Grain boundary energy and curvature in Monte Carlo and cellular automata simulations of grain boundary motion

Mason, Jan

doi:10.1016/j.actamat.2015.04.047

Cited by 42 publications

(15 citation statements)

References 48 publications

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“…In most work, H is assumed to be the inverse of the mean spherical equivalent grain radius. With the emergence of three-dimensional microscopic techniques and simulations, it has become possible to locally measure curvature within voxelized microstructures [10][11][12][13][14][15] and a technique that can be used to measure local grain boundary curvature and correlate it to the crystallography of the grain boundary has recently been reported. 16 The method has been applied to two ferrous alloys and it was found that the curvature varies strongly as a function of the grain boundary plane orientation.…”

Section: Introductionmentioning

confidence: 99%

Grain boundary curvatures in polycrystalline SrTiO₃: Dependence on grain size, topology, and crystallography

et al. 2019

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By mapping grain orientations on parallel serial sections of a SrTiO3 ceramic, it was possible to reconstruct three‐dimensional orientation maps containing more than 3000 grains. The grain boundaries were approximated by a continuous mesh of triangles and mean curvatures were determined for each triangle. The integral mean curvatures of grain faces were determined for all grains. Small grains with fewer than 16 neighbors mostly have positive mean curvatures while larger grains with more than 16 neighbors mostly have negative mean curvatures. It is also possible to correlate the mean curvature of individual triangles with the crystallographic characteristics of the grain boundary. The mean curvature is lowest for grain boundaries with (100) orientations and highest for grain boundaries with (111) orientations. This trend is inversely correlated to the relative areas of grain boundaries and directly correlated to the relative grain boundary energy. The direct correlation between the energy and curvature is consistent with the expected behavior of grain boundaries made up of singular orientations. Furthermore, because both the relative energy and curvature of grain boundaries with (100) orientations are minima in the distributions, these boundaries also have the lowest driving force for migration.

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Section: Introductionmentioning

confidence: 99%

Grain boundary curvatures in polycrystalline SrTiO₃: Dependence on grain size, topology, and crystallography

et al. 2019

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“…The Monte Carlo models simulate curvature-driven grain boundary motion by the random movement of kinks (2D) or ledges (3D) along the grain boundaries controlled by the transition rules. Due to the calculations of grain boundary curvature and energy are ambiguous and the transition rules governing the change of voxel state are often not physically justified, the physical meaning of units of length, time and energy in Monte Carlo models is often unspecified [147]. Nonetheless, the numerical implementation is straightforward and decent computational efficiency can be achieved in the Monte Carlo models, especially since the algorithm is very suitable for parallelization, the Monte Carlo models are still frequently used to model the complex microstructure evolution in materials.…”

Section: Monte Carlo Modelsmentioning

confidence: 99%

A review on the modeling and simulations of solid-state diffusional phase transformations in metals and alloys

Liu

Zhan

2018

Manufacturing Rev.

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Solid-state diffusional phase transformations are vital approaches for controlling of the material microstructure and thus tailoring the properties of metals and alloys. To exploit this mean to a full extent, much effort is paid on the reliable and efficient modeling and simulation of the phase transformations. This work gives an overview of the developments in theoretical research of solid-state diffusional phase transformations and the current status of various numerical simulation techniques such as empirical and analytical models, phase field, cellular automaton methods, Monte Carlo models and molecular dynamics methods. In terms of underlying assumptions, physical relevance, implementation and computational efficiency for the simulation of phase transformations, the advantages and disadvantages of each numerical technique are discussed. Finally, trends or future directions of the quantitative simulation of solid-state diffusional phase transformation are provided.Keywords: Solid-state diffusional phase transformation / numerical simulation / empirical and analytical models / phase-field models / cellular automata / Monte Carlo models / molecular dynamics methods *

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“…[1][2][3] However, the experimental study of grain growth is severely limited by the high temperatures at which it occurs and the optical opacity of polycrystalline samples. Therefore, to systematically examine grain growth phenomena, numerical approaches have been developed using continuum-based grain growth models, 4) including the Monte-Carlo, [5][6][7][8] cellular automaton, [8][9][10][11] vertex or front-tracking, [12][13][14][15][16][17] surface evolver, [18][19][20] and phase-field 7,[21][22][23][24][25][26] models. In particular, the phase-field method has become common because it can accurately address curvature-driven grain boundary migration without explicit boundary tracking.…”

Section: Introductionmentioning

confidence: 99%

Accuracy Evaluation of Phase-field Models for Grain Growth Simulation with Anisotropic Grain Boundary Properties

et al. 2020

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The phase-field method has been widely employed recently for simulating grain growth. Phase-field grain growth models are classified into two types according to their conservation constraints for phase-field variables: the multi-phase-field model and the continuum-field model. In addition, within the multi-phase-field model framework, three models with different formulations exist. These models are reported to accurately simulate grain growth under conditions of isotropic or weakly anisotropic grain boundary energy and mobility. However, for cases of strongly anisotropic grain boundary properties, the accuracy of these models has not yet been examined in detail. In this study, using the continuum-field model and three different multi-phase-field models, systematic grain growth simulations with anisotropic grain boundary energies and mobilities are performed. Through the detailed investigation of the accuracy of the simulated results, the suitability of each model for anisotropic grain growth simulations is revealed. Furthermore, based on the higher-order terms, accuracy improvement of the phase-field models is attempted.

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Grain boundary energy and curvature in Monte Carlo and cellular automata simulations of grain boundary motion

Cited by 42 publications

References 48 publications

Grain boundary curvatures in polycrystalline SrTiO₃: Dependence on grain size, topology, and crystallography

Grain boundary curvatures in polycrystalline SrTiO₃: Dependence on grain size, topology, and crystallography

A review on the modeling and simulations of solid-state diffusional phase transformations in metals and alloys

Accuracy Evaluation of Phase-field Models for Grain Growth Simulation with Anisotropic Grain Boundary Properties

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Grain boundary energy and curvature in Monte Carlo and cellular automata simulations of grain boundary motion

Cited by 42 publications

References 48 publications

Grain boundary curvatures in polycrystalline SrTiO3: Dependence on grain size, topology, and crystallography

Grain boundary curvatures in polycrystalline SrTiO3: Dependence on grain size, topology, and crystallography

A review on the modeling and simulations of solid-state diffusional phase transformations in metals and alloys

Accuracy Evaluation of Phase-field Models for Grain Growth Simulation with Anisotropic Grain Boundary Properties

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Product

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Grain boundary curvatures in polycrystalline SrTiO₃: Dependence on grain size, topology, and crystallography

Grain boundary curvatures in polycrystalline SrTiO₃: Dependence on grain size, topology, and crystallography