scholarly journals Disorder-L10 Transition Investigated by Phase Field Method with CVM Local Free Energy

2001 ◽  
Vol 42 (10) ◽  
pp. 2033-2041 ◽  
Author(s):  
Munekazu Ohno ◽  
Tetsuo Mohri
Keyword(s):  
Free Energy ◽  
Phase Field ◽  
Field Method ◽  
Phase Field Method

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.

Phase Field Calculations with CVM Free Energy within Square Approximation

2007 ◽  
Vol 561-565 ◽  
pp. 1935-1940
Author(s):  
Tetsuo Mohri ◽  
Nao Fujihashi ◽  
Ying Chen
Keyword(s):  
Free Energy ◽  
Phase Field ◽  
Stoichiometric Composition ◽  
Sharp Decrease ◽  
Cluster Variation Method ◽  
Field Method ◽  
Phase Field Method ◽  
Square Lattice ◽  
Variation Method ◽  
Cluster Variation

Phase Field Method is combined with the Cluster Variation Method within the square approximation, and the multiscale ordering behavior from atomistic to microstructural evolution process of ordered domains in the two dimensional square lattice is investigated. The transition temperature is determined at 1:1 stoichiometric composition and it is confirmed that the transition is of the second order. The growth process of the ordered domains is visualized and it is revealed that the sharp decrease of the free energy takes place during the process.

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.

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.

scholarly journals Free Energy Problem for the Simulations of the Growth of Fe2B Phase Using Phase-Field Method

2008 ◽  
Vol 49 (11) ◽  
pp. 2625-2631 ◽  
Author(s):  
Raden Dadan Ramdan ◽  
Tomohiro Takaki ◽  
Yoshihiro Tomita
Keyword(s):  
Free Energy ◽  
Phase Field ◽  
Field Method ◽  
Phase Field Method ◽  
Energy Problem

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.

Growth Dynamics of Single Void during Czochralski Silicon Crystal Growth Using Phase-Field Modeling

2014 ◽  
Vol 576 ◽  
pp. 3-7
Author(s):  
Jin Wang ◽  
Xiao Jun Guan ◽  
Xiang Yu Zhang ◽  
Qing Kai Zeng
Keyword(s):  
Free Energy ◽  
Phase Field ◽  
Vacancy Concentration ◽  
Silicon Crystal ◽  
Growth Dynamics ◽  
Field Method ◽  
Phase Field Method ◽  
Czochralski Silicon ◽  
The Matrix ◽  
Basic Features

To investigate the growth dynamics of the single void during Czochralski silicon growth as well as capture the basic features of the diffusion-controlled dynamic mechanisms, a phase field method has been developed. The free energy of the system involving the chemical free energy and the gradient energy is presented. Numerical tests were performed to examine the capability of this model, and the results show that: the void grows due to the absorption of vacancies in the matrix, which essentially reduces the free energy of the system; with the growth of the void, there forms vacancy concentration gradient towards the void in the matrix; the increase of initial vacancy concentration contributes to a larger void size and growth rate.

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