Thermo-Solutal Modelling of Microstructure Formation during Multiphase Alloy Solidification - a New Approach

Abstract:

This paper shows how to move from a specification of free energy for the solidification of a binary alloy to the dynamical equations using the elegance of a dissipative bracket analogous to the Poisson bracket of Hamiltonian mechanics. A key new result is the derivation of the temperature equation for single-phase thermal-solutal models, which contains generalisations and extra terms which challenge standard models. We also present, for the first time, the temperature equation for thermal multi-phase field models. There are two main ingredients: one, the specification of the free energy in terms of the time and space dependent field variables: $n$-phases $\phi_i$, a concentration variable $c$, and temperature $T$; two, the specification of the dissipative bracket in terms of these variables, their gradients and a set of diffusion parameters, which may themselves depend on the field variables. The paper explains the method within this context and demonstrates its thermodynamic admissibility.

• Periodical: Materials Science Forum (Volumes 790-791)
• Pages: 103-108
• DOI: https://doi.org/10.4028/www.scientific.net/MSF.790-791.103
• Online since: May 2014
• Authors: Peter C. Bollada*, Andrew M. Mullis, Peter K. Jimack
• Keywords: Dissipative System, Non-Equilibrium Thermodynamics, Phase Field, Solidification

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