scholarly journals Lattice Phase Field Model for Nanomaterials

Materials ◽  
2021 ◽  
Vol 14 (23) ◽  
pp. 7317
Author(s):  
Pingping Wu ◽  
Yongfeng Liang
Keyword(s):  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Lattice Parameter ◽  
Grid Spacing ◽  
Field Equations ◽  
Future Directions ◽  
Superlattice Structure ◽  
Field Modeling ◽  
Phase Field Equations

The lattice phase field model is developed to simulate microstructures of nanoscale materials. The grid spacing in simulation is rescaled and restricted to the lattice parameter of real materials. Two possible approaches are used to solve the phase field equations at the length scale of lattice parameter. Examples for lattice phase field modeling of complex nanostructures are presented to demonstrate the potential and capability of this model, including ferroelectric superlattice structure, ferromagnetic composites, and the grain growth process under stress. Advantages, disadvantages, and future directions with this phase field model are discussed briefly.

Convergence of the phase field model to its sharp interface limits

1998 ◽  
Vol 9 (4) ◽  
pp. 417-445 ◽  
Author(s):  
GUNDUZ CAGINALP ◽  
XINFU CHEN
Keyword(s):  
Surface Tension ◽  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Field Equations ◽  
Two Phase ◽  
Cahn Equation ◽  
Phase Field Equations ◽  
Cahn Hilliard Equation ◽  
Surface Tension Model

We consider the distinguished limits of the phase field equations and prove that the corresponding free boundary problem is attained in each case. These include the classical Stefan model, the surface tension model (with or without kinetics), the surface tension model with zero specific heat, the two phase Hele–Shaw, or quasi-static, model. The Hele–Shaw model is also a limit of the Cahn–Hilliard equation, which is itself a limit of the phase field equations. Also included in the distinguished limits is the motion by mean curvature model that is a limit of the Allen–Cahn equation, which can in turn be attained from the phase field equations.

Phase-field modeling of the coupled domain structure and dielectric breakdown evolution in a ferroelectric single crystal

2019 ◽  
Vol 21 (29) ◽  
pp. 16207-16212 ◽  
Author(s):  
Ziming Cai ◽  
Chaoqiong Zhu ◽  
Xiaohui Wang ◽  
Longtu Li
Keyword(s):  
Single Crystal ◽  
Domain Structure ◽  
Phase Field ◽  
Field Model ◽  
Dielectric Breakdown ◽  
Phase Field Model ◽  
Phase Field Modeling ◽  
Field Modeling ◽  
Ferroelectric Single Crystal

The coupled evolution of domain structure and dielectric breakdown is simulated via a phase-field model.

Thermal Kinetics Phase Field Model for the Metals' Solidification - Mathematic Derivation of the Dendrite Growth Phase Field Variable Diffusion Model

2013 ◽  
Vol 364 ◽  
pp. 614-618
Author(s):  
Heng Min Ding ◽  
Lv Chun Pu
Keyword(s):  
Diffusion Model ◽  
Phase Field ◽  
Phase Field Model ◽  
Pure Metal ◽  
Phase Variable ◽  
Field Equations ◽  
Metal Solidification ◽  
Heat Transfer Theory ◽  
Variable Diffusion ◽  
Phase Field Equations

Phase field equations for simulation of dendritic growth have a history of nearly twenty years. The existing phase field equations are directly derived through the Ginzburg-Landau equations. However, though widely used, the physical meaning of each variable in the equations is not clear. So the domestic and foreign researchers have made a lot of mistakes and interpretation. In this paper, with the solid fraction as a phase field variables in the field, based on thermodynamics and heat transfer theory, author gives a rigorous scientific phase variable diffusion model of the pure metal solidification and its derivation process.

