Equation of State and the Thermal Dependence of the Elastic Coefficients of Crystalline Argon

Abstract

An interaction potential of the form A/R¹⁰—B/R⁶ for two argon atoms is assumed. The values of A and B are evaluated using the heat of sublimation and the lattice constant at temperature T=0°K and pressure p=0. By assuming that each atom moves in a potential field because of all the other atoms at rest in their mean positions, a theory is developed for anharmonic vibrations using the perturbation theory for a harmonic oscillator. The partition function for each argon atom is obtained and the equation of state is calculated. The specific‐heat equation obtained represents a correction of the Einstein form. The specific heats at constant pressure are calculated as a function of temperature and deviate from the experimental ones by only 3 percent at low temperatures (15°K—30°K) and only 1 percent at higher temperatures. The isothermal elastic coefficients C₁₁, C₁₂, and C₄₄ are calculated by Born's method without neglecting the part played by the thermal energy. The Cauchy relation is found to be invalid, C₄₄ being about twice C₁₂ at the higher temperatures.