
ciesandcorrespondingly
broadNMR spectra.Potentially
interestingnuclidesare listedin Tables I and 2, which
containa simplecomparison
of therelativeeaseof observation in a liquid sample,basedon resonantfrequency,
spin quantumnumber,and abundance.Thesedata serve
only for rough comparison,however (especiallyfor
solids), becausethey containno material-specificinformation on relaxation rates and line widths.
thatgive background
onthe fundamentals,
aswellas details of applications [2,11,29,33,34,42,61,62,88,116,
141]. Extensive tabulationsof NMR data on silicates
havealsobeenpublished[34,43,56,78,118,128,161].
The utilityof NMR in understanding
thechemistry
and
physicsof materialscomesfromthesmallperturbations
of nuclearspinenergylevels(non-degenerate
only in a
magnetic
field) thatarecaused
by variations
in localelectrondistributions,
by thedistributions
of otherneighboring spins(electronic
or nuclear),andby thetimedependenceof theseinteractions.
Any nuclidewith non-zeronuclear spinthuscan, in principle,be observedby NMR,
butthepracticality
of theexperiment
variestremendously.
Detectionof signalsfrom nuclideswith low naturalabundanceandlow resonantfrequencyis often difficultor im-
possible,
although
isotopic
enrichment
canbeuseful.The
NMR is an elementspecificspectroscopy,
and spectra
are primarily sensitiveto short-range
effects.Thus,like
techniques
suchas x-ray absorption
andM0ssbauerspectroscopy,NMR is a good complementto diffraction
methods,andis particularlyusefulin amorphous
materials
andliquids.NMR canbe highlyquantitative,
with a 1 to
1 correlationbetweensignalintensityand the abundance
of a nuclidein a given structuralsite,regardless
of the
structure.In practice,of course,experiments
mustbecarried out carefully to be accuratelyquantitative.A major
drawbackof NMR is its low sensitivitywhencomparedto
spectroscopies
involvinghigherenergytransitions
(e.g.
visible,infraredandRaman).Interpretations
of solid-state
NMR spectrastill rely primarily on empiricalcorrelations,but theseare now well understoodin a qualitative
sense. Another limitation of NMR is a severe one for the
MineralPhysicsandCrystallography
A Handbookof PhysicalConstants
studyof naturalsilicateminerals:paramagnetic
ionsin
abundances
greaterthana few tenthsof onepercentcan
broadenNMR spectrato the pointof beingimpossible
to
obsee or interpret[87].
Most of the data reportedin the tableshasbeencollectedby high resolutionmagicanglesspinning(MAS)
techniques,with importantcontributionsfrom the new
techniqueof dynamicanglespinning(DAS), and from
singlecrystalandstaticpowderspectra.Figure1 suggests,
AGU
Reference Shelf 2
Copyright1995by theAmericanGeophysical
Union.
303
304
NMR
OF SILICATES
AND
OXIDES
Isoiope
1H
13C
15N
19F
29Si
31p
57Fe
77Se
89y
103Rh
Natural
NMR
frequency
Receptivity
abundance,
%
at 9.4T, MHz
relative
to 29Si
99.99
1.1
0.4
100
4.7
100
2.2
7.6
100
100
400.0
2700
100.6
40.6
376.4
79.5
161.9
12.8
76.3
19.7
12.7
0.48
0.010
2252
1
180
0.002
1.43
0.32
0.09
109Ag
48.2
18.6
0.13
113Cd
19Sn
25Te
129Xe
69Tm
171yb
183W
195pt
12.3
8.6
7.0
26.4
100
14.3
14.4
33.8
88.7
149.2
126.2
-111.2
33.1
70.4
16.6
85.6
3.7
12.2
6.1
15.4
1.5
2.1
0.03
9.1
99Hg
16.8
205T1
207pb
70.5
22.6
71.6
2.7
230.5
83.7
377
5.4
inthisarea.A second
nearly
unique
utililyofMR, that
is just beginningto be applied in the geosciences,is in
Definitions
STEBBS
Isotope
Spin
Natural
abundance,
%
0.02
7.4
Quadrupolar
NMR frequency
Receptivity
moment
x1028,
at 9.4T, MHz
relativeto 29Si
m-2
2H
6Li
1
1
7Li
9Be
3/2
3/2
10B
11B
14N
3
3/2
1
19.58
80.4
99.6
170
23Na
5/2
3/2
0.04
100
25Mg
5/2
0.22
24.5
27A1
33S
35C1
37C1
39K
43Ca
45Sc
47Ti
49Ti
51V
53Cr
55Mn
59Co
61Ni
63Cu
65Cu
67Zn
71Ga
73Ge
75As
81Br
87Rb
87Sr
91Zr
93Nb
95Mo
5/2
3/2
3/2
3/2
3/2
7/2
7/2
5/2
7/2
7/2
3/2
5/2
7/2
3/2
3/2
3/2
5/2
3/2
9/2
3/2
3/2
3/2
9/2
5/2
9/2
5/2
100
0.8
75.5
24.5
93.1
0.15
100
7.3
5.5
99.8
9.6
100
100
1.2
69.1
30.9
4.1
39.6
7.8
100
49.5
27.9
7.0
11.2
100
15.7
0.15
-0.055
-0.10
-0.08
0.05
0.2
-0.22
0.29
0.24
-0.05
0.03
0.4
0.38
0.16
-0.21
-0.20
0.16
0.12
-0.18
0.29
0.31
0.13
0.3
-0.21
-0.22
+0.12
104.3
30.7
39.2
32.7
18.7
27.0
97.3
22.5
22.6
105.4
22.6
98.8
94.4
35.8
106.1
113.7
25.1
122.2
14.0
68.7
108.4
131.3
17.4
37.3
98.2
26.2
99Ru
5/2
12.7
0.08
18.4
0.4
101Ru
5/2
17.1
0.44
20.7
0.7
92.6
100
10.13
0.0028
-0.0008
-0.04
0.05
61.4
59.0
0.004
1.7
155.6
56.2
737
37.5
0.085
0.041
0.01
43.0
128.4
28.9
10.6
360
2.7
-0.026
0.10
54.2
105.9
0.03
250
0.7
560
0.05
9.6
1.8
1.3
0.02
819
0.4
0.6
1035
0.23
475
750
0.11
174
96
0.32
152
0.30
69
133
133
0.51
2.9
1320
1.4
305
306
NMR
OF SILICATES
AND
OXIDES
TABLE 2 (continued)
Isotole
Spin
105Pd 5/2
115in
121Sb
127I
133Cs
137Ba
139La
177Hf
181Ta
187Re
189Os
193Ir
197Au
9/2
5/2
5/2
7/2
3/2
7/2
7/2
7/2
5/2
3/2
3/2
3/2
201Hg
3/2
209Bi
9/2
Quadrupolar
NMR
freqlencyReceptivity
abundance,
moment
x1028,
at 9.4T, MHz
m-2
22.2
0.8
Natural
95.7
57.3
100
100
11.3
99.9
18.5
99.99
62.9
16.1
62.7
100
13.2
100
18.4
relativeto29Si
0.7
0.83
88.1
910
-0.28
96.2
251
-0.79
80.5
257
-0.003
52.8
130
0.28
44.7
0.22
56.8
2.1
163
4.5
16.2
48.0
99
238
2.2
91.8
0.8
31.4
0.7
1.0
1.0
7.6
0.06
0.59
6.9
0.07
0.44
26.6
-0.38
64.9
0.5
381
= 106(samplestandard)/standard.
Thechemical
shift is orientationdependent,and is describedby the
chemicalshift anisotropy(CSA) tensor,whoseprinciple
components
are usuallydenoted511,22, and33 and
which has a unique orientationwith respectto the local
structure(or with respectto crystallographicaxes in a
crystallinematerial).The isotropicchemicalshift,Siso,
is
the averageof thesethreecomponents.For spin1/2 nuclides,5isois observedexperimentally
in liquidswhere
molecularrotationproduces
rapidisotropicaveraging,
and
in solidsby rapid samplespinning(MAS NMR) at the
"magic" angle 0 with respectto the externalfield (0 =
54.7, 1-3cos20
= 0).
For nuclideswith spin I > 1/2, a total of 21 transitionsmay be observable.The frequenciesof thesetransitionsare controlledby the energyof interactions
with the
Fig.1. Static
(non-MAS)
29Sispectra
forquartz.
Top
.-80
-100
-120
spectrumshowsthreemagneticallyinequivalentSi sites;
bottom spectrumshows spectrumfor randomlyoriented
powder;centerspectrumshowseffectof strongpreferred
orientationin a quartz mylonite [132]. Scalesin this and
otherfiguresare in ppm.
STEBBINS
quadrupolar
coupling
constant
QCC=e2qOJh.
Here,eQis
the nuclearquadrupolarmoment,and qis the principle
component
of theelectricfield gradientat thesiteof interest.The full description
of thequadrupolar
interactionrequirestheelectricfield gradienttensorandits orientation
relative to the structure.The deviation from cylindrical
symmetryof this tensoris given by the asymmetryparameterq, which variesfrom 0 to 1. In liquidswith sufficientlyrapidisotropicrotationof molecules,
thefield gradient and the quadrupolarinteractionaverageto zero and
/Sisois observed.In MAS NMR, the central 1/2 to -1/2
transitionremainsshiftedandbroadened
by a secondorder
quadrupolar
interaction;
in DAS NMR,/Sisois shiftedby
307
amongnumberof AI neighbors,
bondangles,and have
beendevelopedthatallow ratherpreciseestimates
of 8 for
tectosilicate structures[34]. A few correlationshave been
portantconstraints
on AI/Si orderingin a numberof minerals.The greatesteffortshavebeenon syntheticzeolites,
becauseof their tremendoustechnologicalimportance
[34,72]. In geochemistry,the most importantexamples
have been in determiningthe orderingstatein feldspars
[64,102,103,120,127,169],
other tectosilicates
[12,53,95,104,117,148], cordierite [107] and sheet sili-
[17,53,103,106].
TO CRYSTALLINE
OXIDES
2.1. 29S i
Isotropic
chemical
shiftsfor29SiandCSAdataare
ber.Thus, for SiO6groups
is therangeof about-180
to -220 ppm relativeto tetramethylsilane(TMS), andis
in nearlyall casesbetweenabout-65 and -120 ppm for
SiO4 groups. Signals near to -150 ppm are probably
from SiO5 groups [58,166].
The secondmostimportanteffectis thatof the number
andidentityof firstcationneighbors.
If bridgingoxygens
Veryrecently,
29SiMASNMRhasbegun
tobeapplied to high pressuremantle phasesthat contain SiO6
tendsto increase
5 byabout5 ppm.Asa result,
295i
MAS NMR spectraof aluminosilicates
oftenhavemultiple, partiallyoverlappingpeaksfor $i sites with varying numbersm of A1neighbors
[Qn(mA1)].Thiseffectis
particularlyobviousand well-exploitedin tectosilicates,
where it has often providedthe key to unravelingquite
complexAI/Si orderingpatterns.Thebondanglebetween
tetrahedrahasa relatedeffect, againbestcalibratedfor tec-
2.2.
27A i
NMR studies
of 27A1in minerals
havebeenreviewed
recently[66], and dataare listedin Tables6 and7. Most
early studiesof this nuclidewere of singlecrystals,with
complete determinationsof quadrupolarcouplingconstants,asymmetryparameters,and electricfield gradient
tensors,but without preciseisotropicchemicalshifts.
The quadrupolar parameters have been shown to be
roughlycorrelatedwith the extentof distortionof the AI
site for both octahedraland tetrahedralgeometries[43].
Single-crystal
work on MgAI204 spinelallowedquantificationof octahedral
andtetrahedral
AI siteoccupancies
and
orderingstate[14].
Asfor29Si,isotropic
shifts
for27A1in oxides
(now
determined most commonly by high resolutionMAS
NMR) are most strongly influencedby coordination
number.Jvaluesfor AIO4 groupsfall roughlyin the
range
of 50to90 ppmrelative
toaqueous
Al(H20)63+,
and for AIO6 groupsin the range of-10
to 15 ppm.
