Theoretical investigation of phase equilibria by the continuous displacement cluster variation method

2009 ◽  
Vol 100 (3) ◽  
pp. 301-307 ◽  
Author(s):  
Tetsuo Mohri
Keyword(s):  
Phase Equilibria ◽  
Theoretical Investigation ◽  
Cluster Variation Method ◽  
Variation Method ◽  
Cluster Variation ◽  
Continuous Displacement

Theoretical Investigation of Alloy Phase Equilibria by Continuous Displacement Cluster Variation Method

2011 ◽  
Vol 172-174 ◽  
pp. 1119-1127
Author(s):  
Tetsuo Mohri
Keyword(s):  
Phase Equilibria ◽  
Lattice Point ◽  
Cluster Variation Method ◽  
Lattice Points ◽  
Variation Method ◽  
Bravais Lattice ◽  
Diffuse Intensity ◽  
Wide Range ◽  
Cluster Variation ◽  
Continuous Displacement

Continuous Displacement Cluster Variation Method is employed to study binary phase equilibria on the two dimensional square lattice with Lennard-Jones type pair potentials. It is confirmed that the transition temperature decreases significantly as compared with the one obtained by conventional Cluster Variation Method. This is ascribed to the distribution of atomic pairs in a wide range of atomic distance, which enables the system to attain the lower free energy. The spatial distribution of atomic species around a Bravais lattice point is visualized. Although the average position of an atom is centred at the Bravais lattice point, the maximum pair probability is not necessarily attained for the pairs located at the neighboring Bravais lattice points. In addition to the real space information, k-space information are calculated in the present study. Among them, the diffuse intensity spectra due to short range ordering and atomic displacement are discussed.

Application of Continuous Displacement Cluster Variation Method to Study Phase Equilibria

2010 ◽  
Vol 654-656 ◽  
pp. 1496-1499
Author(s):  
Tetsuo Mohri
Keyword(s):  
Transition Temperature ◽  
Phase Equilibria ◽  
Lattice Distortion ◽  
Cluster Variation Method ◽  
Variation Method ◽  
Study Phase ◽  
Local Lattice Distortion ◽  
Local Lattice ◽  
Cluster Variation ◽  
Continuous Displacement

Cluster Variation Method (CVM) has been widely recognized as one of the most reliable theoretical tools to study phase equilibria in metallic alloy systems. The conventional CVM, however, does not allow atomic local displacements and, therefore, calculated results often encounter various inconveniences such as the overestimation of transition temperatures. Continuous Displacement Cluster Variation Method (CDCVM) was proposed to circumvent such deficiencies of the conventional CVM. Preliminary studies on an order-disorder phase diagram based on CDCVM indicate that the transition temperature is shifted downward reproducing experimental tendencies. In the present study, lattice thermal vibration effects are also incorporated through Morse potential. It is concluded that the local lattice distortion effects are quite effective to reduce the transition temperature.

Continuous Displacement of “Lattice” Atoms

1992 ◽  
Vol 278 ◽  
Author(s):  
Ryoichi Kikuchi ◽  
Arezki Beldjenna
Keyword(s):  
Interatomic Potential ◽  
Rotational Symmetry ◽  
Cluster Variation Method ◽  
Lattice Points ◽  
Pair Approximation ◽  
Variation Method ◽  
Pair Probability ◽  
Integral Equation Formulation ◽  
Cluster Variation ◽  
Continuous Displacement

AbstractIn the existing CVM (Cluster Variation Method) formulations, atoms are placed on lattice points. A modification is proposed in which an atom can be displaced from a lattice point. The displaced position is written by a vector r, which varies continuously. This model is treated in the CVM framework by regarding an atom at r as a species r. The probability of finding an atom displaced at r in dr is written as f(r)dr, and the corresponding pair probability is written as g(r1, r2)dr1dr2. We formulate using the pair approximation of the CVM in the present paper. The interatomic potential is assumed given, for example as the Lennard-Jones form. The entropy is written in terms of f(r) and g(r1, r2) using the CVM formula. The special feature of the present formulation which is different from the prevailing no-displacement cases of the CVM is that rotational symmetry of the lattice is to be satisfied by the f(r) and g(r1, r2) functions. After the general equations are written in the continuum vector form and in the integral equation formulation, an example of a single-component system is solved by changing integrals into summations over finite intervals. Further we construct simulations of displacement patters in such a way that the pattern satisfies the pair probability distribution which has been calculated as the output of the CVM analysis. The simulated pattern shows the wavy behavior of phonons. Future directions are discussed.

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