Experimental Investigations of Bonding Charges in Diamond and Zinc Blende Structures

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Abstract
A major source of information concerning bonding charges in diamond structures is provided by the weak non-zero forbidden reflections of the type: h + k + l = 4n + 2. In the early determinations of the (222) a lot of attention was devoted to perturbing effects such as "Umweganregung" and lattice defects. Neutron and X-ray diffraction measurements confirmed the electronic origin of the (222) intensity, and established the existence of anharmonic contributions at temperatures above R.T., particularly in the case of the (442) in Si. A non-zero (222) intensity was also found in grey-tin. "Pendellösung" techniques can also be applied, especially in conjunction with high intensity X-ray sources. In the case of III-V semiconducting compounds, such as InSb, reflections for which h + k + l = 4n + 2 are not completely forbidden. They are still interesting for bonding charge density studies, however. Reflections like (200), for example, when compared with the free-atom value, provide information about charge transfer and, or, interstitial charges placed off center along the bond. Reflections like (222) and (2̄2̄2̄) are found different whereas they should be rigorously equal, even considering the violation of Friedel's law owing to anomalous dispersion. Such a difference is a direct indication of asphericity of the valence electrons. 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. It is also found that the difference (222-2̄2̄2̄) decreases gradually with temperature, between 400 K and 16 K. We have interpreted this result by assuming that the amount of tetrahedral distortion and charge transfer vary with temperature.