Elasticity of Phases in Fe-Al-Ti Superalloys: Impact of Atomic Order and Anti-Phase Boundaries

A Quantum-Mechanical Study of Antiphase Boundaries in Ferromagnetic B2-Phase Fe2CoAl Alloy

In this study, we performed a quantum mechanical examination of thermodynamic, structural, elastic, and magnetic properties of single-phase ferromagnetic Fe2CoAl with a chemically disordered B2-type lattice with and without antiphase boundaries (APBs) with (001) crystallographic orientation. Fe2CoAl was modeled using two different 54-atom supercells with atoms on the two B2 sublattices distributed according to the special quasi-random structure (SQS) concept. Both computational models exhibited very similar formation energies (−0.243 and −0.244 eV/atom), B2 structure lattice parameters (2.849 and 2.850 Å), magnetic moments (1.266 and 1.274 μB/atom), practically identical single-crystal elastic constants (C11 = 245 GPa, C12 = 141 GPa, and similar C44 = 132 GPa) and auxetic properties (the lowest Poisson ratio close to −0.1). The averaged APB interface energies were observed to be 199 and 310 mJ/m2 for the two models. The studied APBs increased the total magnetic moment by 6 and 8% due to a volumetric increase as well as local changes in the coordination of Fe atoms (their magnetic moments are reduced for increasing number of Al neighbors but increased by the presence of Co). The APBs also enhanced the auxetic properties.

Impact of Disorder on Properties of Vacancies: A Case Study of B2 and A2 Polymorphs of Non-Stoichiometric Fe2CoAl

We have performed an ab initio study of vacancy-induced changes in thermodynamic, structural and magnetic properties of single-phase ferromagnetic Fe2CoAl with a chemically disordered (i) two-sublattice B2 phase or (ii) single-sublattice A2 phase. The two polymorphs of slightly non-stoichiometric Fe2CoAl (Fe27Co14Al13) were modeled by two different 54-atom supercells with atoms distributed according to the special quasi-random structure (SQS) concept. Both the lower-energy B2 phase and a higher-energy A2 phase possess elastic constants that correspond to an auxetic material that is mechanically stable. The properties of vacancies were computed by systematically removing different atoms (one at a time) from the supercells and quite wide ranges of values of vacancy-related characteristics were obtained. The increase in the level of disorder (when changing from the B2 to the A2 phase) results in an increase in the scatter of calculated values. The Fe and Co vacancies have lower vacancy formation energies than the Al ones. The total magnetic moment of the supercell decreases when introducing Fe and Co vacancies but it increases due to Al ones. The latter findings can be partly explained by an increase of the local magnetic moment of Fe atoms when the number of Al atoms in the first neighbor shell of Fe atoms is reduced, such as due to Al vacancies.

Impact of Antiphase Boundaries on Structural, Magnetic and Vibrational Properties of Fe3Al

We performed a quantum-mechanical study of the effect of antiphase boundaries (APBs) on structural, magnetic and vibrational properties of Fe3Al compound. The studied APBs have the {001} crystallographic orientation of their sharp interfaces and they are characterized by a 1/2〈111〉 shift of atomic planes. There are two types of APB interfaces formed by either two adjacent planes of Fe atoms or by two adjacent planes containing both Fe and Al atoms. The averaged APB interface energy is found to be 80 mJ/m2 and we estimate the APB interface energy of each of the two types of interfaces to be within the range of 40–120 mJ/m2. The studied APBs affect local magnetic moments of Fe atoms near the defects, increasing magnetic moments of FeII atoms by as much as 11.8% and reducing those of FeI atoms by up to 4%. When comparing phonons in the Fe3Al with and without APBs within the harmonic approximation, we find a very strong influence of APBs. In particular, we have found a significant reduction of gap in frequencies that separates phonon modes below 7.9 THz and above 9.2 THz in the defect-free Fe3Al. All the APBs-induced changes result in a higher free energy, lower entropy and partly also a lower harmonic phonon energy in Fe3Al with APBs when compared with those in the defect-free bulk Fe3Al.

