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.

Multi-Scale Phase Field Simulation of Disorder-Order Transition, Combined with Cluster Variation and Path Probability Methods

2009 ◽  
Vol 631-632 ◽  
pp. 401-406
Author(s):  
Munekazu Ohno ◽  
Ying Chen ◽  
Tetsuo Mohri
Keyword(s):  
Phase Field ◽  
Cluster Variation Method ◽  
Field Method ◽  
Phase Field Method ◽  
Variation Method ◽  
Probability Method ◽  
Multi Scale ◽  
Probability Methods ◽  
Cluster Variation ◽  
Path Probability Method

Multi-scale simulation of ordering process from electronic, atomistic scales to microstructural scale was carried out by hybridizing Phase Field Method (PFM) and Cluster Variation Method (CVM). The hybrid model was applied to disorder-L10 ordering process in Fe-Pd system. Furthermore, computation of relaxation constants in the PFM was attempted based on Path Probability Method (PPM) which is the time evolution version of the CVM, within a linearized analysis of order-order relaxation process.

Kinetic Calculation of L10 Ordered System Based on Phase Field Methodand Cluster Variation Method

2002 ◽  
Vol 753 ◽  
Author(s):  
M. Ohno ◽  
T. Mohri
Keyword(s):  
Phase Field ◽  
Relaxation Curve ◽  
Homogeneous System ◽  
Cluster Variation Method ◽  
Phase Field Method ◽  
Variation Method ◽  
Inhomogeneous System ◽  
Atomic Configuration ◽  
Free Energy Surface ◽  
Cluster Variation

ABSTRACTDuring ordering process, anti-site ordering proceeds in atomistic scale and anti-phase domain structure evolves in microstructural scale. In order to describe both the processes, a hybridized calculation of the Phase Field Method(PFM) and Cluster Variation Method(CVM) is attempted. The main objective of the present study is focused on the time evolution of atomic configuration during L10 ordering processes below and above the spinodal ordering temperature and their resultant microstructures. In order to investigate the interplay between atomistic and microstructural processes, we conducted two types of calculations. One is for a homogeneous system without an anti-phase boundary and the other is for an inhomogeneous system in which microstructure is formed by anti-phase domains.For the homogeneous system, the relaxation curve of Long-Range-Order parameter(LRO) indicates a transient appearance of an L12-like atomic configuration below the spinodal ordering temperature. Such an L12–like state corresponds to a saddle point configuration in the CVM free energy surface. When the composition of an alloy is located near L10 + L12 phase field in the phase diagram, the L12–like phase becomes highly ordered state.For the inhomogeneous system, it is implied that the appearance of the L12-like phase affects the resultant microstructure by providing the nucleation sites for the L10 ordered phase.

scholarly journals Towards the First-Principles Investigation of Ordering Dynamics

2005 ◽  
Vol 475-479 ◽  
pp. 3075-3080 ◽  
Author(s):  
Tetsuo Mohri ◽  
Munekazu Ohno ◽  
Ying Chen
Keyword(s):  
First Principles ◽  
Coarse Graining ◽  
Cluster Variation Method ◽  
Field Method ◽  
Energy Functional ◽  
First Principles Calculation ◽  
Phase Field Method ◽  
Variation Method ◽  
Gradient Energy ◽  
Cluster Variation

Phase Field Method (PFM) is hybridized with Cluster Variation Method (CVM) to investigate the ordering dynamics of L10-disorder transition at atomistic and microstructural scales simultaneously. For this, coarse graining operation is attempted on the inhomogeneous free energy functional of CVM. The resultant gradient energy coefficient is found out to be dependent on temperature and order parameters, which is in marked contrast to a conventional PFM formalism. Electronic structure total energy calculations for Fe-Pd system are incorporated to the hybridized scheme and the first principles calculation of microstructural evolution process is attempted.

CVM-based first-principles calculations for Fe-based alloys

2011 ◽  
Vol 1296 ◽  
Author(s):  
Tetsuo Mohri
Keyword(s):  
Free Energy ◽  
First Principles ◽  
Cluster Variation Method ◽  
Phase Field Method ◽  
Variation Method ◽  
Probability Method ◽  
First Principles Calculations ◽  
Wide Range ◽  
Cluster Variation ◽  
Alloy Systems

ABSTRACTCluster Variation Method (CVM) has been recognized as one of the most reliable theoretical tools to incorporate wide range of atomic correlations into a free energy formula. By combining CVM with electronic structure total energy calculations, one can perform first-principles calculations of alloy phase equilibria. The author attempted such CVM-based first-principles calculations for various alloy systems including noble metal alloys, transition-noble alloys, III-V semiconductor alloys and Fe-based alloy systems. Furthermore, CVM can be extended to two kinds of kinetics calculations. One is Path Probability Method (PPM) which is the natural extension of the CVM to time domain and is quite powerful to investigate atomistic kinetic phenomena. The other one is Phase Field Method (PFM) with the CVM free energy as a homogeneous free energy density term in the PFM. The author’s group applied the latter procedure to study time evolution process of ordered domains associated with disorder-L10 transition in Fe-Pd and Fe-Pt systems. CVM has, therefore, a potential applicability for the systematic studies covering atomistic to microstructural scales. It has been, however, pointed out that the conventional CVM is not able to include local lattice relaxation effects and that the resulting order-disorder transition temperatures are overestimated. In order to circumvent such inconveniences, Continuous Displacement Cluster Variation Method (CDCVM) has been developed. Since first-principles CDCVM calculations are still beyond the scope at the present stage, preliminary results on the two dimensional square lattice and an fcc lattice with primitive Lennard-Jones type potentials are demonstrated in the last section.

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.

scholarly journals The 2-D Cluster Variation Method: Topography Illustrations and Their Enthalpy Parameter Correlations

Entropy ◽  
2021 ◽  
Vol 23 (3) ◽  
pp. 319
Author(s):  
Alianna J. Maren
Keyword(s):  
Free Energy ◽  
Nearest Neighbor ◽  
Activation Enthalpy ◽  
Cluster Variation Method ◽  
Variation Method ◽  
Energy Minimum ◽  
Dimensional Parameter ◽  
Free Energy Minimum ◽  
Interaction Enthalpy ◽  
Cluster Variation

One of the biggest challenges in characterizing 2-D image topographies is finding a low-dimensional parameter set that can succinctly describe, not so much image patterns themselves, but the nature of these patterns. The 2-D cluster variation method (CVM), introduced by Kikuchi in 1951, can characterize very local image pattern distributions using configuration variables, identifying nearest-neighbor, next-nearest-neighbor, and triplet configurations. Using the 2-D CVM, we can characterize 2-D topographies using just two parameters; the activation enthalpy (ε0) and the interaction enthalpy (ε1). Two different initial topographies (“scale-free-like” and “extreme rich club-like”) were each computationally brought to a CVM free energy minimum, for the case where the activation enthalpy was zero and different values were used for the interaction enthalpy. The results are: (1) the computational configuration variable results differ significantly from the analytically-predicted values well before ε1 approaches the known divergence as ε1→0.881, (2) the range of potentially useful parameter values, favoring clustering of like-with-like units, is limited to the region where ε0<3 and ε1<0.25, and (3) the topographies in the systems that are brought to a free energy minimum show interesting visual features, such as extended “spider legs” connecting previously unconnected “islands,” and as well as evolution of “peninsulas” in what were previously solid masses.

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.

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