One‐Particle Distribution Functions and Thermodynamics of Crystals with Many‐Body Forces. General Consideration and Investigation of the Properties of the Inert Gas Solids

Abstract

Abstract A crystal is described by a probability density which is not symmetric regarding the interchange of phase‐space coordinates between two molecules. The set of approximate equations for one‐particle distribution functions with many‐body forces is derived from the L IOUVILLE equation. The expression for the H ELMHOLTZ free energy and the equation of state are obtained. The developed method is applied to the determination of the thermodynamic properties of crystalline argon, krypton, and xenon. The nearest‐neighbor distances, internal energies, isothermal and adiabatic compressibilities, linear thermal expansion coefficients, specific heats C v and C p are calculated using the pair potentials of B ARKER ‐P OMPE , of B ARKER ‐B OBETIC , and of L ENNARD ‐J ONES , together with the A XILROD ‐T ELLER three‐body potential. The obtained results are compared with the experimental data and discussed.