The Effect of Valence Electrons and Electron Cloud Distortion upon Intensities in Electron and X-Ray Scattering (Applied to Zinc Oxide)

Abstract

An extensive investigation of electron scattering by zinc oxide has been carried out by Lark-Horovitz and Yearian. The intensity distribution, determined by photographic methods, showed marked anomalies with respect to the intensity distribution of the corresponding x-ray pattern. The visually estimated x-ray intensities seem to be in general agreement with values calculated from approximate Fermi or Pauling-Sherman wave functions, and the marked anomalies appear only in the electron diffraction pattern. The observed intensities have been formally accounted for by assuming a polarization of the $M$ shell of the zinc atom. This hypothesis has been tested by calculating the charge distribution of the $M$ shell in zinc under the effect of the electrostatic fields arising from a partly ionic character of the lattice and its deviation from perfect tetrahedral symmetry. The calculated distortion is too small by a factor of 1/160 to account alone for the observed anomalies. Then the effect due to the valence electrons is considered. A rough agreement with experimental values is obtained with a model in which two valence electrons of each zinc-oxygen pair of nearest neighbors are assumed to be placed in a uniform linear distribution between these neighboring nuclei and the other two in a uniform distribution through the crystal. A more refined model, in which two valence electrons of each zinc-oxygen pair of nearest neighbors are assumed to be distributed over the surface of an ellipsoid with major axis axis along the $c$ axis of the crystal, accounts for the principal anomalies in the electron diffraction intensities, and at the same time gives results which are in agreement with measured x-ray intensities. The importance of the method used as a tool for determining the type of binding in a crystal is discussed.