Main Article Content

О. М. Мельниченко
Н. В. Сторожук
Т. В. Запорожець
А. М. Гусак


The recently developed stochastic kinetic method of the mean-field (stochastic modification of the well-known KMF method) is applied:

- to simulate all stages of decomposition, 

- to study the dependence of the decomposition kinetics on the asymmetry of interactions and diffusion, 

- to study the size effects in the decomposition of nanoparticles, 

- to model the late stages of alloy homogenization.

The possibility of reasonable description of the decomposition and homogenization in binary alloys by the SKMF method has been demonstrated. Namely:

1. Kinetics of spinodal decomposition of the symmetric and asymmetric alloys is studied in details: the time interval is clearly distinguished, during which the characteristic length of the heterogeneity is almost constant (structural "framework"), and the dispersion increases according to the exponential law. 

2. Decomposition of the metastable alloy is characterized by a delay of the second peak formation. It corresponds to the incubation period of nucleation.

3. The existence of the size effect was confirmed. Namely, the decomposition cupola becomes lower and narrower with a decrease the system size.

4. Simple scheme for the simultaneous observation of decomposition and homogenization at the different stages of the process was suggested.  This is provided by an abrupt increase of temperature, which turns the decomposing alloy into a homogenizing alloy.

5. Dispersion at the late stage of homogenization decreases exponentially with time. Thus, the SKMF method is useful not only for research, but, as well, can be used at practical and laboratory works in the course of computational materials science. 

Article Details

Methods of Teaching Physics and Mathematics in Higher Education
Author Biographies

О. М. Мельниченко, The Bohdan Khmelnytsky National University of Cherkasy

Master of Physics (2018)

Н. В. Сторожук, The Bohdan Khmelnytsky National University of Cherkasy

Candidate of physical and mathematical sciences

Т. В. Запорожець, The Bohdan Khmelnytsky National University of Cherkasy

Doctor of physics and mathematics, professor, Head of the teaching and methodical department

А. М. Гусак, The Bohdan Khmelnytsky National University of Cherkasy

Doctor of physical and mathematical sciences, professor Honored Worker of Science and Technology of Ukraine Leading Researcher, Laboratory of Mathematical Physics, Department of Physics of Educational-Scientific Institute of Informational and Eduational Technologies


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