An X-Ray Method of Determining Rates of Diffusion in the Solid State

Abstract

Gold and copper were simultaneously deposited in vacuum by vaporization on a plate of glass, the copper being deposited at a uniform rate while the gold was deposited in one hundred stratified layers in the copper by alternately raising and lowering the temperature of the molybdenum vaporizing trough containing the boiling gold. The translucent deposit so formed had a total thickness of about 10,000A and hence an average interplanar distance of 100A. In an especially constructed constructed x-ray spectrograph selective diffraction of Mo K radiation from these stratified films was observed corresponding to the artificially imposed periodicity of the stratification and the intensity of this diffracted image relative to the direct beam was found to fall off with time so as to indicate a "half-life" for the stratified structure of about two days. This suggests a general method for the study of average rates of diffusion and the determination of diffusion coefficients of solids in solids by utilizing the decay of such stratified films. Simple theoretical considerations should, through the action of diffusion alone, rapidly and automatically lose the higher Fourier harmonics of its periodic density distribution function and retain the fundamental in such a way as to render the determination of the diffusion coefficient quite accurate. The observed behavior of the diffracted maxima seem to support these expectations as does also the absence of any intensity in higher orders than the first. This purification by diffusion probably takes place principally during the depositing process itself while the temperatures are still quite high. Formulae are derived relating the observed rate of decay of the diffracted intensity, the artificial "grating coefficient" of the strata, and the diffusion coefficient. The method seems especially promising for substances and temperatures where diffusion is so slow as to be otherwise quite unobservable because the diffusion time varies as the square of the distance over which atoms must migrate and in this method these distances are so many orders of magnitude smaller than in any other.