The multi-phase-field approach is generalized to treat capillarity-driven diffusion parallel to the surfaces and phase boundaries, i.e., the boundaries between a condensed phase and its vapor and the boundaries between two or multiple condensed phases. The effect of capillarity is modeled via curvature dependence of the chemical potential whose gradient gives rise to diffusion. The model is used to study thermal grooving on the surface of a polycrystalline body. Decaying oscillations of the surface profile during thermal grooving, postulated by Hillert long ago but reported only in few studies so far, are observed and discussed. Furthermore, annealing of multi-nanoclusters on a deformable free surface is investigated using the proposed model. Results of these simulations suggest that the characteristic craterlike structure with an elevated perimeter, observed in recent experiments, is a transient nonequilibrium state during the annealing process.
Domain walls and phase boundaries are fundamental ingredients of ferroelectrics and strongly influence their functional properties. Although both interfaces have been studied for decades, often only a phenomenological macroscopic understanding has been established. The recent developments in experiments and theory allow to address the relevant time and length scales and revisit nucleation, phase propagation and the coupling of domains and phase transitions. This review attempts to specify regularities of domain formation and evolution at ferroelectric transitions and give an overview on unusual polar topological structures that appear as transient states and at the nanoscale. We survey the benefits, validity, and limitations of experimental tools as well as simulation methods to study phase and domain interfaces. We focus on the recent success of these tools in joint scale-bridging studies to solve long lasting puzzles in the field and give an outlook on recent trends in superlattices.
A consistent treatment of the coupling of surface energy and elasticity within the multi-phasefield framework is presented. The model accurately reproduces stress distribution in a number of analytically tractable, yet non-trivial, cases including different types of spherical heterogeneities and a thin plate suspending in a gas environment. It is then used to study the stress distribution inside elastic bodies with non-spherical geometries, such as a solid ellipsoid and a sintered structure. In these latter cases, it is shown that the interplay between deformation and spatially variable surface curvature leads to heterogeneous stress distribution across the specimen.
We propose a combined computational approach based on the multi-phase-field and the lattice Boltzmann method for the motion of solid particles under the action of capillary forces. The accuracy of the method is analyzed by comparison with the analytic solutions for the motion of two parallel plates of finite extension connected by a capillary bridge. The method is then used to investigate the dynamics of multiple spherical solid bodies connected via capillary bridges. The amount of liquid connecting the spheres is varied, and the influence of the resulting liquid-morphology on their dynamics is investigated. It is shown that the method is suitable for a study of liquid-phase sintering which includes both phase transformation and capillary driven rigid body motion.
In this work, we develop an efficient phase-field approach to simulate the grain growth in polycrystalline ceramic materials in the presence of pores with various mobilities and diffusion coefficients. The multi-phase-field model is coupled to the Cahn–Hilliard equation for pore dynamics by interaction functions which describe the interaction of pores with grain boundaries. Two types of the model are suggested with one and two order parameters responsible for the pores. We also show that the model can be applied to the simulation of the interaction of the grain boundaries with coherent and non-coherent particles. The parameters of the model allow us to reproduce the equilibrium dihedral angle in the triple-junction of a pore or a particle and a grain boundary. A drag velocity of the grain boundary in the presence of pores or precipitates was also measured for various diffusion coefficients and grain boundary mobilities. The effects of the pore dynamics on the grain size evolution in ceramic materials was investigated and compared with reported theoretical predictions and experimental data.
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