Stability and motion of arbitrary grain boundary junctions

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• 作者：Jeremy K. Mason ^{jkylemason@gmail.com}
• 关键词：Herring condition ; Grain boundary junction ; Grain growth
• 刊名：Acta Materialia
• 出版年：2017
• 出版时间：15 February 2017
• 年：2017
• 卷：125
• 期：Complete
• 页码：286-295
• 全文大小：1003 K
• 卷排序：125

文摘

The Herring condition is known as the stability condition for a junction line, but the stability conditions for junction points are not readily available. This paper derives stability conditions for arbitrary junction points and allows for anisotropic surface energies and line energies. A junction is considered to be stable when the force on a small neighborhood around the junction vanishes. When the force does not vanish, the junction is expected to move. Equations of motion are derived for the nodes belonging to polygonal curves or triangulated surfaces, and allow for junction lines and junction points to contribute to the drag on a node. The accuracy of the equations of motion is evaluated by the relative error in the rate of volume change of an adjoining grain. They are found to be second-order accurate for nodes on a boundary and first-order accurate for nodes at a junction. A simulation of boundary motion in two dimensions suggests that the equations of motion are of comparable accuracy to alternatives in the literature, and have the advantage of less computational complexity.