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• W2003105910 endingPage "1529" @default.
• W2003105910 startingPage "1518" @default.
• W2003105910 abstract "A new method of analysis is developed for solving the problem of an initially thin source of impurity ions diffusing into a host solid when the mechanism of transport involves a concentration-dependent diffusivity. In order to extract a diffusivity from experimental data we show that the fundamental experiment required is a measurement of the diffusion profile at two different times. The constant and the concentration-dependent contributions to the diffusivity then can be isolated by requiring the initial measured profile to propagate into the final measured profile. The analytic procedure presented here is shown to be a full solution to the problem of a diffusivity that varies linearly with concentration: D(C)=${D}_{0}$(1+ensuremath{alpha}C), where ensuremath{alpha} is the strength of the nonlinear term. A matrix of orthogonal functions determines the time evolution for an arbitrary thin-source initial state. We show that the total diffusant amount is conserved and that the solution is naturally expressed as a power series in ensuremath{alpha}. The persistence of curvature on ln(C)-vs-${x}^{2}$ axes is then derived from the asymptotic (long-time) properties of the nonlinear equation solution. The solution up through order ${ensuremath{alpha}}^{2}$ is then explicitly constructed for an arbitrary thin-source initial state." @default.
• W2003105910 created "2016-06-24" @default.
• W2003105910 creator A5033821744 @default.
• W2003105910 date "1989-01-15" @default.
• W2003105910 modified "2023-09-25" @default.
• W2003105910 title "Thin-source concentration-dependent diffusion: A full solution" @default.
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• W2003105910 doi "https://doi.org/10.1103/physrevb.39.1518" @default.
• W2003105910 hasPubMedId "https://pubmed.ncbi.nlm.nih.gov/9948362" @default.
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