Monte Carlo simulations for a Lotka-type model with reactant surface diffusion and interactions

2001 ◽  
Vol 63 (5) ◽  
Author(s):  
G. Zvejnieks ◽  
V. N. Kuzovkov
2009 ◽  
Vol 289-292 ◽  
pp. 361-368 ◽  
Author(s):  
Andrzej Biborski ◽  
L. Zosiak ◽  
Rafal Abdank-Kozubski

Surprisingly low rate of “order-order” kinetics in stoichiometric NiAl intermetallic known of very high vacancy concentration suggested a specific triple-defect mechanism of ordering/disordering in this system [1]. This mechanism implies a correlation between the concentrations of antisite defects and vacancies; the latters being trapped in triple defects and thus, inactive as atomic migration agents. The process was modelled by means of Monte Carlo (MC) simulations recognised as a powerful tool for such tasks [2], but requiring now the implementation of thermal vacancy thermodynamics. Temperature dependence of vacancy concentration in an AB B2 binary system was determined within an Ising-type model solved first in Bragg-Williams approximation [3] and then by means of MC simulation of a Grandcanonical Ensemble. Without any a priori assumptions concerning the formation of particular types of point defects the model yielded temperature domains where the concentrations of antisite defects and vacancies were proportional. The effect associated with the formation of triple defects appeared for specific values of atomic pair-interaction energies. Moreover, non-stoichiometric A-B systems with the same atomic pair-interaction energies showed the existence of constitutional vacancies at low temperatures. Monte Carlo simulations of “order-order” (disordering) kinetics in B2 AB systems modelled with triple-defect-promoting atomic pair-interaction energies were run with temperature-dependent concentra-tion (i.e. number) of vacancies given by the above model. The simulated relaxations showed two stages: (i) rapid formation of triple defects engaging almost all vacancies present in the system, (ii) very slow process of further generation of antisite defects until the equilibrium concentration was reached. The result reproduced very well the experimental observations [1].


Vacuum ◽  
2001 ◽  
Vol 63 (1-2) ◽  
pp. 127-133 ◽  
Author(s):  
M.A Załuska-Kotur ◽  
A Łusakowski ◽  
S Krukowski ◽  
Z Romanowski ◽  
Ł.A Turski

2008 ◽  
Vol 277 ◽  
pp. 167-175 ◽  
Author(s):  
A.S. Shirinyan ◽  
D.V. Lubyanskyy

The separation kinetics in a binary nanoparticle is studied by means of two-dimensional Monte-Carlo sampling and Ising-type model, where the species exchange positions due to vacancy mechanism. The model is developed in case of a free nanoparticle with a coating shell. The kinetics is shown to depend on the size of a nanosystem. We demonstrate a distinct size-induced freezing effect on kinetics of separation.


1992 ◽  
Vol 96 (9) ◽  
pp. 7144-7154 ◽  
Author(s):  
D. Rostkier‐Edelstein ◽  
S. Efrima

1999 ◽  
Vol 06 (03n04) ◽  
pp. 323-340 ◽  
Author(s):  
F. NIETO ◽  
A. A. TARASENKO ◽  
V. PEREYRA ◽  
C. UEBING

In this paper we study the influence of adsorption-induced surface reconstruction on both the adsorption–desorption kinetics and the surface diffusion of adsorbed particles. The reconstruction is regarded as an order–disorder phase transition, which is described in the framework of the lattice gas formalism by the two-position (2P) model. Adsorption is studied by kinetic Monte Carlo simulations while surface diffusion coefficients are evaluated by using the classical Monte Carlo modeling. Utilizing Monte Carlo simulations we characterize how the behavior of the chemical (D), the jump (DJ) and the tracer (D*) diffusion coefficients depend on the different ordered phases predicted by the model.


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