308
TABLE
3.29Si
NMRdata
forQo,Q1,and
Q2sites
incrystalline
silicates.
mineral
(s)=synthetic
Qosites:
nominal
formula
chondrodite
forsterite(s)
Mg5(SiO4)2(OH,F)2
Mg2SiO4
(s)
monticellite(s)
(s)
Li2SiO4
CaMgSiO4
NaH3SiO4
(s)
Na2H2SiO4-8.5H20
majorite
garnet(s)g Mg4SiVlsilV3012e
(s)
(s)
-Jiso
a
60c
61.9
64.9
66
66.4
67.8
-/511
CSA b
-/522
-J33
reft
[78]
38.8d
55.3
95.4
44
60
94
[78,159]
[78]
[128]
[78]
[78]
68to90f
[101,146]
Ba2SiO4
ot-Ca2SiO4
70.3
70.3
[78]
afwillite
Ca3(HSiO4)2-2H20
71.3,73.3
[34]
larnite(s)
pyrope(s)
Ca-olivine(s)
(s)
(s)
phenacite
ruffle
titanite
andalusite
kyanite
zircon
piemontiteg
I-Ca2S
iO4
Mg3AI2Si3Oi2
e
-Ca2SiO4
Ca3SiO5
CaNaHSiO4
Be2SiO4
<1% SiO2in TiO2
CaTiSiO5
AI2SiO5
AI2SiO5
ZrSiO4
Ca2(AI,Mn,Fe)3
71.4
72.0
73.5
69 to 75h
73.5
74.2
77.2
79.6
79.8
82.3,83.2
81.6
81.9
[78]
grossu
lar
topaz
(Si207)(SiO4)OH
Ca3AI2(SiO4)3
AI2SiO4(OH,F)2
83.4
85.6
(s)
(s)
gehlenite(s)
akermanite(s)
Na6Si207
Li6Si207
Ca2AI2SiO7
Ca2MgSi207
68.4
72.4
72.5
73.7
mnkinite(s)
hemimorphite
Ca3Si207
Zn4Si207(OH)2-H20
74.5,76.0
77.9
[I-Mg2SiO4
79.0
CaA12Si207(OH)'H20
o-Y2Si207
81
81.6,83.5
(s)
o-La2Si207
83.2
(s)
Ca6Si207(OH)6
82.6
[78]
[101]
[78]
[78,124]
[78]
[78]
[139]
[118]
45
78
116
[78,128]
50
79
120
[118,128]
[78]
[118]
[56]
[78]
Q1sites:
(s)
lawsonite
(s)
[78]
[34]
122
74
20
[56]
134
84
[56]
[78]
[78]
[146]
123
92
28
[128]
[34]
[78]
109
109
35
[34,46]
STEBBINS
TABLE 3 (continued)
CSAb
-822
mineral
(s)=synlhetic
nominal formula
-Siso a
-833
[118]
86.4,90.4
(s)
Ca2(AI,Mn,Fe)3
(Si207)(SiO4)OH
In2Si207
87.7
[78]
(s)
piemontiteg
[5-Y2Si207
92.9
[78]
thortveitite
Sc2Si207
95.3
[78]
zunyiteg
AI13Si5020(OH)
14F4
Cli
91.2,96.9
Li2SiO3
74.5
Na2SiO3
BaSiO3
76.8
18
59
156
[78,36]
80
29
71
140
[128]
SrSiO3
85
30
71
154
[128]
Mg2Si206
Mg2Si206
CaMgSi206
82 c
81.8,84.2
73
132
[56,128]
84.8
73
148
[118,128]
(Ca,Na)(Mg,AI)Si206
i
85.4
81
142
[118]
Q2sites:
(s)
(s)
(s)
(s)
orthoenstatite
clinoenstatite(s)
diopside
omphacite
spodumene
jadeire
pyroxene
phase(s)g
alamosite
LiAISi206
NaA1Si206
NaMg0.5
SivI0.5SiTM
206
Pb{ 2Si{ 2036
[781
[78]
91.4
[118]
53
[118]
[78]
91.8
[146]
92.1,97.6
[34]
84.1,86.5,
94.3
prehniteg
tchermakitic
amphibole(s)g
triple-chain
phase(s)g
Sc-Fpargasite(s)
(Q2+Q3)
tremoliteg
hillebrandite(s)
pectolite(s)
foshagite(s)
xonotlite(s)g
walstromitephase
Ca2AI2Si3010(OH)2
Ca2(Mg4AI)(AISi7022)(oI-I):
Na2Mg4Si6016(OH)2
84.6k
NaCa2Mg4ScSi6AI2022F2
Ca2Mgs(Si4Oll)2(OH)2
Ca2SiO3(OH)2
Ca2NaHSi309
Ca4Si309(OH)2
Ca6Si6017(OH)2
Ca3Si309
[139]
83.4,87.4
[18]
85.3
[18]
86 m
[108]
87.2
5O
77
137
[18,128]
86.3
[78]
86.3
[78]
84.8,86.4
86.8
[78]
73.8,78.5,
[58]
79.0
wollastonite
Ca3Si309
87.6,91.71
[5-wollastonite(s)
[-Ca3Si309
89.0
24
85
158
[118]
[78]
309
TABLE 3 (continued)
mineral
(s)=synthetic
nominal formula
-6iso a
Q2sites,
rings:
ps-wollastonite(s) x-Ca3Si309
83.5
(s)
K4H4Si4012
87.5
tourmaline
Na(Mg,Li,A1)3AI6Si6018-88.1
(BO3)3(OH,F)4
i
(s)
Ba7Si7021'
10BaCI2
92.5
benitoite
BaTiS
i309
94.2
wadeite
phase(s)g K2S
iVlsilV309
95.0
-$11
63
CSAb
-i22
63
-/533
141
ref.
[78]
[71,78]
[118]
[34]
[78]
[146]
High P phases,uncertainstructure:
"phase
E"(s)
"phase
Y"(s)g
(s)
Mg2.3Sil.3H2.406
75.7TM
(CaO)xSiVsilVo4
80
-Na2Si205
80.6,81.8
[58]
[146]
ee
(s)g
CaSiVIsiIVo5
88.9
[146]
(s)g
(s)g
Na2S
ivISiTM207
-Na2
SiVIsilVo5
94.4
97.9
ee
ee
(s)g
Na2(S
iVI,siTM)409
97 .0,107.7,
ee
108.9
'{'Mostintensepeak.
Si-O-B
bonds
areconsidered
as"bridging",
placing
theSisites
inberyl
anddatolite
intheQ4andQ3groups,
respectively.
(a)Chemical
shifts
areinppmrelative
totetramethylsilane.
(b)Unless
otherwise
noted,
principle
components
of
CSAtensor
arederived
fromfitting
spinning
sidebands,
andareofrelatively
lowprecision;
orientation
oftensor
withre-
spect
tocrystallographic
axes
maynotbeknown.
Insome
cases,
15iso
andCSAdataarefromdifferent
sources
andmay
therefore
appear
tobeslightly
discrepant
[/Siso
should
= (/511+/522+i33)/3].
Given
typical
errors
inCSAmeasurements,
thisisgenerally
notsignificant.
(c)Broad
peak
(atleast
5ppmwidth).
(d)CSAbased
onsingle
crystal
study.
(e)Additional
dataonsolid
solution
series
given
inreference.
(f)Multiple
peaks
duetopartial
disorder
among
octahedral
Siand
Mg.Mainpeakisat-74.3ppm.(g)Dataforanother
typeofSi sitelisted
elsewhere
intableorinTable
4 or5. (h)
NineSisites,
7 resolved
peaks.
(i) Approximate
formula.
(j) CSA dataaremeans
fortwosites.(k)Twoadditional
peaks
indicate
asmall
amount
ofSi/AIdisorder.
(1)First
peak
isforT1site,second
forT2+T3.(m)Broad
peakconsistent
with considerable
disorder.(n)
Ordering
schemes
canbecomplex,
butcanbecharacterized
fortetrahedral
SiandAI
as(1)disordered,
Al-avoidance
violated;
(2)ordered
according
toAl-avoidance
only;
(3)more
ordered
than
required
byAIavoidance;
(4)fullyordered
ornearly
so;(5)partially
disordered.
(o)Split
peak
reported
by[4].(p)CSAcomponents:
-43,-59,
-147ppm[128].(q)CSAcomponents:
-49,-83,-129ppm[128].(r)CSAcomponents:
-107,-107,-59ppm
[128].(s)small
peak
duetotriple-chain
sitein partially
disordered
phase.
(t)CSAcomponents:
-56,-72,-151
ppm
[128].(u)CSAcomponents:
-54,-70,-161
ppm[128].(v)CSAcomponents
fromsingle
crystal
study:
102.6,
107.0,
109.1
[132].(w)Approximately
5 peaks
resolved
for12sites.(x)Overlapping
peaks
duetomultiple
sites.
(y)End
member:
complex
series
ofpeaks
forintermediate
compositions.
(z)Approximately
8peaks
for15possible
sites.
(aa)8
peaks
for8 sites.
(bb)511=-173.4
ppm;
1522
= [33TM
-183.1
ppm.(cc)Narrow
peak
consistent
withcomplete
Mg/Si
order.(rid)Somewhat
broadened
peakconsistent
withsome
Mg/Sidisorder.
Reference
contains
dataonsolidsolution
withpyrope.(ee)Kanzaki,Stebbins
andXue,unpublished
data.
(s)=synthetic
nominal
formula
-Siso
a
ordering
staten
ref.
Q3sites,
layeraluminosilicates
:
margarite
CaA12(A12Si2010)(OH)2 75.5
phlogopite
KMg3AlSi3010(F,OH)2
84to87
phlogopite(s)e KMg3AISi3010(OH)2
83.2,87.0?,90.7
palygorskite MgAIS
i4010(OH)2'4H20
84.9,91.7,96.8
beidellite
Na0.3AI2(AI0.3Si2.7010)
muscovite
illitee
KAI2S
iA13010(O
H)2
KAI2SiAI3010(OH)2
i
lepidolite
KLi2AI(AISi3010)(F,OH)2
89m
dickite
kaolinite
endellite
AInSi4010(OH)8
AI4Si4010(OH)8
AI4Si4010(OH)
10'8H20
90.9
91.5
93.1
pyrophyllite
AI2Si4010(OH)2
94.0
4
5
3
88,94
[78]
[60,78]
[20]
[34]
[34]
(oI-I)2
montmorillonite (AI,Mg)2Si4010(OH)2'4H20
89,85
?,81
91rn
5
5
[112]
[60]
[78]
[34]
[78]
[78]
[112,118]
93.7
sepiolite
Mg4Si6015(OH)2'2H20
hectorite
(Mg,Li)2.7Na0.3Si4010(OH)2 95.3
[34]
92,95,98
[34]
[60]
-4H20
Q3sites,
othersilicates:
sapphirine
e
datolite
sillimanite
tremoliteg
tremolite(s)g
tchermakitic
(M g3.6AI4.4)(AI4.4S
i 1.6)020
CaOSO4(OH)
AI2SiO5
Ca2Mg5(Si4011)2(OH)2
Ca2Mg5(Si4011)2(OH)2
Ca2(Mg4AI)(AlSi7022)(OH)2
73TM
83.0P
86.4q
[19]
[128]
[59,118]
91.7 r
[18]
91.7, 96.9s
[18]
92.1
[18]
Na2Mg4Si6016(OH)2
87.8,91.4
[18]
KFCa4Si8020'H20
92.0
[78]
Mg3Si205(OH)4
Mg3Si4010(OH)2
Ca6(Si6017)(OH)2
Li2Si205
BaSi205
c-Na2Si205
K2Si205
[I-H2Si205
c-H2Si205
94.0
[78]
97.2
[118]
97.6
[78]
92.5 t
[94]
93.5
[94]
94.5 u
[94]
91.5,93,94.5
[94]
98.4,101.9,110
[34]
amphibole(s)g
triple-chain
phase(s)g
apophyllite
serpentine
talc
xonotlite(s)g
(s)
(s)
(s)
(s)
(s)
(s)
101.5
[34]
312
NMR OF SILICATES
AND OXIDES
TABLE 4 (continued)
mineral
(s)=synthetic
nominal formula
-Sisoa
ordering
reft
state n
Q4,silicapolymorphs:
quartz
coesite
cristobalite
tridymite
Si02
Si02
Si02
Si02
107.4 v
[118,126]
108.1,113.9
[126]
108.5
[118,126]
109.3-114.0 TM
[126]
Q4,feldspars
:
low albite e
high albitee
microcline e
sanidine e
anorthite e
anorthite e
NaAISi308
NaAISi308
KAISi308
92.3,96.9,104.3
[103,127]
91 to 112 x
[169]
95.6,97.6,100.6
K0.6Na0.4AlSi308
CaAI2Si208
CaAI2Si208(disordered)
97,101 m
[103,127]
[64]
82.7,84.7,89.3 x
[120]
82.5 to 104.5 x
[102]
[148]
Q4,f eldspathoids
:
camegieite(s)
NaAISiO4
82.2
sodalite
Na8AI6Si6024CI2
84.9
[118]
nepheline
e
kalsilite(s)e
Na3KAI4Si4016
i
85.1',88.4
[148]
KAISiO4
88.8
[148]
cancrinite
NasAI6Si6024CO3
86.3
[8]
scapolite
e
Na4AI3Si9024CI-
92.6,106.2Y
[117]
analcite
Ca4AI6Si6024CO3
NaAISi206-H20
91.6,96.8',102.0
[95]
leucite
KA1Si206
78.7 to 106.7 z
[95]
NaCa2AIsSi5020-6H20
CaAI2Si3010'3H20
Na2AI2Si3010'2H20
Na2AI2Si4012'6H20
CaAI2Si4012'6H20
CaAI2Si7018-7H20
BaAI2Si6016'6H20
CaAI2Si7018-6H20
86.4,89.0,91.7
[118]
86.4,88.8,95.7
[118]
87.7?,95.4
[118]
Q4,zeolites
:
thomsonite
scolectite
natrolite
gmelinite
chabazite
stilbite
harmotone
heulandite
92.0,97.2', 102.5
[72]
94.0,99.47,104.8
[72]
98,101.5'{',108
[72]
95,98.6,102.6,108
95.0 tO 108.0 aa
[72]
[118]
Q4,others:
cordierite
cordierite
petalite
Mg2AI4Si5018(ordered)
Mg2AI4Si5018(disordered)
LiAISi4010
79,1007
[107]
79 to 112 aa
[107]
87 c
[78]
STEBBINS
TABLE 4 (continued)
mineral
nominalformula
(s)=synthetic
-isoa
ref.
ordering
state n
danburite
prehnite
beryle
roedderite
zunyite
CaB2Si208
Ca2AI2Si3010(OH)2
A12Be3Si6018
Na2Mg5Si12030
AI 13Si50 20(OH) 14F4C1
89
98.6
102.3
100.6
128.5
[128]
[139]
[1191
[501
[1181
TABLE5.29SiNMRdataforSiO6andSiO5sites
incrystalline
silicates.
Dataforend-member
compositionsonly. SeeTable 3 for notes.
