Interatomic Interactions in F.C.C.-Ni–Fe Alloys

Abstract

Within the scope of the self-consistent-field (SCF) and mean-SCF (MSCF) approximations, static-concentration-waves and Matsubara-Kanzaki-Krivoglaz lattice statics methods, on the basis of state-of-the-art diffraction data concerning coherent and diffuse scattering of radiations in (dis)ordered f.c.c.-NiFe alloys for various composition-temperature regions, and on the basis of data of independent magnetic measurements, the regular parameterization and estimation of 'pair-wise' interatomic interactions of the various nature (namely, 'direct' short-range 'electrochemical' and magnetic contributions as well as indirect long-range 'strain-induced' interaction) have been carried out taking into account their concentration and temperature dependences. As shown unfortunately, many of available 'electrochemical' interaction parameters obtained with use of the well-known ab initio and semi-phenomenological computational methodologies are limited in their applications for the statisticalthermodynamic analysis of f.c.c.-Ni-Fe alloys because most of them are contrary to the regularities of a 'mixing'-energy symmetry and, as a result, to the symmetries of observed L1 2 -Ni 3 Fe-, L1 0 -NiFe-or L1 2 -Fe 3 Ni-type ordered phas- Fiz. Met. 2010, т. 11, сс. 413- The temperature dependence of total 'mixing' energy is mainly due to the significant temperature-dependent magnetic contribution to it, and there is no need to take into account the effects of both substitutional correlations between atoms and many-particle interatomic-force interactions for characterization of microstructures developed by atomic ordering and (or) solid-phase precipitation in f.c.c.-Ni-Fe alloys. As expected, within the scope of the MSCF approximation, the estimated energy parameters of 'exchange' interactions in 1 st coordination shell, J NiNi (r I ) and J NiFe (r I ), correspond to the ferromagnetic interaction between magnetic moments in Ni-Ni and Ni-Fe atomic pairs, and J FeFe (r I ) corresponds to the antiferromagnetic interaction between magnetic moments in Fe-Fe atomic pairs.У рамках наближень самоузгодженого (СУП) та середнього самоузгоджено-го (ССУП) полів, метод статичних концентраційних хвиль (СКХ) і статики ґратниці Мацубари-Канзакі-Кривоглаза, на основі сучасних дифракцій-них даних стосовно когерентного та дифузного розсіяння випромінення у (не)впорядкованих стопах ГЦК-Ni-Fe в широкій концентраційно-темпера-турній області, а також за даними незалежних магнетних мірянь виконано систематичну параметризацію та кількісний розрахунок енергій «парних» міжатомових взаємодій різної природи (а саме, «прямих» близькосяжних «електрохемічного» й магнетного внесків, а також непрямої далекосяжної «деформаційної» взаємодії) із врахуванням їх концентраційної і темпера-турної залежностей. Недвозначно показано, що більшість значень параме-трів «електрохемічних» взаємодій компонентів, наведених у спеціялізова-ній науковій літературі, яких було оцінено із застосуванням відомих «першопринципних» та напівфеноменологічних обчислювальних методо-логій, на жаль, не зад...

Thermodynamics of f.c.c.-Ni–Fe Alloys in a Static Applied Magnetic Field

“…Following [15,[25][26][27][28][29], we consider a substitutional f.c.c.-Ni-Fe alloy, which consists of two magnetic constituents and is characterized by two types of a spatial order, notably, magnetic and atomic orders. It is worth noting that the presented analysis is based solely on the local magnetic moments model, which is valid within the lattice-gas approximation only and cannot be applied to the description of the "itinerant" magnetism of "quasi-free" electrons.…”

“…It is worth noting that the presented analysis is based solely on the local magnetic moments model, which is valid within the lattice-gas approximation only and cannot be applied to the description of the "itinerant" magnetism of "quasi-free" electrons. Nonetheless, a reader can find both approaches and their comparative analysis based on a reciprocal-space symmetry consideration in recent critical reviews [27,28]; the comprehensive list of references to the most salient literature on this matter can be found elsewhere [29]. Thus, the configuration-dependent part of the classical Heisenberg Hamiltonian of considered Ising-type interacting system can be presented in the form [16,30] as follows:…”

“…The indices (α, β) designate the types of atoms (Fe, Ni), c α (r) is a local random variable (1 or 0) of substitution of f.c.c.-lattice site r by an α atom, S α (r) is the spin operator of α atom situated at the site r, μ B is the Bohr magneton, g α is the Landé factor of α atom. J αβ (r − r ) and W αβ (r − r ) are the magnetic ("exchange") and "paramagnetic" (actually "electrochemical" together with "strain-induced" [15,[25][26][27][28][29]) "pairwise" interatomic-interaction energies, respectively. One can see that, in (1), the possible influence of the applied magnetic field with induction B on the spatial configuration of ions by means of their magnetic moments is taken into account explicitly (see, for details, [3,4,15,27,28]).…”

“…J αβ (r − r ) and W αβ (r − r ) are the magnetic ("exchange") and "paramagnetic" (actually "electrochemical" together with "strain-induced" [15,[25][26][27][28][29]) "pairwise" interatomic-interaction energies, respectively. One can see that, in (1), the possible influence of the applied magnetic field with induction B on the spatial configuration of ions by means of their magnetic moments is taken into account explicitly (see, for details, [3,4,15,27,28]). From the chosen configuration Hamiltonian, one can proceed with the statistical thermodynamics description of the atomic and magnetic orders of an alloy by applying the self-consistent field (SCF) and mean self-consistent field (MSCF) approximations, respectively, [3,4,[30][31][32] in a combination with the static concentration wave (SCW) method (see, e.g., [30,32]).…”

“…Equations (4a) and (4b) are obtained by the differentiation of expression (2a) and (2b) with respect to order parameters, η, σ Fe , and σ Ni . Such equations neglecting the influence of an applied magnetic field can be found elsewhere [15,[25][26][27][28][29]. Thus, using (2a), (2b), (4a), and (4b) and knowing the quantitative information about the Fourier components of "paramagnetic" interatomic "mixing" and magneticmoment "exchange" energies (for two quasi-wave vectors, k Γ (000) and k X (001), in the 1st BZ only), in particular, about their temperature-concentration dependences, one can estimate the critical-point and equilibrium parameters for f.c.c.-Ni-Fe alloys within the whole (T-c)-domain under the influence of a static applied magnetic field.…”