Temperature dependence of positron annihilation in tin

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 $T$, $S=0.511(1+32\mathrm{}\times {10}^{-6\mathrm{}}T)$ was observed up to $T=420\mathrm{}\pm 10$ 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 $H_{1v}^F=14\mathrm{}{k}_B{T}_t$ where $k_B$ is the Boltzmann constant and $T_t$ the threshold temperature for the appearance of thermal vacancies. A value $H_{1v}^F=0.51\mathrm{}\pm 0.01$ 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.