!
mineral
(s)=synthetic
nominal
fo.rmula
-5i,o
a
ref.
thaumasite
ilmenite
phase(s)
stis
hovite(s)
perovskite
phase(s)
perovskite
phase(s)
pyroxene
phase(s)g
majorite
garnet(s)g
wadeite
phase(s)g
(s)
(s)
Ca3siVI(oH)6(SO4)(CO3)
15H20
MgSiVlo3
SiVIo2
MgSiVlo
3
CaSiVlo3
NaMg0.5
SivI0.5SiTM
206
Mg4SiVisiIV3012e
K2siVIsiIV309
siVI50(PO4)6
SiVIP207
179.6
bb
181.0
cc
191.3
191.7
cc
194.5
194.7
cc
197.6
dd
203.1
214.0,217.0
220c
[48,139]
[146]
[146]
[63]
[146]
[146]
[101,146]
[146]
[158]
[158]
CaSiVIsiIVo5
-Na2SiVIsiIVo5
Na2S
iVIsiTM
207
Na2(SiVI,siIV)409
(CaO)xSiVIo2
193.4
199.8
200.4
202.4
208.6
[146]
ee
ee
ee
[146]
(CaO)xSiVsiIVo4
g
150.0
[146]
Si06, uncertainstructure:
(s)g
(s)g
(s)g
(s)g
"phase
X"(s)
Si05, uncertainstructure:
"phase
Y"
313
:314
NMR
OF SILICATES
AND
OXIDES
$i TM
siVl
j
-200
Fig.2. 29SiMASspectrum
forahigh
pressure,
MgSiO3
garnet.
Themultiplicity
oftetrahedral
sites
results
frompartial
disorder
among
six-coordinated
SiandMgneighbors
[101].Blackdotmarks
spinning
side
band.
TABLE
6.27A1
NMRdata
AIO4
sites
incrystalline
silicates
and
oxides.
Data
foranumber
ofclay
minerals,
synthetic
zeolites,
sheetsilicates,
andphosphates
havebeenexcluded
forbrevity.
Mineral
nominal
formula
.(s)=synthefic
Qosites:
(s)
QCC,
MHz
Ba5AI208
Siso
a,b
ref.
ppm
2.3
0.8
5.47
6.02
0
0
80
[92]
72
[92]
76.0
72c
[43,79,129]
Qosites,
AlTMneighbors:
zunyite
AIVI12AIIVsi5020(OH)
14F4CI
garnet
phase(s)
Gd3AI2VIAI3IVo12
garnet
phase(s)
Y3AI2VIAI3IVo12
spinel
(disordered)(s)
(Mg,AI)
TM(Al,Mg)vI204
[43]
[86,92,163]
(s)
(s)
(s)
(s)
[5-A1203
y-A1203
ri-A1203
z-AI203
64
66
62
64
(s)
BaAIVI9AIVAIIV2019
70
[92]
[92]
[92]
[92]
[92]
Q1sites:
(s)
KAIO2.1.5H20
5.0
0.25
81
[92]
KAlO2'H20
0t-BaAl2On.2H20
"
6.5
3.4
5.1
0.6
0.5
0.9
83
81
80
[92]
Q2sites:
(s)
(s)
[92]
[92]
STEBBINS
315
TABLE 6 (continued)
Mineral
nominal formula
(s)=synthetic
Q3sites,
layer
aluminosilicates
:d
CaAiVI2(AI
TM2Si2010)(OH)2
margarite
phlogopite
e
KMg3AISi3010(F,OH)2
muscovite
illite e
KAIVI2S
iA1TM
3010(OH)
2
KAI2SiAI3010(OH)2
f
hectorite
(Mg,Li)3Na0.3Si4010(OH)24 H20
penninite
xanthophyllite
QCC,
Siso
a,b
MHz
ppm
4.2
2.1
ref.
76
[73]
69 c
[20,60,111]
72
[73]
72.8
[54,60]
66 c
IdOl
(Mg,AIVI)6(Si,AllV)4010(OH)8
f
Ca2(Mg,AI
VI)6(S
i,AlTM)4010(OH)4
f
2.8
72
[731
2.8
76
[73]
KAIO2-0.5H20
Ca12AI14033
5.6
77
[921
0.2
85
[92]
0.53
64.5
[43,731
75 c
[19]
Q3sites,
others:
(s)
(s)
AIVIAIIVSiO5
sillimanite
11
6.77
(Mg3.6AIVI4.4)(A1TM
4.4S
i1.6)020
sapphirine
Q4sites,
silicaanalogs:
berlinite(s)
AlPOn
tridymitephase(s)
ALPO4
cristobalite
phase(s) ALPO4
4.09
0.37
44.5
[43,93]
0.75
0.95
39.8
[93]
1.2
0.75
42.5
[931
3.29
0.62
63.0
[43,64,73,103,169
3.22
0.21
60.9
[43,64,73,103,169
62,55 c
Q4sites,
feldspars:
albite e
microcline e
NaAISi308
KAISi308
CaAI2Si208
8.5
0.66
0z00
7.4
0.76
00i0
6.8
0.65
m000
6.3
0.88
m0i0
5.5
0.42
mz00
4.90
0.75
4.4
0.53
2.6
0.66
0.94
0.32
anorthite, 0zi0
mzi0
[133]g,[64]
Q4sites,
feldspathoids:
sodalite e
NasA16Si6024CI2
nepheline
kalsilite(s)e
scapolite
e
Na3KAI4Si4016
f
analcite
leucite
62.9
61.0,63.5
[73,961
[53,73]
KAISiO4
61.7
[53]
Na4AI3Si90 24CI-Ca4AI6Si6024CO3
NaAISi206'H20
KAISi206
58.0 c
[117]
59.4
[73]
61,65,69 c
[1041
316
NMR
OF SILICATES
AND
OXIDES
TABLE 6 (continued)
Mineral
(s)=synefic
nominal
formula
QCC,
MHz
rl
Jiso
a,b
ppm
ref.
Q4sites,zeolites:
thomsonite
scolecfite
natrolite
gmelinite
chabazite
mordenite
gismondite
NaCa2AI5Si5O20'6H20
CaAI2Si3010.3H20
Na2AI2Si3010'2H20
Na2AI2Si4012-6H20
CaA12Si4012'6H20
(Na2,K2,Ca)AI 2Si 10024'7H 20
CaAI2Si208-4H20
1.66
0.50
62.7
62.5,66.4
64.0
59.9
59.4
55.8
56.4
[73]
[73]
[43,73]
[73]
[73]
[73]
[73]
Q4sites,
others:
cordierrite,T1
T5
Mg2AI4Si5018'nH20
prehnite
Ca2AlVIAIIVsi3010(OH)2
9.0
13-LiAIO2
,-LiAIO2
[3-NaA102
KAIO2
BaAI204
T1AIO2
1.9
3.2
1.4
1.1
2.4
(s)
....
(s)
....
(s)
(s)
Ca3AI206,AI(1)
, AI(2)
Ca12AI14033,Al(1)
, AI(2)
CanAI6013
CanAI6013'3H20
"
8.69
9.30
9.7
3.8
2.4
1.8
5.4
(s)
CaAI204
h
(s)
....
CaAI407, AI(1)
, AI(2)
6.25
9.55
(s)
VI
CaAI
9AIV AIIV 2019,Q0
2.0
(s)
(s)
(s)
(s)
(s)
(s)
10.6
5.6
0.38
0.34
[43]
[43]
60
[139,#179]
0.56
0.7
0.5
0.7
0.4
83.0
81.3
80.1
76.0
78.0
69
[92,125]
[92]
[921
[92]
[92]
[92]
0.32
0.54
0.40
0.70
0.95
0.5
0.45
79.5
78.25
85.9
80.2
80.3
78
79
Ca-aluminates:
[122]
[122]
[123]
[123]
[91]
[91]
[9]
4)
75.5
69.5
[123]
[123]
65
[91]
a)Relative
toAI(H20)63+.
(b)Peak
positions
corrected
forsecond
order
quadrupolar
shift
have
been
included
where
possible.Wherethiscorrection
is notmade,MASpeakpositions
andwidths
will depend
somewhat
onthemagnetic
field
used.(c) MASpeakposition;
fiisoat slightly
higher
frequency.
(d)See[162]forextensive
dataonclayminerals.
(e)
Approximate
formula.(f) Reference
includes
dataonothersolidsolution
compositions.
(g)Reference
includes
highT
studyof phasetransition.(h) Rangeof damfor six sites.
STEBBINS
Mineral
nominal
formula
(s)=synthetic
QCC,
MHz
Siso
a,b
ref.
ppm
AI05 sites:
(s)
andalusite,
AI2
augelite
senegalite
(s)
(s)
AIV2Si207
AlVIAlVSiO5
AlVIAlV(OH)3PO4
AIVIAIV(OH)3PO4.H20
A12Ge207
LaAIGe207
vesuvianite
10.5
5.9
5.7
=2.7
8.8
7.2
0.6
0.70
0.85
29
36.0
30.9
36.0
[41]
0.4
0.3
36
35
[8O]
41.1
[100]
16.0
[43,55]
Ca19All1Mg2Si
18068(OH)
10f
[3A3,73]
[7]
[7]
[8O]
A106 sites:
corundum
ot-A1203
2.39
chrysoberyl,All
AI 2
spinel(ordered)
BeA1204
2.85
2.85
3.68
0.94
0.76
0
MgAI204
(disordered)
gahnite
ZnA1204
3.68
futile
= 1% A1203 in TiO2
2.8
1.0
(s)
A12TiO5
[43]
[43]
[43]
1lC
[86,163]
-6.5
[143]
6c
[143]
[43]
beryl
Be3A12Si6018
3.09
[43]
euclase
HBeA1SiO5
5.17
0.70
[43]
vesuvianite
Ca19AI11Mg2Si
18068(OH)
l0f
prehnite
Ca2AIVIAlIVsi3010(OH)2
<1
spodumene
kyanite,All
AI2
LiAIS i206
AI2SiO5
2.95
10.04
3.70
0.94
0.27
0.89
15
5.0
[43,129]
6.53
0.59
7.5
[43,73]
9.37
0.38
13
[43,129]
8.93
15.6
0.46
0.08
4.0
12
[43,73]
AI3
AI4
sillimanite
andalusite,
All
AIVIAIIVsio5
AIVIAlVsio5
sapphirine
garnet
(s)
garnet
"YAG"(s)
(Mg3.6AIVI4.4)(AIIV
4.4Si.6)020
Gd3A12VIA13IVo12
Y3AI2VIA13IVo12
grossular
almandine
Ca3AI2Si3012
(Fe,Mg)3AI2Si3012
pyrope
f
Mg3AI2Si30!2
<0.1 0
0.63 0
3.61
1.51
2.5
[100]
4.5
[66,139]
[43]
[43,73]
[23,43]
8c
[19]
0.8
[43,79,129]
[43]
[43]
[43]
2.4c
[82,101]
317
318
NMR
OF SILICATES
AND
OXIDES
TABLE 7 (continued)
Mineral
nominal
formula
QCC,
(s)=synelic
zoisite,AI 1,2
Ca2AI3Si3012OH
8.05
AI3
epidote,All
MHz
Ca2AI2(Fe,AI)Si3012OH
AI2
8isoa,b
ref.
ppm
0.46
[43]
18.5
0.16
[43]
9.8
0.2
[43]
4.6
0.34
[43]
0.38
[43]
topaz
1.67
margarite
6.3
11
[73]
2.2
[73]
5.9
[54,60]
penninite
xanthophyllite
CaAl
VI2(AIIV2s
i2010)
(OH)2
KAIVI2s
iAlIV3010(OH)2
KAI2$iA13010(OH)2
f
(Mg,AI
VI)6(Si,AlIV)4010(OH)8
f
Ca2(Mg,AIVI)6
(Si,AIIV)4010(OH)4
f
1.4
10
[73]
2.0
11
[73]
kaolinite
AI4Si4010(OH)8
4c
[60]
pyrophyllite
AI2Si4010(OH)2
4c
[60]
smectite
(Ca,Na)(AI,Mg)4(S
i,AI)8020(OH)4
f
4c
[60]
muscovite
illite e
gibbsite(s)
AI(OH)3, AI(1)
"
augelite
senegalite
, A(2)
AIVIAIV(OH)3PO4
AIVIAIV(OH)3PO4-H20
1.97
0.73
10.4
[123]
4.45
0.44
11.5
[123]
4.5
1.0
0.3
[7]
=3.8
1.7
[7]
10.2
Ca-aluminates:
(s)
CaAI204' 10H20
2.4
(s)
(s)
Ca3AI206-6H2
Ca4AI207'l 3H20
0.71
(s)
CaAIVI9AIVAIIV2019
1.5
<1
ettringite(s)
(s)
Ca6AI209'3S03-32H20
Ca4AI207'SO3' 12H20
9Si [2,66,88].
ManyMASNMRstudies
of 27A1of solids
havereportedonly peakpositions,whichare generallyshiftedto
frequencies
lowerthanSiso
by thesecond
orderquadrupolar interaction.Quadrupolar
shiftscanbe aslargeas20 or
more ppm for data collectedat relativelylow magnetic
fieldsand/orfor siteswith largefield gradients,
butcanbe
0.09
1.8
0.36
1.7
[123]
12.36
[123]
10.20
[123]
=0
[91]
16
[91]
13.10
[123]
11.80
[123]
0.19
STEBBINS
319
AivI
sheet
silicates,
forexample,
27A1MASNMRdatahave
beenshownto agreewell with siteassignments
basedon
stoichiometry [5,20,52,60,162]. In MgAI204 spinel
A!TM
?oooc
theeffectof temperature
on disorder(Figure3).
