Strain-Enhanced Diffusion in Metals. II. Dislocation and Grain-Boundary Short-Circuiting Models

Abstract

Rapid diffusion along dislocation cores generally enhances the average bulk diffusion in a dislocated crystal. If each diffusing atom has at least several opportunities to make rapid excursions along various dislocation cores, Hart has shown that DT/DT0 = 1+fDP/DT0. DT is the average bulk diffusivity, DT0 is the diffusivity in the dislocation-free lattice, f is the fraction of atoms in dislocation pipes, and DP is the diffusivity along dislocation pipes. Under these conditions, the diffusion-penetration is increased by the short-circuiting but the general shape of the penetration curve is unaffected. When the dislocations are static, each diffusing atom must visit a number of dislocations, and a necessary condition for the Hart relation to hold is 2(DT0t)½>ld, where t is the diffusion time, and ld is the dislocation spacing. When this condition fails (for example, at lower temperatures), and when the dislocations are static, it is demonstrated that the amount of short-circuiting is greatly reduced and that the dislocations become essentially ``clogged.'' However, if the dislocations move through the crystal, as they do in plastic deformation, the situation is quite different, since in this case the dislocations may visit the diffusing atoms rather than vice versa. In such cases, the short-circuiting may again be randomized and the enhancement can be as large as (but no larger than) the result given by Hart, even if 2(DT0t)½<ld. In certain cases, this type of short-circuiting can produce very large relative enhancements. A parallel development is given for short-circuiting due to grain boundaries. In particular, it is shown that grain boundary migration and recrystallization, which occurs repeatedly during deformation of metals with low stacking fault energy, can, for temperatures equal to or less than about half the melting temperature, lead to a greatly increased diffusion coefficient without altering the general shape of the penetration curve. A number of the results established in this work (Part II) are used in Part III (to be published) where a comprehensive interpretation of recent experimental work in the field is carried out. Part I consists of an analysis of point defect models for strain-enhanced diffusion.