Temperature dependence of positron annihilation in tin

Abstract

The Doppler broadening of the positron annihilation line in tin has been studied as a function of temperature in the range 295-640 K. The line shape was measured with an intrinsic germanium spectrometer and was analyzed in terms of a parameter $S$ which measures the peak-to-area ratio. A slow linear rise of $S$ with temperature $T$, $S=0.511(1+32\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}T)$ was observed up to $T=420\ifmmode\pm\else\textpm\fi{}10$ K followed by a steeper rise at higher temperatures. If this steeper rise is attributed to the onset of thermal vacancy effects, the monovacancy formation enthalpy ${H}_{1v}^{F}$ can be calculated using the semiempirical relationship ${H}_{1v}^{F}=14{k}_{B}{T}_{t}$ where ${k}_{B}$ is the Boltzmann constant and ${T}_{t}$ the threshold temperature for the appearance of thermal vacancies. A value ${H}_{1v}^{F}=0.51\ifmmode\pm\else\textpm\fi{}0.01$ eV is obtained. At the melting point, $S$ is found to increase abruptly and remain essentially constant thereafter. Cyclings of the sample temperature around the melting point revealed a large hysteresis effect, which is attributed to supercooling.