Thermo-solutal modelling of microstructure formation during multiphase alloy solidification - a new approach

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 φi, 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.