2D Phase-Field Simulation of the Directional Solidification Process

2014 ◽  
Vol 704 ◽  
pp. 17-21 ◽  
Author(s):  
Alexandre Furtado Ferreira ◽  
José Adilson de Castro ◽  
Ivaldo Leão Ferreira
Keyword(s):  
Directional Solidification ◽  
Phase Field ◽  
Field Model ◽  
Solid Phase ◽  
Morphological Evolution ◽  
Phase Field Model ◽  
Columnar Dendrite ◽  
Liquid Region ◽  
Field Equations ◽  
Cu Alloy

The microstructure evolution during the directional solidification of Al-Cu alloy is simulated using a phase field model. The transformation from liquid to solid phase is a non-equilibrium process with three regions (liquid, solid and interface) involved. Phase field model is defined for each of the three regions. The evolution of each phase is calculated by a set of phase field equations, whereas the solute in those regions is calculated by a concentration equation. In this work, the phase field model which is generally valid for most kinds of transitions between phases, it is applied to the directional solidification problem. Numerical results for the morphological evolution of columnar dendrite in Al-Cu alloy are in agreement with experimental observations found in the literature. The growth velocity of the dendrite tip and the concentration profile in the solid, interface and liquid region were calculated.

ERGODICITY FOR THE PHASE-FIELD EQUATIONS PERTURBED BY GAUSSIAN NOISE

2011 ◽  
Vol 14 (01) ◽  
pp. 35-55 ◽  
Author(s):  
VIOREL BARBU ◽  
GIUSEPPE DA PRATO
Keyword(s):  
Invariant Measure ◽  
Phase Field ◽  
Gaussian Noise ◽  
Phase Field Model ◽  
Field Equations ◽  
Von Neumann ◽  
Neumann Theorem ◽  
Phase Field Equations ◽  
Unique Invariant Measure ◽  
Von Neumann Theorem

We prove that the transition semigroup associated with the phase-field equations perturbed by a Gaussian noise has an invariant measure and it is irreducible and strong Feller. This implies by Doob's theorem that it possesses a unique invariant measure which is ergodic and strongly mixing. This implies the ergodicity of the flow associated with the phase-field model of phase transition in the sense of Birkhoff–von Neumann theorem. Such a result seems to be new in this context.

Phase Field Modeling for Grain Growth of Static Recrystallization of Deformed Alloys

2011 ◽  
Vol 399-401 ◽  
pp. 1785-1788
Author(s):  
Ying Jun Gao ◽  
Zhi Rong Luo
Keyword(s):  
Grain Growth ◽  
Phase Field ◽  
Field Model ◽  
Static Recrystallization ◽  
Phase Field Model ◽  
Free Energy Function ◽  
Phase Field Modeling ◽  
Field Modeling ◽  
Storage Energy ◽  
Good Agreement

A multi-state free energy function for deformation alloy with storage energy is proposed to simulate the microstructure evolution of static recrystallization with phase field model. The grain growth and grain size distribution during recrystallization are discussed. The simulation results are in good agreement with other theoretical or experimental results.

DESIGN OPTIMIZATION OF A FERROELECTRIC NANO-ACTUATOR USING PHASE-FIELD MODELING

2014 ◽  
Vol 1674 ◽  
Author(s):  
Ananya Renuka Balakrishna ◽  
John E. Huber
Keyword(s):  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Two Dimensional ◽  
Phase Field Modeling ◽  
Ferroelectric Crystal ◽  
Surface Conditions ◽  
Field Modeling ◽  
Working Principle ◽  
Ferroelectric Switching

ABSTRACTA ferroelectric crystal with charge-free surface conditions contains polarized domains which can form a flux closure with zero net polarization. In the presence of an external electric field, the flux closure in a two-dimensional continuum reorients its spontaneous polarization to align with the field. Based on this concept of ferroelectric switching coupled with mechanical straining, we demonstrate the working principle of a ferroelectric nano-actuator. The behavior of the actuator is explored under the action of electro-mechanical loading and its mechanism is simulated with a 2D phase-field model. The design of nano-actuator is modified to achieve greater actuation displacements by bending a thin device.

