Transcript Document
Physics 590
“International Tables of Crystallography”
“Everything you wanted to know about beautiful flies, but were afraid to ask.”
Schönflies
Gordie Miller (321 Spedding) Proposed Plan
(1) What basic information is found on the
space group
pages… (2) Stoichiometry of the unit cell (Wyckoff sites) (3) Site (point) symmetry of atoms in solids (4) Solid-solid phase transitions (group-subgroup relationships) (5) Diffraction conditions – what to expect in a XRD powder pattern.
References
Space Groups for Solid State Scientists
, G. Burns and A.M.Glazer
(Little mathematical formalism; prose style)
International Tables for Crystallography
( http://it.iucr.org/ )
Bilbao Crystallographic Server
( www.cryst.ehu.es
) (Comprehensive resources for all space groups) 1
What can we learn from the International Tables?
BaFe
c
2
As
2 Space Group: I4/mmm Lattice Constants: a = 3.9630 Å c = 13.0462 Å Asymmetric Unit: Ba (2a): Fe (4d): 0 ½ As (4e): 0 0 0 0 0 ¼ 0.3544
Intensity (Arb. Units) (hkl) Indices h + k + l = even integer (2n) (013)
a b
(002) (004) (011) (112) (200) (116) (213) (015) (215) (028) 2θ (Cu Kα)
2
Typical
Space Group
Pages…
Symbolism Point Symmetry Features Stoichiometry Structure of Unit Cell Diffraction Extinction Conditions Subgroup/Supergroup Relationships
3
Symbolism Point Group of the Space Group Crystal System
S
4
Space Group
Symmetry Operation
Proper Rotation (by 2π/
n
) Identity Inversion (
x
,
y
,
z
) (–
x
,–
y
,–
z
) Mirror plane Principal Axis Mirror plane Principal Axis Improper Rotation
Molecules Schönflies Notation
C n
(
C E = C
1 2 ,
C
3 ,
C
4 , …)
i = S
2
h
v
,
= S
1
d
(=
S n
=
h
S
1 )
C n
(
S
3 ,
S
4 ,
S
5 , …)
Solids International Notation
“
n
” (2, 3, 4, …) 1 1
/m
(
n/m
is the designator)
m =
2
n n
(3, 4, 5, )
D
vs. 4 :
B A B A B C A
S
4
4 3 C C
C
4 ccw D
σ
h
D C A D B 4
S
4 3
4