X-ray determination of valence-electron charge density and its temperature dependence in indium antimonide

Abstract

Quasiforbidden reflections ($h+k+l=4n+2\mathrm{}$) for the InSb structure are weak but very sensitive to asphericity of valence electrons. A number of these reflections have been measured in perfect crystals of InSb with $\mathrm{Cu}-K\alpha$, at temperatures between 16 and 400°K. The (200) reflection was found 14% greater than the free-atom value at 300°K, an indication of ionic charge transfer from In to Sb. The (222) and (¯ 2 ¯ 2 ¯ 2) differed by 17% at 300°K, whereas they should be rigorously equal for the ZnSe structure. Such a difference is a direct indication of asphericity of the valence electrons. This difference is reduced to 5% for the (442), and vanishes for the (622), which gives useful information concerning the form factor of the valence charge. A phenomenological two-parameter model based on a tetrahedral distortion of the valence charge density and a charge transfer from In to Sb provides excellent fitting with experiment. The bond-charge model with a Gaussian form factor, on the other hand, gave a poorer description than that based on free-atom spherical charge densities. It is found that the difference (222-¯ 2 ¯ 2 ¯ 2) changes gradually with temperature, from 41% at 16°K to 13% at 400°K. Such a variation cannot be explained by attributing a Debye-Waller factor different from that of the core to the valence charge. We have interpreted this result by assuming that the amount of tetrahedral distortion and charge transfer vary with temperature.