An alternative use of Kieffer's lattice dynamics model using vibrational density of states for constructing thermodynamic databases

Abstract

We use Kieffer's model to represent the vibrational density of states (VDoS) and thermodynamic properties of pure substances in pressure-temperature space. We show that this model can be simplified to a vibrational model in which the VDoS is represented by multiple Einstein frequencies without significant loss of accuracy in thermodynamic properties relative to experimental data. The resulting analytical expressions for thermodynamic properties, including the Gibbs energy, are mathematically simple and easily accommodated in existing computational software for making thermodynamic databases. We show for aluminium, platinum, orthoenstatite and forsterite that thermodynamic properties can be represented with comparable accuracy as with Kieffer's model with the same number of fitting parameters as in the Mie-Grüneisen-Debye model. We demonstrate that the method enables to achieve thermodynamic properties with superior accuracy relative to the Mie-Grüneisen-Debye method. The method is versatile in the sense that it allows incorporating dispersion of Grüneisen parameters. It is possible to extend the formalism to include other physical effects, such as intrinsic anharmonicity in the same way as in vibrational models based on Kieffer's formalism.