First-Principles Approach to Thermodynamics

Abstract

Phase diagrams and thermodynamical data play key roles in the field of materials science and engineering. They give us information on phase stabilities and process conditions, which are a sort of guide maps for materials design. Therefore, huge thermodynamical data have been accumulated by many researchers so far, which are listed in several databases, such as NIST-JANAF Thermochemical Tables and Thermochemical Data of Pure Substance (Barin). However, the coverage of the available data is still limited due to a great number of compounds on the earth. On the other hand, rapid development of computational power enables us to evaluate many physical properties from first principles in recent years. They include thermodynamical properties at finite temperatures, e.g., specific heats, enthalpies, entropies, and free energies, though first-principles calculations, i.e., electronic structure calculations, have been considered to be able to evaluate only total energies at absolute zero. In this article, I would detail a first-principles approach to thermodynamical properties which readers here are familiar with. The key is the technique to evaluate “vibrational free energies”, which mainly determine the temperature dependences of thermodynamical properties of solid phases. In general, the harmonic and quasi- harmonic approximations are employed to analyze the lattice vibrations, and they are reasonable in most solid phases. In the case of gas phases, rotational and translational free energies should be taken into account in addition to the vibrational free energies. I would be happy if you could find the great potential of “first-principles thermodynamics” in this article.