Phase-Field Model for Spinodal Decomposition of Dilute Solute Field in Al-Ag Alloy

2011 ◽  
Vol 415-417 ◽  
pp. 1168-1170
Author(s):  
Ying Jun Gao ◽  
Zhi Rong Luo
Keyword(s):  
Free Energy ◽  
Spinodal Decomposition ◽  
Phase Field ◽  
Phase Field Model ◽  
Free Energy Density ◽  
Field Method ◽  
Energy Functional ◽  
Phase Field Method ◽  
Fourth Power ◽  
Free Zone

The typical Landau free energy functional with the fourth power of a solute composition field is not suitable for representing spinodal decomposition of a dilute Ag solute field in Al-Ag alloy. Facing this challenge, a new free energy density function is proposed for spinodal decomposition of a dilute Ag solute field of Al-Ag alloy. The evolution of the solute field in Al-4.2% Ag alloy is studied by phase-field method using this new function. The simulated results reveal that the precipitate free zone (PFZ) around the precipitated phase is an ellipse and its width is about two times that of phase, while in the region far from PFZ, a GPZ pattern of Ag solute field appears due to spinodal decomposition.

A Phase-Field Model for the Formation of Martensite and Bainite

2014 ◽  
Vol 922 ◽  
pp. 31-36 ◽  
Author(s):  
Tansel T. Arif ◽  
Rong Shan Qin
Keyword(s):  
Free Energy ◽  
Phase Field ◽  
Materials Science ◽  
Current Model ◽  
Phase Field Model ◽  
Field Method ◽  
Field Variable ◽  
Phase Field Method ◽  
Cubic Symmetry ◽  
Chemical Free Energy

The phase field method is rapidly becoming the method of choice for simulating the evolution of solid state phase transformations in materials science. Within this area there are transformations primarily concerned with diffusion and those that have a displacive nature. There has been extensive work focussed upon applying the phase field method to diffusive transformations leaving much desired for models that can incorporate displacive transformations. Using the current model, the formation of martensite, which is formed via a displacive transformation, is simulated. The existence of a transformation matrix in the free energy expression along with cubic symmetry operations enables the reproduction of the 24 grain variants of martensite. Furthermore, upon consideration of the chemical free energy term, the model is able to utilise both the displacive and diffusive aspects of bainite formation, reproducing the autocatalytic nucleation process for multiple sheaves using a single phase field variable. Transformation matrices are available for many steels, one of which is used within the model.

Numerical Simulation of Spinodal Deposition in Cu–6at.%Ni–3at.%Si Ternary Alloy Using of Phase Field Method

2011 ◽  
Vol 704-705 ◽  
pp. 1410-1415 ◽  
Author(s):  
Yong Qiang Long ◽  
Ping Liu ◽  
Yong Liu ◽  
Shu Guo Jiao ◽  
Bao Hong Tian
Keyword(s):  
Spinodal Decomposition ◽  
Ternary Alloy ◽  
Phase Field ◽  
Elastic Energy ◽  
Early Stage ◽  
Phase Field Model ◽  
Field Method ◽  
Phase Field Method ◽  
Growth Exponent ◽  
Dynamics Calculation

Based on Cahn-Hilliard nonlinear diffusion equation, the phase field model has been established for ternary alloy spinodal decomposition, which directly couples with Calphad thermodynamics and dynamics calculation and takes into account the effect of the coherent elastic energy. The simulated microstructures of spinodal decomposition were carried out in the isothermally-aged of Cu-6at.%Ni-3at.%Si alloy. The results indicate that the spinodal decomposition takes place at the early stage of Cu-6at.%Ni-3at.%Si alloy aging at temperatures of 723K, forming two-phases mixture of Cu-rich and Ni/Si-rich, and the decomposition microstructures are distributed in a semi-interconnected labyrinth-like form. Under the effect of the coherent elastic energy, the decomposition microstructures demonstrate the obvious anisotropic characteristics, and present interconnected rectangular stripes aligned along [10] and [01] directions. The growth of the decomposition microstructures is in accordance with the growth law of growth exponentn≈0.29, slightly less than the LSW’s prediction.

