On the Interaction of Inclusions with Migrating Grain Boundaries
The interaction energy of a grain boundary with a precipitate particle or inclusion of a second phase is considered in detail. When the nature of the inclusion is considered, two regimes emerge: (a) the grain boundary may enter and pass through certain coherent inclusions, leaving them coherent; (b) more commonly, the grain boundary may envelop and bypass the inclusion, causing one which was coherent to lose coherency. The maximum pinning force exerted by an inclusion or particle on a boundary depends on its nature.
A simple differential equation describes the equilibrium of a segment of boundary which is pushed between particles. Numerical integration gives the shape of the boundary. These shapes are complicated by having double curvature, and depend on the nature and spacing of the inclusions. However, certain characteristics of the shape depend only on the pressure, or driving force, acting on the boundary tending to make it migrate. This means that the local pressure on a grain boundary can be measured by measuring its shape, much as the local stress in a crystal can be calculated from the local curvature of a dislocation.
KeywordsFull Line Boundary Energy Precipitate Particle Equilibrium Shape Critical Position
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