Fast grain boundary diffusion and rate-limiting surface exchange reactions in polycrystalline materials

摘要: Analytical solutions to the diffusion equations for fast grain boundary in polycrystalline solids of finite thickness bounded by two parallel surface planes are presented. The coefficient may be higher several orders magnitude than bulk (volume) coefficient. microstructure sample has been modeled means an isolated as well array boundaries. concentration assumed vary continuously during process, exchange reactions diffusing species considered fairly slow and equilibrium between constant source (gas phase) is not attained. Two different cases at interface sample/diffusion taken into account, viz. negligible diffusion. pertinent analytical allow calculation two-dimensional profiles thin films average semi-infinite systems. In addition, time dependence total amount exchanged solid calculated. theoretical results interpreted terms Harrison’s classification regimes. model enables both type-A type-B kinetics. case kinetics expressions effective proposed, which depend on corresponding values, specimen, respective condition.