Incubation Time at Decomposition of Solid Solution – Stochastic Kinetic Mean-Field Versus Monte Carlo Simulation

Authors

DOI:

https://doi.org/10.15407/ujpe65.6.488

Keywords:

nucleation, Monte Carlo method, solid solution, binodal, spinodal, supersaturation, noise, stochastic kinetic mean-field

Abstract

The comparison of two simulation techniques applied to the nucleation in a supersaturated solid solution is made. The first one is the well-known Monte Carlo (MC) method. The second one is a recently developed modification of the atomistic self-consistent non-linear mean-field method with the additionally introduced noise of local fluxes: Stochastic Kinetic Mean-Field (SKMF) method. The amplitude of noise is a tuning parameter of the SKMF method in its comparison with the Monte Carlo one. The results of two methods for the concentration and temperature dependences of the incubation period become close, if one extrapolates the SKMF data to a certain magnitude of the noise amplitude. The results of both methods are compared also with the Classical Nucleation Theory (CNT).

References

W. Ostwald. Zeitschrift fur physikalische. Chemie 22 (1), 289 (1897). https://doi.org/10.1515/zpch-1897-2233

J.W.P. Schmelzer, A.S. Abyzov. How do Crystals Nucleate and Grow: Ostwald's Rule of Stages and Beyond (Springer, 2017) [ISBN: 978-3-319-45899-1]. https://doi.org/10.1007/978-3-319-45899-1_9

A.M. Gusak, T.V. Zaporozhets, Y.O. Lyashenko, S.V. Kornienko, M.O. Pasichnyy, A.S. Shirinyan. Diffusion-controlled solid state reactions. In: Alloys, Thin Films, and Nanosystems (Wiley, 2010) [ISBN: 978-3-527-40884-9]. https://doi.org/10.1002/9783527631025

D. Turnbull, J.C. Fisher. Rate of nucleation in condensed systems. J. Chem. Phys. 17 (1), 71 (1949). https://doi.org/10.1063/1.1747055

K. Kelton, A.L. Greer. Nucleation in Condensed Matter: Applications in Materials and Biology (Elsevier, 2010) [ISBN: 978-0-08-042147-6].

O.Y. Liashenko, A. Gusak, F. Hodaj. Spectrum of heterogeneous nucleation modes in crystallization of Sn-0.7 wt Cu solder: Experimental results versus theoretical model calculations. J. Mater. Sci.: Mater. Electron. 26 (11), 8464 (2015). https://doi.org/10.1007/s10854-015-3516-z

Nucleation Theory and Applications, edited by J.W.P. Schmelzer (Wiley, 2006) [ISBN-13: 978-3-527-40469-8, ISBN-10:3-527-40469-8].

V.V. Slezov. Kinetics of First-Order Phase Transitions (Wiley, 2009) [ISBN: 978-3-527-40775-0]. https://doi.org/10.1002/9783527627769

A.S. Abyzov, J.W. Schmelzer. Kinetics of segregation processes in solutions: Saddle point versus ridge crossing of the thermodynamic potential barrier. J. Non-Crystalline Solids 384, 8 (2014). https://doi.org/10.1016/j.jnoncrysol.2013.04.019

J.W. Schmelzer, A.S. Abyzov, J. Moller. Nucleation versus spinodal decomposition in phase formation processes in multicomponent solutions. J. Chem. Phys. 121 (14), 6900 (2004). https://doi.org/10.1063/1.1786914

A.S. Abyzov, J.W. Schmelzer, L.N. Davydov. Heterogeneous nucleation on rough surfaces: Generalized Gibbs' approach. J. Chem. Phys. 147 (21), 214705 (2017). https://doi.org/10.1063/1.5006631

F. Soisson, G. Martin. Monte Carlo simulations of the decomposition of metastable solid solutions: Transient and steady-state nucleation kinetics. Phys. Rev. B 62 (1), 203 (2000). https://doi.org/10.1103/PhysRevB.62.203

Z. Erdelyi, M. Pasichnyy, V. Bezpalchuk, J.J. Toman, B. Gajdics, A.M. Gusak. Stochastic kinetic mean field model. Comp. Phys. Commun. 204, 31 (2016). https://doi.org/10.1016/j.cpc.2016.03.003

