A generalization of Grüneisen's theory of solids and its application to solid argon

Publisher Website
Google Scholar
Abstract
The quasi-harmonic model of a solid (a harmonic model which takes only partial account of anharmonicity) is examined and a general notation established. The theory involves the quantities [ϵi][n] ≡(Vn /vi ) (∂nvi/∂Vn ), where vi are the spectral frequencies. By evatuatisg averages of [ϵi][n] appropriate at high and low temperatures it is shown that Grüneisen-type assumptions are reasonable for the inert gas solids. This confirms work by Barron on Grüneisen's γ (in our notation γ=−< [ϵ i ][1]AV). Grüneisen's equation of state pV= −VU 0 ′(V)+γUT , where UT and U 0, are the thermal and non-thermal contributions to the internal energy U, is extended to yield an equation of the form V/KT=V 2 U 0 ″(V)+γ'UT-γ2TCV wehereγ′(=<[ϵi][2]Av) is a 'second' Grüneisen constant. It may be estimatad from measurements of the variation of compressibility with temperature in much the same way as the first Grüneisen constant γ is determined from measurements on expansivity, specific heat and compressibility. Experimental results for argon are compared with the theory, assuming a Lennard-Jones 6–12 potential. Good agreement is obtained except above 40°K where anharmonicity must be considered explicitly. Our estimates of γ are consistent with those of previous writers; from the theory we conclude that for argon γ′ has a value of about 10 and this is confirmed by a direct use of experimental results on compressibility.

This publication has 17 references indexed in Scilit: