Effective diffusion coefficient and correlation effects in periodic grain boundaries

Abstract

Grain boundary tracer diffusion is treated as a correlated walk in a periodic system with multiple jump frequencies. Along with the usual defect-induced correlations, the non-uniformity of the boundary structure itself gives rise to additional correlations, which are called “structural” correlations. These are present also under the interstitial mechanism of atomic migration and play an important role in boundary diffusion. To study them separately a model of diffusion taking into account only structural correlations is developed. Based on this model a method is proposed for exact and approximate calculations of the effective diffusion tensor and the correlation factors using recursive relations between displacement S-vectors associated with different sites in the boundary. Applying this method and direct Monte Carlo simulations, diffusion behaviour in a simplified grain boundary structure is investigated. Depending on the distribution of “easy” and “difficult” diffusion jumps and the tracer binding energies in the structure, the structural correlation effects range from very weak to very strong, in the latter case being associated with a trapping effect. The situation where both defect-induced and structural correlations are present is discussed in detail. Under certain conditions the two types of correlation can be treated separately in terms of the encounter model.