Thermodynamical functions for crystals with large unit cells such as zircon, coffinite, fluorapatite, and iodoapatite fromab initiocalculations

We derive thermodynamical functions for some large unit cell ionocovalent crystals from the well known quasiharmonic free energy model with the help of ab initio calculations. In order to keep the computation time within reasonable bounds the ab initio assessment applies only to the cohesive energy as a function of volume, Poisson's ratio, and the harmonic vibration frequencies at the Γ point for the unit cell at zero static pressure. These quantities are obtained by solving the electronic Schr\"odinger equation in the framework of the electronic density functional theory using available packages. Thermal contributions are estimated using the Debye model for acoustic modes and the extended Gr\"uneisen method for optical modes. We have estimated in this way the thermodynamical functions of some crystals relevant to radioactive waste management such as zircon, coffinite, fluorapatite, and, in the end, iodoapatite, which is able to immobilize ¹²⁹I. For zircon, coffinite, and fluorapatite for which the main thermodynamical functions are experimentally known, the enthalpy of formation in standard conditions is determined within $6%$ of the experimental value, and heat capacities at constant pressure are well reproduced, within $5%,$ at any temperature up to the dissociation temperature. For iodoapatite there are as yet no published experimental thermochemical data to compare to the present theoretical results.