MODELING OF THE KINETICS OF THE ALLOYS DECOMPOSITION AND HOMOGENIZATION BY THE MEAN- FIELD METHOD

Main Article Content

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

Abstract

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

Section
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

References

Slezov V. V., Sagalovich V. V. (1987). Diffusive decomposition of solid solutions. Soviet Physics Uspekhi, 30(1), 23.

Slezov V. V. (2009). Kinetics of first order phase transitions. New Jersey: John Wiley & Sons.

Avila-Davila E. O., Lopez-Hirata V. M., Saucedo-Muñoz M. L. (2016). Application of Phase-Field Method to the Analysis of Phase Decomposition of Alloys. Modeling and Simulation in Engineering Sciences. InTech.

Jablonski P. D., Hawk J. A. (2017). Homogenizing advanced alloys: thermodynamic and kinetic simulations followed by experimental results. Journal of Materials Engineering and Performance, 26(1), 4-13.

Gusak A. M., Zhusov V. V., Mokrov A. P. (1989). Mathematical simulation of the initial stage of prediffusion homogenization in sintering of a powder mixture. Soviet Powder Metallurgy and Metal Ceramics, 28(8), 623-626.

Gusak A. M., Lucenko G. V. (1998). Interdiffusion and solid state reactions in powder mixtures – one more model. Acta materialia, 46(10), 3343.

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

A. I. Rusanov. (1978). Phasengleichgewichte und Grenzflächenerscheinungen. Berlin: AkademieVerlag.

Schmelzer J., Schweitzer F. Phys. Chem. (Leipzig). (1985) 266, 943; (1989) 270, 5; (1990) 271, 565.

Schmelzer J. W., Abyzov A. S. (2014). Comments on the thermodynamic analysis of nucleation in confined space. Journal of Non-Crystalline Solids, 384, 2.

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

Gusak A. M., Kovalchuk A. O., Straumal B. B. (2013). Interrelation of depletion and segregation in decomposition of nanoparticles. Philosophical Magazine. 93(14), 16771689.

Martin G. (1990). Atomic mobility in Cahn’s diffusion model. Physical Review B. 41 (4), 2279.

Erdélyi Z., Beke D. L., Nemes P., Langer G. A. (1999). On the range of validity of the continuum approach for nonlinear diffusional mixing of multilayers. Philosophical Magazine A, 79(8), 1757.

Erdélyi Z., Szabó I. A., Beke D. L. (2002). Interface sharpening instead of broadening by diffusion in ideal binary alloys. Physical review letters, 89(16), 165901.

Csik A., Langer G. A., Beke D. L., Erdélyi Z., Menyhard M., Sulyok A. (2001). Interdiffusion in amorphous Si/Ge multilayers by Auger depth profiling technique. Journal of Applied Physics, 89(1), 804.

Erdélyi Z., Katona G. L., Beke D. L. (2004). Nonparabolic nanoscale shift of phase boundaries in binary systems with restricted solubility. Physical Review B., 69(11), 113407.

Beke D. L., Erdélyi Z. (2006). Resolution of the diffusional paradox predicting infinitely fast kinetics on the nanoscale, Physical Review B., 73(3), 035426.

Erdélyi Z., Beke D. L., Taranovskyy A. (2008). Dissolution and off-stoichiometric formation of compound layers in solid state reactions. Applied Physics Letters, 92(13), 133110.

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.

Stochastic Kinetic Mean-Field. Electronic resource: http://skmf.eu/

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. Prog. Phys. Met., 18(3), 205.

Bezpalchuk V., 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.

Bezpalchuk V., Pasichnyy M., Gusak A. (2016). Application of a Stochastic Kinetic Mean Field (SKMF) Method to Ordering Substitutional Atoms in Macro- and Nanosize F.C.C. Lattices. Metallofiz. Noveishie Tekhnol. (Physics of Metals and Advanced Technologies), 38(9), 1135.

Bezpalchuk V., Rusenko D., Gusak A. (2017). Influence of the Intermediate Nanointerlayer on a Kinetics of Phase Formation and Ordering in Thin Films – Mean Field Kinetic Simulation. Metallofiz. Noveishie Tekhnol. (Physics of Metals and Advanced Technologies), 39(7), 865.

Gusak Andriy, Zaporozhets Tetiana. (2018). Martin’s Kinetic Mean-Field Model Revisited – Frequency Noise Approach versus Monte Carlo / A. Gusak, T. Zaporozhets // Metallofiz. Noveishie Tekhnol. (Physics of Metals and Advanced Technologies), 40 (11), 1415.