Inter-atomic potential energy and Grüneisen parameter: A new method for equation of state of solids

• We present exact relation for Grüneisen γγ in terms of inter-atomic potential energy ϕϕ.
• It reverses approximation made by Dugdale–MacDonald.
• Numerical solution using experimental data gives γγ, ϕϕ and EOS of Al, Cu, Pb and Au.
• Good agreement with alternative calculations.
• Method applicable to conductors or non-conductors.

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 γγ (as a function of the specific volume VV of the material) in terms of the specific inter-atomic potential energy ϕ(V)ϕ(V). Existing expressions for γγ in the literature are usually approximations in terms of total pressure PP. There is a variety of such “(γ,P)(γ,P)” formulas and one needs experience in deciding which to use in any particular application. The alternative “(γ,ϕ)(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 ϕϕ, dϕ/dVdϕ/dV, γγ, dγ/dVdγ/dV 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.