An Ab Initio Study of Magnetism in Disordered Fe-Al Alloys with Thermal Antiphase Boundaries

We have performed a quantum-mechanical study of a B2 phase of Fe70Al30 alloy with and without antiphase boundaries (APBs) with the {001} crystallographic orientation of APB interfaces. We used a supercell approach with the atoms distributed according to the special quasi-random structure (SQS) concept. Our study was motivated by experimental findings by Murakami et al. (Nature Comm. 5 (2014) 4133) who reported significantly higher magnetic flux density from A2-phase interlayers at the thermally-induced APBs in Fe70Al30 and suggested that the ferromagnetism is stabilized by the disorder in the A2 phase. Our computational study of sharp APBs (without any A2-phase interlayer) indicates that they have moderate APB energies (≈0.1 J/m2) and cannot explain the experimentally detected increase in the ferromagnetism because they often induce a ferro-to-ferrimagnetic transition. When studying thermal APBs, we introduce a few atomic layers of A2 phase of Fe70Al30 into the interface of sharp APBs. The averaged computed magnetic moment of Fe atoms in the whole B2/A2 nanocomposite is then increased by 11.5% w.r.t. the B2 phase. The A2 phase itself (treated separately as a bulk) has the total magnetic moment even higher, by 17.5%, and this increase also applies if the A2 phase at APBs is sufficiently thick (the experimental value is 2–3 nm). We link the changes in the magnetism to the facts that (i) the Al atoms in the first nearest neighbor (1NN) shell of Fe atoms nonlinearly reduce their magnetic moments and (ii) there are on average less Al atoms in the 1NN shell of Fe atoms in the A2 phase. These effects synergically combine with the influence of APBs which provide local atomic configurations not existing in an APB-free bulk. The identified mechanism of increasing the magnetic properties by introducing APBs with disordered phases can be used as a designing principle when developing new magnetic materials.

A Quantum-Mechanical Study of Clean and Cr-Segregated Antiphase Boundaries in Fe3Al

We present a quantum-mechanical study of thermodynamic, structural, elastic, and magnetic properties of selected antiphase boundaries (APBs) in Fe3Al with the D03 crystal structure with and without Cr atoms. The computed APBs are sharp (not thermal), and they have {001} crystallographic orientation. They are characterized by a mutual shift of grains by 1/2〈100〉a where a is the lattice parameter of a cube-shaped 16-atom elementary cell of Fe3Al, i.e., they affect the next nearest neighbors (APB-NNN type, also called APB-D03). Regarding clean APBs in Fe3Al, the studied ones have only a very minor impact on the structural and magnetic properties, including local magnetic moments, and the APB energy is rather low, about 80 ± 25 mJ/m2. Interestingly, they have a rather strong impact on the anisotropic (tensorial) elastic properties with the APB-induced change from a cubic symmetry to a tetragonal one, which is sensitively reflected by the directional dependence of linear compressibility. The Cr atoms have a strong impact on magnetic properties and a complex influence on the energetics of APBs. In particular, the Cr atoms in Fe3Al exhibit clustering tendencies even in the presence of APBs and cause a transition from a ferromagnetic (Cr-free Fe3Al) into a ferrimagnetic state. The Fe atoms with Cr atoms in their first coordination shell have their local atomic magnetic moments reduced. This reduction is synergically enhanced (to the point when Fe atoms are turned non-magnetic) when the influence of clustering of Cr atoms is combined with APBs, which offer specific atomic environments not existing in the APB-free bulk Fe3Al. The impact of Cr atoms on APB energies in Fe3Al is found to be ambiguous, including reduction, having a negligible influence or increasing APB energies depending on the local atomic configuration of Cr atoms, as well as their concentration.