Diffusion dynamics of defects in Fe and Fe-P systems

Gordon, Stewart M.J.; Kenny, Steven D.; Smith, Roger

doi:10.1103/physrevb.72.214104

Cited by 12 publications

(3 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The KMC method has extensively been employed to study defects of varying dimensionality [55][56][57][58][59][60][61]. Here we study a prototype model of surface defects diffusing on a lattice.…”

Section: A Prototype Model For Diffusion Of Surface Vacanciesmentioning

confidence: 99%

An overview of spatial microscopic and accelerated kinetic Monte Carlo methods

Chatterjee

Vlachos

2007

J Computer-Aided Mater Des

423

400

View full text Add to dashboard Cite

The microscopic spatial kinetic Monte Carlo (KMC) method has been employed extensively in materials modeling. In this review paper, we focus on different traditional and multiscale KMC algorithms, challenges associated with their implementation, and methods developed to overcome these challenges. In the first part of the paper, we compare the implementation and computational cost of the null-event and rejection-free microscopic KMC algorithms. A firmer and more general foundation of the null-event KMC algorithm is presented. Statistical equivalence between the null-event and rejection-free KMC algorithms is also demonstrated. Implementation and efficiency of various search and update algorithms, which are at the heart of all spatial KMC simulations, are outlined and compared via numerical examples. In the second half of the paper, we review various spatial and temporal multiscale KMC methods, namely, the coarse-grained Monte Carlo (CGMC), the stochastic singular perturbation approximation, and the τ -leap methods, introduced recently to overcome the disparity of length and time scales and the one-at-a time execution of events. The concepts of the CGMC and the τ -leap methods, stochastic closures, multigrid methods, error associated with coarse-graining, a posteriori error estimates for generating spatially adaptive coarse-grained lattices, and computational speed-up upon coarse-graining are illustrated through simple examples from crystal growth, defect dynamics, adsorption-desorption, surface diffusion, and phase transitions.

show abstract

Section: A Prototype Model For Diffusion Of Surface Vacanciesmentioning

confidence: 99%

An overview of spatial microscopic and accelerated kinetic Monte Carlo methods

Chatterjee

Vlachos

2007

J Computer-Aided Mater Des

423

400

View full text Add to dashboard Cite

show abstract

“…This accounts for a total rate difference of factor 5.4 between M07 and A04. As the use of the A04 potential is prevalent in point defect simulations in iron, 4,7,[21][22][23][24][35][36][37] we will also use it for reasons of comparability, but will compare with results obtained with M07 in certain cases.…”

Section: A Small Vacancy Clustersmentioning

confidence: 99%

Understanding long-time vacancy aggregation in iron: A kinetic activation-relaxation technique study

et al. 2014

View full text Add to dashboard Cite

Vacancy diffusion and clustering processes in body-centered cubic (bcc) Fe are studied using the kinetic Activation-Relaxation Technique (k-ART), an off-lattice kinetic Monte Carlo (KMC) method with on-the-fly catalog building capabilities. For mono-and di-vacancies, k-ART recovers previously published results while clustering in a 50-vacancy simulation box agrees with experimental estimates. Applying k-ART to the study of clustering pathways for systems containing from 1 to 6 vacancies, we find a rich set of diffusion mechanisms. In particular we show that the path followed to reach a hexavacancy cluster influences greatly the associated mean-square displacement. Aggregation in a 50-vacancy box also shows a notable dispersion in relaxation time associated with effective barriers varying from 0.84 to 1.1 eV depending on the exact pathway selected. We isolate the effects of long-range elastic interactions between defects by comparing to simulations where those effects are deliberately suppressed. This allows us to demonstrate that in bcc Fe, suppressing longrange interactions mainly influences kinetics in the first 0.3 ms, slowing down quick energy release cascades seen more frequently in full simulations, whereas long-term behavior and final state are not significantly affected.

show abstract

“…Recently in some papers, defect structures in α-Fe were discussed using Monte Carlo (MC) technique [1,2], ab initio density functional (PP) model [3][4][5], and molecular dynamics (MD) simulation [6]. Iron exists in different phases, namely α-Fe (room temperature to 768 • C, bcc structure, lattice constant a = 5.48 AU, and ferromagnetic), β-Fe (768 • C to 910 • C, bcc structure, a = 5.48 AU, and nonmagnetic), γ-Fe (910 • C to 1400 • C, fcc structure, a = 6.73 AU, and paramagnetic), and δ-Fe (1400 • C to 1535 • C, bcc structure again).…”

Section: Introductionmentioning

confidence: 99%