| The presence of extended defects in crystalline solids (e.g., dislocations, cracks, grain boundaries) can significantly alter their mechanical and transport properties. In this dissertation I examine the impact of defects on long-ranged diffusion, focusing in particular on the roles of cracks and grain boundaries in this process. More specifically, I employ kinetic Monte Carlo simulation and analytical methods to explore the effects of elastic deformation, in the crack case, and defect geometry, in the grain-boundary case, on solute transport in a solid. In the crack case, the biased diffusive transport of solute to a crack is studied as an example of a complex trapping problem. A novel kinetic, lattice-gas Monte Carlo simulation and associated coupled rate equations, along with continuum solutions to a diffusive boundary-value problem, are employed to describe quantitatively solute transport near a crack. In a regime where the crack loading is dominated by an externally imposed tensile stress, the segregation behavior is obtained and interpreted in terms of the elastic fields generated by the crack. In a regime where solute loading of the crack becomes important, it is found that this loading enhances segregation and leads to small correlations in diffusive motion. In the grain-boundary case, the impact of segregating impurities on grain-boundary diffusion is investigated using a kinetic Monte Carlo simulation of boundary transport on a lattice that is appropriate for both slab and pipe geometries. More specifically, the grain-boundary diffusivity is determined as a function of impurity concentration using an analog of the experimental sectioning method. The retardation of diffusion that results from segregation is interpreted in terms of site-blocking models that reflect the local free volume available to a diffusing tracer. The results of this investigation are then interpreted in the context of experimental determinations of grain-boundary diffusivity in doped ceramic oxides. Finally, as I have considered idealized defects in this work, I conclude with a discussion of possible extensions of my results to incorporate more realistic grain-boundary structures and to model a fully three-dimensional crack. |
