Intensity Distribution in X-Ray and Electron Diffraction Patterns. X-Ray Atom Factors of Zinc in Zinc Oxide and Chemical Binding

Abstract

Electron diffraction patterns of zinc oxide show intensities markedly deviating from the ones calculated under the assumption of a spherically symmetrical electron distribution in the atom. Possible explanations were suggested on the basis of a shift of the electron cloud with respect to the nucleus, a distortion of the crystal lattice, a distortion of the electron cloud, and particularly of the valence electrons, or effects of dynamical reflection of the electron waves not taken into account in the kinematic theory. For a final decision between these possibilities, x-ray diffraction patterns from a flat sample of zinc oxide have been obtained photographically, with monochromatic Cu $K\alpha$ radiation, and the relative intensities measured. From these results it is possible to calculate the x-ray atom factors for zinc, and thus to construct theoretical electron diffraction curves. These reproduce the essential features of the electron diffraction experiments of K. Lark-Horovitz and H. J. Yearian. Therefore, the observed intensity anomaly must be due to anomalous $F$ factors in the expression for electron diffraction intensity ${\mathrm{}(Z-F)\mathrm{}}^2{\left[\frac{\left(sin\theta \right)}{\lambda }\right]}^{-4\mathrm{}}$ rather than to effects of dynamical reflection neglected in the kinematic theory. This is also in agreement with the explanation by James and Johnson since the x-ray intensities of our experiments are in better agreement with the theoretical values obtained by using the distorted charge distribution as calculated by James and Johnson, than they are with values based upon the symmetrical distribution of Pauling and Sherman. Discrepancies at larger values of $\frac{\left(sin\theta \right)}{\lambda }$ are discussed in connection with temperature and order-disorder effects: the combination of electron diffraction and x-ray patterns allows one to distinguish between intensity anomalies due to distortion of the electron cloud and effects due to some other factors such as order-disorder.