Abstract
We rationalize diffusion in solids on the basis of a differential equation of balance expressing conservation of momentum for the diffusing species. The balance equation contains a tensor, modelling the stress supported by the diffusing species, and a diffusive force vector, modelling the exchange of momentum between the diffusing species and the species of the solid matrix. These two quantities, which are not identified in classical diffusion interpretations, are the basic ingredients of the theory. The effect of state and constitution of interdiffusing materials is reflected in the form of the constitutive equations for the stress and the diffusive force. Within our framework, the main results of classical theories are rigorously derived in a unified manner. New interesting findings are also deduced and their implications are discussed. The applicability of the theory to a variety of problems, ranging from metallurgy to polymer physics and geophysics, is illustrated.
Zusammenfassung
Wir beschreiben die Diffusion in festen Körpern auf der Basis von Bilanzdifferentialgleichungen, die die Erhaltung des Impulses der diffundierenden Teilchen ausdrücken. Die Bilanzgleichung enthält einen Tensor, der die durch das diffundierende Material hervorgerufenen Spannungen beschreibt und den Vektor einer Diffusionskraft, die den Impulsaustausch zwischen dem diffundierenden Medium und der Festkörpermatrix beschreibt. Diese zwei Größen, die in den klassischen Behandlungen des Diffusionsproblems nicht festgestellt wurden, sind die tragenden Säulen für diese Theorie. Zustand und Beschaffenheit der austauschenden Materialien werden durch konstitutive Gleichungen für die Spannungen und die diffusive Kraft beschrieben. Innerhalb dieses Rahmens werden die grundlegenden Ergebnisse der klassischen Theorie streng auf einheitliche Weise hergeleitet. Neue, interessante Ergebnisse werden abgeleitet und ihre Folgerungen besprochen.
Die Anwendbarkeit der Theorie auf verschiedene Problemstellungen, von der Metallurgie über Polymerphysik bis zur Geophysik, wird aufgezeigt.
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Aifantis, E.C. On the problem of diffusion in solids. Acta Mechanica 37, 265–296 (1980). https://doi.org/10.1007/BF01202949
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DOI: https://doi.org/10.1007/BF01202949