Ultrasonic parameters in the born model of the sodium and potassium halides

Abstract

Available experimental data at 295°K on the ultrasonic elastic constants and their temperature variation, the specific heat, and the thermal expansion of the sodium and potassium halides have been collected and inspected for smoothness in each sequence when plotted against nearest neighbor distance. In the same way, ultrasonic data on the pressure derivatives of the elastic constants have been reviewed and, in the case of NaBr, NaI, KF and KI, measured. The resulting smooth thermodynamic data have been used to obtain values of the constant volume temperature coefficient of the isothermal bulk modulus, d ln B T d T) V and of d B T d P) T . The former is found to be rou − 0.7 × 10 −4deg −1 for both halide sequences. It arises in the vibrational entropy of the crystal and appears as a correction in expressions giving the repulsive exponent in the two-parameter empirical Born model. The usual procedure of using compression data to obtain dlnB T d T) V results in an erratic correction that occasionally amounts to more than 10 per cent of the repulsive parameter; on the other hand, the ultrasonically based correction is strikingly smooth at about 2 per cent. Experimental values of d B T d P) T are nearly invariant among these eight alkali halides at a value of 5.4. The Born model correctly predicts this magnitude but also predicts a systematic trend with repulsive exponent significantly greater than that found. Born-Hildebrand equations of state based on the ultrasonic parameters should provide improved estimates of V( P) relations; these do compare fairly well with X-ray data for NaF, NaCl and NaI to pressures on the order of the bulk modulus. Neither comparison with experiment will distinguish, however, for the whole group between the version of the Born model based on a power law repulsive potential and that based on an exponential law.