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.

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.

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.

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.

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.

Sign in / Sign up

Export Citation Format

Share Document