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

CuGaS2 and CuInS2 are typical AIBIIIC2VI 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 AIBIIIC2VI chalcopyrites. The sublattice distortion in AIIBIVC2V 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.