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

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.

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Theoretical Investigation of Coarsening Process of L10-Ordered Domain Based on Phase Field Method and Cluster Variation Method

MATERIALS TRANSACTIONS ◽

10.2320/matertrans.43.2189 ◽

2002 ◽

Vol 43 (9) ◽

pp. 2189-2192 ◽

Cited By ~ 6

Author(s):

Munekazu Ohno ◽

Tetsuo Mohri

Keyword(s):

Theoretical Investigation ◽

Phase Field ◽

Cluster Variation Method ◽

Field Method ◽

Phase Field Method ◽

Variation Method ◽

Cluster Variation

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Phase Field Calculations with CVM Free Energy within Square Approximation

Materials Science Forum ◽

10.4028/www.scientific.net/msf.561-565.1935 ◽

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.

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Multicritical phase diagrams of the ferromagnetic spin- Blume–Emery–Griffiths model with repulsive biquadratic coupling including metastable phases: The cluster variation method and the path probability method with the point distribution

Journal of Magnetism and Magnetic Materials ◽

10.1016/j.jmmm.2007.05.005 ◽

2008 ◽

Vol 320 (1-2) ◽

pp. 8-24 ◽

Cited By ~ 15

Author(s):

Mustafa Keskin ◽

Osman Canko

Keyword(s):

Phase Diagrams ◽

Cluster Variation Method ◽

Metastable Phases ◽

Variation Method ◽

Probability Method ◽

Point Distribution ◽

Cluster Variation ◽

Path Probability Method

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

MRS Proceedings ◽

10.1557/proc-753-bb5.44 ◽

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.

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Towards the First-Principles Investigation of Ordering Dynamics

Materials Science Forum ◽

10.4028/www.scientific.net/msf.475-479.3075 ◽

2005 ◽

Vol 475-479 ◽

pp. 3075-3080 ◽

Cited By ~ 5

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.

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