Semi-Empirical Parameterization of Interatomic Interactions and Kinetics of the Atomic Ordering in Ni-Fe-C Permalloys and Elinvars
Authors: Tatarenko Valentin A. , Bokoch S.M. , Nadutov V.M. , Radchenko Taras M. , Park Yong Bum 
Published: March 2009

Within the framework of the lattice-statics and static fluctuation-waves’ methods, the available energies of strain-induced interaction of interstitial–interstitial, interstitial–substitutional and substitutional–substitutional impurity atomic pairs are collected and analysed for f.c.c.-(Ni,Fe)–C solutions allowing for discrete atomic structure of the host-crystal lattice. The lattice spacings, elasticity moduli and/or quasi-elastic force parameters of the host-crystal lattice, and concentration coefficients of the dilatation of solid-solution lattice due to the respective solutes are selected as the input numerical experimental data used. The above-mentioned interaction energies prove to have non-monotonically decreasing (‘quasi-oscillating’) and anisotropic dependences on discrete intera-tomic radius-vector, and themselves are strong and long-range. In all f.c.c.-(Ni,Fe)-base solutions, there is strain-induced attraction in many co-ordination shells. In general, the strain-induced interaction between impurity atoms in γ-Fe is weaker than in α-Ni (but in some solid solutions, it may prove to be of the same order). The verification of applicability of the approximation of strain-induced interaction of impurities for f.c.c.-(Ni,Fe)–C alloys (by means of analysis of thermodynamic C activity and ‘short-range order’ parameters of C-atoms’ distribution revealed by Mössbauer spectroscopy) showed that it must be supplemented with additional short-range (‘electrochemical’) repulsion in the first co-ordination shell. Nevertheless, in any case, the strain-induced interaction of impurity atoms must be taken into account for analysis of structure and properties of f.c.c.-(Ni,Fe)-base solutions. The Monte Carlo simulation procedures applied for constitution of a nanoscale Fe–C-austenite crystallite and based on analysis of the dependences of numbers of the different atomic configurations on C–C interatomic-interaction energies reveal correlation between the potential energy of such a modelling system and the numbers of iterations as well as Monte Carlo steps for the approach to constrained equilibrium. As shown by the example of austenite, for adequate representation of the experimental data on thermodynamic C activity, one needs to take into account for computations the ‘electrochemical’ (direct) and strain-induced (indirect) contributions to C–C interaction. The estimated sets of energies of such a total interaction within the first several interstitial co-ordination shells with rated radii are presented, and optimal set is selected, which optimally corresponds to experimental concentration and temperature dependences of C activity and the Mössbauer-spectroscopy data on the nearest neighbourhoods of Fe atoms with octahedral C interstitials. The ‘equilibrium’ relative parts of the different atomic Fe–C and C–C configurations (depending on C–C interaction energies) are determined. The Khachaturyan–Cook microscopic approach is considered to relate the time dependence of the long-range order (LRO) or short-range order to atomic diffusion. It enables to use the data of measurements of time dependence of radiation diffraction or diffuse-scattering intensity for a Ni–Fe solid solution for calculation of both probabilities of elementary atomic-migration jumps to different lattice sites per unit time and ‘exchange’ or vacancy-controlled diffusion coefficients, respectively. By the use of quantitative experimental information about the Curie temperatures, TC, and neutron diffuse-scattering intensities for disordered f.c.c.-Ni–Fe alloys, it is possible to evaluate the Fourier components, w~tot(k), of effective Ni–Fe atomic ‘mixing’ energies (inclusive the competing exchange interactions of respective permanent magnetic moments) taking into account both long-range ‘paramagnetic’ (‘electrochemical’ + ‘strain-induced’) and Ising-type magnetic contributions that drive the long-range ordering. Magnetism and ‘chemical’ (atomic) LRO in f.c.c.-Ni1cFeFecFe alloys are analysed within the self-consistent mean-field approximation, in which the statistical thermodynamics of the non-stoichiometric L12(Ni3Fe)-type permalloy (as well as L10(NiFe)-type elinvar) is determined by several energy parameters {w~tot(k)}. There is a revealed interplay of magnetism and long-range atomic ordering with the order–disorder transformation temperatures, TK, (below TC) appreciably different from the corresponding isolated TK values (above TC). The interplay of these two phenomena is examined along two lines, i.e. through the estimation of both temperature–cFe dependence of spatial LRO parameter and magnetisations of Ni and Fe subsystems. As shown, not only the temperature-dependent phase states of such binary f.c.c. alloys can be reproduced, but also the dependence of TK vs. cFe, including the observed asymmetry of phase-diagram curves due to the T- and cFe-dependent magnetic contribution to the effective interatomic interactions etc. As revealed for f.c.c.-Ni–Fe alloy with the use of single relaxation-time kinetics approximation for calculation of equilibrium intensity values, the magnetic contribution to the ‘mixing’ energy of atoms (in low-spin states) of this alloy facilitates its atomic ordering, and the presence of atoms with essentially different spins may cause the virtually abrupt phase transition from paramagnetic state into magnetic one. The optimal sets of exchange-interaction energy parameters for f.c.c. Ni–Fe alloy are selected. As shown, the doping of small amounts of interstitial C impurities most likely increases ferromagnetic component of bond of Ni spins with Fe spins, reduces ferromagnetic component of bond of Ni spins with Ni spins, and in-creases antiferromagnetic component of bond of Fe spins with Fe spins in an f.c.c.-Ni–Fe alloy.