XRD - Ag NPG
XRD - Ag NPG
XRD - Ag NPG
Materials Characterization
Importance of X-ray Diffraction
Basics
Diffraction
X-ray Diffraction
Crystal Structure and X-ray Diffraction
Different Methods
Phase Analysis
Texture Analysis
Stress Analysis
Particles Size Analysis
..
Summary
Materials Characterization
C(Z )
I K Bi (V V k) n
SWL
Use of Filter
Metals
Copper: FCC
-Iron: BCC
Zinc: HCP
Silver: FCC
Aluminium: FCC
Ceramics
SiC: Diamond Cubic
Al2O3: Hexagonal
MgO: NaCl type
Diffraction
Scattering
Interaction with a single particle
Diffraction
Interaction with a crystal
Scattering Modes
0.9
0.8
0.7
0.6
Intensity
0.5
0.4
0.3
0.2
0.1
0
-15 -10 -5 0 5 10 15
1
0.9
0.8
0.7
0.6
Intensity
0.5
0.4
0.3
0.2
0.1
0
-15 -10 -5 0 5 10 15
Minima Maxima
sin n sin 2n 1
n = 1, 2,..
a
n = 0, 1,.. 2a
Youngs Double slit experiment
n=2d.sin in out
n: Order of reflection
d: Plane spacing 2
a
= 2 2 2
h k l
: Bragg Angle
n 1
d sin d
2 sin 2
Geometry of Braggs law
*The term reflection is only notional due to symmetry between incoming and
outgoing beam w.r.t. plane normal, otherwise we are only talking of diffraction.
Reciprocal lattice vectors
Used to describe Fourier analysis of electron concentration
of the diffracted pattern.
x
x y
Reciprocal space
bc
a* Reciprocal lattice of FCC is BCC
a (b c ) and vice versa
ca
b*
a (b c ) 001
a b a
c* 010
a (b c ) b
100
Ewald sphere
1 2
d hkl
1 k'
2 hkl
hkl
k
Ewald sphere
Limiting sphere
Ewald sphere
J. Krawit, Introduction to Diffraction in Materials Science and Engineering, Wiley New York 2001
Two Circle Diffractometer
www.serc.carleton.edu/
Hong et al., Nuclear Instruments and Methods in Physics Research A 572 (2007) 942
NaCl crystals in a tube facing X-ray beam
Powder Diffractometer
(100)
(110)
(111)
(200)
(210)
(211)
(220)
(330)(221)
(310)
(311)
(222)
(320)
(321)
Calculated Patterns for a Cubic Crystal
(400)
(410)
Structure Factor
N
Fhkl f n e 2 i ( hun kvn lwn )
Intensity of the diffracted beam |F|2
1
h,k,l : indices of the diffraction plane under consideration
u,v,w : co-ordinates of the atoms in the lattice
N : number of atoms
fn : scattering factor of a particular type of atom
Permitted Reflections
Zone axis
Transmission Zone axis Reflection
crystal
crystal
Film
Useful for determining lattice parameters with high precision and for
identification of phases
Indexing a powder pattern
Braggs Law
n = 2d sin
0.9
t
B cos B
http://ww1.iucr.org/cww-top/crystal.index.html
Actual Pattern
Phase Identification
Crystal Size
Crystal Quality
Texture (to some extent)
Crystal Structure
Analysis of Single Phase
2() d () (I/I1)*100
27.42 3.25 10
31.70 2.82 100
45.54 1.99 60
53.55 1.71 5
56.40 1.63 30
Intensity (a.u.)