The numerical modeling of cell freezing in binary solution under subcooling conditions

2019 ◽  
Vol 30 (6) ◽  
pp. 3005-3025
Author(s):  
Przemysław Smakulski ◽  
Sławomir Pietrowicz ◽  
Jun Ishimoto
Keyword(s):  
Numerical Modeling ◽  
Free Energy ◽  
Numerical Calculation ◽  
Phase Field ◽  
Field Method ◽  
Energy Functional ◽  
Phase Field Method ◽  
Phase Front ◽  
Content Type ◽  
Free Energy Functional

Purpose This paper aims to describe and investigate the mathematical models and numerical modeling of how a cell membrane is affected by a transient ice freezing front combined with the influence of thermal fluctuations and anisotropy. Design/methodology/approach The study consists of mathematical modeling, validation with an analytical solution, and shows the influence of thermal noises on phase front dynamics and how it influences the freezing process of a single red blood cell. The numerical calculation has been modeled in the framework of the phase field method with a Cahn–Hilliard formulation of a free energy functional. Findings The results show an influence scale on directional phase front propagation dynamics and how significant are stochastic thermal noises in micro-scale freezing. Originality/value The numerical calculation has modeled in the framework of the phase field method with a Cahn–Hilliard formulation of a free energy functional.

Phase Field Model for Influence of Edge Dislocation on Precipitation

2011 ◽  
Vol 415-417 ◽  
pp. 1482-1485
Author(s):  
Chuang Gao Huang ◽  
Ying Jun Gao ◽  
Li Lin Huang ◽  
Jun Long Tian
Keyword(s):  
Edge Dislocation ◽  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Field Method ◽  
Phase Field Method ◽  
Second Phase ◽  
Free Energy Function ◽  
Phase Nucleation ◽  
Good Agreement

The second phase nucleation and precipitation around the edge dislocation are studied using phase-field method. A new free energy function is established. The simulation results are in good agreement with that of theory of dislocation and theory of non-uniform nucleation.

scholarly journals The Effects of Inhomogeneous Elasticity and Dislocation on Thermodynamics and the Kinetics of the Spinodal Decomposition of a Fe-Cr System: A Phase-Field Study

Metals ◽  
2020 ◽  
Vol 10 (9) ◽  
pp. 1209
Author(s):  
Wooseob Shin ◽  
Jeonghwan Lee ◽  
Kunok Chang
Keyword(s):  
Spinodal Decomposition ◽  
Phase Field ◽  
Early Stage ◽  
Field Method ◽  
Phase Field Method ◽  
Precipitate Size ◽  
System A ◽  
Phase Separation Kinetics ◽  
Cr Concentration ◽  
Cr System

The effects of inhomogeneous elasticity and dislocation on the microstructure evolution of α′ precipitate in a Fe-Cr system was investigated using a Computer Coupling of Phase Diagrams and Thermochemistry (CALPHAD)-type free energy incorporated phase-field method. In order to simulate the precipitation behavior by phase-field modeling in consideration of inhomogeneous elasticity, a Multiphysics Object-Oriented Simulation Environment (MOOSE) framework was used, which makes it easy to use powerful numerical means such as parallel computing and finite element method (FEM) solver. The effect of inhomogeneous elasticity due to the compositional inhomogeneity or the presence of dislocations affects the thermodynamic properties of the system was investigated, such as the lowest Cr concentration at which spinodal decomposition occurs. The effect of inhomogeneous elasticity on phase separation kinetics is also studied. Finally, we analyzed how inhomogeneous elasticity caused by compositional fluctuation or dislocation affects microstructure characteristics such as ratio between maximum precipitate size with respect to the average on early stage and later stage, respectively.

