Tracer Diffusion and Ordering in FCC Structures - Stochastic Kinetic Mean-Field Method vs. Kinetic Monte Carlo

Bezpalchuk, V. M.; Kozubski, R.; Pasichnyy, Mykola; Гусак, А. М.

doi:10.4028/www.scientific.net/ddf.383.59

Cited by 7 publications

(3 citation statements)

References 14 publications

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“…Therefore, it looks reasonable to use SKMF for modelling of nucleation behaviour, keeping in mind the interrelation (8). It might be a good tool to check and distinguish the alternative theories of nucleation [22][23][24], especially in the sharp concentration gradients [25,26].…”

Section: Discussionmentioning

confidence: 99%

Martin’s Kinetic Mean-Field Model Revisited—Frequency Noise Approach versus Monte Carlo

Гусак¹,

Zaporozhets²

2018

Metallofiz. Noveishie Tekhnol.

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Development of the non-linear kinetic mean-field model suggested by GeorgeMartin in 1990 is discussed. Its steady-state limit is shown to coincide with Khachaturyan's model. It is proved rigorously that Martin's model and its 3D version always provide decrease of free energy and are unable to model any overcoming of free-energy barrier, including nucleation. To enable nucleation processes within the mean-field models, the introduction of noise is necessary. Contrary to common way of noise introduction (noise of concentration), we introduce the noise of jump frequencies as a basic reason of fluctuations. The new method is called as Stochastic Kinetic Mean Field (SKMF). In this paper, we investigate and compare the dispersion and spatial correlations of concentration fluctuations by three methods-direct Monte Carlo simulation, numeric simulation by SKMF method, and analytic approximation within the scope of SKMF. Comparison confirms the correspondence of frequency noise to the averaging over finite number of Monte Carlo runs (over finite number of copies of the canonical ensemble).

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Section: Discussionmentioning

confidence: 99%

Martin’s Kinetic Mean-Field Model Revisited—Frequency Noise Approach versus Monte Carlo

Гусак¹,

Zaporozhets²

2018

Metallofiz. Noveishie Tekhnol.

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“…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].…”

Section: Introductionmentioning

confidence: 92%

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

Pasichna

2019

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Uu; 82.56.Lz MODELING OF CONCENTRATION AND TEMPERATURE DEPENDENCIES OF INCUBATION TIME AT DECOMPOSITION OF SOLID SOLUTION BY MONTE CARLO METHOD * The article presents the application of Monte Carlo method to the kinetics of nucleation at the decomposition of a binary solid solution with a face-centered cubic lattice. We built a phase diagram of a binary solid solution by Monte Carlo method and found the dependence of incubation time on supersaturation of solid solution at different reduced temperatures in metastable regions. Obtained results of the computer experiment are compared with the classical nucleation theory, in which the nucleus is born at once with almost optimal composition, and then just grows.

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“…Після цього метод кінетичного середнього поля (KMF), за рахунок введення динамічного шуму Ланжевена, був перетворений в стохастичний кінетичний середньо-польовий метод (SKMF [7,21]). Подальший розвиток методу та його застосування можна знайти в [22][23][24][25].…”

Section: основи методів Kmf і Skmfunclassified

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2019

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Tracer Diffusion and Ordering in FCC Structures - Stochastic Kinetic Mean-Field Method vs. Kinetic Monte Carlo

Cited by 7 publications

References 14 publications

Martin’s Kinetic Mean-Field Model Revisited—Frequency Noise Approach versus Monte Carlo

Martin’s Kinetic Mean-Field Model Revisited—Frequency Noise Approach versus Monte Carlo

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

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