Tracer Diffusion and Ordering in FCC Structures - Stochastic Kinetic Mean-Field Method vs. Kinetic Monte Carlo

2018 ◽  
Vol 383 ◽  
pp. 59-65 ◽  
Author(s):  
Volodymyr Bezpalchuk ◽  
Rafal Abdank-Kozubski ◽  
Mykola Pasichnyy ◽  
Andriy Gusak
Keyword(s):  
Activation Energy ◽  
Monte Carlo ◽  
Kinetic Monte Carlo ◽  
Mean Field ◽  
Field Method ◽  
Activation Energies ◽  
Tracer Diffusion ◽  
Atomistic Modelling ◽  
Fcc Alloys ◽  
Diffusion Activation

Recently developed method of atomistic modelling (SKMF) is applied to order-disorder transitions in FCC alloys and to tracer diffusion in the ordered L12 structure. Results correlate with Kinetic Mote-Carlo modelling. Difference of diffusion activation energies of two species is found. Activation energy of ordering is close to one of minority component diffusion.

scholarly journals Kinetic Monte Carlo Simulation of Clustering in an Al-Mg-Si-Cu Alloy

Materials ◽  
2021 ◽  
Vol 14 (16) ◽  
pp. 4523
Author(s):  
Qilu Ye ◽  
Jianxin Wu ◽  
Jiqing Zhao ◽  
Gang Yang ◽  
Bin Yang
Keyword(s):  
Activation Energy ◽  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Kinetic Monte Carlo ◽  
Complex Interaction ◽  
Cu Alloy ◽  
Cu Alloys ◽  
Simulation Results ◽  
Small Clusters ◽  
First Time

The mechanism of the clustering in Al-Mg-Si-Cu alloys has been a long-standing controversial issue. Here, for the first time, the mechanism of the clustering in the alloy was investigated by a Kinetic Monte Carlo (KMC) approach. In addition, reversion aging (RA) was carried out to evaluate the simulation results. The results showed that many small-size clusters formed rapidly in the early stages of aging. With the prolongation of aging time, the clusters merged and grew. The small clusters formed at the beginning of aging in Al-Mg-Si-Cu alloy were caused by initial vacancies (quenching vacancies). The merging and decomposition of the clusters were mainly caused by the capturing of vacancies, and the clusters had a probability to decompose before reaching a stable size. After repeated merging and decomposition, the clusters reach stability. During RA, the complex interaction between the cluster merging and decomposition leaded to the partial irregular change of the hardness reduction and activation energy.

Mean field rate theory and object kinetic Monte Carlo: A comparison of kinetic models

2008 ◽  
Vol 382 (2-3) ◽  
pp. 77-90 ◽  
Author(s):  
R.E. Stoller ◽  
S.I. Golubov ◽  
C. Domain ◽  
C.S. Becquart
Keyword(s):  
Monte Carlo ◽  
Kinetic Models ◽  
Kinetic Monte Carlo ◽  
Mean Field ◽  
Rate Theory ◽  
Object Kinetic Monte Carlo

scholarly journals Theoretical Analysis and Atomistic Modelling of Diffusion and Stability of Pure Element Hollow Nanospheres and Nanotubes

2008 ◽  
Vol 277 ◽  
pp. 21-26 ◽  
Author(s):  
Alexander V. Evteev ◽  
Elena V. Levchenko ◽  
Irina V. Belova ◽  
Graeme E. Murch
Keyword(s):  
Molecular Dynamics ◽  
Monte Carlo ◽  
Kinetic Monte Carlo ◽  
Middle Part ◽  
Dynamics Simulation ◽  
Vacancy Mechanism ◽  
Pure Element ◽  
Hollow Nanosphere ◽  
Analytical Analysis ◽  
Atomistic Modelling

