Main Article Content

D. M. Fenech
M. O. Pasichnyy
A. M. Gusak


The application of Stochastic Kinetic Mean Field approach to the kinetics of nucleation at the decomposition of supersaturated binary solid solution is presented. The dependencies of incubation time on the noise amplitude and the supersaturation are obtained. SKMF modeling demonstrates the validity of Classical Nucleation Theory. The logarithm of nucleation time is inversely proportional to the squared supersaturation. The logarithm of nucleation time is a linear function of the inverse squared noise amplitude.

Article Details

Materials Physics
Author Biographies

D. M. Fenech, The Bohdan Khmelnytsky National University of Cherkasy

Master's student of Educational-Scientific Institute of Informational and Eduational Technologies

M. O. Pasichnyy, candidate of physical and mathematical sciences, associate professor, head of the chair of physics

The Bohdan Khmelnytsky National University of Cherkasy

A. M. Gusak, 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


Beinke D., Oberdorfer C., Schmitz G. (2016). Towards an accurate volume reconstruction in atom probe tomography. Ultramicroscopy, 165, 34-41. Retrieved from

Amouyal Y., Schmitz G. (2016). Atom probe tomography – A cornerstone in materials characterization. MRS Bulletin, 41(1), 13-18. Retrieved from

Park J. H., Schneider N. M., Grogan J. M., Reuter M. C., Bau H. H., Kodambaka S., Ross F. M. (2015). Control of electron beam-induced Au nanocrystal growth kinetics through solution chemistry. Nano letters, 15(8), 5314-5320. Retrieved from

Schmelzer J. W., Abyzov A. S. (2018). Crystallization of glass-forming melts: New answers to old questions. Journal of Non-Crystalline Solids, 501, 11-20. Retrieved from

Schmelzer J. W., Abyzov A. S., Möller J. (2004). Nucleation versus spinodal decomposition in phase formation processes in multicomponent solutions. The Journal of chemical physics, 121(14), 6900-6917. Retrieved from

Soisson F., Martin G. (2000). Monte Carlo simulations of the decomposition of metastable solid solutions: Transient and steady-state nucleation kinetics. Physical Review B, 62(1), 203-214. Retrieved from

Erdélyi Z., Pasichnyy M., Bezpalchuk V., Tomán J. J., Gajdics B., Gusak A. M. (2016). Stochastic kinetic mean field model. Computer Physics Communications, 204, 31-37. Retrieved from

Bezpalchuk V., Abdank-Kozubski R., Pasichnyy M., Gusak A. (2018). Tracer Diffusion and Ordering in FCC Structures-Stochastic Kinetic Mean-Field Method vs. Kinetic Monte Carlo. Defect and Diffusion Forum, 383, 59-65. Retrieved from

Bezpalchuk V. M., Kozubski R., Gusak A. M. (2017). Simulation of the tracer diffusion, bulk ordering, and surface reordering in fcc structures by kinetic mean-field method. Uspehi fiziki metallov (Progress in Physics of Metals), 18(3), 205-233. Retrieved from

Wang Y., Banerjee D., Su C. C., Khachaturyan A. G. (1998). Field kinetic model and computer simulation of precipitation of L12 ordered intermetallics from fcc solid solution. Acta materialia, 46(9), 2983-3001. Retrieved from

Gusak A., Zaporozhets T. (2018). Martin’s Kinetic Mean-Field Model Revisited – Frequency Noise Approach versus Monte Carlo. Metallofizika i Noveishie Tekhnologii (Metallophysics and Advanced Technologies), 40(11), 1415-1435. Retrieved from

Storozhuk N. V., Sopiga K. V., Gusak A. M. (2013). Mean-field and quasi-phase-field models of nucleation and phase competition in reactive diffusion. Philosophical Magazine, 93(16), 1999-2012. Retrieved from

Rusanov A. I. (1967). Phase equilibria and surface phenomena. Leningrad: Khimiya (in Russ.).

Schmelzer J., Ulbricht H. (1987). Thermodynamics of finite systems and the kinetics of first-order phase transitions. Journal of Colloid and Interface Science, 117(2), 325-338. Retrieved from

Shirinyan A. S., Gusak A. M. (2004). Phase diagrams of decomposing nanoalloys. Philosophical Magazine, 84(6), 579-593. Retrieved from