Simulation of diffusion in nanocrystalline materials : continuum approach ; Simulation der Diffusion in nanokristallinen Materialien : Kontinuum-Methode

Nowadays diffusion profiles can be measured on the scale of hundred nanometers, allowing one to analyze diffusion processes very close to interfaces. It is also obliged by the existence of nanocrystalline materials which are characterized by grain sizes of the order of hundred nanometers. For diffusion measurements in nanocrystalline materials short diffusion times and/or small temperatures are necessary in order to apply standard procedures for determining grain boundary diffusivities. This is particularly important when the diffusion profiles are supposed to be measured in the type-B kinetics. However, the standard procedures are based on different assumptions and, thus, can lead to erroneous results when used under extreme conditions. In the present work classical grain boundary diffusion models are re-examined with respect to the following effects: 1) short diffusion times 2) realistic microstructures in the type-B as well as -A kinetics, including segregation effects 3) space charge layers typically present in ionic materials and their role in both the B- and A-diffusion regimes. Accordingly, each effect is discussed in a separate chapter of the present dissertation. Errors in determining the grain boundary diffusivities due to each effect are given together with suggestions and improved procedures which allow one to better find the grain boundary diffusivities or substantially reduce the errors. Some of the procedures discussed are unique in the sense that they are based on pure mathematics and provide exact values of the grain boundary diffusivities. Also, numerical errors arising in the course of integrations used in the present study are seriously discussed. For example, the procedure to simulate grain boundary diffusion under conditions of long and short diffusion times by using the finite element method was established. ; Heute können Diffusionsprofile in der Größenordnung von einhundert Nanometer gemessen werden. Dadurch ist es möglich, Diffusionsprozesse in der Nähe der Grenzfläche zu analysieren. ...