2.3. 170
Although
170 canbeobserved
atnatural
abundance
in
liquidsand in highly symmetricalsitesin crystallineoxides[6], applicationsto silicateshavegenerallybeenlimited by the necessityof workingon isotopically
enriched
samples.The data assembledin Table 8 havebeen obtained at high magnetic fields by the fitting of MAS,
DAS spectra,or static spectra.For somematerials,the
latter can be quite informative,but neglectof chemical
shiftanisotropycanleadto discrepancies
[131].
Themostobvious
effecton 170 spectra
of silicates
with tetrahedralSi is the distinctionbetweenbridgingand
non-bridgingoxygens.Theformer generallyhave much
covalent
character
of
the
M-O
bonds
lZ,O0OC
250
-15o
Fig.3. 27A1
MASspectra
forMgAI204
spinel
quenched
from the two temperatures
shown.Featuresotherthanthe
two labeledpeaksarespinningsidebands.The increase
in
theintensity
oftheAITMpeakindicates
anincrease
indisorderwith temperature
[86].
centlyincluded
9Be,13C,19F,25Mg,31p,35C1
' 39K,
45Sc
' 47Ti' 51V,89y, 93Nb' 119Sn
' 129Xe
' and207pb.
remarkably
effectiveforresolving
170NMRpeaks
for
structurallysimilar but crystallographically
distinctsites
in silicates [89].
2.4.
Other
Nuclides
ple,allowthese
sites
tobeeasily
distinguished
by 1lB
NMR. Many applicationsof this relationship,
as well as
the effect of coordinationnumberon iso,have been
cations
(especially
7Li+and23Na+)
andanions
(especially
19F-),andonphase
transitions
inmaterials
withabundant
nuclides
of highLarmor
frequency
(e.g.7Li,19F,23Na,
27A1,
93Nb)[8,109,136,138].
Thefirstof these
reports
extensivework on perovskite-structured
oxides.Most of
thesestudieshave been done at relatively low magnetic
fields and consistprimarily of relaxationtime measurements.As such,quantificationof resultsoften requires
320
NMR
OF SILICATES
AND OXIDES
TABLE
8.170 NMRdata
forcrystalline
oxides
and
silicates.
Some
data
forsynthetic
zeolites,
aswellasoxysalts
andoxide
superconductors
areexcluded
forbrevity.
Insilicates,
"BO"signifies
bridging
oxygen,
"NBO"
non-bridging
oxygen.
Mineral
nominal
formula
{s)=synthefic
miscellaneous
MHz
Siso
a,
tel
ppm
oxides:
(S)
periclase(s)
(s)
(s)
(s)
ruffle(s)
anatase(s)
(s)
baddeleyite
(s)
(s)
(s)
(s)
(s)
(s)
zincite(s)
(s)
(s)
(s)
litharge(s)
cuprite(s)
(s)
(s)
(s)
BeO
MgO
CaO
SrO
BaO
TiO2
TiO2
Ti203
ZrO2
ZrO2(tetmgonal)
87ZRO2-13MgO
(cubic)
HfO2
La203(octahedral
site)
" (tetrahedral
site)
CeO2
VO2
ZnO
CdO
HgO(yellow)
SnO
PbO
Cu20
Ag20
KMnO4
=0.02
=0.014
<.005
<.005
<.005
<1.5
< 1.1
<2.6
<0.9,1.0
< 1.4
<1.1,0.9
<1.4
<2.2
M)
--0.13
7.1
2.3
0.9
=0
=0
<0.4
K2WO4,
site1f
"
"
aluminum
QCC,
, site2
, site3
26b
47b
294b
390b
629b
590c
558c
503c
325,402
c
383c
=355
d
267,335
c
469c
590c
878c
--755,815
d
- 18b
=60
121e
251
294
-193
-277
1197
[154]
[154]
[154]
[154]
[154]
[6]
[6]
[6]
[6]
[6]
[6]
[6]
[6]
[6]
[6]
[6]
[6,154]
[154]
[154]
[6]
[6]
[6]
[6]
[115]
437
[115]
429
422
[115]
[115]
oxides:
corundum(s)
(s)
(s)
(s)
(s)
It-alumina(s)
{z-A1203,
OALisite
'-A1203,
OA!4site
q-A1203,OAI4site
5-A1203,
OAI4site
0-A1203,
OAI4site
" , OAI3site
11A1203'Na20
2.17
1.8
1.6
1.6
1.2
4.0
<2.2
0.55
0.6
75c
73c
73c
72c
72c
79c
76c
[13,156]
[156]
[156]
[156]
[156]
[156]
[6]
STEBBINS
TABLE 8 (continued)
Mineral
nominal formula
(s)=synthetic
QCC,
iisoa,
MHz
ppm
ref.
hydroxides:
boehmite(s)
bayerite(s)
brucite
1.15
0.13
70.0 c
[125,156]
5.0
0.5
40 c
[156]
AI(OH)3, A12OHsite
Mg(OH)2
6.0
0.3
40 c
[156]
6.8
0.0
25g
[157]
Mg2SiO4, NBO
3.3h
2.8h
3 .Oh
2.9h
2.7h
2.5h
2.8h
72i
64i
49i
134i
[89]
orthosilicates:
forsterite(s)
lamite(s)
"
, NBO
"
,NBO
Ca2SiO4, NBO
"
, NBO
"
, NBO
"
, NBO
[89]
[89]
[89]
128i
122i
122i
[89]
86i
64i
69i
57i
61i
59i
62i
70i
70i
115i
114i
107i
97i
103i
88i
75i
75i
67
[89]
[89]
[89]
chain silicates:
diopside(s)
clinoenstatite(s)
wollastonite(s)
ps-wollastonite
(s)
CaMgSi206, NBO
2.83
0.13
"
, NBO
2.74
0.00
"
, BO
4.39
0.36
Mg2Si206, NBO
"
, NBO
"
,NBO
"
,Nito
"
, BO
"
, BO
Ca3Si309, NBO
"
, NBO
"
, NBO
"
, NBO
"
, NBO
"
, NBO
"
, BO
"
, BO
"
, BO
-CaSiO3J,
NBO
2.9h
3.6h
3.6h
4.2h
5.1h
5.2h
2.3h
2.6h
2.2h
2.0h
2.9h
2.6h
4.8h
4.8h
4.7h
[89]
[89]
[891
[89]
[89]
[891
[89]
[89]
[89]
[89]
[891
[891
[89]
[891
[89]
[89]
[89]
2.1
0.1
94 c
[153]
"
, NBO
2.3
0.1
91 c
[153]
"
, BO
3.8
0.2
75 c
[1531
2.1
0.1
108 c
[153]
-SrSiO3J,NBO
"
, NBO
2.2
0.1
105 c
[153]
"
, BO
4.1
0.4
80 c
[153]
321
322
NMR
OF SILICATES
AND
OXIDES
TABLE 8 (continued)
Mineral
(s)=synthetic
(s)
nominal formula
. .
QCC,
MHz .
BaSiO3J,
NBO
8isoa'
ppm.....
ref.
2.1
0.1
169c
[153]
....
NBO
1.6
0.1
159c
[153]
....
BO
3.7
0.4
87c
[153]
3.2
40g
[157]
5.8
50g
[157]
7.3
0g
[157]
5.3
0.13
40k
[131]
3.2
3.1
4.6
0.2
0.2
0.1
32c
31 c
44 c
[152]
[152]
[ 152]
4.45
0.35
62.5
[165]
4.90
0.2
97.0
[165]
6.50
0.13
109.5
[165]
talc(s)
Mg3Si4010(OH)2,NBO
....
BO
, MgOH site
frameworksilicates:
Na-A zeolite(s)
SiO2
(seereference),Si-O-AI, BO
Na-Y zeolite(s)
(seereference),Si-O-AI, BO
cristobalite(s)
"
, Si-O-AI, BO
highpressuresilicates:
wadeitephase(s)
K2siVIsilV309,
silV-o-siTM
"
stishovite(s)
, silV-o-si vI
SiO2
Notesfor Table 8:
a) Relative to H20.
(b) From MAS data,little or no correctionfor QCC needed. (c) From simulationof MAS
data. (d) Uncorrectedfor QCC. (e) From MAS, correctedusingQCC from staticspectrum. (f) For site 1'
c11=564,c22=530,c33=217ppm; for site2: c11=567,c22=518,c33=202ppm; for site 3:c11=561c22=497,
c33=208
ppm. (g) Basedonstaticspectrum,
CSAnotincluded.(h) QCCgivenis actuallythe"quadrupolar
prod-
uct".PQ=QCCx(l+
12/3)1/2;
0.87<QCC<PQ
[89].(i)Derived
from
DASdata
at twomagnetic
fields.
(j)More
sitesarepresentthanareresolved
in MAS spectra.(k) Fit of staticspectrum
gives311=c22=60,
333=-10ppm.
informationobtainableby diffractionmethods.Becauseof
the wide and continuousrangesof compositions
studied,
andthe frequentmodel-dependent
natureof thestructural
conclusions,
I havetabulated
onlya few29SiMASdata
some tabulations [34], as well as extensive discussionof
silicate, oxide,
iesof nuclides
notincluded
here,especially
l lB, 19F,
23Na,and31p.
3. APPLICATIONS
TO
AMORPHOUS
SOLIDS,
GLASSES,
AND MELTS
3.1. 29S i
Therelativelyclear relationships
betweenisoand Q
speciesin crystallinesilicateshasled to a numberof attemptsto quantifytheir abundancein glasses.Separate
STEBBINS
323
TABLE9.29SiNMRdataforglasses
ofsimple,
crystalline
stoichiometry.
Composition
-fiiso, ppm
.
SiO2
111.5
FWHM,
ppm
12
[44,98]
NaAISi308
98.7
16
[98]
NaAISi206
NaAISiO4
KAISi308
CaAI2Si208
CaA12SiO6
92.8
18
[94]
86.0
13
100.5
15
Mg3A12Si3012
Ca3AI2Si3012
Na2Si409
K2Si409
87.9
15
[94,98]
83.4
11
[94,981
82.3
17
[7O]
80.1
13
[70]
105.6,92.2
105.1,94.3
Li2S i205
Na2Si205
K2Si205
102.7*,91.0,81.1*
99.5' ,88.7,77.7'
103.3* ,90.8,79.5'
N a2SiO3
84.8* ,76.0,66.8*
MgSiO3
CaMgSi206
CaSiO3
[941
[94,98]
82.3
81.3
80.6
13,11
[77,166]
11,10
[77,166]
14',12,10'
[771
12',10,8'
[771
11',11,7'
[77]
10',7,5'
[77]
20
16
14
[7O]
[7O]
[7O]
Notesfor Table 9:
Uncertaintiesare generallyat least0.5 ppmin peakpositionsandwidths.
*Partiallyresolvedshoulder
data [9,77].
324
NMR
OF SILICATES
AND
OXIDES
is highlydisordered
withrespect
to localstructure[ 1,22].
Siv
SiTM
12 GPa
i bar
-gO
-10
-160
-200
Themostdramatic
findings
from27A1
MASNMRin
glasses
hasbeenthecleardetection
of five andsixcoordinatedA1 in a varietyof compositions,
includingthosein
the SIO2-A1203 binary [105,110,113] and in some
dependent.Studieshaveincludedextensive
workon alkali
and alkaline earth aluminosilicates [35,65,98] and Ca,
temperatures
(Tg).Thisapproach
hasbeenusedto show
thatQ speciesdistributions,as well as overalldisorderin
bondangles,do indeedbecomemorerandomwith increasing T [9,135].
Studiesof alkali silicateglasses
quenchedfrom liquids
at pressures
to 12 GPa haveshownthepresence
of six coordinatedSi (Figure4), and for the firsttimedemonstrated
the existence of five coordinated Si [147,166,167]. The
latter
phosphorus-rich
glasses
[27]and boroaluminates
[15,97].
In the CaO - A1203 - SiO2 ternary, non-tetrahedral
AI is
abundantonly in compositions
closeto the SIO2-A1203
join [ 114].In carefullyquantifiedstudies
of glasscompo-
sitions
withM+120/AI203or M+20/AI203< 1.0,it
hasbeenshownthat high coordinatedAI is undetectable
andthuscomprises
lessthana few percentof thetotalAI
[65,98]. However,high-coordinate
A1 hasbeendetectedin
onlyslightlyperaluminous
glasses
nearto theMgAI204SiO2 join [83].
3.3. 170
As in crystals,the primarydistinctionamongO sites
detectedby NMR of glassesis thatbetweenbridgingand
non-bridgingoxygens(Figure5). Staticspectracansometimes be more informative than MAS data. Systematic
compositional
effectson thechemicalshiftsfor NBO sites
have been noted [61], as have pressureeffectson O site
distribution[ 165]. Very recently,it hasbeendemonstrated
that170DASNMRcanaccurately
quantify
bondangles
andoxygen sitedistributions
[36].
at low abundance
3.4.
Water
in
Glass
Bothstatic
"wideline"
andhighspeed
1HMASstudies
have detectedand quantified OH- and molecularH20
[30,68].
2HNMRhasdistinguished
among
water
species
in glasses,as well, and hasprovidedsomedynamicalin-
STEBBINS
formation
[31].In hydrous
NaAISi308
glass,
23Na,27A1,
and29SiMASandCPMASspectra
wereinterpreted
as
indicatingthatOH is boundsoleyto Na with thepossibility of protonatedbridging oxygens [67,69], whereasin
hydrousbinaryalkali silicateglasses[85,139]andin $iO2
325
onlysingle170,23Na
' 27A1,
and29Sipeaks,
forwhich
orientationaleffectsthat lead to broadeningin a solid,includingchemicalshift anisotropyand quadrupolarcouplings, are fully averaged[38,81,121,142,149,151].The
averagepeak positioncan still give structuralinformation
however,sinceit is a quantitativeweightedmeanoverall
speciespresent.This approachhas shown,for example,
that when aluminum oxides, aluminates, and fluorides
melt, the mean AI coordinationnumberdecreases[40,81].
