A Simulation Study of Tracer Diffusion Concentration Profiles Resulting from the Transition from Dislocation Pipes to a
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A Simulation Study of Tracer Diffusion Concentration Profiles Resulting from the Transition from Dislocation Pipes to a Grain Boundary Slab Irina V Belova and Graeme E Murch Diffusion in Solids Group, Dept. Mechanical Engineering The University of Newcastle, Callaghan, NSW 2308 AUSTRALIA ABSTRACT In the present study we examine the well-known analysis in which the dislocation pipe diffusivity is determined by means of a grain boundary type analysis of the tail of a tracer concentration depth profile. We use a Monte Carlo grid method for testing the analysis. The results show that the analysis is really only satisfactory when the spacing between the dislocations is roughly twice the diffusion length (Dlt)1/2 where Dl and t are the lattice diffusivity and time respectively. INTRODUCTION It is well accepted that dislocations and grain boundaries provide short circuit paths for diffusion. In order to study short circuit diffusion experimentally the standard tracer diffusion techniques of tracer deposition, annealing and sectioning are normally used. In the case of isolated short circuit paths (meaning that the lattice diffusion length is small compared with the distance between the short circuit paths) there are close to exact solutions available to describe the tracer concentration depth profiles for diffusion from the instantaneous tracer source and the constant tracer source, see for example the following reviews [1-4]. The solution involving dislocation pipes allows for variable dislocation densities assuming a hexagonal array of parallel pipes normal to the source [5]. The lower symmetry of grain boundary slabs compared with dislocation pipes has meant that an accurate solution for variable densities of grain boundaries is difficult to obtain but a Monte Carlo solution has recently been provided [6]. The isolated dislocation pipe problem involving an instantaneous tracer source has a solution where the logarithm of the tracer concentration in the tail of the concentration depth profile is linear with distance y. Similarly, the isolated grain boundary slab problem involving an instantaneous tracer source has a solution where the logarithm of the tracer concentration in the tail of the profile is proportional to y6/5. Low angle grain boundaries (< 15° disorientation angle) can be described by a regular array of discrete dislocations separated by sections of (strained) crystal [7]. It is of interest to see how quickly the linear solution ln c vs y (dislocation pipes) approaches the ln c vs y6/5 (grain boundary slabs) solution as the spacing of dislocation pipes along a line decreases and effectively become a grain boundary slab. In particular, the following equation is sometimes used to obtain the dislocation pipe diffusivity Dd from the grain boundary diffusivity Db [1, 8] D δλ Dd a 2 = b (1) π
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where a is the effective radius of the dislocation pipe, δ is the boundary width and λ is the spacing between dislocations [1, 8]. In order to address this phenomenologically conceived problem we use a Monte Carlo g
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