Off-lattice pattern recognition scheme for kinetic Monte Carlo simulations

Nandipati, Giridhar; Kara, Abdelkader; Shah, Syed Islamuddin; Rahman, Talat S.

doi:10.1016/j.jcp.2011.12.029

Cited by 21 publications

(19 citation statements)

References 41 publications

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“…The strength of this approach is that a known event can be efficiently matched to a new geometry by using existing subgraph matching algorithms (60). Alternatively, a grid-based approach to pattern recognition of local environments avoids the explicit definition of bonds and retains the fast matching property (61). A weakness of these methods is that graph edges or grid entries are discrete, so there is a trade-off between the size of the environment used to describe an event and the number of graphs in the database.…”

Section: Kdb: Kinetic Databasementioning

confidence: 99%

Atomistic Simulations of Activated Processes in Materials

Henkelman

2017

Annu. Rev. Mater. Res.

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Activated processes in materials are important for many of the properties that make them function. Batteries and catalysts are examples for which understanding how the component materials function on a timescale of milliseconds to seconds is critical to making improvements in a rational way. Modeling materials over these long timescales, relative to the timescale of atomic vibrations, is one of the grand challenges of the field. Transition state theory is central to bridging this timescale gap, and in the materials community, the harmonic approximation and the determination of saddle points to quantify reaction rates are ubiquitous. In this review, single-and doubleended methods for saddle point finding are discussed, as well as how finding saddle points can be used in the adaptive kinetic Monte Carlo method to model materials properties on the timescale of activated processes. Applications of surface diffusion and chemistry, phase boundary migration, and solid-solid phase transitions are presented.

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Section: Kdb: Kinetic Databasementioning

confidence: 99%

Atomistic Simulations of Activated Processes in Materials

Henkelman

2017

Annu. Rev. Mater. Res.

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“…A recent extension to three dimensions has a similar scaling with interaction range. 14 Another interesting idea, put forward by El-Mellouhi et al, 9 is to store the local environments around active atoms in terms of their bonding topology. An algorithm called NAUTY (Ref.…”

Section: E Previous Workmentioning

confidence: 99%

Database of atomistic reaction mechanisms with application to kinetic Monte Carlo

Terrell

Welborn

Chill

et al. 2012

The Journal of Chemical Physics

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Kinetic Monte Carlo is a method used to model the state-to-state kinetics of atomic systems when all reaction mechanisms and rates are known a priori. Adaptive versions of this algorithm use saddle searches from each visited state so that unexpected and complex reaction mechanisms can also be included. Here, we describe how calculated reaction mechanisms can be stored concisely in a kinetic database and subsequently reused to reduce the computational cost of such simulations. As all accessible reaction mechanisms available in a system are contained in the database, the cost of the adaptive algorithm is reduced towards that of standard kinetic Monte Carlo.

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“…Several KMC methods are available and are implemented depending on the investigated time and space scales. Atomistic kinetic Monte Carlo (AKMC) methods monitor the positions of all atoms on the lattice [8][9][10] or over the space [11,12]. The variant method is commonly known as object kinetic Monte Carlo (OKMC), rather simulate diffusing entities like defect-solute clusters [13].…”

Section: Introductionmentioning

confidence: 99%

Absorption kinetics of vacancies by cavities in Aluminum: numerical characterization of sink strengths and first-passage statistics through Krylov subspace projection and eigenvalue deflation

Kaur,

Athènes,

Creuze

2021

Preprint

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Modeling the microstructural evolution of metal and alloys, specifically under irradiation, is essential to predict the aging properties of materials. Many models are based on a transition rate matrix describing the jump frequencies of defects and involve a master equation governing the time evolution of a state probability vector. Here, we present non-stochastic numerical techniques to characterize the motion of individual defects migrating over long distances prior to recombining or being absorbed by another defect, resorting to the theory of absorbing Markov chains. These important events are fully determined by their first-passage time distribution to distant locations, no-passage distribution ,and walker fluxes to the sinks. We show that these functions can be efficiently computed using a method combining Krylov subspace projection and eigenvalue deflation. For a model system describing the absorption of a vacancy by a cavity in aluminum, the use of a small Krylov subspace deflated by the unique eigenmode corresponding to the quasi-stationary distribution is sufficient to capture the kinetics of the defect absorption faithfully. This method can be used in kinetic Monte Carlo simulations to perform stochastic non-local moves or in cluster dynamics simulations to compute sink strengths.

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Off-lattice pattern recognition scheme for kinetic Monte Carlo simulations

Abstract: openAccessArticle: FalsePage Range: 3548-3548doi: 10.1016/j.jcp.2011.12.029Harvest Date: 2016-01-12 15:09:32issueName:cover date: 2012-05-01pubType

Cited by 21 publications

References 41 publications

Atomistic Simulations of Activated Processes in Materials

Atomistic Simulations of Activated Processes in Materials

Database of atomistic reaction mechanisms with application to kinetic Monte Carlo

Absorption kinetics of vacancies by cavities in Aluminum: numerical characterization of sink strengths and first-passage statistics through Krylov subspace projection and eigenvalue deflation

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