Schlegel description of grain form evolution in grain growth

Patterson, Burton R.; Rule, David; DeHoff, R. T.; Tikare, Veena

doi:10.1016/j.actamat.2013.03.013

Cited by 19 publications

(28 citation statements)

References 9 publications

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“…The self-similarity that is observed with respect to both, the scaled size distribution as well as the time-independent Aboav-Weaire relation, is known to be coupled for normal grain growth to three distinct topological transitions in 2D namely neighbor switching events T1, edge disappearing events T2, and grain disappearance events T3. [49][50][51] The edge disappearance events-which are topological transitions from a grain's perspective-can only happen as part of the other two events. Nevertheless, each grain is known to undergo a sequence of those T2 events during annealing independent of the stage of growth during normal grain growth.…”

Section: Resultsmentioning

confidence: 99%

Texture Controlled Grain Growth in Thin Films Studied by 3D Potts Model

Zöllner

2019

Advcd Theory and Sims

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Thin films have numerous applications in optics, mechanics, and electricity, where the grain microstructure and the corresponding crystallography are key factors influencing materials properties as well as coarsening kinetics. However, even today this problem is often tackled by 2D means of treating thin films as quasi-2D objects. In the present work, it is shown by modified 3D Potts model simulations that not only is the third dimension non-negligible, but also how texture changes the growth kinetics, when the percentage of low angle grain boundaries varies systematically.

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Section: Resultsmentioning

confidence: 99%

Texture Controlled Grain Growth in Thin Films Studied by 3D Potts Model

Zöllner

2019

Advcd Theory and Sims

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“…And, the Aboav-Weaire law is recently observed to be not valid for the Poisson-Voronoi microstructure [16,27]. All these results demonstrated the fact that although different cellular structures share many features in common, structures resulting from different formation or evolution processes can be different to some extent.…”

Section: The Relationship Between Topology and Geometrymentioning

confidence: 94%

“…The simplest way to classify the topology of a grain involves counting its number of edges [16,24]. This is the topological characterization most commonly quoted in the literature.…”

Section: Distribution Of Edgesmentioning

confidence: 99%

“…Historically, the topology of a grain has been commonly described by using only its number of edges in two dimensions or faces in three dimensions, i.e., the number of its first nearest neighbors [8][9][10][11][12][13][14]. Some good works have recently been done to provide a more detailed topological description of a grain [15,16] and analyze the affinities of a pair with different face classes in grain structures [17]. Some important topological relations concerning the first nearest neighbors have been summarized in the past, such as the Aboav-Weaire law [2,3] on nearest-neighbor topological correlations, the Lewis law [4] on the statistics of grain area, and the von Neumann-Mullins law [5,6] on the growth rate of individual grains.…”

Section: Introductionmentioning

confidence: 99%

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Long-range topological correlations of real polycrystalline grains in two dimensions

Wang

Liu

Chen

et al. 2014

Materials Characterization

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“…. , T t } of truncation trees provides a more detailed description of the polytope than merely the number of triangular faces [12,13].…”

Section: Figmentioning

confidence: 99%

Roundness of grains in cellular microstructures

et al. 2017

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Many physical systems are composed of polyhedral cells of varying sizes and shapes. These structures are simple in the sense that no more than three faces meet at an edge and no more than four edges meet at a vertex. This means that individual cells can usually be considered as simple, three-dimensional polyhedra. This paper is concerned with determining the distribution of combinatorial types of such polyhedral cells. We introduce the terms fundamental and vertextruncated types and apply these concepts to the grain growth microstructure as a testing ground. For these microstructures we demonstrate that most grains are of particular fundamental types, whereas the frequency of vertex-truncated types decreases exponentially with the number of truncations. This can be explained by the evolutionary process through which grain growth structures are formed, and in which energetically unfavorable surfaces are quickly eliminated. Furthermore, we observe that these grain types are 'round' in a combinatorial sense: there are no 'short' separating cycles that partition the polyhedra into two parts of similar sizes. A particular microstructure derived from the Poisson-Voronoi initial condition is identified as containing an unusually large proportion of round grains. This Round microstructure has an average of 14.036 faces per grain, and is conjectured to be more resistant to topological change than the steady-state grain growth microstructure.

show abstract

Schlegel description of grain form evolution in grain growth

Cited by 19 publications

References 9 publications

Texture Controlled Grain Growth in Thin Films Studied by 3D Potts Model

Texture Controlled Grain Growth in Thin Films Studied by 3D Potts Model

Long-range topological correlations of real polycrystalline grains in two dimensions

Roundness of grains in cellular microstructures

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