65.70 1.42 20
76.08 1.25 30
84.11 1.15 30
89.94 1.09 5
I1: Intensity of the strongest peak
Procedure
Note first three strongest peaks at d1, d2, and d3
In the present case: d1: 2.82; d2: 1.99 and d3: 1.63
Search JCPDS manual to find the d group belonging to the
strongest line: between 2.84-2.80
There are 17 substances with approximately similar d2 but only 4
have d1: 2.82
Out of these, only NaCl has d3: 1.63
It is NaClHurrah
Specimen and Intensities Substance File Number
2.829 1.999 2.26x 1.619 1.519 1.499 3.578 2.668 (ErSe)2Q 19-443
2.82x 1.996 1.632 3.261 1.261 1.151 1.411 0.891 NaCl 5-628
2.824 1.994 1.54x 1.204 1.194 2.443 5.622 4.892 (NH4)2WO2Cl4 22-65
2.82x 1.998 1.263 1.632 1.152 0.941 0.891 1.411 (BePd)2C 18-225
Caution: It could be much more tricky if the sample is oriented or textured or your goniometer is not
calibrated
Presence of Multiple phases
d () I/I
1
More Complex
Pattern of Cu2O Remaining
3.01 Lines 5
Several permutations combinations possible 2.47 I/I1 72
d () I/I1 d
e.g. d1; d2; and d3, the first three strongest lines () 2.13 28
3.020 9 Observed Normalized
show several alternatives 2.09 * 100
Then take any of the two lines together 2.465 and 100 match 3.01 5 7
1.80 * 52
It turns out that 1st and 3rd strongest lies belong
2.135 37Patternto
2.47
for Cu
72 1.50 20
100
Cu and then all other peaks for Cu1.743 can be 1d () 2.13I/I1 28
1.29 9
39
separated out 2.088 100 1.28 * 18
1.510 27 1.50 20 28
Now separate the remaining lines and normalize 1.808 46 1.22 4
171.278 1.29 9 1.08 * 13 20
the intensities 1.287 20
1.0436 5 0.98 5
phase is Cu2O 1.0674 2 0.98 5 7
0.9038 3 0.91 4
No Strain 2
Uniform Strain
d strain 2
Non-uniform Strain
2
d
Broadeing b 2 2 tan
d
Texture in Materials
Fiber Texture
A particular direction [uvw] for all grains is more or less parallel to
the wire or fiber axis
e.g. [111] fiber texture in Al cold drawn wire
Double axis is also possible
Example: [111] and [100] fiber textures in Cu wire
Sheet Texture
Most of the grains are oriented with a certain crystallographic plane
(hkl) roughly parallel to the sheet surface and certain direction [uvw]
parallel to the rolling direction
Notation: (hkl)[uvw]
Texture in materials
Also, if the direction [u1v1w1]
is parallel for all regions, the
structure is like a single
However, the direction
crystal
[u1v1w1] is not aligned for all
regions, the structure is like a
mosaic structure, also called
as Mosaic Texture
B B
Grazing angle (very small, ~1-5)
Film or Coating
Substrate
B1B2
Diffraction
i.e. from hkl
No Diffraction plane
from hkl
occurs
plane
B1B B2
B
008
0014
006
0016
0010
0012
0022
0018
004
0028
0026
0024
0020
*
Bismuth Titanate thin
films on oriented
Only one type of peaks
2216
It apparent that films
SrTiO3 (110)
are highly oriented
10 20 30 40 50 60 70 80 90
4016/
0416
014
SrTiO3 (111)
10 20 30 40 50 60 70 80 90
o
2 ( )
Degree of orientation
[uvw] corresponding
to planes parallel to
Film the surface
Substrate
Side view
But what if the planes when looked from top have random orientation?
Top view
Pole Figure
SrTiO3 (100) SrTiO3 (110) SrTiO3 (111)
2 1
1
1 2
2
1 3
2 1
1 2 3
1
2 3 2
2
1 3
3 (100) planes
Film inclined at 54.7
to (110) plane,
SrTiO3 (100) Two (100) planes
separated by
inclined at 45 to (110)
120
plane in opposite
directions STO(111)
BNdT(001)
STO [100] 45
54.7
STO(110)
STO(111)
STO(100)
(a.u.)
(a.u.)
FWHM = 0.171
Intensity
B
Intensity
32.432.4 33.0
32.6 32.832.8
17.833.233.2
17.4 17.6 32.6 17.8 18.0
33.0 18.2
17.5 17.6 17.7
() ()
Order Disorder Transformation
Structure factor is dependent on the presence
of order or disorder within a material
Present in systems such as Cu-Au, Ti-Al, Ni-
Fe
Order-disorder transformation at specific
compositions upon heating/cooling across a
critical temperature
Examples: Cu3Au, Ni3Fe
Order Disorder Transformation
Structure factor is dependent on the presence
of order or disorder within a material.
Complete Disorder
Example: AB with A and B atoms
randomly distributed in the lattice
Lattice positions: (000) and ( )
Atomic scattering factor
favj= (fA+fB)
Structure Factor, F, is given by
F = f exp[2i (hu+kv+lw)]
= favj [1+e( i (h+k+l))] A
= 2. favj when h+k+l is even B
= 0 when h+k+l is odd
The expected pattern is like a BCC crystal
Order Disorder Transformation
Complete Order
Example: AB with A at (000) and B at ( )
Disordered Cu3Au
Ordered Cu3Au
Instrumentation
Diffractometer
Source
Optics
Detector
XYZ translation
XY movement to choose
area of interest
X-ray generation
X-ray tube ( = 0.8-2.3 )
Liquid metal
Rotating anode
Small angle anode Large angle anode
http://www.coe.berkeley.edu/AST/srms
Moving charge emits radiation
Electrons at v~c
Reduction in intensity of K
Mono-chromator remove K2
Si Graphite
Beam Profile
Mirror Parallel beam
Source
Soller slit
Detector Mirror
Sample
Para-focusing Source
Detector
Sample
Point focus Source
Detector
Sample
Comparison
Parallel beam Para-focusing
X-rays are aligned X-rays are diverging
Lower intensity for bulk Higher intensity
samples
Higher intensity for small Lower intensity
samples
Instrumental broadening Instrumental broadening
independent of orientation dependent of orientation of
of diffraction vector with diffraction vector with
specimen normal specimen normal
Choose 2 range