Two-dimensional hopping diffusion across material interfaces

Deppe, J.; Wallis, R. F.; Nachev, I.; Bałkanski, M.

doi:10.1016/0022-3697(94)90028-0

Cited by 12 publications

(8 citation statements)

References 17 publications

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“…Note that the expressions for the displacement field are valid only if either (a) the dislocation line is an axis of sixfold symmetry or (b) every axis is an axis of evenfold symmetry. A dislocation with Burgers vector b = 1 3 [2110] on the (0110) slip plane was chosen, as it satisfies the first condition, i.e., the Z axis is one of sixfold symmetry. It is possible to construct a dislocation with the same Burgers vector on the (0001) slip plane, but we observed that on the (0001) slip plane, the edge dislocation dissociates into Shockley partials with mixed character.…”

Section: B Vacancy Energetics In the Vicinity Of An Edge Dislocationmentioning

confidence: 99%

“…It has been used to study a variety of phenomena such as surface and bulk diffusion 3,4 , microbial ecologies 5 , cascade annealing 6,7 , and thin film growth 8,9 . A number of enhancements over the last few decades have resulted in improved methods such as absorbing Markov chains 10 , adaptive kMC 11 , object kMC 12 , and accelerated superbasin kMC 13 .…”

Section: Introductionmentioning

confidence: 99%

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Method to account for arbitrary strains in kinetic Monte Carlo simulations

et al. 2013

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We present a method for efficiently recomputing rates in a kinetic Monte Carlo simulation when the existing rate catalog is modified by the presence of a strain field. We use the concept of the dipole tensor to estimate the changes in the kinetic barriers that comprise the catalog, thereby obviating the need for recomputing it from scratch. The underlying assumptions in the method are that linear elasticity is valid, and that the topology of the underlying potential energy surface (and consequently, the fundamental structure of the rate catalog) is not changed by the strain field. As a simple test case, we apply the method to a single vacancy in zirconium diffusing in the strain field of a dislocation, and discuss the consequences of the assumptions on simulating more complex materials.

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Section: B Vacancy Energetics In the Vicinity Of An Edge Dislocationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Method to account for arbitrary strains in kinetic Monte Carlo simulations

et al. 2013

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“…Kinetic Monte Carlo (KMC) is one of the more efficient scale-bridging methods, which we adopt here for this charge-transport problem. KMC approaches for modeling ion and electron transport can be roughly divided into two categories, (1) those that rely on empirical data for diffusion coefficients and diffusion rates − and (2) those in which these properties are calculated using finer-scale molecular dynamics or quantum mechanics techniques. − A major implementation challenge of KMC methods is that unless a complete catalogue of all possible events is created, the simulation will never realize all possible processes, which limits the predictive value. To overcome this challenge, several transition-state search algorithms have been proposed .…”

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confidence: 99%

Kinetic Monte Carlo Study of Ambipolar Lithium Ion and Electron–Polaron Diffusion into Nanostructured TiO₂

Sushko

Kerisit

et al. 2012

J. Phys. Chem. Lett.

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Nanostructured titania (TiO 2 ) polymorphs have proved to be promising electrode materials for next-generation lithium ion batteries. However, there is still a lack of understanding of the fundamental microscopic processes that control charge transport in these materials. Here, we present microscopic simulations of the collective dynamics of lithium ion (Li + ) and chargecompensating electron−polarons (e − ) in rutile TiO 2 nanoparticles in contact with an idealized conductive matrix and electrolyte. Kinetic Monte Carlo simulations are used, parametrized by molecular-dynamics-based predictions of activation energy barriers for Li + and e − diffusion. Simulations reveal the central role of electrostatic coupling between Li + and e − on their collective drift diffusion at the nanoscale. They also demonstrate that a high contact area between the conductive matrix and rutile nanoparticles leads to undesirable coupling-induced surface saturation effects during Li + insertion, which limits the overall capacity and conductivity of the material. These results help provide guidelines for design of nanostructured electrode materials with improved electrochemical performance. SECTION: Energy Conversion and Storage; Energy and Charge Transport

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“…Another class of methods, which has been mostly used for studying material science systems [9][10][11][12], is the kinetic Monte Carlo (KMC) [13] approach, which builds on the fact that for most material systems the dynamical evolution consists of stochastic jumps from one metastable state to another, where the system stays in a state for a sufficiently long-time to lose its memory before making a transition to the next state. Thus, if the underlying dynamics is Markovian, this characteristic can be exploited to evolve the system from one state to another over long times.…”

Section: Introductionmentioning

confidence: 99%

Computing long time scale biomolecular dynamics using quasi-stationary distribution kinetic Monte Carlo (QSD-KMC)

Agarwal

Hengartner

Gnanakaran

et al. 2019

The Journal of Chemical Physics

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It is a challenge to obtain an accurate model of the state-to-state dynamics of a complex biological system from molecular dynamics (MD) simulations. In recent years, Markov State Models have gained immense popularity for computing state-to-state dynamics from a pool of short MD simulations. However, the assumption that the underlying dynamics on the reduced space is Markovian induces a systematic bias in the model, especially in biomolecular systems with complicated energy landscapes. To address this problem, we have devised a new approach we call quasi-stationary distribution kinetic Monte Carlo (QSD-KMC) that gives accurate long time state-to-state evolution while retaining the entire time resolution even when the dynamics is highly non-Markovian.The proposed method is a kinetic Monte Carlo approach that takes advantage of two concepts: (i) the quasistationary distribution, the distribution that results when a trajectory remains in one state for a long time (the dephasing time), such that the next escape is Markovian, and (ii) dynamical corrections theory, which properly accounts for the correlated events that occur as a trajectory passes from state to state before it settles again.In practice, this is achieved by specifying, for each escape, the intermediate states and the final state that has resulted from the escape. Implementation of QSD-KMC imposes stricter requirements on the lengths of the trajectories than in a Markov State Model approach, as the trajectories must be long enough to dephase.However, the QSD-KMC model produces state-to-state trajectories that are statistically indistinguishable from an MD trajectory mapped onto the discrete set of states, for an arbitrary choice of state decomposition. Furthermore, the aforementioned concepts can be used to construct a Monte Carlo approach to optimize the state boundaries regardless of the initial choice of states. We demonstrate the QSD-KMC method on two one-dimensional model systems, one of which is a driven nonequilibrium system, and on two well-characterized biomolecular systems. * gnana@lanl.gov † afv@lanl.gov arXiv:1905.09975v2 [physics.chem-ph]

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Two-dimensional hopping diffusion across material interfaces

Cited by 12 publications

References 17 publications

Method to account for arbitrary strains in kinetic Monte Carlo simulations

Method to account for arbitrary strains in kinetic Monte Carlo simulations

Kinetic Monte Carlo Study of Ambipolar Lithium Ion and Electron–Polaron Diffusion into Nanostructured TiO₂

Computing long time scale biomolecular dynamics using quasi-stationary distribution kinetic Monte Carlo (QSD-KMC)

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Two-dimensional hopping diffusion across material interfaces

Cited by 12 publications

References 17 publications

Method to account for arbitrary strains in kinetic Monte Carlo simulations

Method to account for arbitrary strains in kinetic Monte Carlo simulations

Kinetic Monte Carlo Study of Ambipolar Lithium Ion and Electron–Polaron Diffusion into Nanostructured TiO2

Computing long time scale biomolecular dynamics using quasi-stationary distribution kinetic Monte Carlo (QSD-KMC)

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Kinetic Monte Carlo Study of Ambipolar Lithium Ion and Electron–Polaron Diffusion into Nanostructured TiO₂