V. Bezpalchuk, R. Kozubski, M. Pasichnyy, A. Gusak. Tracer diffusion and ordering in FCC structures-stochastic kinetic Mean-Field Method vs. Kinetic Monte Carlo. Defect and Diffusion Forum 383, 59 (2018). https://doi.org/10.4028/www.scientific.net/DDF.383.59

A. Gusak, T. Zaporozhets. Martin's kinetic mean-field model revisited-frequency noise approach versus Monte Carlo. Metallofiz. Noveish. Tekhnol. 40 (11), 1415 (2018). https://doi.org/10.15407/mfint.40.11.1415

B. Gajdics, J.J. Toman, H. Zapolsky, Z. Erdelyi, G. Demange. A multiscale procedure based on the stochastic kinetic mean field and the phase-field models for coarsening. J. Appl. Phys. 126 (6), 065106 (2019). https://doi.org/10.1063/1.5099676

N.V. Storozhuk, K.V. Sopiga, A.M. Gusak. Mean-field and quasi-phase-field models of nucleation and phase competition in reactive diffusion. Philosophical Magazine 93 (16), 1999 (2013). https://doi.org/10.1080/14786435.2012.746793

A.A. Smirnov. Molecular Kinetic Theory of Metals (Nauka, 1966) (in Russian) [ISBN: 978-5-02].

A.A. Kodentsov, G.F. Bastin, F.J.J. Van Loo. The diffusion couple technique in phase diagram determination. J. Alloys and Compounds 320 (2), 207 (2001). https://doi.org/10.1016/S0925-8388(00)01487-0

J.C. Zhao. Reliability of the diffusion-multiple approach for phase diagram mapping. J. Mater. Sci. 39 (12), 3913 (2004). https://doi.org/10.1023/B:JMSC.0000031472.25241.c5

Z. Erdelyi, M. Pasichnyy, V. Bezpalchuk, J.J. Toman, B. Gajdics, A.M. Gusak. Stochastic kinetic mean field model. Comp. Phys. Commun. 204, 31 (2016). https://doi.org/10.1016/j.cpc.2016.03.003

A. Gusak, T. Zaporozhets, N. Storozhuk. Phase competition in solid-state reactive diffusion revisited-stochastic kinetic mean-field approach. J. Chem. Phys. 150 (17), 174109 (2019). https://doi.org/10.1063/1.5086046

C. Hin, J. Lepinoux, J.B. Neaton, M. Dresselhaus. From the interface energy to the solubility limit of aluminium in nickel from first-principles and kinetic Monte Carlo calculations. Mater. Sci. Engin.: B 176 (9), 767 (2011). https://doi.org/10.1016/j.mseb.2011.02.023

A. Biborski, L. Zosiak, R. Kozubski, R. Sot, V. Pierron-Bohnes. Semi-grand canonical Monte Carlo simulation of ternary bcc lattice-gas decomposition: Vacancy formation correlated with B2 atomic ordering in A-B intermetallics. Intermetallics 18 (12), 2343 (2010). https://doi.org/10.1016/j.intermet.2010.08.007

M. Pasichnyy, A. Gusak. Modeling of phase competition and diffusion zone morphology evolution at initial stages of reaction diffusion Defect and Diffusion Forum 237, 1193 (2005). https://doi.org/10.4028/www.scientific.net/DDF.237-240.1193

C. Michaelsen, K. Barmak, T.P. Weihs. Investigating the thermodynamics and kinetics of thin film reactions by differential scanning calorimetry. J. Phys. D: Appl. Phys. 30 (23), 3167 (1997). https://doi.org/10.1088/0022-3727/30/23/001

Downloads

Published

2020-06-09

How to Cite

Pasichna, V. M., Storozhuk, N. V., & Gusak, A. M. (2020). Incubation Time at Decomposition of Solid Solution – Stochastic Kinetic Mean-Field Versus Monte Carlo Simulation. Ukrainian Journal of Physics, 65(6), 488. https://doi.org/10.15407/ujpe65.6.488

Issue

Section

General physics