Effect of Vacancy Diffusion on Mössbauer Line Broadening

Recent Mössbauer-effect experiments on iron in copper and iron in gold indicate that the line broadening due to diffusion is about a factor of 2 smaller than the value predicted by the independent-jump model of Singwi and Sjölander. A model for vacancy diffusion is advanced which results in Mössbauer spectra that are Lorentzian in shape with a broadening $\Delta \epsilon$ that is proportional to the average diffusive jump rate ${\tau }_D^{-1\mathrm{}}$, as is also the case for the independent-jump model. The slope of $\Delta \epsilon$ vs ${\tau }_D^{-1\mathrm{}}$ is related to the probability for a vacancy to dissociate completely from a Mössbauer atom and can be inferred from the correlation factor. The model indicates that the broadening can range from 0 in the highly correlated limit to a value less than $2\hslash {\tau }_D^{-1\mathrm{}}$ in the uncorrelated limit.