Experimental and Theoretical Study of Phonon Scattering from Simple Point Defects in Sodium Chloride

Abstract

Thermal-conductivity measurements have been made as a function of temperature on sodium chloride crystals containing the nine monovalent substitutional impurities: ${\mathrm{F}}^{\ensuremath{-}}$, ${\mathrm{Br}}^{\ensuremath{-}}$, ${\mathrm{I}}^{\ensuremath{-}}$, ${\mathrm{Li}}^{+}$, ${\mathrm{K}}^{+}$, ${\mathrm{Rb}}^{+}$, ${\mathrm{Ag}}^{+}$, ${\mathrm{Tl}}^{+}$, and ${\mathrm{Cu}}^{+}$. These measurements extend over the temperature range 1.2 to 300\ifmmode^\circ\else\textdegree\fi{}K. All of the systems showed a lowering of the curves which is asymmetric which respect to the peak. In order to explain this behavior, the Debye approximation in the expression for the thermal-conductivity integral has been relaxed. Phonon data were calculated using the shell model for 64 000 points in the Brillouin zone. From these data a density of states and frequency-averaged group velocities were obtained and then used in the conductivity integral. In addition, exact relaxation rates were obtained, via a Green's-function formalism derived by Klein, for a simple model for the defect in the lattice, which assumed a change of mass at the defect site and a change of force constant to the six nearest neighbors. The changes in force constant were obtained using a Born-Meyer repulsive potential between the ions. New equilibrium positions of the surrounding ions were obtained from published literature and from a method using the static Green's functions. The results for the change in force constant varied considerably, so that this parameter was considered to be semivariable in the analysis. Depressions of the conductivity curve were predicted at approximately the same positions as found experimentally. The predicted high-temperature depressions occurred at slightly lower temperatures than the experimental ones and the strengths did not agree very well with experiment. The degree to which the theory successfully predicted the experimental curves is related to the size of the strain field about the impurity. Thus it is hoped that a more sophisticated model containing long-range effects will improve the fit.