Temperature Dependence of the Debye-Waller Factor of Platinum

Abstract

The Mössbauer absorption spectrum of the 99-keV gamma ray of ${\mathrm{Pt}}^{195}$ in platinum metal has been studied from 20 to 100°K. In a separate experiment to be published later, the internal-conversion coefficient $\alpha$ was found to be $\alpha =7.2\mathrm{}\pm 0.7$. Using this value of $\alpha$ the fraction of recoilless emission $f_s$ and recoilless absorption $f_a$ are $f_s\left(20\mathrm{}°\mathrm{K}\right)=0.089\mathrm{}\pm 0.002$, $f_s\left(77\mathrm{}°\mathrm{K}\right)=0.021\mathrm{}\pm 0.003$, and $f_a\left(20\mathrm{}°\mathrm{K}\right)=0.129\mathrm{}\pm 0.008$, $f_a\left(77\mathrm{}°\mathrm{K}\right)=0.043\mathrm{}\pm 0.011$. The half-life of the 99-keV level is ${\tau }_{\frac{1}{2}}=(1.7\mathrm{}\pm 0.2){10}^{-10\mathrm{}}$ sec in agreement with the electronic measurement ${\tau }_{\frac{1}{2}}\approx 1.4\times {10}^{-10\mathrm{}}$ sec. The Debye temperature ${\theta }_{\mathrm{DW}}$ determined from the Debye-Waller factor is in good agreement with a calculation based on the quasi-harmonic approximation. The Debye temperature extrapolates to ${\theta }_{\mathrm{DW}}=(234\mathrm{}\pm 6)°$K at 0°K and is essentially independent of temperature up to 100°K.