Interdiffusion in many dimensions: mathematical models, numerical simulations and experiment
| Autor: | Bogusław Bożek, Marek Zajusz, Marek Danielewski, Lucjan Sapa, Katarzyna Tkacz–Śmiech |
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| Rok vydání: | 2020 |
| Předmět: |
Mathematical model
Computer science General Mathematics Computation 010103 numerical & computational mathematics 01 natural sciences 010101 applied mathematics Mechanics of Materials Consistency (statistics) Key (cryptography) General Materials Science Statistical physics 0101 mathematics Diffusion (business) Material properties |
| Zdroj: | Mathematics and Mechanics of Solids. 25:2178-2198 |
| ISSN: | 1741-3028 1081-2865 |
| DOI: | 10.1177/1081286520923376 |
| Popis: | Over the last two decades, there have been tremendous advances in the computation of diffusion and today many key properties of materials can be accurately predicted by modelling and simulations. In this paper, we present, for the first time, comprehensive studies of interdiffusion in three dimensions, a model, simulations and experiment. The model follows from the local mass conservation with Vegard’s rule and is combined with Darken’s bi-velocity method. The approach is expressed using the nonlinear parabolic–elliptic system of strongly coupled differential equations with initial and nonlinear coupled boundary conditions. Implicit finite difference methods, preserving Vegard’s rule, are generated by some linearization and splitting ideas, in one- and two-dimensional cases. The theorems on the existence and uniqueness of solutions of the implicit difference schemes and the consistency of the difference methods are studied. The numerical results are compared with experimental data for a ternary Fe-Co-Ni system. A good agreement of both sets is revealed, which confirms the strength of the method. |
| Databáze: | OpenAIRE |
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