Incubation Time at Decomposition of Solid Solution – Stochastic Kinetic Mean-Field Versus Monte Carlo Simulation
DOI:
https://doi.org/10.15407/ujpe65.6.488Keywords:
nucleation, Monte Carlo method, solid solution, binodal, spinodal, supersaturation, noise, stochastic kinetic mean-fieldAbstract
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
How to Cite
Issue
Section
License
Copyright Agreement
License to Publish the Paper
Kyiv, Ukraine
The corresponding author and the co-authors (hereon referred to as the Author(s)) of the paper being submitted to the Ukrainian Journal of Physics (hereon referred to as the Paper) from one side and the Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine, represented by its Director (hereon referred to as the Publisher) from the other side have come to the following Agreement:
1. Subject of the Agreement.
The Author(s) grant(s) the Publisher the free non-exclusive right to use the Paper (of scientific, technical, or any other content) according to the terms and conditions defined by this Agreement.
2. The ways of using the Paper.
2.1. The Author(s) grant(s) the Publisher the right to use the Paper as follows.
2.1.1. To publish the Paper in the Ukrainian Journal of Physics (hereon referred to as the Journal) in original language and translated into English (the copy of the Paper approved by the Author(s) and the Publisher and accepted for publication is a constitutive part of this License Agreement).
2.1.2. To edit, adapt, and correct the Paper by approval of the Author(s).
2.1.3. To translate the Paper in the case when the Paper is written in a language different from that adopted in the Journal.
2.2. If the Author(s) has(ve) an intent to use the Paper in any other way, e.g., to publish the translated version of the Paper (except for the case defined by Section 2.1.3 of this Agreement), to post the full Paper or any its part on the web, to publish the Paper in any other editions, to include the Paper or any its part in other collections, anthologies, encyclopaedias, etc., the Author(s) should get a written permission from the Publisher.
3. License territory.
The Author(s) grant(s) the Publisher the right to use the Paper as regulated by sections 2.1.1–2.1.3 of this Agreement on the territory of Ukraine and to distribute the Paper as indispensable part of the Journal on the territory of Ukraine and other countries by means of subscription, sales, and free transfer to a third party.
4. Duration.
4.1. This Agreement is valid starting from the date of signature and acts for the entire period of the existence of the Journal.
5. Loyalty.
5.1. The Author(s) warrant(s) the Publisher that:
– he/she is the true author (co-author) of the Paper;
– copyright on the Paper was not transferred to any other party;
– the Paper has never been published before and will not be published in any other media before it is published by the Publisher (see also section 2.2);
– the Author(s) do(es) not violate any intellectual property right of other parties. If the Paper includes some materials of other parties, except for citations whose length is regulated by the scientific, informational, or critical character of the Paper, the use of such materials is in compliance with the regulations of the international law and the law of Ukraine.
6. Requisites and signatures of the Parties.
Publisher: Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine.
Address: Ukraine, Kyiv, Metrolohichna Str. 14-b.
Author: Electronic signature on behalf and with endorsement of all co-authors.
.png){kind=small}