943 'C
temperatures
greater
than21000
C,andhaveincluded
systematicwork on the effectsof compositionon the structure and dynamics in the CaO-AI203-SiO2 system
[21,84].
741 'C
69O 'C
639 C
85 'C
At lower temperatures,
incompleteexchangeandaveragingoccurs,and, in favorablecases,NMR line shapes
canbe analyzedto measuretheratesof exchange.The rate
of exchangeof Si amongvariousanionicspecies,andthat
of O betweenbridgingand non-bridgingsites,are fundamentallytied to diffusionand viscousflow. In K2Si409
liquid, for example(Figure 5), simulationsof high tem-
perature
170and29Silineshapes
gives
results
thatcan
be usedto accuratelypredictthe viscosity,assuminga
simpleEyring model for flow [38,145]. 2-D exchange
NMR spectroscopy
just above the glasstransitionalso
suggests
that exchangeamongQ speciesis of key importancein flow even in the very high viscosityrange[39].
A series of relaxation time measurements has shown that
25 'C
.... I'"'1'""1
4OO
.... I""l""i'r"i
40O
Acknowledgements.
I wouldlike to thankmy numerous
colleagueswho sentreprintsandpreprintsandallowedme to
Fig.5. Hightemperature
170spectra
forK2Si409liquid. "bo" and "nbo"showcontributions
from bridging
and non-bridgingoxygens[145]. Note collapseto single,
narrowline causedby exchangeof species.
T. Ahrens,andan anonymous
reviewer,andacknowledge
the
support of the National Science Foundation, grant
#EAR9204458.
326
NMR
OF SILICATES
AND
OXIDES
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MOssbauerSpectroscopyof Minerals
Catherine
1.
McCammon
INTRODUCTION
positions
andthehyperfineparameters
aregivenin Table
2. Suggested
referencesfor furtherinformationare listedin
Table 3.
3.
containing
57Feand18 containing
9Sn, accompanied
by
relativeto theabsorber,
shiftingtheenergyspectrum
due
to the Dopplereffect.Spectraare commonlyplottedas
percenttransmission
versussourcevelocity (energy).
Selected references to important experimental
A transmissionMOssbauerspectrometeris very
simple,and typically consistsof a y-ray source,the
absorber(sample)and a detector.The sourceis moved
referencematerialon M0ssbauerspectroscopy.
2.
EXPERIMENT
THEORY
considerations
are given in Table 4, while Table 5 lists
somecommon
applications
of M0ssbauer
spectroscopy
to
mineralstudies.This chapteronly includesreferences
to
transmission
studies;howeverthe techniquecanalsobe
performedin a scatteringgeometryto studysurface
properties(e.g., [ 105, 121, 127]).
Shelf 2
MINERAL
DATA
observed,
althoughunfavourable
nuclearproperties
limit
thenumberof commonly
usednuclei.57Feis by far the
mostpopularisotope,followedby 9Sn. Both the 14.4
keV transitionin S7Feand the 23.88 keV transitionin
AGU
4.
332
MCAMMON
(3)
(2)
(1)
(4)
excited
state
ground
state
Ire nucleus
Isomershift
Quadrupole
splitling
Magnetic
splilling
I
Eo
Fig. 1. Illustration
of hyperfine
interactions
for57Fenuclei,showing
thenuclear
energyleveldiagram
for
(1) a bare nucleus,(2) electricmonopoleinteraction(isomershift), (3) electricquadrupoleinteraction
(quadrupole
splitting),and(4) magnetic
dipoleinteraction
(hyperfinemagnetic
splitting).Eachinteraction
is
shownindividually,accompaniedby the resultingM0ssbauerspectrum.
I
1.00
0.98
0.96
0.94
0.92
-4.0
-2.0
0.0
2.0
4.0
Velocity (mm/s)
Fig. 2. M0ssbauerspectrum
of orthopyroxene
with composition
Fe0.sMg0.2SiO3
showingtwo quadrupole
doublets,
onecorresponding
to Fe2+in theM 1 site(45%of totalarea)andonecorresponding
to Fe+ in the
M2 site (55% of total area).
334
M)SSBAUER SPECTROSCOPY
Chemicalcompositions
are given exactlyas reportedby
the authors(even if the resulting compositionsare not
electrostatically
neutral).Data for differingcompositions
are providedfor the major mineralgroupsto illustratethe
dependence
of hyperfineparameters
on composition.
The
relative areas of subspectracan be used as a rough
approximationto relative abundance,e.g. [97], but note
thatsiteproportionsoftenvary betweendifferentsamples
of the samemineral.For example,the amountof Fe+
may depend strongly on foe conditions, and the
distribution
of
iron
cations
between
different
Unit
Isomershift (b')
Description
Energydifferencebetweensourceandabsorber
nucleiresultingfromeffects
including differencesin valence state, spin state and coordinationof
absorberatoms.Experimentallyone observesa singleline shiftedfrom a
referencezero pointby theisomershift plusthesecond-order
Dopplershift
(SOD), a smallthemudshiftdue to atomicvibrations.
mm s-1
The experimental
shiftof thecentmidof a M0ssbauer
trmn froma zero
referencepoint.The contribution
from the SOD is similarin moststandard
materials,so for purposes
of comparisonthe isomershift is often takento
be equalto thecentreshift.
Quadrupolesplitting
mm s-1
Experimentally
oneobserves
a doubletin S7Fe
and9Sn spectra
withcomponentsof equalintensityand linewidthin the idealrandomab,sorbercase.
The quadrupole splitting is given by the energy separationbetween
components.
Hyperfinemagneticfield
Tesla
(H)
forS7Fespectra
in thesimplest
case.Foranidealrandom
absorber
withno
quadrupoleinteractionthe linewidthsof the peaksare equalwith intensity
ratio 3:2:1:1:2:3. The separationof peaks 1 and 6 is proportionalto the
magnitudeof the hyperfinemagneticfield.
Line width (F)
Relative area(/)
mm s-1
Relative proportionof subspectrumarea to the total area. Each site normally contributesa subspectrum
(e.g. a quadrupoledoublet)whoseareais
approximatelyrelatedto therelativeabundance
of thatparticularsitewithin
the absorber.
MCAMMON
335
TABLE2. Determination
of linepositions
for57Fe14.4keV transition
Hyperfineinteractions
present
Line positions
- eleclricmonopole
L =CS
- electric
monopole
+ magnetic
dipole(AE2= 0)
-electricmonopole
+ quadrupole
+ magnetic
dipole
(special
caseof axiallysymmetric
electricfield
gradient
andI/4g/HI >> IAEa21)
L = /2IINH
L2= l/2#NH
La= /2I H
Ln= /21 H
Ls= /21 H
L = /2/& H
/ gm= 0.11882mms4 T-
/ gat2= 0.067899mms4 T'
- electricmonopole+ quadrupole
+ magnetic
dipole
(general
case)
TABLE 3. Suggested
refereaces
for Mtlssbauer
s[troscopy
Refexence
Type
Book
Bancroft,G.M. MOssbauerSpectroscopy.
An Introductionfor Inorganic Chemistsand Geochemists.McGraw Hi!l, New York, 1973.
336
M(SSBAUER SPECTROSCOPY
TABLE 3. (continued)
Reference
Type
Journal
Data Resource
Stevens,J.G., Pollack, H., Zhe, L., Stevens, V.E., White, R.M. and Gibson, J.L. (eds.) Mineral:
TABLE 4. MethodologyReferences
Experimentalaspect
Reference
Absorber thickness
[74, 99]
[16, 28]
[18,50]
Absorberhomogeneity
Preferred orientation of absorber
[95, 96]
Saturation effects
[97, 99, 120]
Isomer shift reference scales
[6]
Goodness of fit criteria
[31, 37, 58, 103]
Conventionsfor reportingM6ssbauerdata [117]
Geometric effects
Application
Reference
Oxidation state,including
intervalence
chargetransfer
Site occupancies,
includingFe3+/Fe
Site coordination
[15, 22]
[13,85]
[66, 108]
[23, 25]
Semi-quantitative
phaseanalysis
Phase transitions
Magneticstructure
Amphibolestructure
Mgs.7Fe.3Si8022(OH)2
Fe6.2Mgo.
sSi8022(OH
h
RT
RT
AEa
mm s-
CS(Fe)
mm s-
Tesla
1.16(1)
1.13(1)
1.16(1)
1.07(1)
2.76(1)
1.81(1)
2.79(1)
1.55(1)
0.07
0.93
0.69
0.31
site
VlFe2+
XaFe2+
XaFe2+
VFe+
Ref
[107]
[53]
MCAMMON
TABLE 6. (continued)
CaXSisOz(OH)ff
AFQ
1.27(1)
1.30(1)
1.27(1)
1.14(1)
1.12(1)
0.40(1)
3.17(1)
2.39(1)
1.86(1)
2.87(1)
2.36(1)
0.44()
RT
0.34(1)
1.76(1)
RT
1.20(1)
0.41(1)
2.44(1)
0.86(1)
0.40
1.14(3)
1.16(3)
0.23(5)
2.67(5)
2.38(5)
0.70(3)
0.70
1.15(1)
0.29(1)
2.41(1)
0.98(1)
0.98
1.22(1)
1.21(1)
2.31(1)
1.60(1)
0.94
0.36(1)
0.30(2)
1.08(1)
1.20(4)
0.35(1)
2.06(1)
1.54(3)
1.67(1)
1.90(8)
1.94(1)
0.92
0.31(5)
3.51(1)
3.46(1)
0.24(1)
3.56(1)
0.33(1)
0.55(1)
3.49(1)
0.58(1)
3.60(1)
1.39(1)
0.48(5)
1.11(1)
0.33(1)
1.73(1)
1.20(1)
1.03(2)
1.06(2)
0.48(2)
2.48(2)
2.01(2)
1.32(2)
77 K
X=Mg4.7Feo.3
Nal.sCao.
lXSisO22(OI-I)2
X=Fen.oMgo.3
CS(Fe)
mms '1
Absorber
RT
0.59
0.31
0.10
0.36
0.19
0.45
site
Ref
VXFe2+
VXFe2+
XaFe2+
XaFe2+
VFe2+
VIFe-
[113]
[4O]
Andalusite
(Alo.96Feo.
oaMno.
ol)2SiO5
[1]
Babingtonite
Ca2Fel.7Mno.aSi5014(OH)
0.60
VIFe2+
XaFe3+
[21]
rife2+
XaFe2+
Fe3+
[33]
rife2+
VIFe+
[57]
VIFe2+
channel Fe2+
[47]
VlFe3*
XaFe3*
XaFe2+
Fe 2+
XaFe3*
[36]
VllIFe2+
VmFe2+
XaFe3*
VmFe2+
XaFe3*
XaFe3+
VmFe2+
XaFe3+
VmFe2+
XaFe2*
Fe3+
[89]
[131]
VFe2+
Fe3+
[109]
WFe2*
VmFe2+
VmFe3+
[73]
Chlorite
XSiz9AIz4(OI-I)7.901
o
RT
X=Mg2.2Fe2.3Mno.
1
0.21
0.09
Chloritoid
Fe1.7Mgo.aA14Si20]o(OHh
RT
0.02
Clay minerals
Cordierite
A13Mg.9Feo.2A1SisO
Epidotestructure
Ca2XSi302(OH)
X=A12.2Feo.s
YAI.7Fe.2Si30
2(OH)
Y=Cal.2Ceo.sLao.2
RT
RT
RT
0.06
0.08
0.58
0.09
0.33
[36]
Garnet structure
FeaA12Si3012
RT
1.29(1)
Fe2+3Fe3+2Si3012
RT
1.31( 1)
quenched
from9.7 GPa,1100C
Mg2Cao.sFeo.sXSi3012
RT
X=All.sCro.5
Ca3FeaSi30
i2
RT
0.36(1)
1.28(1)
0.36(1)
0.41(1)
Ca2.sFeo.7A1].3Si3012 R'I;
1.26(1)
0.39(1)
Mgo.9Feo.
lSiO3
quenched
from 18GPa,1800C
RT
1.26(1)
1.11(1)
0.54
0.46
0.84
0.16
0.17
0.83
0.80
0.10
0.10
p]
p]
[7]
[92]
Grandidierite
Mgo.9Feo.1A13BSiO9
RT
0.94
0.06
llvaite
CaFe3Si208(OH)
a
RT
0.27
0.35
0.38
TABLE 6. (continued)
Absorber
CS(F)
AE{2
mm s-1
site
Ref
Tesla
Kyanite
(Alo.sFeo.
o2)SiO
Micagroupb
Ko.9NaoaXAISi30
o(OH
X=Al.7Feo.2Mgo.
KXAIo.sSi3Olo(OH)2
X=Mgz6Feo.6
KXAISi30o(OH)2
RT
0.38(2)
0.99(2)
RT
1.21(1)
1.14(1)
0.36(1)
1.12(1)
0.19(1)
1.02(1)
1.06(1)
0.31(1)
1.o6()
0.28(1)
2.99(1)
2.12(1)
0.86(1)
2.63(1)
0.56(1)
2.52(1)
2.08(1)
o.8o(1)
2.34(1)
0.66(1)
0.89(2)
0.95(2)
0.84(2)
0.19(4)
0.94(2)
0.99(2)
0.23(4)
1.13(1)
0.39(1)
1.91(2)
2.39(2)
1.33(2)
1.23(4)
1.98(2)
2.36(2)
0.70(4)
2.75(2)
0.91(2)
RT
0.46(1)
0.68(1)
RT
1.20(1)
1.14(1)
2.35(1)
1.86(1)
0.32
1.12(1)
0.44(5)
1.58(1)
0.98(5)
0.08
0.36(1)
0.43(4)
0.14(4)
0.18(1)
1.22(8)
0.59(8)
0.08
1.18(1)
1.13(1)
1.30(1)
1.26(2)
1.29(1)
1.28(1)
1.19(1)
0.42(1)
0.14(1)
0.39(1)
2.49(1)
1.91(1)
0.46
RT
RT
X=Mg.6Fe.2Mno.Tio.
