A Simple Expression for the Gruneisen Parameter and Its Relation with Rao' s Rule

Abstract

The concept of a constant relating thermal and mechanical properties was first proposed by Griineisen /1/ for solids. In the quasi-harmonic model of lattice dynamics the change of anharmonicity in lattice vibration frequency Rao' s acoustical parameter (K) of a liquid is an important quantity as it is related to the C1 parameter and the Gruneisen parameter. The acoustic parameter can be expressed as /15/ where u is the bulk sound velocity in liquid.1) Bhubaneswar 751007, India.

Relationship of Triple Point Solid Volume with Thermo‐Acoustic Parameters and Structural Distortion in Quasi‐Spherical Molecular Liquids by the Corresponding State Correlations

“…where us = (g'VJN)1'3 is the intermolecular separation at the triple point, V, the limiting solid volume at the triple point, a, the limiting value of the equilibrium molecular diameter, CT* = (g'V*/N)1'3 is the hard-core molecular diameter, and the constant factor A = ( C~~/ G , ]~ is characteristic of the substance. Equation (10) shows that the estimated value of A' = 1.038 is very close to that for the ratio (a,/o*) or the cube root ofthe ratio (V,/V*) for quasi-spherical molecular liquids [6].…”

“…For simple liquids having f.c.c. structure, Z' decreases from about 12 to about 10 at the triple point/melting point and further to about 4 at the critical point [8, 111. In view of the theoretical considerations and suggestions [5,6], the expressions for 2 , (, and g' in an expanded liquid region at any temperature may be written as [5] Z' = z m ( V m / V ) 9 (1)…”

“…A"/A' = C*/a = 1.963. (9) At the triple point, the molar volumes can be shown to be related to the molecular diameters as [6] v,p* = (a,/rJ*)3 = A p,…”

“…Using (7) and (10) to (12) the expression for the nearest-neighbour number Z , of a liquid at the triple point [6] can be related to the molecular diameters through the parameters A and A' for the liquid as…”

“…The triple point solid volume V, has been found to be a very useful tool for investigating thermo-acoustic properties [l, 21, locating the solid-liquid phase transition [3], and examining the melting behaviour of substances [4]. The significance of the idea of corresponding state correlations [2,5,6] and the liquid structure distortion parameter [5,7] in describing the physico-chemical and thermo-acoustic properties of liquids has been discussed. In the present work, an attempt has been made to obtain simple relations for the triple point solid volume V, and the I) Sri Aurobindo Marg, New Delhi 110016, India.…”