SHORT RANGE ORDERING AND LOCAL DISPLACEMENT OF ALLOYS STUDIED BY CVM

2012 ◽  
Vol 01 (02) ◽  
pp. 1250018 ◽  
Author(s):  
TETSUO MOHRI
Keyword(s):  
Short Range ◽  
Lattice Distortion ◽  
Cluster Variation Method ◽  
Real Space ◽  
Variation Method ◽  
Diffuse Intensity ◽  
Local Lattice Distortion ◽  
Wide Range ◽  
Local Lattice ◽  
Cluster Variation

Cluster Variation Method (CVM) is a powerful statistical mechanics means to investigate phase equilibria of an alloy. The advantageous feature of the CVM stems from the fact that wide range of atomic correlations which play an important role at the phase transition is efficiently incorporated into the free energy formula. Hence, configurational fluctuation can be systematically studied through the calculations of correlation functions in the real space and short range order diffuse intensity spectrum in the k-space. However, one of the deficiencies of the conventional CVM is the fact that local lattice distortion (local atomic displacement) is not correctly dealt with. In order to improve such shortcomings, Continuous Displacement Cluster Variation Method (CDCVM) has been developed. In the CDCVM, local lattice distortion is mapped onto the configurational freedom of a multi-component alloy on a rigid (uniformly deformable) lattice. With CDCVM, the applicability of CVM is enlarged and the calculations of diffuse intensity spectrum originating from local lattice distortion can be performed.

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.

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.

Local Lattice Distortion and Chemical Short Range Order in High Entropy Alloys

2020 ◽  
Author(s):  
Yuan-Yuan Tan ◽  
Ming-Yao Su ◽  
Zhou-Can Xie ◽  
Zhong-Jun Chen ◽  
Yu Gong ◽  
...  
Keyword(s):  
Short Range ◽  
Short Range Order ◽  
Lattice Distortion ◽  
Range Order ◽  
High Entropy Alloys ◽  
Local Lattice Distortion ◽  
High Entropy ◽  
Local Lattice

scholarly journals Local Lattice Distortion Caused by Short Range Charge Ordering in LiMn2O4

2013 ◽  
Vol 82 (9) ◽  
pp. 094601 ◽  
Author(s):  
Katsuaki Kodama ◽  
Naoki Igawa ◽  
Shin-ichi Shamoto ◽  
Kazutaka Ikeda ◽  
Hidetoshi Oshita ◽  
...  
Keyword(s):  
Short Range ◽  
Lattice Distortion ◽  
Charge Ordering ◽  
Local Lattice Distortion ◽  
Local Lattice

Short-Range Chemical Order and Local Lattice Distortion in a Compositionally Complex Al 8Cr 17Co 17Cu 8Fe 17Ni 33 Alloy

2019 ◽  
Author(s):  
Andrea Fantin ◽  
Giovanni Orazio Lepore ◽  
Anna M. Manzoni ◽  
Sergey Kasatikov ◽  
Tobias Scherb ◽  
...  
Keyword(s):  
Short Range ◽  
Lattice Distortion ◽  
Local Lattice Distortion ◽  
Chemical Order ◽  
Local Lattice

A data-driven approach to approximate the correlation functions in cluster variation method

2021 ◽  
Author(s):  
Abhishek Kumar Thakur ◽  
Rajendra Prasad Gorrey ◽  
Vikas Jindal ◽  
Krishna Muralidharan
Keyword(s):  
Correlation Functions ◽  
Short Range ◽  
Cluster Variation Method ◽  
Data Driven ◽  
Variation Method ◽  
Internal Variables ◽  
Data Driven Approach ◽  
Cluster Variation ◽  
Bcc Phase

Abstract The cluster variation method (CVM) is one of the thermodynamic models used to calculate phase diagrams considering short range order (SRO). This method predicts the SRO values through internal variables referred to as correlation functions (CFs), accurately up to the cluster chosen in modeling the system. Determination of these CFs at each thermodynamic state of the system requires solving a set of nonlinear equations using numerical methods. In this communication, a neural network model is proposed to predict the values of the CFs. This network is trained for the BCC phase under tetrahedron approximation for both ordering and phase separating systems. The results show that the network can predict the values of the CFs accurately and thereby Helmholtz energy and the phase diagram with significantly less computational burden than that of conventional methods used.

Real Space Multiple Scattering Description of Alloy Phase Stability

1991 ◽  
Vol 253 ◽  
Author(s):  
P. E. A. Turchi ◽  
M. Sluiter
Keyword(s):  
Multiple Scattering ◽  
Phase Stability ◽  
Antiphase Boundary ◽  
Cluster Variation Method ◽  
Real Space ◽  
Variation Method ◽  
Study Phase ◽  
Interfacial Energies ◽  
Cluster Variation ◽  
The Stability

ABSTRACTWe present a brief overview of the advanced methodology which has been recently developed to study phase stability properties of substitutional alloys, including order-disorder phenomena and structural transformations. The approach is based on the real space version of the Generalized Perturbation Method, first introduced by Ducastelle and Gautier, within the Korringa-Kohn- Rostoker multiple scattering formulation of the Coherent Potential Approximation. Temperature effects are taken into account with a generalized meanfield approach, namely the Cluster Variation Method. The viability and the predictive power of such a scheme will be illustrated by a few examples, among them: (1) the ground state properties of alloys, in particular the ordering tendencies for a series of equiatomic bcc-based alloys, (2) the computation of alloy phase diagrams with the case of fcc and bcc-based Ni-Al alloys, (3) the calculation of antiphase boundary energies and interfacial energies, and (4) the stability of artificial ordered superlattices.

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