Application of Stochastic Kinetic Mean-Field method to nucleation, ordering, and phase competition in reactive diffusion
2Department of Solid State Physics, University of Debrecen, Hungary
3M. Smoluchowski Institute of Physics, Jagiellonian University, Poland
Recently, nonlinear self-consistent version of the atomistic kinetic mean-field model suggested by George Martin [1], later applied to the systems with strong diffusion asymmetry [2] and generalized to 3D case [3], was essentially developed [4,5]. New development, SKMF (Stochastic Kinetic Mean-Field), contains Langevin noise of jump frequencies. Noise enables overcoming the barriers in first-order transformations. Nucleation is a natural topic for application of SKMF since noise helps to overcome the nucleation barrier. Application of SKMF to the following problems is discussed:
1. Nucleation rate in the decomposition of the regular solid solution with positive mixing energy as a function of noise amplitude and composition.
2. Decomposition of solid solution (C=1/8) with negative mixing energy with the formation of the ordered phase A3B (C=1/4) and weak solid solution. Nucleation rate as a function of the noise amplitude.
3. Ordering kinetics in FCC structures. Correlations with the tracer diffusivities.
4. Size and surface effects in ordering for nanosystems.
5. Ordering in the sharp concentration gradients.
6. Phase competition in A-B reactive diffusion with the formation of A3B, AB, AB3 phases.
7. SKMF model of phase formation and competition in exothermic SHS reactions.
[1] Martin, G. Phys. Rev. B 41, 2279-2283 (1990).
[2] Erdélyi, Z., Sladecek, M., Stadler, L., Zizak, I., Langer, G., Kis-Varga, M., Beke D., Sepiol, B. Science,306(5703), 1913-1915. (2004).
[3] N. Storozhuk, K. Sopiga, A. Gusak. Philosophical Magazine 93, 1999-2012 (2013).
[4] Erdélyi, Z., Pasichnyy, M., Bezpalchuk, V., Tomán, J. J., Gajdics, B., Gusak, A.M.
Computer Physics Communications. (2016), http://dx.doi.org/10.1016/j.cpc.2016.03.003
[5] http://skmf.eu
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