Structural dependence of birefringence in the chalcopyrite structure. Refinement of the structural parameters of ZnGeP2 and ZnSiAs2

Abstract

We have found that, as a consequence of the experimentally observed geometrical regularity of the BC₄ tetrahedra in ${\mathrm{A}}^{\mathrm{II}}{\mathrm{B}}^{\mathrm{IV}}{\mathrm{C}}_2^{\mathrm{V}}$ crystals with the chalcopyrite structure, the birefringence of the crystals depends on the anisotropic polarizability of the $\mathrm{A–C}$ bonds only. This has allowed us to predict the birefringence of several ${\mathrm{A}}^{\mathrm{II}}{\mathrm{B}}^{\mathrm{IV}}{\mathrm{C}}_2^{\mathrm{V}}$ crystals for which reliable experimentally determined values are not available. To provide additional crystal structure data, as required for the predictions, we have refined the structural parameters of ZnGeP₂ and ZnSiAs₂ by the method of least squares with counter measured single crystal x‐ray diffraction data; the positional parameters (estimated standard errors in parentheses) are x_P=0.25816 (0.00044) and x_As=0.26575 (0.00012). Final values of the conventional agreement index R were 0.029 and 0.022 for ZnGeP₂ and ZnSiAs₂, respectively. The GeP₄ and SiAs₄ tetrahedra are regular within experimental error. Experimentally determined bond distances are: $\mathrm{Zn–P}\text{,\hspace{0.17em}2.375\hspace{0.17em} (0.002)\hspace{0.17em} Å;\hspace{0.17em}}\mathrm{Ge–P}\text{,\hspace{0.17em}2.324\hspace{0.17em} (0.002)\hspace{0.17em} Å;\hspace{0.17em}}\mathrm{Zn–As}\text{,\hspace{0.17em}2.454\hspace{0.17em} (0.001)\hspace{0.17em} Å;\hspace{0.17em}}\mathrm{and}\hspace{0.17em}\mathrm{Si–As}\text{,\hspace{0.17em}2.352\hspace{0.17em} (0.001)\hspace{0.17em} Å}$ .