Volume-based thermoelasticity: Thermal expansion coefficients and the Grüneisen ratio

In an extension of our current studies of volume-based thermodynamics and thermoelasticity (VBT), we here consider the parameters at ambient temperature of the dimensionless Grűneisen ratio (or Grűneisen parameter), γth, which is a standard descriptor of the thermophysical properties of solids: γth=αKTVm/Cv=αVm/βCv It has earlier been established that the isothermal volume compressibility, β (which is the reciprocal of the bulk modulus, KT), and the ambient-temperature heat capacity, Cp, are strongly linearly correlated with the molar volume, Vm, among groups of materials with similar structures. Here, we examine possible correlations between the volumetric thermal expansion coefficient, α (the remaining Grűneisen parameter), and molar volume. Using the high-temperature limiting value, a°, as a surrogate for α, we find that α is essentially uncorrelated with volume among a range of materials. As a consequence of the lack of correlation through volume of α with the other Grűneisen parameters, we conclude that the dimensionless Grűneisen ratio at ambient temperatures itself is thereby poorly constant across materials and cannot be reliably used for predictive purposes. It is noted that, for thermodynamic reasons, the values of γth generally range from about 0.5 to 3, clustering around 2.