### Abstract

In present work we discuss the problem of introducing stochasticity into 3D atomistic kinetic mean-field simulations. As this is a new approach for simulating the time evolution of material systems, it should be positioned in the field of available methods. Compared to the most used stochastic techniques: while atomistic kinetic Monte Carlo (KMC) methods generate microstates of the system they simulate, stochastic kinetic mean-field (SKMF) seems to generate mesostates of the system during a finite time-window. Previously, strong interrelation have been found for the dispersion of composition fluctuations in ideal solutions between SKMF states and averaged KMC states. In present work we compare the statistical nature of fluctuations in the two approaches in case of equilibrium solid solutions with non-zero mixing energies. At the investigated high temperature cases we show how at a certain noise amplitude in SKMF the composition fluctuations can be related to results received by averaging a certain number of independent KMC states. Furthermore, the correlation between the neighboring sites, emerging because of the chemical interactions, shows the same statistical behavior in both methods as well.

Original language | English |
---|---|

Article number | 109251 |

Journal | Computational Materials Science |

Volume | 171 |

DOIs | |

Publication status | Published - Jan 1 2020 |

### Fingerprint

### Keywords

- Fluctuation phenomena
- Mean-field
- Monte Carlo
- Noise
- Regular solution
- Statistical mechanics of model systems
- Thermodynamics of solutions

### ASJC Scopus subject areas

- Computer Science(all)
- Chemistry(all)
- Materials Science(all)
- Mechanics of Materials
- Physics and Astronomy(all)
- Computational Mathematics

### Cite this

*Computational Materials Science*,

*171*, [109251]. https://doi.org/10.1016/j.commatsci.2019.109251

**The effect of introducing stochasticity to kinetic mean-field calculations : Comparison with lattice kinetic Monte Carlo in case of regular solid solutions.** / Zaporozhets, Tetyana V.; Taranovskyy, Andriy; Jáger, Gabriella; Gusak, Andriy M.; Erdélyi, Z.; Tomán, János J.

Research output: Contribution to journal › Article

*Computational Materials Science*, vol. 171, 109251. https://doi.org/10.1016/j.commatsci.2019.109251

}

TY - JOUR

T1 - The effect of introducing stochasticity to kinetic mean-field calculations

T2 - Comparison with lattice kinetic Monte Carlo in case of regular solid solutions

AU - Zaporozhets, Tetyana V.

AU - Taranovskyy, Andriy

AU - Jáger, Gabriella

AU - Gusak, Andriy M.

AU - Erdélyi, Z.

AU - Tomán, János J.

PY - 2020/1/1

Y1 - 2020/1/1

N2 - In present work we discuss the problem of introducing stochasticity into 3D atomistic kinetic mean-field simulations. As this is a new approach for simulating the time evolution of material systems, it should be positioned in the field of available methods. Compared to the most used stochastic techniques: while atomistic kinetic Monte Carlo (KMC) methods generate microstates of the system they simulate, stochastic kinetic mean-field (SKMF) seems to generate mesostates of the system during a finite time-window. Previously, strong interrelation have been found for the dispersion of composition fluctuations in ideal solutions between SKMF states and averaged KMC states. In present work we compare the statistical nature of fluctuations in the two approaches in case of equilibrium solid solutions with non-zero mixing energies. At the investigated high temperature cases we show how at a certain noise amplitude in SKMF the composition fluctuations can be related to results received by averaging a certain number of independent KMC states. Furthermore, the correlation between the neighboring sites, emerging because of the chemical interactions, shows the same statistical behavior in both methods as well.

AB - In present work we discuss the problem of introducing stochasticity into 3D atomistic kinetic mean-field simulations. As this is a new approach for simulating the time evolution of material systems, it should be positioned in the field of available methods. Compared to the most used stochastic techniques: while atomistic kinetic Monte Carlo (KMC) methods generate microstates of the system they simulate, stochastic kinetic mean-field (SKMF) seems to generate mesostates of the system during a finite time-window. Previously, strong interrelation have been found for the dispersion of composition fluctuations in ideal solutions between SKMF states and averaged KMC states. In present work we compare the statistical nature of fluctuations in the two approaches in case of equilibrium solid solutions with non-zero mixing energies. At the investigated high temperature cases we show how at a certain noise amplitude in SKMF the composition fluctuations can be related to results received by averaging a certain number of independent KMC states. Furthermore, the correlation between the neighboring sites, emerging because of the chemical interactions, shows the same statistical behavior in both methods as well.

KW - Fluctuation phenomena

KW - Mean-field

KW - Monte Carlo

KW - Noise

KW - Regular solution

KW - Statistical mechanics of model systems

KW - Thermodynamics of solutions

UR - http://www.scopus.com/inward/record.url?scp=85072277272&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85072277272&partnerID=8YFLogxK

U2 - 10.1016/j.commatsci.2019.109251

DO - 10.1016/j.commatsci.2019.109251

M3 - Article

AN - SCOPUS:85072277272

VL - 171

JO - Computational Materials Science

JF - Computational Materials Science

SN - 0927-0256

M1 - 109251

ER -