Hybrid approach to computer design “self-healing” ferritic steels: quantum mechanical calculations, statistical and physico-empirical models, thermodynamic optimization and forecasting

Abstract

Abstract The analysis of experimental data on neutron-structural studies of the sigma-phase of the alloys of the Fe-Cr system, obtained by Yakel, was carried out, which made it possible to introduce the concept of coordination spheres with an average radius around atoms located on all five sublattices of the crystal structure of sigma-phase. This analysis made it possible to develop a simplified statistical three-sub-lattice model for the sigma-phase in order to calculate the structural and thermodynamic properties taking into account its homogeneity region in Fe-(Cr, V, Mo) systems. The functional of the free mixing energy of the sigma-phase is written down as a function of the pair energies of the atoms of the components located on different sublattices of the sigma-phase, as well as the configurational entropy in the Gorsky-Bragg-Williams approximation. A system of equations of state is obtained by minimizing the free energy functional over different configurations. The independent energy parameters of the model are calculated by “linking” to the results of quantum mechanical calculations of the total energy and mixing energy of the sigma-phase of stoichiometric compositions for the ground state relative to sigma-phases of pure components. The solution of the system of equations of state allows one to calculate the distribution of atoms of both components over all sublattices of the sigma-phase, thermodynamic properties depending on the composition and temperature. In order to take into account the effect of temperature on the magnetic component of the free energy of mixing for the sigma phase, within the framework of the Inden-Hillert-Jarl model, estimates of the mean magnetic moment and Curie temperature are made for both the sigma phase of the Fe and the concentration dependences in the Fe-V system.