Phase-Field Models for Microstructure Evolution

Abstract

The phase-field method has recently emerged as a powerful computational approach to modeling and predicting mesoscale morphological and microstructure evolution in materials. It describes a microstructure using a set of conserved and nonconserved field variables that are continuous across the interfacial regions. The temporal and spatial evolution of the field variables is governed by the Cahn-Hilliard nonlinear diffusion equation and the Allen-Cahn relaxation equation. With the fundamental thermodynamic and kinetic information as the input, the phase-field method is able to predict the evolution of arbitrary morphologies and complex microstructures without explicitly tracking the positions of interfaces. This paper briefly reviews the recent advances in developing phase-field models for various materials processes including solidification, solid-state structural phase transformations, grain growth and coarsening, domain evolution in thin films, pattern formation on surfaces, dislocation microstructures, crack propagation, and electromigration.

Nonlinear stress-strain behavior and stress-induced phase transitions in soft Pb(Zr1−xTix)OSeo1, Franzbach2, Koruza3 et al. 2013Phys. Rev. B496261View full textAdd to dashboardCite

“…Ferroelastic stress-strain hysteresis curves for unpoled PZT 40,45,47,49,55, and 60 specimens at 25, 200, and 400 °C are presented in Figure 3. It is apparent that with increasing temperature there is a corresponding decrease in the coercive stress, maximum strain, and remanent strain in all compositions.…”

“…46 The evolution of the polarization of the ferroelectric domain can be determined in response to an external mechanical load by expanding Equation (3) to account for the proper crystal symmetry in three dimensions 47 and enforcing the following equilibrium conditions:…”

“…This was found to be sufficiently small to allow for program convergence and smooth polarization evolution. Simulations were performed for PZT 40,45,47, and 49 using the material parameters in Table 1. During calculations an arbitrarily large uniaxial compressive stress of 50 GPa was utilized to ensure a saturated remanent state, which was defined as the stress above which no increase in remanent strain was found.…”

Extended smoothed boundary method for solving partial differential equations with general boundary conditions on complex boundaries

“…This equation can also be used as a model for evaporationcondensation dynamics [38,39]. Here, we use the Allen-Cahn equation to examine the evaporation of a droplet on a rough surface.…”

Phase-field model for grain boundary grooving in multi-component thin films

“…The functional derivatives of the free energy with respect to ψ and c i are If there is no segregation, all Y i are zero and we recover (12) and (13). The equilibrium on sublattice i, given by δG/δc i = 0, is independent of the other sublattices.…”