Methods of evaluation of elastic constants and several other properties using radial distribution functions

Abstract

The I₁ and I₂ integrals defined by Schofield are evaluated for the hard-sphere, square-well, and Lennard-Jones potential functions. We have also presented calculations of I₁ and I₂ integrals from Ascarelli's modified compressibility equation. These I₁ and I₂ values are used in the evaluation of second- and third-order elastic constants. A relationship between (C₁₁₁/C₁₁) and the pressure variation of bulk modulus C₁ has been derived. This is found to give results in fair agreement with experiment. Using the Collin-Raffel's equation of viscosity, the effective mass of the liquid molecule is deduced, and from the effective mass the diffusion coefficient has been calculated. Using Zwanzig's and Mountain's equation, the high-frequency moduli G_∞ and K_∞ have been computed, and from this the dilation modulus M_∞ has been calculated and compared with experiment. We use Takeno's and Goda's equation to evaluate C_L and C_T, the longitudinal and transverse sound velocities, respectively, and hence the Poisson ratio σ_s. Thus the present investigation involves the use of I₁ and I₂ integrals, which in turn are dependent on the microscopic properties; g(r), the radial distribution function; and u(r), the potential function.