1. “International Tables of Crystallography”
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
What basic information is found on the space group pages…
Stoichiometry of the unit cell (Wyckoff sites)
Site (point) symmetry of atoms in solids
Solid-solid phase transitions (group-subgroup relationships)
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 (
Bilbao Crystallographic Server (
(Comprehensive resources for all space groups)

2. BaFe2As2 What can we learn from the International Tables? c b a
Space Group: I4/mmm
Lattice Constants: a = Å
c = Å
Asymmetric Unit:
Ba (2a): 0 0 0
Fe (4d): ½ 0 ¼
As (4e): a b c
Intensity
(Arb. Units)
(hkl) Indices
h + k + l = even integer (2n)
(013)
(112)
(200)
(116)
(213)
(015)
(004)
(215)
(028)
(002)
(011)
2θ (Cu Kα)

3. Typical Space Group Pages…
Symbolism
Diffraction
Extinction
Conditions
Point Symmetry Features
Stoichiometry
Structure of Unit Cell
Subgroup/Supergroup
Relationships

4. C4 σh 𝟏 Symbolism Molecules Solids Symmetry Operation
Point Group of
the Space Group
Crystal
System
Space Group
Molecules
Solids
Symmetry Operation
Schönflies Notation
International Notation
Proper Rotation (by 2π/n)
Cn (C2, C3, C4, …)
“n” (2, 3, 4, …)
Identity
E = C1 1
Inversion (x,y,z)  (–x,–y,–z)
i = S2
Mirror plane  Principal Axis
h = S1
/m (n/m is the designator)
Mirror plane  Principal Axis
v , d (= S1)
m =
Improper Rotation
Sn = h  Cn (S3, S4, S5, …) D C B A B A B A C D C D D
ccw C C4 σh 𝟏 A B