Inter-atomic potential energy and Grüneisen parameter: A new method for equation of state of solids. (May 2015)

• Record Type: Journal Article
• Authors: Parish, Peter G.; Moore, John
• Is Part Of: Journal of physics and chemistry of solids. Volume 80(2015:May)
• Page Start: 39
• Page End: 51
• Publication Date: 2015-05
• Subjects: Metals -- Inorganic compounds -- High pressure -- Equations-of-state -- Thermodynamic properties; Solids -- Periodicals; Solides -- Périodiques; Solids; Periodicals; 530.41
• DOI: 10.1016/j.jpcs.2014.12.017
• Languages: English
• ISSNs: 0022-3697

Abstract

Abstract: This paper presents a rational foundation for the computation of equation of state (EOS) data for solids at high pressure. We demonstrate a new method which makes use of an accurate relation expressing the Grüneisen parameter γ (as a function of the specific volume V of the material) in terms of the specific inter-atomic potential energy ϕ ( V ) . Existing expressions for γ in the literature are usually approximations in terms of total pressure P . There is a variety of such " ( γ, P ) " formulas and one needs experience in deciding which to use in any particular application. The alternative " ( γ, ϕ ) " relationship presented here is both unique and exact within the Debye and harmonic approximations and allows the individual terms of the EOS to be determined separately. It is rigorously derived in this paper and solved numerically, using experimental input data for aluminium, copper, lead and gold, to predict ϕ, d ϕ / d V, γ, d γ / d V and EOS data for the four metals. Comparison is made with existing computations in the literature showing good agreement. The method can be applied to any metal or non-metal using experimental input data from any suitable volume-dependent locus. Highlights: We present exact relation for Grüneisen γ in terms of inter-atomic potential energy ϕ . It reverses approximation made by Dugdale–MacDonald. Numerical solution using experimental data gives γ, ϕ and EOS of Al, Cu, Pb and Au. Good agreement with alternative calculations. Method applicable to conductors or non-conductors.