A simple thermodynamic description of the combined Einstein and elastic models

TL;DR

This paper extends the Einstein model by incorporating elastic energy and volume-dependent oscillator frequencies to develop a comprehensive thermodynamic description of solids, accurately predicting properties like thermal expansion and compressibility.

Contribution

It introduces a combined Einstein-elastic model with volume-dependent frequencies and static elastic energy terms for improved thermodynamic predictions.

Findings

Model accurately predicts thermal expansion of solid argon.

Theoretical results align well with experimental data.

Provides a practical equation of state for solids.

Abstract

Simple application of the Einstein model combined with the elastic description of solid state is developed. The frequency of quantum oscillators has been assumed as volume dependent and, furthermore, elastic energy terms of static character have been included to complete the description. Such an extension enables to construct the complete thermodynamics. In particular, the model yields practical equation of state and describes the thermal expansion coefficient as well as the isothermal compressibility of solids. The thermodynamic properties resulting from the Gibbs free-energy analysis have been calculated and illustrated in figures. Some comparison of the theoretical results with experimental data for solid argon has been made.