Fisika Zat Padat I: Dosen: Dr. Iwantono, M.Phil Jurusan Fisika Fmipa-Ur
Fisika Zat Padat I: Dosen: Dr. Iwantono, M.Phil Jurusan Fisika Fmipa-Ur
Fisika Zat Padat I: Dosen: Dr. Iwantono, M.Phil Jurusan Fisika Fmipa-Ur
SISTEM KRISTAL
Kita tahu bahwa kisi ruang tiga dimensi
dibentuk dari pengulangan tiga vektor
translasi
non-coplanar
a,
b,
c.
Berdasarkan
parameter
kisi
kita
mempunyai 7 sistem kristal populer.
Bravais memperlihatkan bahwa titik
identik pada 7 sistem kristal dapat di atur
secara spasi membentuk 14 jenis pola
regular yang dikenal dengan Kisi Bravais
SISTEM KRISTAL
Crystal system
Cubic
a= b=c
= ==90
Tetragonal
a = b c
= ==90
Orthorhombic a b c
= ==90
Monoclinic
abc
= =90
Triclinic
abc
90
Trigonal
a= b=c
= =90
Hexagonal
a= b c
==90
=120
14 BRAVAIS LATTICES
S.No
Crystal Type
Symbol
Cubic
Bravais
lattices
Simple
Tetragonal
Body
centred
Face
centred
Simple
Orthorhombic
Body
centred
Simple
Base
centred
2
3
4
5
6
7
F
P
8
9
10
Body
centred
Face
centred
Monoclinic Simple
11
I
F
P
12
Triclinic
Base
centred
Simple
13
Trigonal
Simple
14
Hexgonal
Simple
a1= a2 =a3
a1 a 2 a 3
a1
(4,3)
(0,0)
5a + 3b
b
a
[001]
[011]
[101]
[010]
[111]
[1 10]
[100]
[110]
Family of directions
Index
<100>
3x2=6
<110>
6 x 2 = 12
<111>
4x2=8
Symbol
Alternate
symbol
[]
<>
[[ ]]
Particular direction
Family of directions
(0,3,0)
(2,0,0)
Intercepts 1
Plane (100)
Family {100} 3
Intercepts 1 1
Plane (110)
Family {110} 6
Intercepts 1 1 1
Plane (111)
Family {111} 8
(Octahedral plane)
(111)
Family of {111} planes within the cubic unit cell
d111 a / 3 a 3 / 3
The (111) plane trisects the body diagonal
Direction
number of parts
[100]
[010]
[001]
(100)
[011]
(k + l)
(010)
[101]
(l + h)
(001)
[110]
(h + k)
[111]
(h + k + l)
The portion of the central (111) plane as intersected by the various unit cells
Summary of notations
Alternate
symbols
Symbol
Direction
Plane
Point
[]
[uvw]
<>
<uvw>
()
(hkl)
{}
{hkl}
..
.xyz.
::
:xyz:
Particular direction
Family of directions
Particular plane
(( ))
Family of planes
[[ ]]
Particular point
Family of point
[[ ]]
d hkl
a
h k l
2
Condition
h even
midpoint of a
(k + l) even
(h + k + l) even
body centre
midpoint of body diagonal
Index
Number of
members in a
cubic lattice
(100)
(110)
(111)
(210)
6
12
8
24
(211)
(221)
(310)
24
24
24
(311)
(320)
(321)
24
24
48
dhkl
d100 a
d110 a / 2 a 2 / 2
d111 a / 3 a 3 / 3
Multiplicity factor
Cubic
Hexagonal
Tetragonal
Orthorhombic
Monoclinic
Triclinic
hkl
48*
hk.l
24*
hkl
16*
hkl
8
hkl
4
hkl
2
hhl
24
hh.l
12*
hhl
8
hk0
4
h0l
2
hk0
24*
h0.l
12*
h0l
8
h0l
4
0k0
2
hh0
12
hk.0
12*
hk0
8*
0kl
4
hhh
8
hh.0
6
hh0
4
h00
2
h00
6
h0.0
6
h00
4
0k0
2
* Altered in crystals with lower symmetry (of the same crystal class)
00.l
2
00l
2
00l
2
c
a
Kemasan optimum
(0,433a)
I)
a1 1 a x y z
2
1 a x y z
a
2 2
a 1 a x y z
3 2
face-centered cubic
a1 ax
a 2 ay
a az
3
a1 1 a x y
2
1
a 2 2 a y z
a 1 a z x
3 2
a1 1 a x y z
2
body-centered cubic
1 a x y z
a
2 2
a 1 a x y z
3 2
0.74
FCC
(0,3535a)
HEXAGONAL SYSTEM
40
Triclinic (Simple)
90
o
a b c
Monoclinic (Simple)
= = 90o, 90o
a b c
ORTHORHOMBIC SYSTEM
Orthorhombic (FC)
= = = 90o
a b c
TETRAGONAL SYSTEM
Tetragonal (P)
= = = 90o
a = b c
Tetragonal (BC)
= = = 90o
a = b c
RHOMBOHEDRAL (R) OR
TRIGONAL
DIAMOND STRUCTURE
C, Si, Ge, -Sn
45
Crystal Structures of
Elements
Kittel, pg. 23
46
Intercepts 1 1 -
Plane (1 1 2 0)
(h k i l)
i = (h + k)
a2
a1
a3
a2
a1
Intercepts 1 -1
Intercepts 1 -1
Miller (1 1 0 )
Miller (0 1 0)
Miller-Bravais (1 1 0 0 )
Miller-Bravais (0 1 1 0)
a3
a2
Intercepts 1 -2 -2
Plane (2 1 1 0 )
a1
Intercepts 1 1 -
Plane (1 1 2 0)
Intercepts 1 1 - 1
Plane (1 1 2 1)
Intercepts 1 1 1
Plane (1 0 1 1)
Directions Directions are projected onto the basis vectors to determine the components
[1120]
a1
a2
a3
Projections
a/2
a/2
Normalized wrt LP
1/2
1/2
Factorization
Indices
[1 1 2 0]
X-RAY DIFFRACTION
XY = a sin
X
Diffracted light
a sin = n
X-ray
Tube
Incident radiation
Reflected radiation
1
2
Z
Y
Transmitted radiation
Incident radiation
Reflected radiation
1
2
Z
Y
Transmitted radiation
2d sin = n
Braggs Law
e.g. X-rays with wavelength 1.54 are reflected from planes with d=1.2.
Calculate the Bragg angle, , for constructive interference.
= 1.54 x 10-10 m,
2d sin n
n
sin
2d
1
d = 1.2 x 10-10 m, =?
n=1 :
= 39.9
n=2 :
2d sin = n
We normally set n=1 and adjust Miller indices, to give
2dhkl sin =
(n/2d)>1
(2 0 0) reflection, d=2.5
n=1,
=17.93o
n=2,
=38.02o
n=3,
=67.52o
no reflection for n4
2d sin = n
or
2dhkl sin =
1 h k l
2
2
2
2
d
a
b c
2
1 h k l
2
d
a2
2
d 18
2
11 0
0.056
2
6
d = 4.24
d = 4.24
n
sin
2d
1
n=1:
= 10.46
= (1 1 0)
n=2:
= 21.30
= (2 2 0)
n=3:
= 33.01
= (3 3 0)
n=4:
= 46.59
= (4 4 0)
n=5:
= 65.23
= (5 5 0)
2dhkl sin =
SEKIAN
TERIMAKASIH