1
CaXAIz7sil.201o(OH)2
X=Mg2.3Alo.7Feo.
RT
Olivine
Fe2SiO4
CaFeSOn
Mgo.s3Feo.7SiO4
Fe2+o.Fe3+SiO4
310 K
400 K
310 K
290 K
Orthoclase
KAlo.95Feo.
osSi3Os
Osumilite
XMgl.nFeo.9A14.4
sil 0.3030
X=Ko.9NaoA
Perovda'te structure
Mgo.95Feo.
osSiO3
RT
Pyrophyllite
Fe,2Mgoa
Alo.1SiOlo(OH)
2
Pyroxenestructure
FeSiO3
RT
RT
77 K
Mgo.ssFeo.
lsSiO3c
77 K
CaFei206
CaMgo.9Feo.2Sil.906
RT
NaFei206
RT
RT
3.13(1)
2.00(1)
3.06(1)
2.16(1)
2.22(1)
1.07(1)
1.62(1)
0.30(1)
[94]
0.08
[41]
0.05
0.87
0.38
[39]
0.62
0.59
[76]
0.33
0.08
0.30
[671
0.70
0.48
0.52
0.70
0.30
0.51
0.41
0.08
0.41
0.59
0.68
0.92
0.85
0.07
0.54
rife2+
rife2+
VIFe2+
VFe3*
VFe2+
rife2+
VFea*
VIFe2+
VFe3*
[lll]
VFea*
[19]
VIFe2+
channel Fee+
[46]
XXIFe2+
Fe a*
[80]
VFea*
VFea*
VFea*
[26]
[lll]
[111]
[68]
[38]
0.50
0.50
0.20
[12]
0.80
0.50
[38]
[54]
0.50
[10]
McCAMMON
339
TABLE 6. (continued)
Absorber
CaFeAISiO6
Serpentine
(M..Ol)35i205(O4
antigorite
(Mgo.Feo.oOaSi:Os(OHh
chrysotile
(Mgo.13Feo.
g7)3Si205(OI-I)4
CS(Fe)
mm S'1
Tesla
site
Ref
RT
0.22(1)
0.35(1)
1.58(2)
0.99(2)
0.11
0.87f
IVFe3+
VIFe3+
[3]
RT
1.12(1)
0.36(4)
1.14(1)
0.38(3)
0.27(4)
1.15(2)
1.16(1)
0.36(4)
2.70(1)
0.70(5)
2.74(2)
1.08(1)
0.30(3)
2.79(1)
2.21(2)
0.70(5)
0.68
0.32
0.39
0.29
0.32
0.30
0.52
0.18
VFe2+
VFe3+
VFe2+
VFe3*
xaFe3*
rife2+
VFe2+
XaFe3+
[102]
RT
0.38(2)
0.16(50)
1.11(3)
0.5(10)
0.79
0.21
VIFe3*
IVFe3+
[101]
RT
0.37(1)
0.37(1)
0.24()
0.35(1)
0.37(1)
1.13(1)
0.23(1)
0.65(1)
0.54(1)
0.81(1)
1.35(1)
2.65(1)
0.65
0.35
0.09
0.55
0.30
0.06
XaFe3+
XaFe3+
IVFe3*
XaFe3+
VIFe3+
XaFee+
[11o]
1.09(1)
0.18(5)
1.05(1)
0.27(5)
2.62(1)
0.37(5)
2.78(1)
0.93
0.07
0.94
VFe2+
Fe3'
VFe2+
[92]
RT
0.96(1)
0.98(1)
0.92(1)
0.60(1)
2.50(1)
2.13(1)
1.17(1)
0.83(1)
RT
1.15(1)
2.63(1)
RT
0.21(1)
0.35(1)
0.48()
RT
1.06(1)
1.09(3)
0.27(5)
RT
RT
[102]
[102]
Sillimanite
(do.J%.o2hSiOs
Smectite minerals
Cao.2XSi3.6.401
o(OH)2
X=Fel.9Mgo.1
Cao.2XSi3.sAlo.3Ol
o(OH)2
RT
X=Fel.nMgl.2
Spinelstructure
y-Fe2SiO4
RT
quenchedfrom 8 GPa,1000C
y-Mgo.ssFeo.
5SiO4
RT
quenchedfrom 18 GPa,1700C
0.06
[110]
[92]
Fe 3*
Staurolite
XA19Si402o(On)2
X=Fel.1Mgo.sZno.3Tioa
0.23
0.40
0.31
0.06
rVFe2+
rVFe2+
lVFe2+
VIFe3*
[5]
1.25(1)
0.96(1)
0.81(1)
0.14
0.55
0.31
rVFe3+
XaFe3*
VIFe3*
[61]
2.76(1)
2.29(3)
0.37(5)
0.19
0.77
0.04
VFe2+
XaFee+
Fe3*
[92]
Talc
(Mgo.9Feo.)3Si40
o(OHh
Titanite
CaTio.9Feoa
SiO5
Wadsleyite
-(]V[..16)2SiO4
quenchedfrom 15.5 GPa,1800C
Yoderite(Mg2AI3.6Feo.3Mno.1)6A12S
i4015(OH)
2
RT
0.36(1)
1.00(1)
VFe'/VIFe'
spectral
datawerefittedusinga relaxation
model
b spectra
aremorerealistically
described
withhyperfine
parameterdistributions,see [98]
c see[59] for a compilationof data
smallamountof additionalcomponent
present
340
MSSBAUER SPECTROSCOPY
TABLE7.57Fe
M6ssbauer
dataforselected
oxide
andhydroxide
minerals
Absorber
AE
mm s-
CS(Fe)
mm s-
Tesla
0.39(1)
0.38(1)
0.95(1)
0.55(1)
site
Ref
Akagandite
l-FeOOH
RT
0.39
VFe3+
0.61
rife3+
[84]
Feroxyhite
8'-FeOOH
Fem'hydrite
FesHO84H20
RT
0.4(1)
0.4(1)
- 0.1(1)
+1.1(1)
44.8(5)
39.3(5)
0.60
VFe3*
0.40
VFe3+
[35]
RT
0.35(1)
0.62(1)
RT
0.35(1)
-0.3(1)
38.4(5)
RT
0.38(5)
- 0.21(5)
52.1(5)
RT
1.07(1)
0.70(1)
VlFe2*
[44]
RT
RT
0.30(1)
1.06(1)
0.55(1)
0.53(1)
rife3+
XqFe2+
[65]
[72]
RT
0.22(5)
0.37(5)
+0.08(5)
+0.02(4)
0.33
VFe3+
[11]
0.67
rife3+
RT
0.35(5)
0.34(5)
RT
0.37(1)
0.37(1)
0.52(1)
0.90(1)
Goethite
ct-FeOOH b
Haematite
ct-Fe203c
[122]
llmenite
FeTiO3
Lepidochrocite
y-FeOOH
Magnesiowt2stite
Mgo.sFeo.20
Maghemite
y-Fe203
Perovskite
Ca.Tio.8FeoaO3
50.2(1)
50.5(1)
VFe3+
[83]
0.54
VFe3+
[29]
0.46
rife3+
Pseudobrookite
FeaTiO5
Spinelstructure
Fe3On
FeCr204
FeA12On
ZnFe2On
MgFe2On
310K
0.63(1)
0.05(10)
0.05(10)
RT
0.63(1)
0.27(1)
0.90(1)
RT
RT
RT
0.91(1)
0.33(1)
0.37(1)
1.57(1)
0.41(1)
quenchedfrom 1000C
Zno.7
Mgo.5Feo.
5A12On
Fe2TiO4
d
Tapiolite
FeTa206
Wastite
Feo.950e
51.0(2)
52.6(2)
0.48(1)
RT
0.46
XaFe2-5+ [56]
0.15
0.39
XaFe2-5+
VeFe3*
0.36
rVFe2+
IVFe2+
VFe3+
reFe3+
0.64
VFe3+
0.29(2)
0.78(2)
0.11
XaFe3+
0.92(2)
0.89(2)
0.23(2)
0.81(2)
0.76
0.13
rVFe2*
IVFe2+
RT
0.83(1)
1.91(8)
RT
1.11(2)
3.15(5)
1.00(1)
0.22(1)
0.42(1)
RT
0.93(1)
0.60(5)
spectradata were fitted with a distributionmodel
see[87]fora discussion
of theeffectofA1substitution
and
varying crystal size
45.7(1)
44.6(1)
48.9(1)
Fe2+
XaFe2+
0.43
0.48
VFe2+
VFe2+
0.09
VeFe3*
[93]
[93]
[781
[91]
[128]
[77]
[106]
[79]
octahedral
andtetrahedral
sites
inFe2TiO
4have
been
distinguished
usingextemalmagnetic
fields[123]
thereisconsiderable
controversy
overfittingmodels,
see[75]
for a review
MCAMMON
TABLE8.57FeM6ssbauer
dataforselected
sulphide,
selenide
andtellurideminerals
Absorber
site
Ref
1.15(3)
VlFe2+
[64]
0.83(2)
2.69(2)
VIFe2+
[17]
RT
0.39(1)
0.22(1)
RT
0.25(3)
RT
0.26(1)
0.45(1)
RT
RT
0.43(1)
0.72(1)
0.22(1)
1.2
0.20(1)
RT
RT
0.30(1)
0.45(1)
RT
RT
RT
RT
CS(Fe)
AE2
mm s-
mm s-
RT
0.26(3)
RT
Tesla
Arsenopyrite
FeAsS
Berthierite
FeSb2S4
Bornite
CusFeS4
Chalcopyrite
CuFeS2
[27]
35.7(5)
ntFe3+
[63]
XaFe2+
[124]
lVFe2.5+
ntFe2*
ntFe3+
[631
[491
1.65(1)
1.28(2)
VIFe2+
VlFe2+
[641
[119]
0.27(1)
0.39(1)
0.47(1)
0.51(1)
0.58(1)
0.50(1)
VlFe2+
XaFe2+
VIFe2+
[119]
[1191
[119]
0.36(1)
0.65(1)
0.32(1)
IVFcZS+?
VFca*
[69]
RT
0.31(1)
0.61(1)
VlFe2+
[119]
285 K
0.69(1)
0.68(1)
0.67(1)
RT
0.67(3)
0.67(3)
0.60(10)
RT
0.57(1)
2.90(1)
RT
0.39(2)
1.07(2)
RT
0.58(1)
0.37(1)
2.28(1)
0.33(1)
0.29(1)
0.59(1)
0.58(1)
0.55(1)
0.26(1)
0.54(1)
0.00(2)
0.70()
Cobaltite
(Co,ge)AsS
Cubanite
CuFeaSa(ortho)
CuFeaS(cubic)
L611ingitestructure
FcAs2
FSb2
Marcasite
33.1(5)
0.46
0.54
structure
FS 2
FeSea
FeTea
Pentlandite
Fe4.2Coo.lNi4.7S8
Pyrite
FeS2
Pyrrhotite
Feo.89
S
Sphalerite
Zno.95Feo.osS
0.82
0.18
- 0.48
- 0.59
-0.45
30.2(5)
25.7(5)
23.1(5)
0.41
0.36
0.23
XaFe2+
XaFe2+
XaFe2+
0.54
IVFe2+
IVFe2+
[431
lVFe2+
[491
IVFe2.5+
[129]
lVFe2+
mFe3+
[24]
VlFe2+
lVFe2+
lVFe2+
VlFeZS+?
ntFe3+
[125]
[001
0.46
Stannite
Cu2FeSnS4
Sternbergite
AgFe2S3
27.8(2)
Tetrahedrite
Cua.9Ag2Fe.
Sb4S
Thiospinelminerals
FeNi2S4
FeCr2S4
F%S4
RT
RT
RT
0.60
0.40
0.93
0.06'
31.0(5)
31.1(5)
0.66
0.34
[115]
341
342
MOSSBAUER SPECTROSCOPY
TABLE 8. (continued)
Absorber
FeIn2S4
Co2.9Feo.1
S4
Troilite
FeS
RT
RT
CS(Fe)
AEQ
mm s-1
mm s-1
Tesla
0.88(1)
0.25(1)
0.23(1)
3.27(1)
0.25(1)
RT
0.76(4)
RT
0.69(3)
0.69(3)
0.45
0.55
- 0.88
31.0(5)
site
Ref
VFe2+
VFe3+
VFe3+
[491
[130]
XaFe2+
Ds]
0.54
lVFe2+
[43]
0.46
VFe2+
Wurtzite
Zno.95Feo.osS
0.56(10)
TABLE 9. S7FeM6ssbauer
datafor selected
carbonate,
phosphate,
sulphate
andtungstate
minerals
Absorber
CS(Fe)
mm s-
AEQ
mm s-
site
Ref
Tesla
Siderite
FeCO3
RT
1.24(1)
1.80(1)
VFe2+
[481
RT
1.25(1)
1.48(3)
WFe2+
[341
RT
1.11(2)
1.49(3)
rife2+
[51]
RT
0.40(5)
I. 15(5)
WFe3+
[62]
RT
1.13(2)
1.53(3)
rife2*
[51]
RT
1.21(1)
2.98(1)
0.22
rife2+
[10]
1.18(1)
0.38(1)
0.40(1)
2.45(1)
1.06(1)
0.61(1)
0.21
0.38
0.19
WFe2+
WFe3+
WFe3+
Ankerite
Ca.lX(CO3)2
X=Mgo.sFeo.3Mno.
