Crystal chemistry and Calphad modeling of the σ phase

Electronic structure calculations are employed in order to investigate the cohesive properties (lattice parameter, enthalpy of formation, and bulk modulus) of random Fe-Cr alloys as a function of composition and magnetic state, as well as to derive the chemical and magnetic exchange interactions of the constituent atoms. The calculations predict certain anomalies in the cohesive properties of ferromagnetic alloys at a concentration of about $7\text{ }\text{at}\text{ }%$ Cr; these anomalies may be related to the changes in Fermi-surface topology that occur with composition in this alloy system. The obtained interatomic interactions are used as parameters in the configurational (Ising) and magnetic (Heisenberg) Hamiltonians for modeling finite-temperature thermodynamic properties of the alloys. We discuss the approximations and limitations of similar modeling approaches, investigate the origin of existing difficulties, and analyze possible ways of extending the theoretical models in order to capture the essential physics of interatomic interactions in the Fe-Cr or similar alloys where magnetism plays a crucial role in the phase stability.

Electronic structure and effective chemical and magnetic exchange interactions in bcc Fe-Cr alloys

Ab initio perturbation-theory techniques, such as the generalized perturbation method and magnetic force theorem, are used to determine the Heisenberg exchange interaction parameters and the effective cluster interactions in Fe-rich bcc Fe-Cr alloys in different magnetic states. We establish a direct connection between chemical and magnetic exchange interactions, as well as their dependence on the global magnetic state of the alloy. These findings have important implications for phase equilibria in magnetic alloys. In particular, we demonstrate that the experimentally reported concentration interval of anomalous ordering in Fe-Cr alloys is determined by the thermal history of the alloys through the value of global magnetization at the annealing temperature.

First-principles theory of magnetically driven anomalous ordering in bcc Fe-Cr alloys

Structure, state, transformations and interactions of iron oxide shell with the iron metallic core in aerosol Fe nano-particles has been studied by X-ray and electron diffraction, TEM, Mossbauer spectroscopy and magnetization measurements. A strong influence of the state of nanoparticles oxide shell has been revealed on their magnetization, coercive force and hysteresis loop shift. A long-term passivation of the particles has been shown to be caused by the primary amorphous oxide. The passivation ability of the oxide shell becomes essentially worse after heat treatment of powder, resulting in its crystallization. Basing on the obtained results, a qualitative mechanism of passivation for nanoparticles covered with amorphous oxide shell has been suggested.

Aerosol Fe Nanoparticles with the Passivating Oxide Shell

One of the many singularities of Frank-Kasper phases is their ability to accommodate extremely large composition ranges by atom mixing on the different sites of the crystal structures. This phenomenon will be reviewed in the present paper with special emphasis on the experimental demonstration of this phenomenon, the theoretical calculation of disordered structures and the modeling of these phases.

Non-Stoichiometry and Calphad Modeling of Frank-Kasper Phases

The structure and hyperfine fields of Fe1−xCrx (x=0.0236–0.803) nanoparticles (average size of 27±2 nm) are studied at room temperature by combined x-ray diffraction and Mossbauer spectroscopy techniques. They are produced by fast evaporation of bulk alloys at 3 Torr Ar pressure. The bulk alloys of any composition are shown to exhibit a bcc structure, whereas the nanoparticles demonstrate a mixture of bcc and tetragonal σ phases in the Cr range from 24.4 to 83.03 at. %. At the Cr content of 2.36 at. % the lattice constant for nanoparticles is larger than that of the bulk alloy, though the values of hyperfine fields on Fe nuclei do not differ. The Mossbauer spectrum of nanoparticles contains an oxide doublet in addition to the sextet specific to that of the bulk alloy. In both cases the width of the sextet lines is rather narrow. However, even at ∼8 at. % Cr the lines of the sextet are broadened so much that it can be decomposed by two-three components. This is explained by freezing the high-temperature ferromagnetic fcc phase regions in the bcc lattice. As the Cr content increases, the Mossbauer spectra become more complex, transforming finally into a paramagnetic singlet. A complete ferromagnetic→paramagnetic transition is observed for the bulk alloy at 68 at. % Cr and for nanoparticles at 35 at. % Cr. The results are discussed under the assumption that at high temperatures the alloys are not homogeneous and exhibit fluctuations of the composition. With decrease of temperature these fluctuations result in decomposition of the alloy into two phases for nanoparticles whereas they are frozen at the cluster level in the bulk alloys holding a macroscopic homogeneity.

S. V. Essine

Papers

Structure and Mössbauer spectra for the Fe–Cr system: From bulk alloy to nanoparticles