Dependence of Dendritic Growth on Convention with PFM Simulation

2011 ◽  
Vol 689 ◽  
pp. 85-90
Author(s):  
Chang Sheng Zhu ◽  
Jin Gui ◽  
Zhi Ping Wang ◽  
Feng Li
Keyword(s):  
Flow Field ◽  
Computational Methods ◽  
Binary Alloy ◽  
Phase Field ◽  
Dendritic Growth ◽  
Field Model ◽  
Phase Field Model ◽  
Field Equations ◽  
Dendritic Branches ◽  
Solute Composition

A binary alloy PFM (Phase-Field Model) which incorporates the flow field equations is constructed considering the dependence of microstructure on convention. Al-Cu binary alloy is investigated numerically based on the model, and the reasonable computational methods is studied for solving PFM, the effect of convention on dendritic growth and microsegregation patterns is implemented successfully. The computed results indicate that, the larger convention velocity U, the more developed the upstream dendritic branches is, and the more acutely the solute composition in the upstream dendritic solid fluctuates is. But the severity of microsegregation ahead of interface reduces. Nevertheless, the more undeveloped the downstream dendritic branches, the more acutely the solute composition in the the downstream dendritic solid fluctuates is, but the severity of microsegregation ahead of interface aggravates.

Phase-Field Modeling of Dendritic Solidification in Undercooled Droplets Processed by Electromagnetic Levitation

2006 ◽  
Vol 508 ◽  
pp. 431-436 ◽  
Author(s):  
Peter K. Galenko ◽  
Dieter M. Herlach ◽  
G. Phanikumar ◽  
O. Funke
Keyword(s):  
Phase Field ◽  
Dendritic Growth ◽  
Field Model ◽  
Phase Field Model ◽  
Electromagnetic Levitation ◽  
Dendritic Solidification ◽  
Field Modeling ◽  
Theoretical Predictions ◽  
Forced Convective Flow ◽  
Undercooled Melts

The results on modeling dendritic solidification from undercooled melts processed by the electromagnetic levitation technique are discussed. In order to model the details of formation of dendritic patterns we use a phase-field model of dendritic growth in a pure undercooled system with convection of the liquid phase. The predictions of the phase-field model are discussed referring to our latest high accuracy measurements of dendrite growth velocities in nickel samples. Special emphasis is given to the growth of dendrites at small and moderate undercoolings. At small undercoolings, the theoretical predictions deviate systematically from experimental data for solidification of nickel dendrites. It is shown that small amounts of impurities and forced convective flow can lead to an enhancement of the velocity of dendritic solidification at small undercoolings.

scholarly journals 3D Phase Field Modeling of Multi-Dendrites Evolution in Solidification and Validation by Synchrotron X-ray Tomography

Materials ◽  
2021 ◽  
Vol 14 (3) ◽  
pp. 520
Author(s):  
Shuo Wang ◽  
Zhipeng Guo ◽  
Jinwu Kang ◽  
Meishuai Zou ◽  
Xiaodong Li ◽  
...  
Keyword(s):  
Phase Field ◽  
Field Model ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Phase Field Model ◽  
Computationally Efficient ◽  
X Ray ◽  
Cu Alloy ◽  
Field Modeling ◽  
Micro Tomography

In this paper, the dynamics of multi-dendrite concurrent growth and coarsening of an Al-15 wt.% Cu alloy was studied using a highly computationally efficient 3D phase field model and real-time synchrotron X-ray micro-tomography. High fidelity multi-dendrite simulations were achieved and the results were compared directly with the time-evolved tomography datasets to quantify the relative importance of multi-dendritic growth and coarsening. Coarsening mechanisms under different solidification conditions were further elucidated. The dominant coarsening mechanisms change from small arm melting and interdendritic groove advancement to coalescence when the solid volume fraction approaches ~0.70. Both tomography experiments and phase field simulations indicated that multi-dendrite coarsening obeys the classical Lifshitz–Slyozov–Wagner theory Rn−R0n = kc(t−t0), but with a higher constant of n = 4.3.

Sign in / Sign up

Export Citation Format

Share Document