Approximations to the Whipple solution for grain boundary diffusion and an algorithm for their avoidance

This paper concerns the Whipple model for grain boundary diffusion. In particular, it examines the various approximations that have been used to calculate solute concentration from the equation provided by Whipple. Included are approximations intended to permit the determination of grain boundary diffusivities from experimental data, An algorithm is presented which avoids these approximations. It is demonstrated that the algorithm is robust in the face of moderate experimental error, and, unlike an alternative, can be used to minimize the impact of that error. (C) 1997 American Institute of Physics.