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