Volume-based thermoelasticity: Thermal expansion coefficients and the Gruneisen ratio
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NOTICE: this is the author’s version of a work that was accepted for publication in Journal of Physics and Chemistry of Solids. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Physics and Chemistry of Solids, 73, 1 (2012). DOI http://dx.doi.org/10.1016/j.jpcs.2011.10.008
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 Gruneisen ratio (or Gruneisen 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 Gruneisen parameter), and molar volume. Using the high-temperature limiting value, α°, 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 Gruneisen parameters, we conclude that the dimensionless Gruneisen 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.
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