Remarks on some open problems in phase-field modelling of solidification

Abstract

Three different topics in phase-field modelling of solidification are discussed, with particular emphasis on the limitations of the currently available modelling approaches. First, thin-interface limits of two-sided phase-field models are examined, and it is shown that the antitrapping current is in general not sufficient to remove all thin-interface effects. Second, orientation-field models for polycrystalline solidification are analysed, and it is shown that the standard relaxational equation of motion for the orientation field is incorrect in coherent polycrystalline matter. Third, it is pointed out that the standard procedure to incorporate fluctuations into the phase-field approach cannot be used in a straightforward way for a quantitative description of nucleation.

22 pages, 3 figures

References in corpus (5)

• Quantitative Phase Field Model of Alloy Solidification
• On the growth and form of spherulites
• Quantitative phase-field modeling of two-phase solidification
• Phase Field Theory of Heterogeneous Crystal Nucleation
• Phase field theory of polycrystalline solidification in three dimensions

Cited by in corpus (9)

• Phase-field-crystal models for condensed matter dynamics on atomic length and diffusive time scales: an overview
• Phase-field modeling of crystal nucleation in undercooled liquids -- A review
• Theoretical and numerical study of lamellar eutectoid growth influenced by volume diffusion
• An orientation-field model for polycristalline solidification with a singular coupling between order and orientation
• Tensorial mobilities for accurate solution of transport problems in models with diffuse interfaces
• A hybrid level-set / embedded boundary method applied to solidification-melt problems
• Contact melting and the structure of binary eutectic near the eutectic point
• Classical nucleation theory in the phase-field crystal model
• Nucleation of crystal surfaces with corner energy regularization