Effect of Force-Constant Changes on the Lattice Specific Heat of KCl:Tl

Abstract

A detailed study of the effects of force-constant changes produced by noninteracting ${\mathrm{Tl}}^{+}$ impurity ions on the lattice specific heat of KCl has been made. Numerical computations have been performed for three impurity concentrations, 1, 3, and 5 mole% of ${\mathrm{Tl}}^{+}$, and the results are compared with the experimental data of Karlsson. The effects of force-constant changes on the specific heat are seen to be quite large. The temperature dependence of the observed specific heat has been explained successfully by Green's-function theory in the temperature range 1-10 °K. The force-constant change due to ${\mathrm{Tl}}^{+}$ in KCl is seen to be small and the impurity behaves essentially as a mass defect. Finally, the low-concentration theory is seen to be adequate for understanding the experimental results even at relatively higher concentration of impurities (5 mole% of ${\mathrm{Tl}}^{+}$) present in a crystal.