A theoretical and atomistic study of diffusion and stability of a pure element hollow nanosphere and nanotube is performed. The shrinkage via the vacancy mechanism of these hollow nano-objects is described analytically. Using Gibbs-Thomson boundary conditions an exact solution of the kinetic equation in quasi steady-state at the linear approximation is obtained. The collapse time as a function of the geometrical sizes of the hollow nano-objects is determined. Kinetic Monte Carlo simulation of the shrinkage of these nano-objects is performed: it confirms the predictions of the analytical analysis. Next, molecular dynamics simulation in combination with the embedded atom method is used to investigate diffusion by the vacancy mechanism in a Pd hollow nanosphere and nanotube. It is found that the diffusion coefficient in a Pd hollow nanosphere and nanotube is larger near the inner and external surfaces compared with the middle part of a nanoshell. The molecular dynamics results provide quite a strong but indirect argument that a real pure element hollow nanosphere and nanotube may not shrink as readily via the vacancy mechanism as compared with the predictions of the analytical analysis and kinetic Monte Carlo simulations.

scholarly journals Evaluating the Benefits of Kinetic Monte Carlo and Microkinetic Modeling for Catalyst Design Studies in the Presence of Lateral Interactions

2020 ◽  
Author(s):  
Xiao Li ◽  
Lars Grabow
Keyword(s):  
Monte Carlo ◽  
Kinetic Monte Carlo ◽  
Computational Cost ◽  
Mean Field ◽  
Catalyst Design ◽  
Mean Field Approximation ◽  
Lateral Interactions ◽  
Trend Prediction ◽  
Co Oxidation Reaction ◽  
Coverage Effects

<div>Popular computational catalyst design strategies rely on the identification of reactivity descriptors, which can be used along with Brønsted−Evans−Polanyi (BEP) and scaling relations as input to a microkinetic model (MKM) to make predictions for activity or selectivity trends. The main benefit of this approach is related to the inherent dimensionality reduction of the large material space to just a few catalyst descriptors. Conversely, it is well documented that a small set of descriptors is insufficient to capture the intricacies and complexities of a real catalytic system. The inclusion of coverage effects through lateral adsorbate-adsorbate interactions can narrow the gap between simplified descriptor predictions and real systems, but mean-field MKMs cannot properly account for local coverage effects. This shortcoming of the mean-field approximation can be rectified by switching to a lattice-based kinetic Monte Carlo (kMC) method using cluster expansion representation of adsorbate−adsorbate lateral interactions. </div><div><br></div><div>Using the prototypical CO oxidation reaction as an example, we critically evaluate the benefits of kMC over MKM in terms of trend prediction accuracy and computational cost. After confirming that in the absence of lateral interactions the kMC and MKM approaches yield identical trends and mechanistic information, we observed substantial differences between the two kinetic models when lateral interactions were introduced. The difference, however, is mainly manifested in the absolute rates, surface coverages and the optimal descriptor values, whereas relative activity trends remain largely intact. Moreover, the nature of the rate-determining step as identified using Campbell’s degree of rate control is also consistent between both approaches. Considering that the computational cost of MKM is ca. three orders of magnitude lower than for a kMC simulation, the MKM approach does provide the best balance between accuracy and efficiency when used in the context of computational catalyst screening.</div><div><br></div>

scholarly journals Micro-Kinetic Modelling of CO-TPD from Fe(100)—Incorporating Lateral Interactions

Catalysts ◽  
2019 ◽  
Vol 9 (4) ◽  
pp. 310 ◽  
Author(s):  
Thobani Gambu ◽  
R. Abrahams ◽  
Eric van Steen
Keyword(s):  
Monte Carlo ◽  
Kinetic Modelling ◽  
Kinetic Monte Carlo ◽  
Mean Field ◽  
Temperature Programmed Desorption ◽  
Lateral Interactions ◽  
Field Techniques ◽  
Co Dissociation ◽  
The Mean ◽  
Temperature Programmed