1
Ferberite
FeWOn
Jarosite
KFea(SOn)e(OH)
6
Wolframite
Feo.sMno.sWO4
Vivianire
Feo0a)2-8H20
Absorber
CS(Fe)
mm s-
zQ
mm s-
Tesla
site
Ref
Iron
ct-Fe
298 K
0.00
+0.001(2)
33.04(3)
Fe
[126]
33.8(7)
Fe
DO]
Fe
[41
Fe
[4]
Kamacite
~Feo.9sNio.os
RT
0.02(1)
RT
-0.08(1)
FeNi
RT
0.02(1)
Taenite
0.40(2)
28.9(2)
McCAMMON
343
T
RT
Berndtite,$nS2
Cassiterite,SnO2
RT
CS(SnO
2)
AEi2
mm $-1
mm S-1
.03(5)
0.00
0.40(5)
site
Ref
VlSn4+
VSn4+
[8]
[132]
VlSn4+
VSSn4+
VSn2+
VlSn4+
[9]
[9]
[8]
[6]
Garnet structure
RT
CaaFei.sAlo.1Sno.1S
iaO12
YCa2Sn2Fe302
Herzenbergite,SnS
Incaite, Pb3.sFeSn4Sb2S
13.s
Malayite, CaSnSiO5
Mawsonite,Cu6Fe2SnSa
Ottemannite,Sn2S3
RT
Romarchite, SnO
RT
- 0.14(5)
0.07(5)
3.23(3)
.3(4)
3.29(5)
- 0.07(2)
1.46(5)
3.48(5)
1.10(5)
2.64(2)
Spinelstructure
Co2SnOn
Mn2SnO4
Zn2SnO4
Mg2SnO4
Stannite,Cu2Feo.9Znoa
SnS4
Stannoidite,Cus(Feo.sZno.2)aSn2S
2
RT
RT
RT
RT
RT
RT
0.30(4)
0.25(4)
0.24(4)
0.12(4)
1.45(5)
1.48(5)
RT
RT
RT
RT
RT
0.42(5)
0.42(5)
0.85(5)
0.66
0.98(5)
1.32(4)
0.00(5)
0.95(5)
Sn2+
0.34
0.29
VSn4+
reSn4+
Sn2+
0.71
VlSn4+
[104]
[132]
[8]
1.31(1)
VISn2+
[60]
0.80(8)
0.75(8)
0.75(8)
1.20(8)
0.00(5)
0.00(5)
WSn4+
VSn4+
VSn4+
VSn4+
reSn
4+
reSns+
[52]
[52]
[52]
[52]
[132]
[132]
Sn
Sn
[118]
[118]
Tin
c-Sn
300 K
2.02(2)
15-Sn
300 K
2.55(1)
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Litterst, F. J. and Amthauer, G.,
Electron delocalization in ilvaite,
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346
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86.
1991.
Clay
1988.
Minerals,
15,
87.
71-77,
88.
69,
1984.
1977.
Goldanskii-Karyagineffect versus
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Murad,E. andSchwertmann,
U.,
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and
troscopy
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Fe3' in tri99.
DeCarreau,
A.
and
Manceau,
A., Spectroscopic
and
250-254, 1985.
McCaramon, C. A., Rubie, D.C.,
Ross II, C. R., Seifert, F. and
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H. St. C., M6ssbauer
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1992.
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0VlgFe204)
from powder XRD structural refinements and M6ssbauer spectroscopy. Amer. Mineral., 77,
1958.
725-740,
spectraof 57Fe0.05Mg0.95SiO
3
91.
Mineral.,
77,
894-897,
92.
fluoresentyon Gammastrahlungin
Muir,
Mineral.,
22,
689-694,
1984.
1992.
84.
317-325,
96.
161-173,
928-936,
23,
95.
Influence
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83.
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Stewart
187-221,
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82.
in
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81.
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80.
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1987.
79.
In
1981.
94.
and limita-
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78.
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76.
85.
1984.
75.
10, 250-255,
93.
466, 1993.
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and Heller-Kallai,
L., M6ssbauer
Amer.
1979.
phyllo-
Mineral.,
64,
colouredceramicpigments.Trans.
McCAMMON
Experimental techniquesfor conversion electron M6ssbauer spectroscopy. Hyper. Inter., 13, 199219, 1983.
Schmidbauer, E. and Lebkilchner-
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196-200,
1987.
Robinson (ed.),
520-522,
CRC
1981.
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Burragato
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Seifert,
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distributions.
F.
and
Olesch,
62, 547-553,
M.,
1977.
1346-1354,
Amer.
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73,
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1992.
J.W.
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114.
Mineral.,
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113.
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Massbauerspectroscopic
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112.
J. G.,
of 57Fe in anthophyllite.Phys.
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1972.
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Wintenberger, M.,
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P., Magnetic
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Cskiagite")
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1993.
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Yamanaka,
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119Snin stannite,stannoidite,and
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61,
Vol. 2
Subject Index
actinides, bulk moduli, 131
activationenergy,apparent,crystals,
238
activationenergy,diffusion,274
activationvolume,apparent,crystals,
238
temperatureand thermalpressure,
black-bodyemission,dependenceon
wavelengthat different
temperatures,300
bondingproperties,minerals,291
elastic moduli, 68
mantle mineral data, 85
borates
thermalexpansivity,specificheat,
78
albite
calcite,spectra,296
phasediagrams,249-252
viscosity,214
alkali feldspar,phasediagrams,250
alloys,shearviscosity,221-224
Coblecreep,crystals,240
coesite,phasediagrams,249
compression
curves,shockwaves,172
calcium oxide
convective flow
76
aluminates
NMR spectra,325
See also calcium-aluminates
aluminosilicates,layer
A1-27 NMR data, 315
Si-29 NMR data, 311
aluminum
dimensionless
parameters,Debye
temperatureand thermalpressure,
oxides
dimensionless
parameters,Debye
temperatureandthermalpressure,
75
elastic moduli, 69
mantle mineral data, 85-86
O- 17 NMR data, 320
thermalexpansivity,specificheat,
elastic constants, and
velocities, 70
amorphousmaterials
bulk moduli, 134
NMR spectra,303,322-325
amphiboles
diffusion, 277
M/3ssbauer
spectra,336-337
andalusite,M/3ssbauer
spectra,337
andesite,shearviscosity,215
anelasticity,melts,209-217
anorthite,phasediagrams,249-251
Arrheniusequation,diffusion,274
Arrheniuslaw, crystals,238
asymmetryparameter,NMR spectra,307
augite,phasediagrams,255
babingtonite,
M/3ssbauer
spectra,337
basalt, diffusion, 274, 282-283
Beer-Lambertlaw, absorption,295
beta-spinel,
plasticity,245
bibliography,M/3ssbauer
spectroscopy,
335-336
elastic moduli, 65
mantle mineral data, 83
mantle, 227
mantle viscosity,229
coordinationnumber,NMR spectra,307
core,outer, viscosity,218-226
correspondence
principle,elasticity,
228
thermalexpansivity,specificheat,
elastic constants, and
velocities, 73
corundum
phasediagrams,251
See also aluminum
oxide
creep,climb-controlled,
crystals,
carbon-bearing
minerals,bulk moduli,
117-118
239-240
creep,glide-controlled,crystals,239
creep,power-law
carbonates
high-temperature
electrical
conductivity,189
mineral data, 3
M/Sssbauer
spectra,342
shockwaveequationof state,160
thermalexpansion,32
chain silicates
chargetransferband,297
chemical diffusion, 271
chlorite,M/3ssbauer
spectra,337
chloritoid,M/3ssbauer
spectra,337
clay minerals,M/3ssbauer
spectra,337
clinoenstatite,
phasediagrams,253-254
clinopyroxene
phasediagrams,254, 256
plasticproperties,244
closuretemperature,diffusion,274
cobalt silicate
dislocations, 240
mantleviscosity,
creep,quasisteady-state,
crystals,237
crystals,237
See also diffusioncreep;dislocation
creep;Harper-Dom creep;
Herring-Nabarrocreep
creepmechanism,mantleviscosity,227
cristobalite,phasediagrams,249
critical resolvedshearstress,yield
strength,245
cross-slip,dislocations,240
crystal-fieldabsorptions,
297
crystallographic
data,minerals,1-17
crystals
plasticrheology,237-247
Seealsocubiccrystals;hexagonal
crystals;orthorhombiccrystals;
trigonalcrystals
crystalstructure,mineraldata, 1-17
cubiccrystals,elasticmoduli,46-48
cyclosilicates
bulk moduli, 107-110
mineral data, 5-6
dimensionless
parameters,Debye
349
Vol. 2
INDEX
Debye temperature,mantleminerals,
75-79
deformation-mechanism
maps,plastic
deformation, 241
deformation mechanism, mantle
viscosity,227
diamond-anvil
electricalproperties,minerals,185-208
cell
equationsof state,98-101
high-pressure
minerals,245-246
dielectricpermittivity, 185
diffusion, 304
elements,
GroupIII., bulkmoduli,126
elements,GroupIV, bulk moduli,126-128
elements,GroupV, bulk moduli, 128
elements,GroupVI, bulk moduli,128-129
elements,GroupVII, bulk moduli,129
elastic moduli, 46
dislocations, 240
olivine, 243-244
phasediagrams,254-257
phaserelations,25
plasticproperties,244
enthalpy
silicates, 269-290
See also chemical diffusion
diffusionalflow, mantleviscosity,227
diffusion
coefficients
silicates, 270-273
See also chemical diffusion;
effectivebinarydiffusion
coefficients; interdiffusion;
multicomponent
diffusion;
phenomenological
diffusion
mantle minerals, 90
minerals, 21-23
phasetransformations,
23-27
entropy
mantle minerals, 90
minerals, 21-23
phasetransformations,
23-27
epidote,M/3ssbauer
spectra,337
equationsof state
coefficients; self-diffusion
coefficient;thermodynamic
staticcompressionmeasurements,
98-142
See alsoMie-Gruneisenequationof
diffusion creep
crystals,239
dislocations, 240
diopside
phasediagrams,253-257
plasticproperties,244
dislocationcreep,crystals,239
dislocations,crystals,239
dynamictopography,
mantleviscosity,
229
dynamicyielding,shockwaves, 174-175
Earth-formingminerals
phasediagrams,248-268
spectra,291-302
Earthrotation,mantleviscosity,231
effectivebinarydiffusion
coefficients, 273
elasticconstants,
isotropic,mantle
minerals, 69-74
elasticity,geologicalmaterials,45-63
elasticlimit, crystals,237
elasticmoduli, isotropic,P and T
derivatives, 57-58
crystals,46-56
mantlemineralsat high temperature,
64-97
melts, 209
electricalconductivity,185
minerals, 291
pointdefects,187-188
silicates
fusion,enthalpy,25
gamma-spinel,
plasticity,245-246
garnet,grossular
dimensionlessparameters,Debye
temperatureand thermalpressure,
76
multicomponent,273
diffusion
Seealsomagnesiumsilicate
framework
state
fayalite
crystalfield absorptionspectra,299
phasediagrams,256
see also iron silicate
Fe-57
M/3ssbauer
spectroscopy,
332-335
feldspars
A1-27 NMR data, 315
diffusion, 275-276
log electricalconductivityvs.
partialpressure,205
phasediagrams,248-252
Si-29 NMR data, 312
viscosity,214
feldspathoids
AI-27 NMR data, 315
diffusion, 279
log electricalconductivityvs.
partialpressure,205
Si-29 NMR data, 312
ferropseudobrookite,
phasediagrams,259
ferrosilite,phasediagrams,255
elastic moduli, 65
mantle mineral data, 83
phasediagrams,257
thermalexpansivity,specificheat,
elastic constants, and
velocities, 73
thermoelastic
properties,93-94
garnet,majorite
phasediagrams,253
plasticity,245
garnet,pyrope-rich
dimensionless
parameters,Debye
temperatureand thermalpressure,
76
elastic moduli, 65
mantle mineral data, 83
phasediagrams,256-257
thermalexpansivity,specificheat,
elastic constants, and
velocities, 73
garnet
diffusion, 280
elastic moduli, 47-48
Massbauerspectra,337
phasediagrams,248, 256-257
gases,shockwave equationof state,
144-145
geochemistry,
304
geodeticstudies,coreviscosity,219
geoid,mantleviscosity,227
geoidanomaly,positivemassanomaly,
231
geoidinversion,mantleviscosity,
232-234
geomagnetism
studies,coreviscosity,
220
geophysics,
304
germanares,
phasetransitions,25
Gibbsfree energy,vs. temperature,23
glasses
bulk moduli, 134
diffusion, 269-290
elasticity,45-63
elastic moduli, 56
forsterite
heatcapacity,20
NMR spectra,322-325
phasetransitions,212
shockwave equationof state,166-168
heatcapacity,19
phasediagrams,254-256
thermoelastic
properties,92-93
Vol. 2
INDEX
glasstransition,heatcapacity,20-21
grain-boundary
sliding,crystals,239
grandidierite,
M0ssbauerspectra,337
iron-sulfuralloys,liquid, shear
viscosity,223
iron-titaniumoxides,phasediagrams,
248, 258-260
halides
hightemperatureelectrical
conductivity,189-190
log electricalconductivityvs.
