Multicomponent alloy solidification: Phase-field modeling and simulations

Abstract

A general formulation of phase-field models for nonisothermal solidification in multicomponent and multiphase alloy systems is derived from an entropy functional in a thermodynamically consistent way. General expressions for the free energy densities, for multicomponent diffusion coefficients, and for both weak and faceted types of surface energy and kinetic anisotropy are possible. A three-dimensional simulator is developed to show the capability of the model to describe phase transitions, complex microstructure formation, and grain growth in polycrystalline textures.

Modeling fracture cementation processes in calcite limestone: a phase-field study

“…A thermodynamically consistent multiphase-field model Nestler et al (2005) is employed to address the phenomenon of anisotropic crystal growth in calcite veins. The model has been previously applied to address the growth of minerals such as potash alum (Ankit et al 2013), quartz (Ankit et al 2013(Ankit et al , 2015aWendler et al 2016), and calcite (Prajapati et al 2017).…”

Numerical and Experimental Investigations on the Growth of the Intermetallic Mg2Si Phase in Mg Infiltrated Si‐Foams

“…[31] for the expressions), V is the domain occupied by the system, and e is a length parameter related to the width of the diffuse interface. The phase-field evolution equation is derived by the variational approach and reads…”

Phase-field simulations of nuclei and early stage solidification microstructures

“…From MD predictions [25], an additional energy of triple line order is essentially of relevance for small (nanometer) length scales. To account for this effect in the multiphase-field formulation [26], the anisotropic gradient energy density a(φ, ∇φ) in the functional is extended by a third order term ∼θ αβη φ η of the form…”

“…For the MD simulations, the crystal-melt interface in the pure Ni system is modelled by the interatomic potential using the embedded atom method and the system is considered as an isothermal, isobaric N PT ensemble with 32 000 atoms, [29,30]. The PF model is based on a standard formulation presented in [13,26], for example. The MD simulations were set up in a domain with an initial Ni melt undercooled by 300 K. A nucleus forms naturally by homogeneous nucleation and grows to extend approximately 50Å in each dimension.…”

“…This approach has been used to model solidification, microstructure formation in solids and motion of grain boundaries. PF models include formulations for the case of a pure substance [3], for multicomponent systems [4][5][6], for polycrystalline structure [7,8] as well as for the phase transition where multiple different phases are involved: eutectic [9][10][11], peritectic [10] and monotectic [12] systems.…”