Thermal Conductivity of Potassium Chloride Crystals Containing Calcium

The details of the phonon scattering produced by point imperfections in insulating crystals has been determined from measurements of the thermal conductivity of six single crystals of KCl from 3°K to 30°K as a function of the concentration of point imperfections. These imperfections were produced by the addition of Ca${\mathrm{Cl}}_2$, which was incorporated into the KCl crystals as a substitutional impurity during growth from the melt. At temperatures above 15°K the mean free path of the phonons decreases inversely with increasing calcium concentration. The average scattering cross section of a calcium ion—potassium ion vacancy complex increases as the fourth power of the temperature for low temperatures, and becomes equal to the geometrical cross section of the vacancy at a temperature of about $\frac{{\theta }_D}{6}$. Below 15°K the phonon scattering by colloids of precipitated calcium chloride produces a large thermal resistivity in the impure crystals. The thermal conductivity of "pure" KCl at low temperatures is limited mainly by isotope and boundary scattering. The theoretical expressions as given by Klemens for combining thermal resistivities which possess different temperature dependences have been calculated, and have been applied to the present results. The agreement between Klemens' theory and the present experiment as to both the magnitude and the temperature dependence of the thermal resistivity is considered to be satisfactory.