The analysis of grain boundary diffusion measurements

Whipple's exact solution of the grain boundary diffusion problem is evaluated numerically and the results presented in graphical form suitable for immediate application to the commoner types of experimental measurement of D ́, the grain boundary diffusion coefficient. This enables a detailed comparison to be made between the results obtained using the exact solution and the approximate but commonly employed Fisher solution. The most interesting result is that indiscriminate use of the Fisher equation may lead to anomalously high activation energies for grain boundary diffusion, especially in low angle boundaries. The Whipple solution is also compared with another exact solution due to Suzuoka, which employs a different surface condition from the one assumed by Whipple. For the sectioning method of measurements the two solutions will give nearly the same value of D ́. This is a distinct advantage for this method over others, for the conditions prevailing at the surface in a grain boundary experiment are not easily controllable. Mathematical treatments of grain boundary diffusion by other authors are briefly mentioned. Most of these give results already contained in the Whipple solution.