Piezoelectric nonlinear optic CuGaS2 and CuInS2 crystal structure: Sublattice distortion in AIBIIIC2VI and AIIBIVC2V type chalcopyrites

CuGaS₂ and CuInS₂ are typical ${\mathrm{A}}^{\mathrm{I}}{\mathrm{B}}^{\mathrm{III}}{\mathrm{C}}_2^{\mathrm{VI}}$ members of the chalcopyrite structure family. The lattice constants of tetragonal CuGaS₂ are a = 5.34741 ± 0.00007 and c = 10.47429 ± 0.00006 Å at 298 °K, and of CuInS₂ are a = 5.52279 ± 0.00007 and c = 11.13295 ± 0.00022 Å at 298 °K. Both materials have four formulas in a unit cell with space group I 42d. A total of 984 reflections for CuGaS₂ and 1413 for CuInS₂ were measured with PEXRAD, and the resulting 134 symmetry‐independent CuGaS₂ and 310 CuInS₂ structure factors, in least‐squares refinement, led to final agreement factors of 0.029 and 0.038, respectively. Both materials are slightly nonstoichiometric. Final x coordinates are 0.2593 ± 0.0004 for CuGaS₂ and 0.2295 ± 0.0004 for CuInS₂. As was also found with AgGaS, these values are significantly different from those expected for a geometrically regular B atom tetrahedron. The resulting sublattice distortion is predictable from a linear sum of atomic electronegativities, which is also used to predict the x coordinate and interatomic bond lengths in 17 other ${\mathrm{A}}^{\mathrm{I}}{\mathrm{B}}^{\mathrm{III}}{\mathrm{C}}_2^{\mathrm{VI}}$ chalcopyrites. The sublattice distortion in ${\mathrm{A}}^{\mathrm{II}}{\mathrm{B}}^{\mathrm{IV}}{\mathrm{C}}_2^{\mathrm{V}}$ chalcopyrites is generally small, but also significant. The experimental Cu–S distance is 2.312 ± 0.001 Å in CuGaS₂ and 2.335 ± 0.001 Å in CuInS₂, the Ga–S distance is 2.288 ± 0.001, and In–S is 2.464 ± 0.002 Å. The amplitudes of thermal vibration for the A and B atoms in AgGaS₂, CuGaS₂, and CuInS₂ are essentially isotropic, with considerable anisotropy in the C atom motion.