Atomic, Electronic, and Magnetic Structure of Iron-Based Sigma-Phases
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Atomic, Electronic, and Magnetic Structure of Iron-Based Sigma-Phases Pavel A. Korzhavyi,1 Bo Sundman,1 Malin Selleby,1 and Börje Johansson1,2 1 Department of Materials Science and Engineering, Royal Institute of Technology (KTH), SE-100 44 Stockholm, SWEDEN; 2 Condensed Matter Theory Group, Department of Physics, Uppsala University, SE-751 21 Uppsala, SWEDEN. ABSTRACT A combination of ab initio total energy calculations with Calphad approach is applied to model the site occupancy and thermodynamic properties of the Fe-Cr, Co-Cr, Fe-V, and Fe-Mo binary sigma-phases as a function of composition and temperature. For each binary sigma-phase the parameters of the model are the ab initio calculated total energies of so-called end-member compounds, which represent all the 25=32 variants of complete occupancy of each of the five crystallographically inequivalent sites by one or the other alloy component. The paramagnetic state of the sigma-phases has been taken into account within the disordered local moment approach. The Fe and Co atoms are found to retain high spin moments when they occupy highcoordination-number sites in the structure. Using our model we were able to reproduce the experimentally observed site occupancy in the FeCr sigma-phase. The calculated site occupancies in the Co-Cr, Fe-V, and Fe-Mo sigma-phases are also presented and discussed.
INTRODUCTION Sigma-phases are complex tetragonal structures [1] (structure type D8b) that form in transition metal alloys having the average number of s+d electrons in the interval 6.2 – 7.4. These phases, which may form during solidification or heat treatment, cause embrittlement of transition metal alloys such as stainless steels or Ni-based superalloys. A well known example is the FeCr σ-phase, whose formation has a deleterious effect on the mechanical properties of stainless steels. Like other σ-phases, the FeCr phase possesses a relatively high degree of chemical disorder among its five crystallographically inequivalent sites. Among these lattice sites (see table I) one finds two kinds of icosahedrally coordinated sites (IC sites 1 and 4) and three types of sites with high coordination numbers (high-CN sites 2, 3, and 5). It has been found experimentally that the group VIIB and VIII elements tend to occupy the IC sites (10 out of the 30 atomic positions in the structure), while the remaining 20 atomic positions of high-CN sites are preferentially occupied by the group VB and VIB elements [2]. Accurate site-occupancy data have been obtained [3] for the Fe-Cr binary σ-phase using X-ray diffraction experiments on single crystals, whereas for the majority of σ-phases only qualitative ordering schemes are available. The aims of the present theoretical study were to investigate the electronic structure and to derive the site occupancy in the Fe-Cr, Co-Cr, Fe-V, and Fe-Mo sigma-phases, as a function of composition and temperature, from ab initio calculated total energies for the complete set of 25=32 end member compounds (all the variants of integral site occupancy
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