X-Ray Dispersion and Atomic Electron Cloud Distortion in Zinc Crystals

Monochromatic x-rays of wave-lengths 1.54A ($\mathrm{Cu} K\alpha$) and 1.433A ($\mathrm{Zn} K\alpha$) were diffusely scattered at angles $\phi$ varying from 24° to 120° from single crystals of zinc (${\lambda }_K=1.28\mathrm{}\mathrm{A}$) whose orientation angles $\psi$ were 0° and 90°. The intensity of the diffusely scattered rays was found to vary with $\frac{\left(sin \frac{1}{2}\phi \right)}{\lambda }$ according to Jauncey's theoretical formula for the region of wave-lengths close to the $K$ critical absorption wave-length of the scattering crystal. In the case of the scattering of $\mathrm{Cu} K\alpha$ rays the decrement $\Delta f$ in the atomic structure factor was 2.5 as compared with Hönl's value of 2.3. For the less intense $\mathrm{Zn} K\alpha$ rays $\Delta f$ was 3.65 as compared with Hönl's value of 2.8. The difference in the latter case is probably due to experimental error. More interesting was the "dip" or "valley" found in the diffuse scattering $S(\psi =0^{\circ })$ values in the region of $\frac{\left(sin \frac{1}{2}\phi \right)}{\lambda }=0.3\mathrm{}{\mathrm{A}}^{-1\mathrm{}}$. After considering various possible causes for this dip, it was finally decided that the cause of the dip is a corresponding dip in the atomic structure factor $f(\psi =0^{\circ })$ values in this region. The maximum difference, $f(\psi ={90}^{\circ })-f(\psi =0^{\circ })$ is about 6 electrons. This is greater than the previous value of 2.4 electrons and indicates a larger and deeper distortion of the electron cloud of a zinc atom in the crystal than had previously been imagined.