Thermal grain boundary grooving with anisotropic surface free energy in three dimensions

Zhang, W.; Gladwell, I.

doi:10.1016/j.jcrysgro.2004.12.157

Cited by 12 publications

(13 citation statements)

References 16 publications

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“…Finally, we present some anisotropic variants of the simulation in Figure 21, where we recall that these experiments are motivated by the AFM image shown in Zhang and Gladwell (2005, Fig. 7).…”

Section: Anisotropic Flowsmentioning

confidence: 99%

“…Numerical studies for coupled mean curvature flow and surface diffusion in three space dimensions are so far restricted to very simplified geometries, see e.g. Zhang and Gladwell (2005); Wakai et al (2005); Kanel et al (2006). Let us mention here that Kanel et al (2006) study a radially symmetric grain and that Wakai et al (2005) compute for a simplified model, where the fourth order flow by surface diffusion is replaced by the second order conserved mean curvature flow.…”

Section: Introductionmentioning

confidence: 99%

“…The next experiment is inspired by the AFM image shown in Zhang and Gladwell (2005, Fig. 7), which shows three grain boundaries inside a tricrystal meeting its surface.…”

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confidence: 99%

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Finite-element approximation of coupled surface and grain boundary motion with applications to thermal grooving and sintering

2010

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We study the coupled surface and grain boundary motion in bi-and tricrystals in three space dimensions, building on previous work by the authors on the simplified two dimensional case. The motion of the interfaces, which in this paper are presented by two-dimensional hypersurfaces, is described by two types of normal velocities: motion by mean curvature and motion by surface diffusion. Three hypersurfaces meet at triple junction lines, where junction conditions need to hold. Similarly, boundary conditions are prescribed where an interface meets an external boundary, and these conditions naturally give rise to contact angles. We present a variational formulation of the flows, which leads to a fully practical finite element approximation that exhibits excellent mesh properties, with no mesh smoothing or remeshing required in practice. For the introduced parametric finite element approximation we show well-posedness and, in general, unconditional stability, i.e. there is no restriction on the chosen time step size. Moreover, the induced discrete equations are linear and easy to solve. A generalization to anisotropic surface energies is straightforward. Several numerical results in two and three space dimensions are presented, including simulations for thermal grooving and sintering. Three dimensional simulations featuring quadruple junction points, nonstandard boundary contact angles and fully anisotropic surface energies are also presented.

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Section: Anisotropic Flowsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Finite-element approximation of coupled surface and grain boundary motion with applications to thermal grooving and sintering

2010

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“…Then Herring stated that ''Combining Eqs. (13) and (14) gives for the potential motivating diffusion or evaporation…”

Section: Article In Pressmentioning

confidence: 99%

“…In Refs. [10][11][12][13], the authors studied the evolution of periodic/infinite surface in 3D with anisotropic surface free energies of different levels. An extra corner energy term is added in the model in Ref.…”

Section: Introductionmentioning

confidence: 99%

Evolution of crystal morphologies to equilibrium by surface diffusion with anisotropic surface free energy in three dimensions

Zhang

2006

Journal of Crystal Growth

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Surface motion of single crystals driven by anisotropic surface diffusion

Zhang

2008

Comput. Visual Sci.

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Thermal grain boundary grooving with anisotropic surface free energy in three dimensions

Cited by 12 publications

References 16 publications

Finite-element approximation of coupled surface and grain boundary motion with applications to thermal grooving and sintering

Finite-element approximation of coupled surface and grain boundary motion with applications to thermal grooving and sintering

Evolution of crystal morphologies to equilibrium by surface diffusion with anisotropic surface free energy in three dimensions

Surface motion of single crystals driven by anisotropic surface diffusion

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