Relaxation kinetics of the long-range order parameter in a non-uniform system studied by the phase field method using the free energy obtained by the cluster variation method

2003 ◽  
Vol 83 (3) ◽  
pp. 315-328 ◽  
Author(s):  
Munekazu Ohno ◽  
Tetsuo Mohri
Keyword(s):  
Order Parameter ◽  
Cluster Variation Method ◽  
Field Method ◽  
Phase Field Method ◽  
Variation Method ◽  
Range Order Parameter ◽  
Long Range Order ◽  
Uniform System ◽  
Cluster Variation ◽  
Kinetics Of

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.

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.

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.

Interface Energy Calculation of γ-γ′ in Ni-Al System Using the Cluster Variation Method

2007 ◽  
Vol 546-549 ◽  
pp. 1333-1338 ◽  
Author(s):  
Jin Cheng Wang ◽  
M. Osawa ◽  
Tadaharu Yokokawa ◽  
Hiroshi Harada ◽  
Masato Enomoto
Keyword(s):  
Phase Boundary ◽  
Binary Alloy ◽  
Order Parameter ◽  
Interface Energy ◽  
Cluster Variation Method ◽  
Variation Method ◽  
Energy Calculation ◽  
Average Composition ◽  
Cluster Variation ◽  
Anti Phase Boundary

A calculation of the interface energy for the Ni-Al binary alloy, including the inter-phase boundary (IPB) energy and the anti-phase boundary (APB) energy, has been performed using the Cluster Variation Method (CVM) with the tetrahedron approximation within the temperature range of 600°C~1300°C. The calculated IPB energies range between 8 and 13 mJ/m2, while the APB energies range between 24 and 46 mJ/m2. Additionally, the dependence of the average composition and the order parameter on distance with the compositionally diffuse interfacial regions has been computed. The calculation also shows the width of the diffuse IPB increases with the temperature linearly.

Theoretical Study of Glass Transition Based on Cluster Variation Method

2007 ◽  
Vol 539-543 ◽  
pp. 2425-2430 ◽  
Author(s):  
Tetsuo Mohri ◽  
Yoshitaka Kobayashi
Keyword(s):  
Free Energy ◽  
Glass Transition ◽  
Order Parameter ◽  
Cluster Variation Method ◽  
Variation Method ◽  
Bravais Lattice ◽  
Probability Method ◽  
Temperature Dependent Viscosity ◽  
Viscosity Term ◽  
Cluster Variation

Modeling of Glass transition is attempted based on the Cluster Variation Method. Free energy functional of an L10 ordered phase is employed to describe the first order nature of the transition. Free energy contour surface calculated as a function of temperature and an order parameter which simulates an amount of defects provides a generalized stability diagram in which the ideal glass transition temperature is identified as a critical point. Transition kinetics is investigated by Path Probability Method which is the kinetics version of the CVM to time domain. Continuous cooling behavior is calculated by explicitly incorporating the temperature dependent viscosity term based on VFT (Vogel-Fulcher-Tamman) formula. The glass transition is realized as the freezing of the order parameter due to the enhanced viscosity. The extension of the present theoretical scheme to non-Bravais lattice is attempted by Continuous Cluster Variation Method.

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.

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