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Interdiffusion in many dimensions: mathematical models, numerical simulations and experiment. (English) Zbl 1482.74140

Summary: 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 [“Diffusion of carbon in austenite with a discontinuity of composition”, Trans. AIME 180, 430–438 (1949); “Diffusion, mobility and their interrelation through free energy in binary metallic systems”, Trans. AIME 175, 184–201 (1948)]. 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.

MSC:

74N25 Transformations involving diffusion in solids
74S20 Finite difference methods applied to problems in solid mechanics
76R50 Diffusion
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