Temperature Dependence of the Debye-Waller Factor of Platinum

Abstract

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