Linear-thermal-expansion measurements on potassium metal from 2 to 320 K

Abstract

A differential capacitance dilatometer has been used to obtain linear-thermal-expansion measurements on free-standing samples of high-purity potassium metal from 2 to 320 K. The low-temperature results are consistent with a free-electron calculation of the electronic contribution to the thermal-expansion coefficient, while the lattice contribution can be represented by a Gr\"uneisen parameter $\ensuremath{\gamma}$ which varies slowly with temperature from approximately 0.90 at $T=0 \mathrm{to} 1.24$ near the melting point, in agreement with $\ensuremath{\gamma}'\mathrm{s}$ as calculated from high-pressure elastic-constant data. Slight inconsistencies (1% or so) were found for temperatures between 20 and 30 K, and between 100 and 200 K, which are believed to be traceable to the thermal history of the samples. A summary of existing bulk-modulus data is given for use with the $\ensuremath{\gamma}$ calculations. The data are normalized to published bulk-density measurements at 300 K, and the resulting $T=0$ molar volume (43.21 \ifmmode\pm\else\textpm\fi{} 0.02 ${\mathrm{cm}}^{3}$/mole) can be used with the free-electron model to calculate a de Haas-van Alphen frequency which is in excellent agreement with direct determinations. When the smoothed linear-thermal-expansion coefficients are used to calculate ${C}_{V}^{\mathrm{lat}}(T)$ from published results for ${C}_{p}(T)$, anharmonic effects (${C}_{V}$ proportional to $T$) are evident above 100 K, while vacancy effects become important above 250 K.