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Monte Carlo model

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Published: 01 December 2009
Fig. 5 Monte Carlo model simulation of texture-controlled grain growth for a material with two texture components. (a) Comparison of predicted grain-growth kinetics (solid line) and normal grain-growth kinetics (broken line). MU, model lattice units; MCS, Monte Carlo steps. (b) Simulated (100 More
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Published: 01 December 2009
Fig. 6 Monte Carlo model predictions of the grain-size distributions after 15 Monte Carlo steps for the simulation of texture-controlled grain growth in a material with two texture components. (a) For the entire material. (b) For the grains belonging to texture component “A.” MU, model lattice More
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005428
EISBN: 978-1-62708-196-2
... Abstract The misorientation of a boundary of a growing grain is defined not only by its crystallography but also by the crystallography of the grain into which it is growing. This article focuses on the Monte Carlo Potts model that is typically used to model grain growth, Zener-Smith pinning...
Series: ASM Handbook
Volume: 9
Publisher: ASM International
Published: 01 December 2004
DOI: 10.31399/asm.hb.v09.a0003729
EISBN: 978-1-62708-177-1
... of the general capabilities of the various models that can generate microstructure maps and thus transform the computer into a dynamic microscope. These include standard transport models, phase-field models, Monte Carlo models, and cellular automaton models. cellular automaton models computer modeling...
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Published: 01 January 2005
Fig. 12 Monte Carlo (3D) model predictions of (a, b, c) grain structure (2D sections after 1000 MC steps) and (d) grain-growth behavior for materials with various starting textures and assumed grain-boundary properties. (a) Case A, isotropic starting texture and isotropic boundary properties More
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Published: 01 January 2005
Fig. 5 Monte Carlo (three-dimensional) model predictions of (a, b, and c) grain structure (two-dimensional) sections after 1000 Monte-Carlo Steps and (d) grain-growth behavior for materials with various starting textures and assumed grain-boundary properties. (a) Case A, isotropic starting More
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005401
EISBN: 978-1-62708-196-2
... with a strong initial texture showing periods of rapid and slow growth. Source: Ref 22 Texture-controlled grain growth during beta annealing of titanium alloys has been simulated using both the Monte Carlo (Potts) and phase-field modeling approaches. In the work of Ivasishin et al. ( Ref 24 , 25...
Series: ASM Handbook Archive
Volume: 11
Publisher: ASM International
Published: 01 January 2002
DOI: 10.31399/asm.hb.v11.a0003514
EISBN: 978-1-62708-180-1
... element. Examples of the use of probabilistic analysis are presented. The article concludes with an overview of some of the commercially available software programs for performing probabilistic analysis. advanced mean value method failure model first-second-order reliability methods Monte Carlo...
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Published: 01 December 2009
Fig. 5 Relationship between boundary energy and node angle. (a) Continuum system. (b) Monte Carlo Potts model. Each grain orientation is represented by a different gray scale; the boundaries are sharp, being implicitly defined between sites of different orientations. (c) Implementation More
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Published: 01 January 2005
Fig. 10 Microstructural evolution during recrystallization simulated using a hybrid Monte Carlo-Potts cellular automaton model; the white grains are recrystallized. Source: Ref 23 More
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Published: 01 December 2009
Fig. 19 Main simulation models used in materials science and related length and time scales. DFT, density functional theory; MD, molecular dynamics; MC, Monte Carlo. Source: Ref 177 More
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Published: 01 January 2005
Fig. 8 A series of snapshots during a two-dimensional grain-growth simulation using the Monte Carlo-Potts model. The system size is 400 by 400 with periodic boundary conditions and isotropic boundary energies and mobilities. Source: Ref 20 More
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Published: 01 December 2009
proposed for SiO 2 CVD, combining a macroscale finite-element model (FEM) and a ballistic transport and reaction model at the feature scale. A third FEM mesoscale model is used to link both scales. Source: Ref 186 . (c) Monte Carlo simulation of sputtered-aluminum deposition on a 0.025 mm trench. Source More
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Published: 01 December 2009
Fig. 8 Baseline dependences. (a) Normalized grain-boundary energy and mobility (m a = 1) dependence on misorientation. (b) Normalized stored energy dependence on location used in Monte Carlo simulations of recrystallization and grain growth. “A,” “B,” and “C” are energy-level distributions More
Series: ASM Handbook
Volume: 14A
Publisher: ASM International
Published: 01 January 2005
DOI: 10.31399/asm.hb.v14a.a0004027
EISBN: 978-1-62708-185-6
... steel (observations shown in points). Source: Ref 11 Fig. 8 A series of snapshots during a two-dimensional grain-growth simulation using the Monte Carlo-Potts model. The system size is 400 by 400 with periodic boundary conditions and isotropic boundary energies and mobilities. Source: Ref...
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005425
EISBN: 978-1-62708-196-2
... of mechanism-based models, such as those designed to predict phase equilibria (e.g., Calphad), recrystallization and grain growth (Monte Carlo and cellular-automaton techniques), and precipitation and solidification problems (e.g., phase-field methods). The successful implementation of these newer techniques...
Series: ASM Handbook
Volume: 11A
Publisher: ASM International
Published: 30 August 2021
DOI: 10.31399/asm.hb.v11A.a0006803
EISBN: 978-1-62708-329-4
... of the Monte Carlo simulation method and work performed at the Los Alamos National Laboratories at the end of World War II ( Ref 12 ). The limitation of the original method is the large sample size required for convergence, which can become a problem when the individual “deterministic” model evaluation...
Series: ASM Handbook
Volume: 14A
Publisher: ASM International
Published: 01 January 2005
DOI: 10.31399/asm.hb.v14a.a0009002
EISBN: 978-1-62708-185-6
... of microstructure evolution. cellular automata dynamic recovery grain growth hot working microstructure evolution microstructure evolution modeling Monte-Carlo techniques plastic flow recrystallization static recovery texture evolution models thermomechanical processing IN PROCESS DESIGN...
Series: ASM Handbook
Volume: 22B
Publisher: ASM International
Published: 01 November 2010
DOI: 10.31399/asm.hb.v22b.a0005534
EISBN: 978-1-62708-197-9
... effects—of each variable and therefore determining those that can be ignored ( Ref 8 ). For these calculations, the variances are usually determined by Monte Carlo simulations using a crude model that is usually assumed to be adequate for this purpose but not for an accurate description of system behavior...
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005459
EISBN: 978-1-62708-196-2
...,”  “Monte Carlo Models for Grain Growth and Recrystallization,” and “Network and Vertex Models for Grain Growth” in this Volume. Overview of Microstructure Evolution in Nickel-Base Superalloys during Hot Working Experimental observations of the various features and mechanisms of microstructure...