Influence of composition and annealing conditions on the site-occupation in the σ-phase of Fe–Cr and Fe–V systems

Ab Initio Study of Lattice Site Occupancies in Binary Sigma Phases Using a Single-Site Mean Field Model

“…The results are shown in Figure 2 and agree quite well with the available experimental data [2,28]. At very high temperatures the configurational entropy drives the system to a highly disordered distribution of the alloy components on the five σ-phase sublattices.…”

“…Figure 5. The V site occupancies of the (A, B, C, D, E) sublattices versus the V composition, x V , at fixed T = 1,000 K. The full symbols denote the calculated results, the empty symbols represent the available experimental data (error bars within the symbol sizes) [28,32]. J Let us now consider the atomic site distribution in the Fe-V σ-phase with respect to the alloy composition, x V (see Figure 5).…”

Formation energy in Fe–V alloys

“…In practice, the electronic structure calculations were performed for a finite number of the unit cells with a symmetry reduced to a simple tetragonal one (P1 instead of P4 2 /mnm), in which each position (but not the sublattice) was occupied by one type of atoms (Fe or V). The atoms were distributed over the five different sites with the probabilities determined from neutron diffraction measurements 15 which were next altered in the way described below. Differences between total energies (per atom), ∆E (usually called the formation energy), determined for each of these atomic configurations, E σ , and corresponding values obtained for pure constituents, i.e.…”

“…This approach was already successfully applied to the analysis of the formation energy of the σ-phase in the Fe-Cr alloy system 5 . As mentioned above, the σ-phase is characterized by a chemical disorder on all five sublattices, and the concentrations of Fe/V atoms on each of them were determined experimentally 15 . Since both Fe and V atoms are present on all five sublattices, it is useful for further considerations to introduce shortened notations for samples with different sublattice occupancies.…”

“…A better knowledge of conditions of its formation may be helpful for fabrications of materials in which the unwanted phase does not precipitate or its precipitatioin is significantly retarded. On the other hand, due to its complexity (30 atoms per unit cell, five different sublattices, high (12)(13)(14)(15) coordination numbers, and lack of a stoichiometry) make the σ-phase a very challending object for theoretical calculations. They are very helpful for a proper interpretation of measurements, especially those done by means of microscopic methods like Mssbauer spectroscopy or nuclear magnetic resonance, as well as for a better understanding of the results obtained.…”