Thermal Expansion of Alkali Halides at Low Temperatures

A previous calculation of the temperature variation of the Grüneisen function [$\gamma \mathrm{}\left(T\right)=\frac{\beta V}{{\chi }_S{C}_p}$] for rigid-ion models of NaCl indicated a rather deep minimum at low temperatures. No such minimum has been observed for shell models of NaI and KBr. It is here pointed out that approximations employed in the calculations on the rigid-ion model were particularly unsatisfactory at low temperatures, and that the error resulting from these approximations can be assessed independently by calculating the low-temperature limits ${\gamma }_0$ from the volume derivatives of the elastic constants. Such calculations indicate that there can be no deep minimum in $\gamma \mathrm{}\left(T\right)\mathrm{}$ for these models, in general agreement both with the shell-model calculations and with experiment. Dispersion curves for both frequency and Grüneisen parameter as a function of wave vector suggest that $\gamma \mathrm{}\left(T\right)\mathrm{}$ is probably monotonic at low temperatures, but the possibility of a shallow minimum (depth ∼0.01) cannot be excluded.