MSE_442_Lecture_23_Nov 18 2013

More correctly the chemical poten4al gradient across

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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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