Computer modelling of three-dimensional cellular pattern growth

Fuchizaki, Kazuhiro; Kusaba, Takuo; Kawasaki, Kyozi

doi:10.1080/13642819508239038

Cited by 77 publications

(51 citation statements)

References 35 publications

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“…2, where the size distributions FðrÞ in the following simulations depend linearly on r for small grain sizes: the vertex model, 6,10) 2D Monte Carlo model, 7) variational principle, 8) Surface Evolver program 9) and atomic jump model, 11) where n ¼ 2 has been obtained. A slightly increasing m-value with decreasing r in the 3D vertex model 6) may occur from insufficient data for such small grains.…”

Section: Numerical Simulationsmentioning

confidence: 99%

“…On normal grain growth, there have been extensive studies including the curvature-driven growth model, 1) diffusion-like growth model, 2) statistical analysis, 3) stochastic model 4) and numerical simulations. [5][6][7][8][9][10][11][12] Despite a variety of the analyzing methods, most of the studies predict an n-value of 2, and thereby n ¼ 2 has widely been recognized as the theoretical grain growth exponent for normal grain growth. In those studies giving n ¼ 2, however, the obtained size distributions of grains in a steady state are various.…”

Section: Introductionmentioning

confidence: 99%

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Kinetics of Normal Grain Growth Depending on the Size Distribution of Small Grains

2003

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A theoretical relationship is derived between the kinetics of normal grain growth and the size distribution of small grains. When the distribution of the normalized grain size r is proportional to r m around r ¼ 0 in a steady state, the grain growth exponent n is revealed to be m þ 1. The same relationship is also derived from the analysis of the mean field model for particle growth. The validity of this relationship is confirmed from the consistence with existing grain-growth models and numerical simulations. Experimental consistence is observed for the size distribution on sectional surface. It is found that a log-normal function is not a steady-state size distribution for normal grain growth with n ¼ 2, even though it may approximate experimental size distributions. The obtained relationship is also shown to be applicable to particle coarsening by Ostwald-ripening.

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Section: Numerical Simulationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Kinetics of Normal Grain Growth Depending on the Size Distribution of Small Grains

2003

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“…Models that describe grain growth, such as the stochastic method (Monte Carlo method), 3) and topological network models such as the phase field method, 4) front tracking model 5,6) and vertex model, [7][8][9][10] have already been proposed and developed. These models are superior in the sense that they handle the orientations of individual grains, and under certain limited conditions, they can successfully describe…”

Section: Introductionmentioning

confidence: 99%

Proposal of Two-dimensional Local Curvature Multi-vertex Model for Grain Growth Simulation

2016

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A local curvature multi-vertex model was developed. This model is a straightforward two-dimensional topological network model based on physical principles that consider the local curvatures of grain boundaries and the grain boundary tensions at triple junctions. Virtual vertices are set on the grain boundaries in order to calculate the driving forces of grain boundary and triple junction migration. Therefore, the accuracy of the developed model is higher than that of the conventional curvature model and the vertex model. In the proposed model, the generation and annihilation of virtual vertices maintained a proper configuration of virtual vertices, and high accuracy is expected with a suitable set of simulation parameters. The proposed model was verified by the grain growth simulation using adequately determined parameters for the artificially generated specimens with 5 040 grains.

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“…8,9) Since the grain boundary is normally not a straight line, approximation as a straight line is a drawback. In the initial vertex model, virtual vertices are positioned along the grain boundary, which improves the model 10,11) by employing multi-vertices, and the grain boundary is approximated by broken lines. This improved vertex model is based on physical principles, so it is considered to be suitable for describing grain growth.…”

Section: Introductionmentioning

confidence: 99%

“…Also, models that describe grain growth such as the stochastic method (Monte Carlo method) 4) and topological network models, which includes the phase field method, 5) front tracking model 6,7) and vertex model, [8][9][10][11] have already been developed. These models are superior in that they take the crystal orientation of each grain into consideration and describe grain growth under specified conditions.…”

Section: Introductionmentioning

confidence: 99%

Proposal of Grain Growth Model Based on Two-dimensional Local Curvature Multi-vertex Model in the Presence of Pinning Particles

2016

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A grain growth model based on a two-dimensional local curvature multi-vertex model in the presence of pinning particles was developed. This model is a physical model which pursues the minimum total grain boundary energy as the evaluation function, where the unpinning conditions are as follows. The first unpinning condition is that the total energy of the unpinned grain boundary is smaller than the total energy of the pinned grain boundary. The second unpinning condition is that the energy of the grain boundary necessary to surpass the energy barrier is assumed to be smaller than the jumping energy, which is presumably assisted by thermal lattice vibration. Using only the first condition, the Zener pinning effect caused by the finely dispersed particles during normal grain growth was reproduced. With the second condition, the selective abnormal grain growth was reproduced when the abnormally grown grain was surrounded by the grains with low-energy grain boundaries.

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Computer modelling of three-dimensional cellular pattern growth

Cited by 77 publications

References 35 publications

Kinetics of Normal Grain Growth Depending on the Size Distribution of Small Grains

Kinetics of Normal Grain Growth Depending on the Size Distribution of Small Grains

Proposal of Two-dimensional Local Curvature Multi-vertex Model for Grain Growth Simulation

Proposal of Grain Growth Model Based on Two-dimensional Local Curvature Multi-vertex Model in the Presence of Pinning Particles

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