Field kinetic model and computer simulation of precipitation of L12 ordered intermetallics from f.c.c. solid solution

Wang, Y.; Banerjee, D.; Su, Congxue; Khachaturyan, A. G.

doi:10.1016/s1359-6454(98)00015-9

Cited by 277 publications

(180 citation statements)

References 38 publications

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“…Such free energies have been obtained for many different physical situations [16,17,18,19]. The present derivation of the free energy is based upon some of these earlier constructions.…”

Section: Total Free Energymentioning

confidence: 94%

Phase-field model for grain boundary grooving in multi-component thin films

Bouville¹,

Hu²,

Chen³

et al. 2006

Modelling Simul. Mater. Sci. Eng.

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Abstract. Polycrystalline thin films can be unstable with respect to island formation (agglomeration) through grooving where grain boundaries intersect the free surface and/or thin film-substrate interface. We develop a phase-field model to study the evolution of the phases, composition, microstructure and morphology of such thin films. The phase-field model is quite general, describing compounds and solid solution alloys with sufficient freedom to choose solubilities, grain boundary and interface energies, and heats of segregation to all interfaces. We present analytical results which describe the interface profiles, with and without segregation, and confirm them using numerical simulations. We demonstrate that the present model accurately reproduces the theoretical grain boundary groove angles both at and far from equilibrium. As an example, we apply the phase-field model to the special case of a Ni(Pt)Si (Ni/Pt silicide) thin film on an initially flat silicon substrate.

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“…Such free energies have been obtained for many different physical situations [16,17,18,19]. The present derivation of the free energy is based upon some of these earlier constructions.…”

Section: Total Free Energymentioning

confidence: 94%

Phase-field model for grain boundary grooving in multi-component thin films

Bouville¹,

Hu²,

Chen³

et al. 2006

Modelling Simul. Mater. Sci. Eng.

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“…The technique was then applied to nanofilms with diffusion asymmetry in the series of papers by Z. Erdelyi, D. Beke et al [5][6][7][8], extended to 3D [9], and recently generalized to first-order transformations by introducing dynamic noise of jump frequencies in the kinetic master equations ('stochastic KMF' (SKMF) [10].) The Martin's version of KMF approach is not the only one [11][12][13][14]. The mean-field approach is a very popular approximation when interactions between particles are approximated by interactions of particles with some effective field representing an averaged effect 208 V. M. BEZPALCHUK, R. KOZUBSKI, and A. M. GUSAK of the surrounding atoms.…”

Section: Introductionmentioning

confidence: 99%

“…It was intensively developed to calculate, for example, the phase diagram of f.c.c. binary alloys [12], but also to model the kinetics of the phase transformations (for example, precipitation of Ni 3 Al from disordered solution) [13,14]. The fundamental difference between Martin's approach and other kinetic mean-field approaches is the self-consistent introduction of jump frequencies using the actual interaction energies.…”

Section: Introductionmentioning

confidence: 99%

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

2017

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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....

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“…[1][2][3][4] The phase-field model describes a microstructure using a set of conserved or non-conserved field variables. The microstructure evolution can be simulated by a set of equations governing the evolution of the fields under the condition of achieving the minimum of the total free energy of the system.…”

Section: Introductionmentioning

confidence: 99%

“…The microstructure evolution can be simulated by a set of equations governing the evolution of the fields under the condition of achieving the minimum of the total free energy of the system. In previous works on Ni-based alloys, 1,2,4) the difference in elastic constants between the and 0 phases (elastic inhomogeneity) have not been considered in the calculation of the elastic strain energy, because the elastic inhomogeneity is less than 7% in the wide range of temperatures in NiAl binary system. 5) However, it is important to understand the effect of the elastic inhomogeneity on the microstructure evolution, because the elastic inhomogeneity has become about 13% in a practical Ni-based superalloy at high temperatures.…”

Section: Introductionmentioning

confidence: 99%

Phase-Field Simulation of the Effect of Elastic Inhomogeneity on Microstructure Evolution in Ni-Based Superalloys

et al. 2009

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Phase-field simulation is performed to examine the effect of elastic inhomogeneity between the and 0 phases on microstructure evolution of the 0 phase in Ni-based superalloys. For solving the elastic equilibrium equation numerically in the elastically inhomogeneous system, an iterative approach is used. In this simulation, both elastic anisotropy and shear modulus are varied independently based on the elastic constants of a practical Ni-based superalloy. Four different types of anti-phase domains in the 0 phase are also considered in this simulation. The variation of elastic anisotropy affected significantly the manner of both morphology of the 0 phase and distribution function of the 0 particle size, whereas the variation of shear modulus did not affect them.

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Field kinetic model and computer simulation of precipitation of L12 ordered intermetallics from f.c.c. solid solution

Cited by 277 publications

References 38 publications

Phase-field model for grain boundary grooving in multi-component thin films

Phase-field model for grain boundary grooving in multi-component thin films

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

Phase-Field Simulation of the Effect of Elastic Inhomogeneity on Microstructure Evolution in Ni-Based Superalloys

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