The Effect of Temperature on the Intensity of Reflection of X-Rays from Zinc Crystals

Measurements have been made of the intensity of x-rays reflected from powdered zinc crystals at room temperature and at the temperature of liquid air. The atomic structure factors for the zinc atom at these temperatures are found to depend on the orientation of the particular plane from which the reflection of the x-rays takes place. Planes whose normals make small angles $\psi$ with the $c$ axis of the crystal give abnormally low values of the structure factor, while planes for which $\psi$ is large give high values. From the measurements at the two temperatures the temperature factor for the various planes has been determined and with the aid of this factor the structure factor for the atom at rest has been calculated. The structure factor data for the atom at rest do not lie on a smooth curve as one might expect, but are also found to depend on the value of $\psi$. This indicates that the zinc atoms in the crystal do not possess spherical symmetry but are drawn out in the direction of the $c$ axis. The average structure factor curve obtained experimentally has, however, been found to be in satisfactory agreement with a similar curve obtained from the theoretical charge distribution in the atom. The amplitude of thermal vibration of the atoms along various directions in the crystal has been determined. A comparison is made of the root mean square displacement as determined from the x-ray measurements with the average value obtained from specific heat data and a good agreement is found.