Date of download: 12/31/2017 Copyright © ASME. All rights reserved. From: Simulations of Anisotropic Grain Growth Subject to Thermal Gradients Using Q-State Monte Carlo J. Eng. Mater. Technol. 2013;135(4):041005-041005-9. doi:10.1115/1.4025171 Figure Legend: Plot of mobility versus x-position (using Eq. (7)) for mobility constants: α = 0.1 and α = 4.0 × 10−5

Date of download: 12/31/2017 Copyright © ASME. All rights reserved. From: Simulations of Anisotropic Grain Growth Subject to Thermal Gradients Using Q-State Monte Carlo J. Eng. Mater. Technol. 2013;135(4):041005-041005-9. doi:10.1115/1.4025171 Figure Legend: Hexagonal grain elements and definition of orientation angle (ϕ)

Date of download: 12/31/2017 Copyright © ASME. All rights reserved. From: Simulations of Anisotropic Grain Growth Subject to Thermal Gradients Using Q-State Monte Carlo J. Eng. Mater. Technol. 2013;135(4):041005-041005-9. doi:10.1115/1.4025171 Figure Legend: Elliptical (n = 2) Wulff plot with surface energy determination

Date of download: 12/31/2017 Copyright © ASME. All rights reserved. From: Simulations of Anisotropic Grain Growth Subject to Thermal Gradients Using Q-State Monte Carlo J. Eng. Mater. Technol. 2013;135(4):041005-041005-9. doi:10.1115/1.4025171 Figure Legend: Schematic illustrating the computation of the grain aspect ratio (A/B)

Date of download: 12/31/2017 Copyright © ASME. All rights reserved. From: Simulations of Anisotropic Grain Growth Subject to Thermal Gradients Using Q-State Monte Carlo J. Eng. Mater. Technol. 2013;135(4):041005-041005-9. doi:10.1115/1.4025171 Figure Legend: Lattice independent results, showing the convergence of average grain area for a resolution of N = 500 (isothermal, isotropic, Q = 60, t = 1000 MCS)

Date of download: 12/31/2017 Copyright © ASME. All rights reserved. From: Simulations of Anisotropic Grain Growth Subject to Thermal Gradients Using Q-State Monte Carlo J. Eng. Mater. Technol. 2013;135(4):041005-041005-9. doi:10.1115/1.4025171 Figure Legend: The slope of a straight fit through a plot of log R versus log (t) by least squares fitting provides an estimate for the inverse grain growth exponent (1/r). As shown, to a good approximation, the slope (0.49) is in agreement with the power-law prediction (isothermal, isotropic, Q = 60, t = 1000 MCS, N = 500).

Date of download: 12/31/2017 Copyright © ASME. All rights reserved. From: Simulations of Anisotropic Grain Growth Subject to Thermal Gradients Using Q-State Monte Carlo J. Eng. Mater. Technol. 2013;135(4):041005-041005-9. doi:10.1115/1.4025171 Figure Legend: The evolution of the CV at different simulation temperatures (isothermal, isotropic, N = 500, Q = 60, t = 1000 MCS)

Date of download: 12/31/2017 Copyright © ASME. All rights reserved. From: Simulations of Anisotropic Grain Growth Subject to Thermal Gradients Using Q-State Monte Carlo J. Eng. Mater. Technol. 2013;135(4):041005-041005-9. doi:10.1115/1.4025171 Figure Legend: Contours of anisotropic grain growth evolution (isothermal; anisotropic; Q = 60; t = 0 MCS, 100 MCS, 1000 MCS, 4000 MCS; N = 500). (a) t = 0 MCS; (b) t = 100 MCS; (c) t = 1000 MCS; (d) t = 4000 MCS.

Date of download: 12/31/2017 Copyright © ASME. All rights reserved. From: Simulations of Anisotropic Grain Growth Subject to Thermal Gradients Using Q-State Monte Carlo J. Eng. Mater. Technol. 2013;135(4):041005-041005-9. doi:10.1115/1.4025171 Figure Legend: Isotropic and anisotropic grain growth subject to a mobility gradient (α = 0.1, α = 4.0 × 10−5; anisotropic; Q = 60; t = 4000 MCS; N = 500). (a) Isotropic (α = 0.1); (b) isotropic (α = 4.0 × 10−5); (c) isotropic (α = 0.1); (d) isotropic (α = 4.0 × 10−5).

Date of download: 12/31/2017 Copyright © ASME. All rights reserved. From: Simulations of Anisotropic Grain Growth Subject to Thermal Gradients Using Q-State Monte Carlo J. Eng. Mater. Technol. 2013;135(4):041005-041005-9. doi:10.1115/1.4025171 Figure Legend: Average grain area (A) as a function of x-position showing the effect of a mobility gradient (α = 0.1; isotropic; t = 1000 MCS, t = 4000 MCS; Q = 60; N = 500; NDIV = 100)

Date of download: 12/31/2017 Copyright © ASME. All rights reserved. From: Simulations of Anisotropic Grain Growth Subject to Thermal Gradients Using Q-State Monte Carlo J. Eng. Mater. Technol. 2013;135(4):041005-041005-9. doi:10.1115/1.4025171 Figure Legend: Average grain area (A) as a function of x-position for isotropic/isothermal conditions (M = 1.0; t = 100 MCS, 500 MCS, 1000 MCS; Q = 60; N = 500; NDIV = 100)

Date of download: 12/31/2017 Copyright © ASME. All rights reserved. From: Simulations of Anisotropic Grain Growth Subject to Thermal Gradients Using Q-State Monte Carlo J. Eng. Mater. Technol. 2013;135(4):041005-041005-9. doi:10.1115/1.4025171 Figure Legend: Average grain area along the x-axis with changing mobility for both isotropic and anisotropic cases (t = 4000 MCS; Q = 60; N = 500; NDIV = 100); (a) isotropic and (b) anisotropic (see online figure for color)

Date of download: 12/31/2017 Copyright © ASME. All rights reserved. From: Simulations of Anisotropic Grain Growth Subject to Thermal Gradients Using Q-State Monte Carlo J. Eng. Mater. Technol. 2013;135(4):041005-041005-9. doi:10.1115/1.4025171 Figure Legend: Plot of the average AR as a function of position for both isotropic and anisotropic cases (α=0.1; t = 4000 MCS; Q = 60; N = 500; NDIV = 100)

Date of download: 12/31/2017 Copyright © ASME. All rights reserved. From: Simulations of Anisotropic Grain Growth Subject to Thermal Gradients Using Q-State Monte Carlo J. Eng. Mater. Technol. 2013;135(4):041005-041005-9. doi:10.1115/1.4025171 Figure Legend: Plot of orientation angle distribution for the anisotropic (n = 2) case pertaining to three different temperature profiles: isothermal, α = 0.1, and α = 4.0 × 10−5 (t = 4000 MCS; Q = 60; N = 500)