Simulation of the Tracer Diffusion, Bulk Ordering, and Surface Reordering in F.C.C. Structures by Kinetic Mean-Field Method

Abstract

Tracer diffusion and 'chemical' (atomic) ordering processes in two facecentred cubic (f.c.c.) binary systems mimicking Ni 3 Al and FePt were simulated by means of the kinetic mean-field (KMF) method originally proposed by G. Martin in 1990. The systems simulated within the present work were modelled with fixed pair-interaction parameters and saddlepoint energies adopted earlier via the comparison of Monte Carlo method modelling and experimental data. In a simulation of tracer migration as well as ordering, the focus was attracted to comparison of activation energies rather than pre-exponential factors of kinetic coefficients. Generally, the mean-field models cannot properly take into account correlation effect that could be important for the tracer diffusion especially for the B2 structures. However, at least for the f.c.c. structures, application of KMF to diffusion and ordering seems demonstrating very reasonable results qualitatively similar to those obtained in kinetic Monte Carlo (KMC) method and realistic experiments. Modelling of Ni-and Al-tracer diffusion in Ni 3 Al system shows higher diffusivity of Ni atoms as compared with Al ones that is attributed to easier intrasublattice diffusion channel for the Ni atoms in the L1 2 -Ni 3 Al superstructure. Also, the obtained activation energy for the tracer Al atoms is higher, and its value is closer to activation energy of ordering kinetics. Computer experiments for the ordering kinetics showed that, in contrast to exchange mechanism, L1 2 -type ordering kinetics is described via two relaxation times in case of the vacancy diffusion mechanism. Modelling of the discontinuous process of the surface-induced re-orientation of the monatomic Fe and Pt planes in thin FePt film was, in turn, a good test for the stochastic variant of the KMF (SKMF) method. The fact that implementation of the stochastic noise was Fiz. Met. 2017, т. 3, сс. 205- В работе рассматривается диффузия меченых атомов и процесс «хими-ческого» (атомного) упорядочения в двух бинарных системах с гране-центрированной кубической (ГЦК) структурой Ni 3 Al и FePt с использо-ванием среднеполевого кинетического метода (KMF), предложенного Ж. Мартаном в 1990 г. Для указанных систем использовались фикси-рованные значения парных энергий взаимодействия и энергий седловой точки, подобранные ранее путём сравнения моделирования методом Монте-Карло и экспериментальных данных. В моделировании диффу-зии меченых атомов, а также упорядочения их основной акцент на-правлен на сравнение энергий активации, а не предэкспонентных мно-жителей кинетических коэффициентов. В общем случае модели средне-го поля не могут правильно учитывать корреляционный эффект, кото-рый может быть существенным для диффузии меченых атомов, особен-но для структур типа В2. Однако, по крайней мере, для ГЦК-структур, применение KMF к диффузии и упорядочению демонстрирует доста-точно реалистичные результаты, качественно схожие с теми, которые Keywords: kinetic mean-field method, tracer diffusion, ordering kinetics, atomistic simulation, intermetallics....

Modeling of Concentration and Temperature Dependencies of Incubation Time at Decomposition of Solid Solution by Monte Carlo Method

“…Also, we compare our results with the classical nucleation theory [8]. The properties of nucleation are being investigated in parallel with recently developed alternative method SKMF [9][10][11][12].…”

Two Remarks on Wagner Integrated Diffusion Coefficient

“…To illustrate and check the above-mentioned results, we will use atomistic Kinetic Mean Field (KMF) method for the modelling of atomic migration and diffusion-controlled phase transformations on the rigid lattice, suggested by George Martin [8], applied to strongly asymmetric thin-film couples in [9][10][11] and generalized to 3D in [12]. It was developed to include noise, for modelling nucleation and other processes related to overcoming the nucleation barriers [12][13][14][15]. The generalized version of KMF was called SKMF (Stochastic Kinetic Mean Field).…”

“…Yet, more natural is to provide the possibility of fluctuations. Therefore, everywhere below we introduce the noise of local fluxes between neighbouring sites in the form of the noise of jump frequencies and use SKMF instead of KMF method, with the following main kinetic equations [13][14][15]:…”