The experimentally determined temperature programmed desorption profile of CO from Fe(100) is characterized by four maxima, i.e., α1-CO, α2-CO, α3-CO, and β-CO (see e.g., Moon et al., Surf. Sci. 1985, 163, 215). The CO-TPD profile is modeled using mean-field techniques and kinetic Monte Carlo to show the importance of lateral interactions in the appearance of the CO-TPD-profile. The inclusion of lateral interactions results in the appearance of a new maximum in the simulated CO-TPD profile if modeled using the mean-field, quasi-chemical approach or kinetic Monte Carlo. It is argued that α2-CO may thus originate from lateral interactions rather than a differently bound CO on Fe(100). A detailed sensitivity analysis of the effect of the strength of the lateral interactions between the species involved (CO, C, and O), and the choice of the transition state, which affects the activation energy for CO dissociation, and the energy barrier for diffusion on the CO-TPD profile is presented.

scholarly journals An efficient kinetic Monte Carlo to study analyte capture by a nanopore: transients, boundary conditions and time-dependent fields

2021 ◽  
Author(s):  
Le Qiao ◽  
Maxime Ignacio ◽  
Gary W. Slater
Keyword(s):  
Monte Carlo ◽  
Boundary Conditions ◽  
Kinetic Monte Carlo ◽  
Field Method ◽  
Time Dependent ◽  
Pulsed Field

We introduce an efficient KMC algorithm to simulate voltage-driven translocation, as well as a new pulsed-field method to selectively translocate molecules.

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

2020 ◽  
Vol 65 (6) ◽  
pp. 488
Author(s):  
V. M. Pasichna ◽  
N. V. Storozhuk ◽  
A. M. Gusak
Keyword(s):  
Solid Solution ◽  
Monte Carlo ◽  
Mean Field ◽  
Field Method ◽  
Nucleation Theory ◽  
Tuning Parameter ◽  
Classical Nucleation Theory ◽  
Simulation Techniques ◽  
Field Versus ◽  
Temperature Dependences

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).

scholarly journals Evaluating the Benefits of Kinetic Monte Carlo and Microkinetic Modeling for Catalyst Design Studies in the Presence of Lateral Interactions

2021 ◽  
Author(s):  
Xiao Li ◽  
Lars Grabow
Keyword(s):  
Monte Carlo ◽  
Cluster Expansion ◽  
Kinetic Monte Carlo ◽  
Computational Cost ◽  
Mean Field ◽  
Catalyst Design ◽  
Lateral Interactions ◽  
Small Set ◽  
The Mean ◽  
Coverage Effects

<div><p>Popular computational catalyst design strategies rely on the identification of reactivity descriptors, which can be used along with Brønsted−Evans−Polanyi (BEP) and scaling relations as input to a microkinetic model (MKM) to make predictions for activity or selectivity trends. The main benefit of this approach is related to the inherent dimensionality reduction of the large material space to just a few catalyst descriptors. Conversely, it is well documented that a small set of descriptors is insufficient to capture the intricacies and complexities of a real catalytic system. The inclusion of coverage effects through lateral adsorbate-adsorbate interactions can narrow the gap between simplified descriptor predictions and real systems, but mean-field MKMs cannot properly account for local coverage effects. This shortcoming of the mean-field approximation can be rectified by switching to a lattice-based kinetic Monte Carlo (kMC) method using cluster expansion representation of adsorbate−adsorbate lateral interactions.</p>Using the prototypical CO oxidation reaction as an example, we critically evaluate the benefits of kMC over MKM in terms of trend predictions and computational cost when using only a small set of input parameters. After confirming that in the absence of lateral interactions the kMC and MKM approaches yield identical trends and mechanistic information, we observed substantial differences between the two kinetic models when lateral interactions were introduced. The mean-field implementation applies coverage corrections directly to the descriptors, causing an artificial overprediction of the activity of strongly binding metals. In contrast, the cluster expansion in kMC implementation can differentiate among the highly active metals but it is very sensitive to the set of included interaction parameters. Considering that computational screening relies on a minimal set of descriptors, for which MKM makes reasonable trend predictions at a ca. three orders of magnitude lower computational cost than kMC, the MKM approach does provide a better entry point for computational catalyst design.<br></div>

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