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Orientation Field Model for Grain Growth Accounting for Five Crystallographic Degrees of Freedom.

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	Orientation Field Model for Grain Growth Accounting for Five Crystallographic Degrees of Freedom./
Author:	Staublin, Philip David.
Description:	1 online resource (122 pages)
Notes:	Source: Dissertations Abstracts International, Volume: 85-11, Section: B.
Contained By:	Dissertations Abstracts International85-11B.
Subject:	Materials science. -
Online resource:	click for full text (PQDT)
ISBN:	9798382762975

Orientation Field Model for Grain Growth Accounting for Five Crystallographic Degrees of Freedom.
Staublin, Philip David.

Orientation Field Model for Grain Growth Accounting for Five Crystallographic Degrees of Freedom. - 1 online resource (122 pages)

Source: Dissertations Abstracts International, Volume: 85-11, Section: B.

Thesis (Ph.D.)--Northwestern University, 2024.

Includes bibliographical references

A phase field model has been developed for simulation of isothermal grain coarsening in single-phase polycrystals, in two and three dimensions. The model allows the grain boundary energy and mobility to vary with all five macroscopic crystallographic degrees of freedom of the grain boundary, these being the misorientation between adjacent crystals and the inclination of the boundary plane. A continuous orientation field represents the local orientation of the crystal lattice with respect to the computational frame; the orientation field is coupled to an order parameter field with a singular coupling function, to create a finite width diffuse interface representation of a grain boundary. Within the diffuse interface, the orientation field varies smoothly from one grain orientation to that of the adjacent grain. The order parameter and orientation fields are evolved according to Allen-Cahn equations to simulate microstructure evolution.Rotationally invariant quantities which describe the local misorientation as a function of the orientation field are derived. These functions are used in the model free energy density to ensure invariance of the energy with respect to the choice of external reference frame. For the three-dimensional model, a rotationally invariant quantity representing local misorientation is derived based on the infinitesimal rotation tensor, while the grain boundary plane normal vector is defined in terms of gradients of the orientation field rotated into the crystal frame. The three dimensional model is derived in terms of a generalized function of rotationally invariant quantities, allowing variation in the dependence of the grain boundary energy on the five crystallographic degrees of freedom.The two and three dimensional models are demonstrated to reproduce analytical theories of grain boundary motion, including motion by mean curvature and triple junction dihedral angles obeying Young's law. The model does not exhibit anomalous triple junction drag and reproduces the steady-state triple junction velocity predicted by analytical theory. Wulff shapes are reproduced for cubic grain boundary energy anisotropy in the two-dimensional model. Simulations of polycrystalline thin films demonstrates the capability of the model to capture the effect of small angle grain boundaries on grain growth.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2024

Mode of access: World Wide Web

ISBN: 9798382762975Subjects--Topical Terms:

557839
Materials science.
Subjects--Index Terms:

Grain boundaryIndex Terms--Genre/Form:

554714
Electronic books.

Orientation Field Model for Grain Growth Accounting for Five Crystallographic Degrees of Freedom.
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500 $a Advisor: Voorhees, Peter W.
502 $a Thesis (Ph.D.)--Northwestern University, 2024.
504 $a Includes bibliographical references
520 $a A phase field model has been developed for simulation of isothermal grain coarsening in single-phase polycrystals, in two and three dimensions. The model allows the grain boundary energy and mobility to vary with all five macroscopic crystallographic degrees of freedom of the grain boundary, these being the misorientation between adjacent crystals and the inclination of the boundary plane. A continuous orientation field represents the local orientation of the crystal lattice with respect to the computational frame; the orientation field is coupled to an order parameter field with a singular coupling function, to create a finite width diffuse interface representation of a grain boundary. Within the diffuse interface, the orientation field varies smoothly from one grain orientation to that of the adjacent grain. The order parameter and orientation fields are evolved according to Allen-Cahn equations to simulate microstructure evolution.Rotationally invariant quantities which describe the local misorientation as a function of the orientation field are derived. These functions are used in the model free energy density to ensure invariance of the energy with respect to the choice of external reference frame. For the three-dimensional model, a rotationally invariant quantity representing local misorientation is derived based on the infinitesimal rotation tensor, while the grain boundary plane normal vector is defined in terms of gradients of the orientation field rotated into the crystal frame. The three dimensional model is derived in terms of a generalized function of rotationally invariant quantities, allowing variation in the dependence of the grain boundary energy on the five crystallographic degrees of freedom.The two and three dimensional models are demonstrated to reproduce analytical theories of grain boundary motion, including motion by mean curvature and triple junction dihedral angles obeying Young's law. The model does not exhibit anomalous triple junction drag and reproduces the steady-state triple junction velocity predicted by analytical theory. Wulff shapes are reproduced for cubic grain boundary energy anisotropy in the two-dimensional model. Simulations of polycrystalline thin films demonstrates the capability of the model to capture the effect of small angle grain boundaries on grain growth.
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650 4 $a Engineering. $3 561152
650 4 $a Computational physics. $3 1181955
653 $a Grain boundary
653 $a Grain growth
653 $a Orientation-field model
653 $a Phase-field model
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