A phase-field study of domain dynamics in ferroelectric BCT-BZT system

MRS Advances ◽  
2016 ◽  
Vol 1 (40) ◽  
pp. 2783-2788 ◽  
Author(s):  
Soumya Bandyopadhyay ◽  
Tushar Jogi ◽  
Kumaraswamy Miriyala ◽  
Ranjith Ramadurai ◽  
Saswata Bhattacharyya
Keyword(s):  
Free Energy ◽  
Phase Field ◽  
Three Dimensional ◽  
Phase Field Model ◽  
Ginzburg Landau ◽  
Equimolar Composition ◽  
Electrical Boundary Conditions ◽  
Experimental Findings ◽  
Domain Dynamics ◽  
Three Dimensional Simulations

ABSTRACTWe present a thermodynamically consistent phase-field model describing the free energy of perovskite-based BCT-BZT solid solution containing an intermediate morphotropic phase boundaries. The Landau coefficients are derived as functions of composition of zirconium. The electrostrictive and elastic constants are appropriately chosen from experimental findings. The resulting Landau free energy is constructed to describe the stable polarization states as a function of composition. The evolution of the polarization order parameters at a particular composition is described by a set of time-dependent Ginzburg-Landau (TDGL) equations. Additionally, we solve Poisson’s equation and mechanical equilibrium equation to account for the ferroelectric/ferroelastic interactions. We have performed two dimensional and three-dimensional simulations with appropriate electrical boundary conditions to study the effect of external electric field on domain dynamics in BCT-BZT system at the equimolar composition.

scholarly journals On the Diffuse Interface Models for High Codimension Dispersed Inclusions

Mathematics ◽  
2021 ◽  
Vol 9 (18) ◽  
pp. 2206
Author(s):  
Elizaveta Zipunova ◽  
Evgeny Savenkov
Keyword(s):  
Free Energy ◽  
Phase Field ◽  
Field Model ◽  
Three Dimensional ◽  
Phase Field Model ◽  
Diffuse Interface ◽  
State Variables ◽  
Interface Models ◽  
Dispersed Inclusions ◽  
Derivatives Of

Diffuse interface models are widely used to describe the evolution of multi-phase systems of various natures. Dispersed inclusions described by these models are usually three-dimensional (3D) objects characterized by phase field distribution. When employed to describe elastic fracture evolution, the dispersed phase elements are effectively two-dimensional (2D) objects. An example of the model with effectively one-dimensional (1D) dispersed inclusions is a phase field model for electric breakdown in solids. Any diffuse interface field model is defined by an appropriate free energy functional, which depends on a phase field and its derivatives. In this work we show that codimension of the dispersed inclusions significantly restricts the functional dependency of the free energy on the derivatives of the problem state variables. It is shown that to describe codimension 2 diffuse objects, the free energy of the model necessarily depends on higher order derivatives of the phase field or needs an additional smoothness of the solution, i.e., its first derivatives should be integrable with a power greater than two. Numerical experiments are presented to support our theoretical discussion.

scholarly journals Phase-field modeling of grain evolutions in additive manufacturing from nucleation, growth, to coarsening

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Min Yang ◽  
Lu Wang ◽  
Wentao Yan
Keyword(s):  
Additive Manufacturing ◽  
Phase Field ◽  
Field Model ◽  
Three Dimensional ◽  
Phase Field Model ◽  
Nucleation Theory ◽  
Experimental Result ◽  
Classical Nucleation Theory ◽  
Validation Experiment ◽  
Powder Particles

AbstractA three-dimensional phase-field model is developed to simulate grain evolutions during powder-bed-fusion (PBF) additive manufacturing, while the physically-informed temperature profile is implemented from a thermal-fluid flow model. The phase-field model incorporates a nucleation model based on classical nucleation theory, as well as the initial grain structures of powder particles and substrate. The grain evolutions during the three-layer three-track PBF process are comprehensively reproduced, including grain nucleation and growth in molten pools, epitaxial growth from powder particles, substrate and previous tracks, grain re-melting and re-growth in overlapping zones, and grain coarsening in heat-affected zones. A validation experiment has been carried out, showing that the simulation results are consistent with the experimental results in the molten pool and grain morphologies. Furthermore, the grain refinement by adding nanoparticles is preliminarily reproduced and compared against the experimental result in literature.

scholarly journals Phase-field model of precipitation processes with coherency loss

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Tian-Le Cheng ◽  
You-Hai Wen
Keyword(s):  
Phase Field ◽  
Field Model ◽  
Ostwald Ripening ◽  
Phase Field Model ◽  
Energy Criterion ◽  
Field Variable ◽  
Ginzburg Landau ◽  
Underlying Mechanisms ◽  
Flood Fill ◽  
Coherency Loss

AbstractA phase-field model is proposed to simulate coherency loss coupled with microstructure evolution. A special field variable is employed to describe the degree of coherency loss of each particle and its evolution is governed by a Ginzburg-Landau type kinetic equation. For the sake of computational efficiency, a flood-fill algorithm is introduced that can drastically reduce the required number of field variables, which allows the model to efficiently simulate a large number of particles sufficient for characterizing their statistical features during Ostwald ripening. The model can incorporate size dependence of coherency loss, metastability of coherent particles, and effectively incorporate the underlying mechanisms of coherency loss by introducing a so-called differential energy criterion. The model is applied to simulate coarsening of Al3Sc precipitates in aluminum alloy and comprehensively compared with experiments. Our results clearly show how the particle size distribution is changed during coherency loss and affects the coarsening rate.

Phase-Field Simulation of Three-Dimensional Dendritic Growth

2010 ◽  
Vol 97-101 ◽  
pp. 3769-3772 ◽  
Author(s):  
Chang Sheng Zhu ◽  
Jun Wei Wang
Keyword(s):  
Computational Methods ◽  
Phase Field ◽  
Interfacial Energy ◽  
Dendritic Growth ◽  
Field Model ◽  
Three Dimensional ◽  
Phase Field Model ◽  
Computational Time ◽  
Field Simulation ◽  
Undercooled Melt

Based on a thin interface limit 3D phase-field model by coupled the anisotropy of interfacial energy and self-designed AADCR to improve on the computational methods for solving phase-field, 3D dendritic growth in pure undercooled melt is implemented successfully. The simulation authentically recreated the 3D dendritic morphological fromation, and receives the dendritic growth rule being consistent with crystallization mechanism. An example indicates that AADCR can decreased 70% computational time compared with not using algorithms for a 3D domain of size 300×300×300 grids, at the same time, the accelerated algorithms’ computed precision is higher and the redundancy is small, therefore, the accelerated method is really an effective method.

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