On the coarsening of precipitates located on grain boundaries and dislocations

The Lifschitz-Slyozov-Wagner theory of particle coarsening is applied to the case in which all the precipitates lie on grain boundaries. Earlier studies of the grain boundary precipitate coarsening problem have assumed that all mass transfer is limited to the grain boundary region and have shown that in the long time limit the average particle size increases with time as t14. The present investigation considers diffusion of solute to occur both through the bulk material and along the grain boundary. Employing an asymptotic analysis due to Marqusee and Ross, one can show that the time dependent average particle size varies as t13 and the coarsening rate constant depends on both the bulk and grain boundary diffusivities. The case of coarsening of precipitates lying on dislocations is also discussed and again cubic growth kinetics are found.