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Potts model

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Published: 01 December 2009
Fig. 1 Potts model simulation of the microstructural evolution of a silicon steel. Grains that are part of a <110> fiber parallel to the sheet normal, within 15° of the <110> axis, are shown in light gray; <111> fiber grains are shown in white; and <100> fiber grains More
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Published: 01 December 2009
Fig. 4 Different types of boundary conditions used in the Potts model. (a) Surface boundary condition. (b) Mirror boundary condition. (c) Periodic boundary condition. (d) Skew-periodic boundary condition More
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Published: 01 December 2009
Fig. 6 Evolution of microstructure during a Potts model simulation of a two-component system in which the initial distribution of components is equal and R A = R B = 0.5. The A and B components are differentiated by the gray scale. The simulation was performed using a square (1,2 More
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Published: 01 December 2009
Fig. 8 Evolution of microstructure during a Potts model simulation of a two-component system in which the initial distribution of components is unequal and the A-B boundaries have a mobility advantage: f B = 0.05, M A = M B = 1, M AB = 100. The A and B components are differentiated More
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Published: 01 December 2009
Fig. 9 Potts model simulation carried out on a square lattice, using Glauber dynamics and kT s = 0.75. The second phase has an unchangeable index and so pins the primary phase. The simulations were performed using a square (1,2) lattice, Glauber dynamics, metropolis transition probability More
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Published: 01 December 2009
Fig. 12 (a) Three-dimensional equiaxed microstructure grown using the Potts model. (b) Graph showing the desired and the achieved misorientation distribution functions (MDFs) generated by discretizing a texture, allocating orientations to the grains, and then using the swap method to achieve More
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Published: 01 December 2009
Fig. 13 Boundary geometry used to validate the Q -state Potts model for anisotropic grain growth. Boundary conditions are continuous in the x -direction and fixed in the y -direction. The boundary between grain A and grains B and C is the only boundary that moves. θ 1 is the misorientation More
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Published: 01 December 2009
Fig. 14 (a) Measured γ 2 versus nominal γ 2 for Potts model simulations of boundary motion in the system illustrated in Fig. 13 ; kT s = 0.5. (b) Measured μ 1 versus nominal μ 1 for Potts model simulations of boundary motion in the system illustrated in Fig. 13 with μ 2 = 1 More
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Published: 01 December 2009
Fig. 15 Evolution of microstructure during a Potts model simulation of anisotropic grain growth of a single-texture component, using Read-Shockley energies and uniform mobilities. The simulation was performed using a square (1,2) lattice, Glauber dynamics, metropolis transition probability More
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Published: 01 December 2009
Fig. 16 Potts model simulation of anisotropic grain growth. (a) Relationship between misorientation distribution function (MDF) of the evolved system and the energy function. (b) Two-dimensional microstructure growth showing the multijunctions that form with highly anisotropic energy functions More
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Published: 01 December 2009
Fig. 17 Evolution of microstructure during a Potts model simulation of anisotropic grain growth of a single-texture component, using Read-Shockley energies and anisotropic mobilities to show the emergence of an abnormal grain More
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Published: 01 December 2009
Fig. 19 Evolution of microstructure during a Potts model simulation of anisotropic grain growth in a texture gradient, using Read-Shockley energies and anisotropic mobilities. The simulation was performed using a square (1,2) lattice, Glauber dynamics, metropolis transition probability More
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Published: 01 December 2009
Fig. 20 Series of snapshots from a Potts model simulation of an extruded aluminum rod recrystallizing with site-saturated surface nucleation. The light gray indicates a recrystallized grain; the dark-gray grains are unrecrystallized. The system is a 50 × 50 × 200 cylinder, with periodic More
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Published: 01 December 2009
Fig. 23 (a) Snapshot of a pinned microstructure in a Potts model simulation of Zener pinning on a 400 × 400 × 400 lattice, using particles with sizes 3 × 3 × 3. (b) Comparison of pinned grain size with experimental data. Source: Ref 26 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...
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Published: 01 December 2009
, distance of the boundary from the particle center. (b) Comparison of the dimple shape produced by a Potts model and theory. (c) Comparison of the pinning force produced by a Potts model and theory More
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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 December 2009
Fig. 3 Different types of lattice and the neighbor co-ordination used in the Potts model. (a) Two-dimensional (2-D) square lattice. (b) 2-D triangular lattice. (c) Three-dimensional simple cubic lattice 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
Fig. 2 Microstructural evolution of an initially random distribution of spins on a two-dimensional square lattice using the Potts model, periodic boundary conditions, metropolis spin dynamics, and kT s = 0.5. The initial configuration of spins was set by allocating each lattice a random More