Anisotropy in the Atomic Vibrations of Zinc Crystals. I. Evidence from X-Ray Scattering

The results of Brindley's recent experiments on the intensity of the various reflections of Cu $K\alpha$ x-rays from powdered zinc crystals are compared with the results of the measurements made by the authors on the diffuse scattering of x-rays from single zinc crystals. When the method of diffuse scattering is used it is possible to obtain $S$ values for various orientations of the crystal for a given value of $\frac{\left(sin\frac{1}{2}\phi \right)}{\lambda }$. The form of Zener's formula for $M$ for hexagonal crystals is confirmed by our experimental results. We find the root-mean-square thermal displacements of the atoms to be 0.172 and 0.093A, respectively, along and perpendicular to the $c$ axis. These are greater than Brindley's values. They nearly explain the large difference between the $F$ values for the (0002) and ($10\overline{1}0$) reflections. These two reflections possibly give some evidence of asymmetry in the electron structure of the zinc atoms, the structure being more diffuse in the direction of the $c$ axis than normal to this direction.