Author
R.T.P. Whipple
Bio: R.T.P. Whipple is an academic researcher. The author has contributed to research in topics: Grain boundary diffusion coefficient & Grain boundary. The author has an hindex of 1, co-authored 1 publications receiving 598 citations.
Papers
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TL;DR: In this article, a simplified model for studying grain boundary diffusion of one metal into another was proposed, which has obvious application to the study of heat flow in a poorly conducting solid with a metallic fin.
Abstract: Formulae are obtained for the concentration in a poorly diffusing half space bisected by a thin well-diffusing slab, at different times after the edge of the half-space has been suddenly raised from zero to unit concentration. This represents a simplified model for studying ‘grain boundary’ diffusion of one metal into another. The problem also has obvious application to the study of heat flow in a poorly conducting solid with a metallic fin.
610 citations
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TL;DR: In the last 30 years, research efforts by the scientific community intensified significantly, stemming from the pioneering work of Takahashi and co-workers, with the initial development of mixed ionic-electronic conducting (MIEC) oxides.
1,037 citations
TL;DR: In this article, the 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 surface diffusion coefficient.
Abstract: 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.
581 citations
340 citations
TL;DR: In this paper, the self-diffusion of the radioisotope 67Cu in nanocrystalline copper has been measured by serial sectioning with the aid of ion-beam sputtering.
296 citations
TL;DR: In this article, exact solutions of grain boundary diffusion based on the two mathematical conditions assumed for the surface source are discussed for the purpose of application to the experiments by means of sectioning method.
Abstract: Exact solutions of grain boundary diffusion based on the two mathematical conditions assumed for the surface source are discussed for the purpose of application to the experiments by means of sectioning method. It is concluded that the result obtained by either of these solutions is in effect unaffected by possible deviations from the ideal condition, and one of them, the “instantaneous source” solution, is the most successful one in analyzing the problem. The expression for the solutions can be transformed to another type of expression more appropriate to the grain boundary diffusion, and some discussions and numerical evaluations of these solutions over a more extensive range of parameters than previous are given.
252 citations