Thermodynamic model for describing high-entropy oxide phases with the m-type hexaferrite structure

To date, a significant amount of experimental data on the results of the synthesis of high-entropy oxide phases with the M-type hexaferrites structure has been accumulated and their structure and properties have been studied, which allow us to conclude that research in this direction is promising. At the same time, its further development requires work on the creation of theoretical foundations for synthesis of such phases. An important part of theoretical work of this kind should be the thermodynamic description of the studied solid solutions based on M-type hexaferrites, resting on the analysis of experimental data. The aim of this work is to determine what approaches can be used for the thermodynamic description of high-entropy oxides (HEO) with the M-type hexaferrites structure, as well as to form a base of thermodynamic functions describing individual substances involved in the formation of a high-entropy oxide phase of this kind. The analysis of experimental data involving the process and the synthesis results for HEO with the M-type hexaferrites structure, carried out in the course of the study, has made it possible to suggest the use of a two-sublattice phase model, in which the first sublattice is formed by the A type atoms, and the second sublattice by the B12O19 complexes of atoms. Within each of the sublattices, the deviation from ideality is described by the Redlich-Kister polynomials. It is suggested to consider real or hypothetical substances with the АВ12О19 formula as components of a solid solution, where A is Ba, Sr, Pb, Ca; and B is Fe, Al, In, Ga, Ti, Co, Mn, Ni, Zr, Zn, Cu, Cr. For all these substances, the values of the standard enthalpies of formation, standard entropies, and temperature dependences of the isobaric heat capacity have been found. These values are partly borrowed from various sources, though for the most part they are the results of evaluation by various semi-empirical methods. The developed model and values of thermodynamic functions characterizing the individual components of the HEO with the M-type hexaferrite structure made it possible to form a user database within the “FactSage (version 8.0)” software package, which opens up wide opportunities for further work on improving the model, optimizing the model parameters and thermodynamic modeling of the solid-phase synthesis of HEO with the M-type hexaferrites structure.