Rafal Kozubski

Ordering kinetics in Ni3Al by molecular dynamics

We present molecular dynamics simulations of ordering kinetics in the Ni3Al alloy performed within the embedded atom method (EAM) as a scheme for interatomic potentials. The simulation cell containing 1372 atoms was initially perfectly L12-long-range ordered. After having artificially created one vacancy by removing at random one Ni-atom, the dynamics of the system was simulated at constant temperature and pressure. Atoms are found to migrate predominantly via jumps to nearest-neighbour (nn) vacancies. The number of antisites is low in comparison to the total number of atomic jumps. Therefore most of the jumps are ineffective for ordering kinetics causing only temporary change of the chemical order. Accordingly, the jumps creating antisites are most often followed by reverse jumps. Antisite defects are created as nn antisite pairs. This result is in agreement with predictions based on a model originally formulated within Monte Carlo simulations. 2002 Published by Elsevier Science B.V.

Thermotransport in binary system: case study on Ni50Al50 melt

The formalism of thermotransport in a binary system is analysed. Focus is put on a detailed consideration of the heat of transport parameter characterizing diffusion driven by a temperature gradient. We introduce the reduced heat of transport parameter , which characterizes part of the interdiffusion flux that is proportional to the temperature gradient. In an isothermal system represents the reduced heat flow (pure heat conduction) consequent upon unit interdiffusion flux. It is demonstrated that is independent of reference frame and is useful in a practical way for direct comparison of simulation and experimental data from different sources obtained in different reference frames. In the case study of the liquid Ni50Al50 alloy, we use equilibrium molecular dynamics simulations in conjunction with the Green–Kubo formalism to evaluate the heat transport properties of the model within the temperature range of 1500–4000 K. Our results predict that in the presence of a temperature gradient Ni tends to diffuse from the cold end to the hot end whilst Al tends to diffuse from the hot end to the cold end.

Influence of the interatomic potential on thermotransport in binary liquid alloys: case study on NiAl

Abstract Equilibrium molecular dynamics simulation in conjunction with the Green-Kubo formalism is employed to study the transport properties of a model Ni50Al50 melt with the embedded-atom method potential developed in [G.P. Purja Pun, Y. Mishin, Phil. Mag., 2009, 89, 3245]. The principal objective of the work is to quantitatively characterise and analyse thermotransport in the system, i.e. diffusion driven by a temperature gradient. In addition, direct phenomenological coefficients for mass and thermal transport are also evaluated and analysed in the process. Furthermore, the results obtained are compared with previously published data for a different model of Ni50Al50 melt with an alternative embedded-atom method potential for the alloy as well as with experiment where possible. It is found that both potentials are able to consistently predict both direct transport coefficients over a wide temperature range. However, these two potentials are found to be inconsistent in characterising the cross-coupled heat and mass transport, predicting even different directions (sign) of the heat of thermotransport. The origin of this difference is discussed in the paper in detail.

Self-diffusion and ‘order–order’ kinetics in B2-ordering AB binary systems with a tendency for triple-defect formation: Monte Carlo simulation

Self-diffusion of component atoms and ‘order–order’ relaxations in a B2-ordering binary system AB showing a tendency for triple-defect formation were consistently simulated by means of two Monte Carlo techniques. In view of a strict correlation between antisite-defect and vacancy concentrations the Kinetic Monte Carlo (KMC) simulations were implemented with a temperature-dependent vacancy concentration determined by means of Semi-Grand Canonical Monte Carlo (SGCMC) simulations. The Ising model of the system was completed with local-configuration-dependent saddle-point energy parameters related to vacancy mediated atomic jumps. The simulations elucidated the atomistic origin of the experimentally observed low rate of ‘order–order’ relaxations in NiAl, as well as reproduced the experimental relation between the activation energies for ‘order–order’ kinetics and Ni self-diffusion in NiAl. Higher value of the deduced activation energy for atomic migration with respect to the effective energy barriers related to individual atomic jumps indicated their high correlation.

“Order-order” relaxations in intermetallics

Abstract “Order-order” relaxation processes in high-temperature intermetallics occur after an abrupt change of temperature and are controlled by atomic migration in the almost perfect superstructure. The related experiments were carried out using systems being of technological interest and representing three common types of superstructures: L12 (Ni3Al-based quasi-binaries), L10 (FePd, FePt) and B2 (NiAl, FeAl). The corresponding Monte Carlo (MC) simulations of “order-order” kinetics involving the Glauber dynamics implemented with vacancy mechanism for atomic jumps were performed. The studies indicate a crucial role of anti-site-easy-diffusion channels offered by particular superstructures in determining the character of “order-order” processes and their relationship to steady-state self-diffusion. Specific mechanisms of the relaxations in triple-defect B2-ordered binaries are discussed.

