Modelling of multicomponent diffusive phase transformation in solids. (English) Zbl 1202.82032

Chleboun, J. (ed.) et al., Programs and algorithms of numerical mathematics 14. Proceedings of the seminar, Dolní Maxov, Czech Republic, June 1–6, 2008. Prague: Academy of Sciences of the Czech Republic, Institute of Mathematics (ISBN 978-80-85823-55-4). 207-219 (2008).
Summary: Physical analysis of phase transformation of materials consisting from several (both substitutional and interstitial) components, coming from the Onsager extremal thermodynamic principle, leads, from the mathematical point of view, to a system of partial differential equations of evolution type, including certain integral term, with substantial differences in particular phases \((\alpha,\gamma)\) and in moving interface of finite thickness \((\beta)\), in whose center the ideal liquid material behaviour can be detected. The numerical simulation of this process in MATLAB is able to explain some phenomena (e.g. the interface velocity as a function of temperature) better than known simplified models assuming the sharp interface and additional boundary and transfer conditions.
For the entire collection see [Zbl 1194.65013].


82B26 Phase transitions (general) in equilibrium statistical mechanics
82D20 Statistical mechanics of solids
82B24 Interface problems; diffusion-limited aggregation arising in equilibrium statistical mechanics
82B35 Irreversible thermodynamics, including Onsager-Machlup theory