To the Question of Validity Grüneisen Solid State Equation

Abstract

The first justified theory of solid state was proposed by Grüneisen in the year 1912 and was based on the virial theorem. The forces of interaction between two atoms were assumed as changing with distance between them according to inverse power laws. But only virial theorem is insufficient to deduce the equation of state, so this author has introduced some relations, which are correct, when the forces linearly depend on displacement of atoms. But with such law of interaction the phase transitions cannot take place. Debye received Grüneisen equation in another way. He deduced the expression for thermocapacity, using Plank formula for energy of harmonic vibrator. Taking into account the dependence of atomic vibration frequency from distance between atoms, when the forces of interaction are anharmonic, he received the equation of state, which in classical limit turns to Grüneisen equation. The question, formulated by Debye is-How can we come to phase transitions, when Plank formula for harmonic vibrator was used? Debye solved this question not perfectly, because he was born to small anharmonicity. In the presented work a chain of atoms is considered, and their movement is analysed by means of relations, equivalent to virial theorem and theorem of Lucas (disappearing of mean force). Both are the results of variation principle of Hamilton. The Grüneisen equation for low temperature (not very low, where quantum expression for energy is essential) was obtained, and a family of isotherms and isobars are drown, which show the existence of spinodals, where phase transitions occur. So, Grüneisen equation is an equation of state for low temperatures.

Ab-Initio Investigation into the Physical Characteristics of CuInSe2 and CuInTe2 Compounds

“…The C V of the studied systems exhibits distinct behaviors contingent upon the temperature range considered. At elevated temperatures, it tends to approach the Dulong-Petit limit [56] (C V ≈ 3R for monatomic solids). This behavior is a common trait shared by all solids at high temperatures.…”

The Boguslawski Melting Model

“…The theory of Grüneisen was précised in our work [5] and about melting may be formulated following assertions. In Figure 6 of the mentioned work a family of isotherms is drawn, that are curves with maximum.…”

“…So the melting phenomenon was demonstrated, but mathematical difficulties are considerable. It is worthwhile to use the form of dynamical equations that is able to calculate the mean thermal displacement of an atom and mean amplitude of vibration without solving time-dependent dynamical equations [4] [5]. The problem contains in solving algebraic equations, which may be carried out in some cases.…”