Mean field diffusion models for precipitation in crystalline GaAs including surface tension and bulk stresses

Please always quote using this URN:urn:nbn:de:0296-matheon-6749
  • Based on a thermodynamically consistent model for precipitation in gallium arsenide crystals including surface tension and bulk stresses by Dreyer and Duderstadt, we propose different mathematical models to describe the size evolution of liquid droplets in a crystalline solid. The first class of models treats the diffusion-controlled regime of interface motion, while the second class is concerned with the interface-controlled regime of interface motion. Our models take care of conservation of mass and substance. We consider homogenised models, where different length scales of the experimental situation have been exploited in order to simplify the equations. These homogenised models generalise the well-known Lifshitz-Slyozov-Wagner model for Ostwald ripening. Mean field models capture the main properties of our system and are well adapted for numerics and further analysis. Numerical evidence suggests in which case which one of the two regimes might be appropriate to the experimental situation.

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Metadaten
Author:Wolfgang Dreyer, Sven-Joachim Kimmerle
URN:urn:nbn:de:0296-matheon-6749
Referee:Dietmar Hömberg
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2010/04/29
Release Date:2010/04/15
Tag:
Institute:Humboldt-Universität zu Berlin
Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS)
MSC-Classification:35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Bxx Qualitative properties of solutions / 35B27 Homogenization; equations in media with periodic structure [See also 74Qxx, 76M50]
35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Qxx Equations of mathematical physics and other areas of application [See also 35J05, 35J10, 35K05, 35L05] / 35Q74 PDEs in connection with mechanics of deformable solids
35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Rxx Miscellaneous topics (For equations on manifolds, see 58Jxx; for manifolds of solutions, see 58Bxx; for stochastic PDE, see also 60H15) / 35R35 Free boundary problems
65-XX NUMERICAL ANALYSIS / 65Pxx Numerical problems in dynamical systems [See also 37Mxx] / 65P99 None of the above, but in this section
74-XX MECHANICS OF DEFORMABLE SOLIDS / 74Axx Generalities, axiomatics, foundations of continuum mechanics of solids / 74A15 Thermodynamics
74-XX MECHANICS OF DEFORMABLE SOLIDS / 74Fxx Coupling of solid mechanics with other effects / 74F99 None of the above, but in this section
74-XX MECHANICS OF DEFORMABLE SOLIDS / 74Nxx Phase transformations in solids [See also 74A50, 80Axx, 82B26, 82C26] / 74N20 Dynamics of phase boundaries
74-XX MECHANICS OF DEFORMABLE SOLIDS / 74Qxx Homogenization, determination of effective properties / 74Q99 None of the above, but in this section
Preprint Number:698
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