Atomic migration and ordering phenomena in bulk and thin films of FePd and FePt

Abstract “Order–order” kinetics was studied by means of “in situ” and quasi-residual (REST) resistometry in bulk and thin films of L10-ordered FePd and FePt intermetallics. Substantial effect of magnetic ordering on the activation energy for chemical ordering was revealed in FePd. A discontinuous change of ordering dynamics was detected in FePt between 800 and 830 K. The results are consistent with the data of Fe* diffusion in FePt multilayer examined by means of nuclear resonant scattering in grazing-incidence geometry (GINRS). Monte Carlo (MC) simulations of “order–order” processes in L10-ordered bulk FePd and FePt and nano-layered FePt have been carried out using Glauber dynamics with vacancy mechanism of atomic jumps. Multi-time-scale “order–order” relaxations observed in the bulk were predominated in nanolayers by a reorientation of the initial z-variant L10 superstructure into a mixture of x- and y-variants.

Chemical ordering beyond the superstructure in long-range ordered systems

To describe chemical ordering in solid solutions systems Warren-Cowley short-range parameters are ordinarily used. However, they are not directly suited for application to long-range ordered systems, as they do not converge to zero for large separations. It is the aim of this paper to generalize the theory to long-range ordered systems and quantitatively discuss chemical short-range order beyond the superstructure arrangements. This is demonstrated on the example of a non-stoichiometric B2-ordered intermetallic alloy. Parameters of interatomic potentials are taken from an embedded atom method (EAM) calculations and the degree of order is simulated by the Monte Carlo method. Both on-lattice and off-lattice methods, where the latter allows individual atoms to deviate from their regular lattice sites, were used, and the resulting effects are discussed.

Mechanism of “Order-Order” Kinetics in Ll 2 Superstructure Studied by Computer Simulation

Monte Carlo simulations of the isothermal long-range order (LRO) relaxation in A 3 B system with Ll 2 superstructure have been performed within a model based on a vacancy jump mechanism between nearest neighbour lattice sites. The studies aimed at the explanation of the origin of two simultaneous LRO relaxation processes experimentally observed in Ni 3 Al. An effect of pair interaction energies and saddle-point energies (assigned to jumping atoms) was studied. The preference of vacancies for the A-sublattice (face centres), commonly postulated for Ni 3 Al, occurred only for a narrow range of pair-interaction energies within the domain corresponding to Ll 2 ordering. It was found that the appearance of the fast relaxation process is definitely correlated with the efficiency of B-atom jumps, as well as with the values of the saddle-point energies. The results lead to a microscopic model of the “order-order” relaxation in Ll 2 superstructure and yield new indications for the choice of pair-interaction energy parameters applied in Monte Carlo simulations of atomic migration in Ll 2 intermetallic compounds.

Interdiffusion and thermotransport in Ni–Al liquid alloys

ABSTRACT In this paper, we present extensive self-consistent results of molecular dynamics (MD) simulations of diffusion and thermotransport properties of Ni–Al liquid alloys. We develop a new formalism that allows easy connection between results of the MD simulations and the real experiments. In addition, this formalism can be extended to the case of ternary and higher component liquid alloys. We focus on the temperature and composition dependence of the self-diffusion coefficients, interdiffusion coefficients, thermodynamic factor, Manning factor and the reduced heat of transport. The two latter quantities both represent measures of the off-diagonal Onsager phenomenological coefficients. The Manning factor and the reduced heat of transport can be related to experimentally obtainable quantities provided the thermodynamic factor is available. The simulation results for the reduced heat of transport show that for all compositions, in the presence of a temperature gradient, Ni tends to migrate to the cold end. This is in agreement with an available experimental study for a Ni21.5Al78.5 melt (only qualitative result is available so far).

Atomistic origin of the thermodynamic activation energy for self-diffusion and order-order relaxation in intermetallic compounds II: Monte Carlo simulation of B2-ordering binaries

Abstract The validity of previously derived formulae expressing the activation energies for self-diffusion and ‘order–order’ relaxations in intermetallics in terms of the activation energies of more elementary processes involved in the phenomena is tested by simulation of particular binary systems. The simulation results were in good agreement with the tested formulae. It was shown that the relationship between the activation energies observed in triple-defect B2-ordering binaries, where the value of the activation energy for order–order relaxations is substantially lower than that for self-diffusion, does not hold in the case of non-triple-defect binaries. Using the tested formulae, the origin of the effect was elucidated and attributed to the atomistic origin of the tendency for triple-defect disordering.