In this chapter, the crystal structures of sulfides and related chalcogenide compounds (involving Se, Te, As and Sb as well as S) are reviewed with emphasis on mineral phases but with some discussion of related synthetic compounds. Before presenting a systematic account of the principal families, relevant crystal chemical concepts are discussed, and structural classification schemes for these phases are reviewed.

### Crystal chemical concepts

#### Chalcogenide ions.

Chalcogens differ from oxygen by their moderate electronegativity. The Pauling electronegativity of oxygen is 3.44, whereas that of S is 2.58, Se 2.55, and Te 2.1 (Emsley 1994). The Shannon crystal radius of O2− is 1.40 A, that of S2− 1.70 A, Se2− 1.84 A, and Te2− 2.07 A (Shannon 1981). We have estimated the radius of As3− as about 1.78 A, and that of Sb3− as 1.89 A, based on the structures of selected sulfide-pnictides. The difference in polarizability of chalcogens and oxygen is of great structural importance. The electric polarizability (i.e., the value expressing the displacement of the electron cloud relative to the nucleus) is 3.88 × 10−24 cm3 for O2−, but it is 10.2 × 10−24 cm3 for S2−, 10.5 × 10−24 cm3 for Se2−, and 14.0 × 10−24 cm3 for Te2− (Pauling 1927). The polarizability values can also be interpreted as expressing covalency trends of anion-cation bonds and anion-anion interactions in the structure.

The difference between oxygen and chalcogens leads to differences in crystal chemistry of oxides and chalcogenides for nearly all element combinations, exceptions being very few. Structural features of certain chalcogenide categories are in common with hydroxides, which have low-charge and polarizable OH− groups; this is true especially for layer-like structures. There are greater similarities between the above values for S …

Crystal Structures of Sulfides and Other Chalcogenides

Values of crystalline‐solid Debye temperatures depend both on the method and temperature of measurement. Simple relationships between Debye temperatures and such cohesive properties as compressibility and melting point were derived over 60 years ago by Madelung, by Einstein, and by Lindemann. Debye temperatures ΘXR of a number of piezoelectric semiconductors with chalcopyrite structure have been determined at room temperature by x‐ray diffraction. A new series of heat capacity measurements over the temperature range 1.2–40 °K, for four chalcopyrites, give ΘD values at 0 °K. A common proportionality is found between each of these ΘXR and ΘD values and microhardness, and also melting point: Acceptable reproducibility is given for the AIBIIICVI2 chalcopyrites and, separately, the AIIBIVCV2 compounds. Values of Θ are predicted for 15 additional chalcopyrites. Excellent proportionality between Θelastic and compressibility is found for the europium chalcogenides, based on the data of Shapira and Reed.

Debye temperatures and cohesive properties

The crystal structures of CuInSe2 and CuInTe2

Grain boundaries (GBs) in polycrystalline Cu(In,Ga)Se 2 thin fi lms exhibit only slightly enhanced recombination, as compared with the grain interiors, allowing for very high power-conversion effi ciencies of more than 20% in the corresponding solar-cell devices. This work highlights the specifi c compositional and electrical properties of Cu(In,Ga)Se 2 GBs by application of appropriate subnanometer characterisation techniques: inline electron holography, electron energy-loss spectroscopy, and atom-probe tomography. It is found that changes of composition at the GBs are confi ned to regions of only about 1 nm in width. Therefore, these compositional changes are not due to secondary phases but atomic or ionic redistribution within the atomic planes close to the GBs. For different GBs in the Cu(In,Ga)Se 2 thin fi lm investigated, different atomic or ionic redistributions are also found. This chemical fl exibility makes polycrystalline Cu(In,Ga)Se 2 thin fi lms particularly suitable for photovoltaic applications.

Confined and Chemically Flexible Grain Boundaries in Polycrystalline Compound Semiconductors

Optical properties of Cu(In,Ga)Se2 and Cu2ZnSn(S,Se)4

CuGaSe2 and CdGeAs2 crystallize in the chalcopyrite‐type structure. The lattice constants of tetragonal CuGaSe2 are a = 5.5963 ± 0.0001 and c = 11.0036 ± 0.0002 A at 298 °K, those of CdGeAs2 are a = 5.9432 ± 0.0001 and c = 11.2163 ± 0.0003 A at 298°K. The space group is I42d with four formulas in a unit cell. 1747 reflections were measured with PEXRAD for CuGaSe2 and 1892 for CdGeAs2 using MoKα x radiation. Least squares refinement of the structural parameters using 149 symmetry‐independent CuGaSe2 and 300 CdGeAs2 structure factors led to final agreement factors of 0.035 and 0.038, respectively. CuGaSe2 is slightly Cu deficient: the value of the x coordinate in the final model is 0.2431 ± 0.0002, with considerable vibrational anisotropy. CdGeAs2 is stoichiometric: the final model has x = 0.2785 ± 0.0002, also with significant vibrational anisotropy, but less than that in CuGaSe2. The two compounds confirm the pattern of sublattice distortion in AIBIIIC2VI and AIIBIVC2V chalcopyrites previously found. The...

S. C. Abrahams

Papers

Piezoelectric nonlinear optic CuGaSe2 and CdGeAs2: Crystal structure, chalcopyrite microhardness, and sublattice distortion