Three-sublattice model that takes into account the spin density anisotropy, short-range order, and dimensioned factor for the binary Fe-Cr(V, Mo) systems

Abstract

The diffusion properties of the elements entering into the composition of austenitic and ferritic steels are analyzed as functions of the temperature and the time evolution of induced radioactivity. As compared to austenitic steels, ferritic steels are shown to have better diffusion properties and swelling resistance during operation at temperatures up to 650°C under irradiation conditions and can be used as structural materials in the core of a fast neutron reactor. Experimental and calculated (Calphad method) data on the Fe-Cr phase diagram and the thermodynamic properties and the experimental data on the short-range order in Fe-Cr alloys are analyzed, and it is concluded that they are conflicting and that models taking into account the short-range order should be developed. The results of quantum-mechanical calculations of the average magnetic moment for ferromagnetic (FM) iron as a function of the volume are analyzed and used to introduce a concept of partial magnetic moments of the iron atoms located in the first four coordination spheres (1–4 CS). The values of these moments are calculated. The concept of the partial magnetic moments of iron atoms agrees qualitatively with the experimental data on the spin-density anisotropy of the bcc lattice of pure iron. This concept is used to formulate a three-sublattice model for binary FM alloys of Fe-M systems (M is an alloying paramagnetic element). An extended cell whose sites contain 8 bcc cells and 16 atoms per cell and that is isomorphic to a DO3-type crystal lattice is considered. A functional is constructed for the internal energy on the extended 16-atom cell. The dimensioned factor is taken into account in a self-consistent manner, by the expansion of the interaction energies of atoms of both components located in different CSs in the atom displacement with respect to ideal lattice sites. The dimensioned factor is taken into account in the three-sublattice model to obtain a set of equations of state for bcc FM binary iron-rich alloys in a 1–3 CS approximation. The obtained estimates demonstrate that the anisotropy of the distribution of magnetic moments in the bcc iron lattice is responsible for the appearance of a short-range order in bcc FM iron-rich Fe-Cr (V, Mo) binary alloys.