partialpressure,204
mineral data, 8-9
shockwaveequationof state,153-155
hardening,crystals,237
Harper-Domcreep,crystals,240-241
heatcapacity,minerals,18-21
hedenbergite,
phasediagrams,255
Helmholtzfree energy,mantleminerals,
86-87
hematite,phasediagrams,258-260
Herring-Nabarrocreep,crystals,240
hexagonal
crystals,elasticmoduli,48
high-pressure
minerals,l.,antle,245-24,
high-pressure
silicates
mineral data, 8
O-17 NMR data, 322
hollandite,phasediagrams,250
Hugoniotequationof state,minerals,
M0ssbauerspectra,342
phasediagrams,248, 262
iron alloys,bulk moduli, 131-133
iron silicate
elastic moduli, 68
mantle mineral data, 85
isopleths,phasediagrams,249-262
deformation, 241
hydrousminerals,thermalexpansion,
31-32
hydroxides
bulk moduli, 111-117
mineral data, 3
M0ssbauerspectra,340
O- 17 NMR data, 321
thermoelastic
properties,92
magnesiumsilicate
dimensionless
parameters,Debye
temperatureand thermalpressure,
77
elastic moduli, 67
mantle mineral data, 84-85
thermalexpansivity,specificheat,
elastic constants,and
velocities, 71
magnetite,phasediagrams,258-260
manganese
oxide
dimensionless
parameters,Debye
temperatureandthermalpressure,
78
jadeite,phasediagrams,249
kamacite,M/assbauer
spectra,342
kinks, crystals,239
Kroger-Vinknotation,pointdefects,
elastic moduli, 66
mantle mineral data, 83-84
thermalexpansivity,specificheat,
elastic constants, and
velocities, 72
187-188
kyanite,M0ssbauerspectra,338
lanthanides, [::.,ik moduli, 130-131
leucite,phasediagrams,250, 252
liquidalloys,shearviscosity,221-224
liquidmetalstheory,coreviscosity,
143
hydrides,bulk moduli,133-134
hydrostatic
pressure,
plastic
thermalexpansivity,specificheat,
thermalexpansivity,specificheat,
elastic constants, and
velocities, 72
221
manganesesilicate
dimensionless
parameters,Debye
temperatureandthermalpressure,
78
elastic moduli, 68
mantle mineral data, 85
thermalexpansivity,specificheat,
liquids
bulk moduli, 134
diffusion, 269-290
heatcapacity,20
NMR spectroscopy,
303
phasetransitions,212
lithosphere,strength,228
longitudinalviscosity,vs.frequency,
211
lunarglass,shockwaveequationof
state, 168
351
elastic constants,and
velocities, 72
mantle
high-pressure
minerals,245-246
viscosity,227-236
mantle minerals, elastic constants,
64-97
MAS, Seemagicanglesspinning
melting,entropy,23-27
melts
elasticity,45-63
elastic moduli, 55-56
ilmenite,phasediagrams,253, 259-260
ilvaite,M0ssbauerspectra,337
infraredspectroscopy,
Earth-forming
minerals, 291-302
insulators, 186
interdiffusion, 271
intervalence transitions, 297
inverseproblems,mantleviscosity,
231-232
iron,liquid,sheardynamicviscosity,
222
iron-nickelalloys,liquid,shear
viscosity,222-223
iron-oxygenalloys,liquid,shear
viscosity,224
iron-siliconalloys,liquid,shear
viscosity,224-225
magicanglesspinning,NMR spectra,303
magnesiowuestite
phasediagrams,256
plasticity,245
magnesiumaluminumoxide
electricalproperties,185-208
NMR spectra,304, 322-325
viscosityand anelasticity,209-217
Seealsoamorphous
materials;
glasses;liquids;silicatemelts
thermalexpansivity,specificheat,
elastic constants, and
velocities, 70
magnesiumoxide
dimensionless
parameters,Debye
temperatureandthermalpressure,
75
elastic moduli, 65
mantle mineral data, 82-83
mica,M0ssbauerspectra,338
Mie-Gruneisenequationof state,shock
waves, 175
minerals
crystallographic
data, 1-17
elasticity,45-63
electricalproperties,185-208
equationsof state,98-142
Vol. 2
INDEX
M/3ssbauerspectroscopy,
332-347
NMR spectra,304
phasediagrams,248-268
shock wave data, 143-184
thermalexpansion,29-44
thermodynamic
properties,18-28
See also carbon-bearingminerals;
Earth-formingminerals;hydrous
minerals; and the different
M/3ssbauerspectra,338
phasediagrams,252
orthoenstatite,
phasediagrams,254
orthopyroxene
M/3ssbauerspectra,333
phasediagrams,254-255
plasticproperties,244
orthorhombiccrystals,elasticmoduli,
51-52
mineral groups
M/3ssbauer
parameters,
334
M/3ssbauerspectroscopy,
minerals,
332-347
monocliniccrystals,elasticmoduli,
53-54
nephelinite,shearviscosity,215
Nernst-Einstein relation, 186
Newtonian viscosity,crystals,240
nitrates, mineral data, 3
NMR spectroscopy,
Seenuclearmagnetic
resonance spectroscopy
noblegases,bulk moduli,129-130
nuclearmagneticresonance
spectroscopy,
minerals,303-331
nuclides,quadrupolar,NMR parameters,
305-306
olivine
phenomenological
diffusion
orthoclase
orthosilicates
osumilite,M/3ssbauerspectra,338
oxidecomponents,
thermalexpansion,40
oxides,crystalline
AI-27 NMR data, 314-318
O- 17 NMR data, 320
coefficients, 269-270
phlogopite,phasediagrams,248, 261
phosphates
mineral data, 4
M/3ssbauerspectra,342
pigeonite,phasediagrams,254-255
plagioclase,phasediagrams,250-251
Planck function, minerals, 301
plasticdeformation,Seealso
superplastic
deformation
plasticinstability,crystals,238
plasticity,transformation,crystals,
239
platevelocities,mantleviscosity,229
pointdefects,electricalconductivity,
187-188
polarwander,mantleviscosity,231
post-glacialuplift, mantleviscosity,
227, 232
oxides
high temperature
electrical
conductivity,190-192
log electricalconductivityvs.
partialpressure,205
mineral data, 2-3
M/3ssbauer
spectra,
40
nucle,atmagneticresonance
spectroscopy,
303-331
partialmolarheatcapacities,
21
shockwaveequationof state,155-159
thermalexpansion,30-31
vibrations, 297
See also aluminum oxide;
potassiumchloride
dimensionless
parameters,Debye
temperatureand thermalpressure,
79
elastic moduli, 66
mantle mineral data, 84
thermalexpansivity,specificheat,
elastic constants, and
velocities, 74
power-lawcreep,plasticproperties,244
protoenstatite,
phasediagrams,253-254
pseudobrookite,
phasediagrams,259
pyrophyllite,M/3ssbauer
spectra,338
pyroxenes
diffusion, 278-279
iron-titaniumoxide;magnesium
high-temperaturecompression
creep,
244
deformation mechanism, 227-228
oxide;magnesiumaluminumoxide;
M/3ssbauerspectra,338-339
deformationmechanismmap, 241
manganese
oxide
diffusion, 279-280
phasediagrams,248, 253-255
oxygenfugacity
dimensionlessparameters,Debye
crystals,238
quadrupolarcouplingconstant,NMR
temperature
and thermalpressure,
plasticproperties,244
77
spectra,307
elastic moduli, 67
quartz
pargasite,phasediagrams,248, 261
diffusion, 275
high-temperaturecompressioncreep,
periclase,phasediagrams,255
242
phasediagrams,249
peridot,crystal-fieldeffects,298
plasticity,241-242
perovskite
high-temperature
creeplaws,243
spectra,296
high-temperature
compression
creep,
log electricalconductivityvs.
245
staticNMR spectra,306
partialpressure,202-204
mantle mineral data, 85
quasiharmonic
approximation,mantle
Massbauerspectra,338
minerals, 87-89
Massbauerspectra,338
phasediagrams,253,255-256
plasticity,245-246
phasediagrams,248, 255-256
radiativethermalconductivity,
thermalexpansion,38-39
phaserelations,26
minerals, 291
pointdefectmodel,202
phasediagrams,Earth-formingminerals,
248-268
radiative thermal emission, minerals,
point defects,188
301
thermalexpansivity,specificheat,
phasetransformations,
entropy,23-27
elastic constants, and
Ramanspectroscopy,
Earth-forming
phasetransitions,304
crystal-fieldeffects,298
velocities, 71
optical absorptionspectroscopy,
Earth-formingminerals,291-302
Orowan's equation,dislocations,239
phasevelocities,mantleviscosity,
231-232
minerals, 291-302
Rankine-Hugoniot
equations,shock
waves, 172-174
reflectionspectra,minerals,294
Vol. 2
INDEX
time
melts, 209
vs. temperature,212
resonantfrequency,303
rheology,non-Newtonian,melts,215
rheology,plastic,crystals,237-247
rheology,mantleviscosity,227
rhyolite
diffusion, 274, 281-282
shearviscosity,215
ring silicates
M6ssbauerspectra,336-339
nuclearmagneticresonance
spectroscopy,
303-331
phasetransitions,19-27
shockwave equationof state,162-166
thermalexpansion,33-38
vibration of tetrahedra, 293
vibrations, 297
Seealsoamphiboles;chainsilicates;
clinopyroxene;cobaltsilicate;
feldspars;feldspathoids;
framework silicates; iron
silicate;magnesiumsilicate;
manganesesilicate;olivine;
orthopyroxene;orthosilicates;
pyroxenes;ring silicates;sheet
silicates;silicapolymorphs;
See alsocyclosilicates
ringwoodite,Seealsogamma-spinel
ruby,crystal-fieldeffects,298
rutile, phasediagrams,259
sorosilicates
sanidine,phasediagrams,250
sapphirine,
phasediagrams,256
sealevel variations, ice models, 229
seismictomography,mantleviscosity,
229
seismological
studies,coreviscosity,
220
selenides,M/3ssbauer
spectra,341-342
self-diffusion coefficient, 271
semiconductors, 186
serpentine
M6ssbauerspectra,339
phasediagrams,248, 261
shear stress,critical resolved,
crystals,239
shearviscosity,vs. frequency,211
sheet silicates
phasediagrams,248-249
shockwave equationof state,161-162
Si-29 NMR data, 312
silicate melts
hightemperature
electrical
conductivity,201
longitudinalviscosityvs. shear
viscosity,210
silicates,crystalline
AI-27 NMR data, 314-318
Si-29 NMR data, 308-313
silicates
crystallographic
properties,4-8
diffusion, 269-290
hightemperatureelectrical
conductivity,192-200
sillimanite
M6ssbauerspectra,339
phasediagrams,256
smectite,M6ssbauerspectra,339
Sn-119,M6ssbauerspectroscopy,
332-335
sodium chloride
dimensionless
parameters,
Debye
temperatureand thermalpressure,
353
climb-controlledcreep,240
plasticproperties,244
sulfates
mineral data, 4
M/3ssbauerspectra,342
shockwave equationof state,160
thermalexpansion,33
sulfides
M/3ssbauer
spectra,341-342
thermalexpansion,33
superplastic
deformation,crystals,239
taenite,M/3ssbauer
spectra,342
talc, M/3ssbauerspectra,339
tectosilicates, See tektosilicates
tektosilicates, mineral data, 7-8
tellurides
M6ssbauerspectra,341-342
temperature,shockwaves, 175
tetragonalcrystals,elasticmoduli, 50
thermalexpansion
geologicalmaterials,29-44
mantle minerals, 69-74
79
elastic moduli, 66
mantle mineral data, 84
thermalexpansivity,geological
thermalexpansivity,specificheat,
specificheat,mantleminerals,69-74
spinel
AI-27 MAS spectra,319
elastic moduli, 47
high temperatureelectrical
conductivity,192
mantle mineral data, 83
M/3ssbauerspectra,339
phasediagrams,253, 255-256
plasticity,245
Seealsobeta-spinel;gamma-spinel;
ulvospinel
spinquantumnumber,303
standardmaterials,shockwave equation
of state, 168-171
staticcompressiontests,equationsof
state, 98-142
staurolite,M/3ssbauerspectra,339
stishovite,phasediagrams,249, 253
strain, vs. time, 210
stress-strain
materials, 29
thermoelastic
dimensionless
parameters,
mantle minerals, 75-82
thermoelastic
properties,
high-temperature,mantle
minerals, 91-94
tholeiite,shearviscosity,215
tin, M/3ssbauerspectra,343
titanates,phasetransitions,25
titanite
diffusion, 281
M/3ssbauerspectra,339
tracer diffusion coefficient, 271
transmission
electronmicroscopy
high-pressure
minerals,245-246
plasticdeformation,241
quartz,242
tridymite,phasediagrams,249
trigonalcrystals,elasticmoduli,49
tungstates,M/3ssbauerspectra,342
curve
crystals,237
plasticsolid,238
stresscreepcurve,plasticsolid,238
stress exponent
ulvospinel,phasediagrams,259-260
velocity,mantleminerals,69-74
vibrationalspectroscopy
Vol. 2
INDEX
minerals, 291-297
See alsoinfraredspectroscopy;
Raman
spectroscopy
vibrational spectrum,minerals,291
virtification,enthalpy,25
viscoelasticity,melts,209
viscosity,dynamic,outercore,218-226
viscosity,Newtonian,crystals,237
viscosity,non-Newtonian,crystals,237
mantle, 227-236
mantle models, 230
melts, 209-217
pressuredependence,214
temperatedependence,213-214
Seealsolongitudinalviscosity;
Newtonianviscosity;shear
viscosity;volumeviscosity
wuestite,phasediagrams,258-260
X-ray diffractiondata,minerals,1-17
volumeviscosity,vs. frequency,211
wadsleyite,Massbauerspectra,339
water-weakening,quartz,241
water
zeolites
high pressureelectricalconductivity
vs. density,206
phaserelations,27
silicateglasses,324-325
wollastonite,phasediagrams,257