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Comprehensive Guide to Space Groups and Crystallography Techniques in Solid State Physics

Explore the intricacies of crystallography with a focus on space groups and their applications in solid state physics. This guide delves into the essential information found in the International Tables of Crystallography, including the stoichiometry of unit cells, site symmetry of atoms, and solid-solid phase transitions. Learn about diffraction conditions and what to expect in X-ray diffraction (XRD) powder patterns. Comprehensive resources, references, and practical insights are provided to enhance understanding of crystal structures, using BaFe2As2 as a case study.

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Comprehensive Guide to Space Groups and Crystallography Techniques in Solid State Physics

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  1. 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 grouppages… • 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 (http://it.iucr.org/) Bilbao Crystallographic Server (www.cryst.ehu.es) (Comprehensive resources for all space groups)

  2. What can we learn from the International Tables? BaFe2As2 Space Group: I4/mmm Lattice Constants:a = 3.9630 Å c = 13.0462 Å Asymmetric Unit: Ba (2a): 0 0 0 Fe (4d): ½ 0 ¼ As (4e): 0 0 0.3544 c Intensity (Arb. Units) (hkl) Indices h + k + l= even integer (2n) (013) (116) (200) (112) (213) b a (015) (004) (028) (215) (011) (002) 2θ (Cu Kα)

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

  4. Symbolism Point Group of the Space Group Crystal System Space Group Molecules Solids D C B A A A B B C D D C D C ccw σh C4 B A

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