Pore Migration and Grain Growth

When pores are present at grain boundaries, the net driving force of grain boundary migration is the difference between the driving force for the boundary without pores and the inhibition force of pores against boundary migration. The boundary velocity v is then expressed as 

The condition of NMb Mp applies to a system containing (many) pores with low mobilities. In this case pore migration controls the boundary migration. Then, 

On the other hand, for (a small number of) pores with high mobilities, NMf, Mp is satisfied. The migration of the grain boundary is then controlled by its intrinsic mobility (boundary control). The pores do not affect the boundary migration and v is reduced to 

When M, equals MpjN in Eq. (11.8), the grain boundary mobility is the same as the pore mobility (equal mobility). The equal mobility condition on a grain size versus pore size plane can be calculated for any mechanism of pore migration. As an example, consider the pore migration controlled by surface diffusion. In this case the pore mobility Mp = D,, )l Ttr kT) and the boundary mobility M = Z) / r for boundaries without impurity segregation. If N is inversely proportional to the boundary area per grain and is expressed as the number of pores per atom at the boundary,  

For pore/boundary separation, two extreme cases can be considered  

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