Glass Transition within the Cluster Variation Approximation

2007 ◽  
Vol 26-28 ◽  
pp. 723-726
Author(s):  
Tetsuo Mohri
Keyword(s):  
Phase Diagram ◽  
Free Energy ◽  
Glass Transition ◽  
Cluster Variation Method ◽  
Variation Method ◽  
Cluster Variation ◽  
Ordering Transition ◽  
Limiting Case ◽  
The Ideal

The detailed behavior of the free energy of Cluster Variation Method in the vicinity of spinodal ordering transition is examined. The generalized phase diagram proposed in the previous study is modified and spinodal ordering transition is reinterpreted as a limiting case of the ideal glass transition.

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.

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 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.

Thermodynamics of mixing and ordering in the diopside–jadeite system: I. A CVM model

2002 ◽  
Vol 66 (4) ◽  
pp. 513-536 ◽  
Author(s):  
V. L. Vinograd
Keyword(s):  
Free Energy ◽  
Cluster Variation Method ◽  
Solution Calorimetry ◽  
Range Order ◽  
Variation Method ◽  
Energy Of Mixing ◽  
Equilibrium Data ◽  
Thermodynamics Of Mixing ◽  
Cluster Variation ◽  
Free Energy Of Mixing

AbstractSolution calorimetry and phase equilibrium data for the diopside–jadeite system are assessed using a combination of the cluster variation method (CVM) and Redlich-Kister (RK) polynomial expansion. The CVM is used to model part of the free energy of mixing which depends on short-range order (SRO) and long-range order (LRO) effects. The SRO/LRO independent part of the free energy is modelled using an RK polynomial. The parameters of the RK and CVM models are obtained through the fit to the experimental data. The best-fit parameters are used to calculate activity-composition relations and a temperature-composition phase diagram of the diopside–jadeite system.

Phase Diagram of Ni-Pt from Linear Muffin-Tin Orbitals Total Energy Calculations

1991 ◽  
Vol 253 ◽  
Author(s):  
C. Amador ◽  
W. R. L. Lambrecht ◽  
B. Segall
Keyword(s):  
Phase Diagram ◽  
Effective Interaction ◽  
Cluster Variation Method ◽  
Variation Method ◽  
Ordered Structures ◽  
Atomic Sphere ◽  
Sphere Approximation ◽  
Total Energies ◽  
The Difference ◽  
Cluster Variation

ABSTRACTProgress in the calculation of the phase diagram of the Ni-Pt compounds from "first-principles" is reported. Our procedure consists of: (1) calculating total energies for ordered structures as a function of volume and including internal relaxations by means of the linear muffin-tin orbitals method within the atomic sphere approximation; (2) mapping these results onto an Ising model with effective interaction parameters; and (3) calculating the phase diagram by means of the cluster variation method. We identify the elastic energy related to the difference in the Ni and Pt lattice constant as one of the major problems in this system and discuss the convergence of the cluster expansion of the energy.

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