Application of Interface-Tracking Method Based on Phase-Field Model to Numerical Analysis of Isothermal and Thermal Two-Phase Flows

2007 ◽  
Author(s):  
Naoki Takada
Keyword(s):  
Phase Field ◽  
Density Ratio ◽  
Phase Field Model ◽  
Field Method ◽  
Diffuse Interface ◽  
Phase Field Method ◽  
Navier Stokes ◽  
Interface Tracking ◽  
Two Phase Flows ◽  
Two Phase

For interface-tracking simulation of two-phase flows in various micro-fluidics devices, the applicability of two versions of Navier-Stokes phase-field method (NS-PFM) was examined, combining NS equations for a continuous fluid with a diffuse-interface model based on the van der Waals-Cahn-Hilliard free-energy theory. Through the numerical simulations, the following major findings were obtained: (1) The first version of NS-PFM gives good predictions of interfacial shapes and motions in an incompressible, isothermal two-phase fluid with high density ratio on solid surface with heterogeneous wettability. (2) The second version successfully captures liquid-vapor motions with heat and mass transfer across interfaces in phase change of a non-ideal fluid around the critical point.

scholarly journals Application of phase-field method in rechargeable batteries

2020 ◽  
Vol 6 (1) ◽  
Author(s):  
Qiao Wang ◽  
Geng Zhang ◽  
Yajie Li ◽  
Zijian Hong ◽  
Da Wang ◽  
...  
Keyword(s):  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Field Method ◽  
Rechargeable Batteries ◽  
Computational Approach ◽  
Phase Field Method ◽  
Electrochemical Systems ◽  
Material Systems ◽  
Physical And Chemical

AbstractRechargeable batteries have a profound impact on our daily life so that it is urgent to capture the physical and chemical fundamentals affecting the operation and lifetime. The phase-field method is a powerful computational approach to describe and predict the evolution of mesoscale microstructures, which can help to understand the dynamic behavior of the material systems. In this review, we briefly introduce the theoretical framework of the phase-field model and its application in electrochemical systems, summarize the existing phase-field simulations in rechargeable batteries, and provide improvement, development, and problems to be considered of the future phase-field simulation in rechargeable batteries.

Study on Microstructural Evolution of Binary Alloy Crystal Growth in Directional Solidification Process

2013 ◽  
Vol 470 ◽  
pp. 100-103
Author(s):  
Dong Sheng Chen ◽  
Ming Chen ◽  
Rui Chang Wang
Keyword(s):  
Crystal Growth ◽  
Directional Solidification ◽  
Binary Alloy ◽  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Field Method ◽  
Phase Field Method ◽  
Pure Substance ◽  
Columnar Dendrite

PFM (phase field method) was employed to study microstructure evolution, and considering the effect of solute concentration to the undercooling, we developed a phase field model for binary alloy on the basis of pure substance model. In the paper, the temperature field and solute field were coupled together in the phase field model to calculate the crystal growth of magnesium alloy in directional solidification. The simulation results showed a non-planar crystal growth of planar to cellular to columnar dendrite, the comparison of different dendrite patterns were carried out in the numerical simulation, and with the increasing of the anisotropy, the second dendrite arms became more developed.

Thermodynamic Calculation of Al-Cu Eutectic Alloy with Microstructure Simulation Using Phase Field Method

2011 ◽  
Vol 295-297 ◽  
pp. 468-472 ◽  
Author(s):  
Jin Jun Tang ◽  
Jian Zhong Jiang ◽  
Chun Hua Tang ◽  
Da Hui Chen ◽  
Li Qun Hou
Keyword(s):  
Free Energy ◽  
Eutectic Alloy ◽  
Phase Field ◽  
Regular Solution Model ◽  
Field Method ◽  
Phase Field Method ◽  
Multiple Point ◽  
Microstructure Simulation ◽  
Thermo Calc Software ◽  
New Phase

Phase-field method can be used to describe the complicated morphologies of crystal growth without explicitly tracking the complex phase boundaries. The conformation of volume free energy is very important for microstructure simulation with phase-field method. However, the conformation of volume free energy is still correspondingly simple and ideal at present. In this paper, a new conformation method of free energy is mentioned. Free energy of each phase at appointed states is calculated by Thermo-Calc software. In order to avoided calculation, free energy of each phase is fitted by multiple-point function according to sub- regular solution model. It is obtained that the free energy data and phase graph data of α phase, θ phase and L phase in the extension, temperature (791-841) K and component (0-35)Cu(at.%) with Al-Cu eutectic alloy. The new phase model is also founded, and used to calculate microstructure evolution of Al-Cu eutectic alloy.

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