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Unformatted text preview: size Assume that vb can be represented as the product of the driving force for boundary migraGon Fb and the boundary mobility Mb Grain growth process as occurring by transport of atoms across the grain boundary under the driving force of the pressure gradient across the grain boundary. More correctly, the chemical poten4al gradient across the boundary should be used The pressure diﬀerence across the boundary is given by 5 Normal Grain Growth in Dense Solids Assuming that the radius of the boundary is proporGonal to G where α is a geometrical constant that depends on the shape of the boundary Taking the driving force for atomic diﬀusion across the boundary to be equal to the gradient in the chemical potenGal dx = δgb is the grain boundary width The ﬂux of atoms across the boundary is Da is the diﬀusion coeﬃcient for atomic moGon across the grain boundary 6 Normal Grain Growth in Dense Solids The boundary velocity becomes In many analyses, the driving force i...
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 Fall '13

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