LMTO/CVM and LAPW/CVM Calculations of the Nial-Niti Pseudobinary Phase Diagram

1990 ◽  
Vol 213 ◽  
Author(s):  
Benjamin P. Burton ◽  
Jean E. Osburn ◽  
Alain Pasturel
Keyword(s):  
Nearest Neighbor ◽  
Equations Of State ◽  
Cluster Variation Method ◽  
Variation Method ◽  
Two Phase ◽  
Pairwise Interactions ◽  
Phase Fields ◽  
Pseudobinary Phase Diagram ◽  
Total Energies ◽  
Cluster Variation

ABSTRACTLinear Muffin Tin Orbital and Linearly Augmented Plane Wave calculations of equations of state were performed for observed and hypothetical ordered structures in the NiAl-NiTi system. Total energies were parameterized in both the Connolly-Williams and ∈-G approximations, and the resulting parameters were used to calculate theoretical phase diagrams by the cluster variation method. Third nearest neighbor Al-Ti pairwise interactions are predicted to be strongly repulsive, and to be a major cause of observed B2+L21 two phase fields.

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.

Phase Transformations in Hexagonal-Close-Packed Alloys: Analysis with the Cluster Variation Method

1992 ◽  
Vol 291 ◽  
Author(s):  
Ryan Mccormack ◽  
Mark Asta ◽  
Gerbrand Ceder ◽  
Didier de Fontaine
Keyword(s):  
Nearest Neighbor ◽  
Binary Alloys ◽  
Cluster Variation Method ◽  
Variation Method ◽  
Temperature Phase ◽  
Hexagonal Close Packed ◽  
Cluster Configuration ◽  
Cluster Variation ◽  
Polyhedron Method ◽  
Pair Interactions

ABSTRACTWe present a study of the hexagonal close-packed (hcp) Ising model for binary alloys within the cluster variation approximation. Groundstates of order stabilized by nearest-neighbor (NN) pair, triplet, and tetrahedron interactions were determined using the cluster configuration polyhedron method; no previous hcp ground-state study has considered all of these interactions. We predict physically realizable groundstates with stoichiometries A, AB (3 distinct structures), A2B, A3B, and A4B3. The previously unpredicted A4B3 structure is stabilized by multiatom (i.e. triplet, tetrahedron) interactions, while the others are stabilized by the two NN pair interactions. The Cluster Variation Method (CVM) was used to calculate the finite-temperature phase-equilibria for prototypical binary alloys. We present the first ordering phase diagrams computed with the CVM which contain all relevant groundstates for both isotropic and anisotropic NN pair interactions.

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.

Vacancy Ordering in the Basal Plane of YB2Cu3Oz

1987 ◽  
Vol 99 ◽  
Author(s):  
L. T. Wille ◽  
A. Berera ◽  
D. De Fontaine ◽  
S. C. Moss
Keyword(s):  
Ground State ◽  
Basal Plane ◽  
Nearest Neighbors ◽  
Cluster Variation Method ◽  
Variation Method ◽  
Two Dimensional ◽  
Pairwise Interactions ◽  
Vacancy Ordering ◽  
Superconducting Compound ◽  
Cluster Variation

ABSTRACTThe ordering in the Cu-O basal plane of the high Tc superconductor YBa2Cu3Oz is investigated. Asymmetric pairwise interactions between nearest and next nearest neighbors are assumed. Ordering instabilities in two-dimensional k-space are mapped out as a function of the interactions and the ordered ground state superstructures consisting of occupied and empty oxygen sites are determined. A temperature-composition phase diagram is calculated by means of the Cluster Variation Method. The thermodynamic behavior of the superconducting compound is discussed in the light of these results.

scholarly journals The 2-D Cluster Variation Method: Initial Findings and Topography Illustrations

2021 ◽  
Author(s):  
Alianna J. Maren
Keyword(s):  
Free Energy ◽  
Energy Minimization ◽  
Nearest Neighbor ◽  
Temporal Correlation ◽  
Cluster Variation Method ◽  
Variation Method ◽  
Dimensional Parameter ◽  
Free Energy Minimization ◽  
Cluster Variation ◽  
Two Parameters

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 and the interaction enthalpy. Initial investigations with two different representative topographies (``scale-free-like'' and ``rich club-like'') produce interesting results when brought to a CVM free energy minimum. Additional phase space investigations, where one of these two parameters has been set to zero, identify useful parameter ranges. Careful comparison of the analytically-predicted configuration variables versus those obtained when performing computational free energy minimization on a 2-D grid show that the computational results differ significantly from the analytic solution. The 2-D CVM can potentially function as a secondary free energy minimization within the hidden layer of a neural network, providing a basis for extending node activations over time and allowing temporal correlation of patterns.

scholarly journals Chain length probability distribution — equivalence of ASYNNNI and 1d Ising model

Open Physics ◽  
2008 ◽  
Vol 6 (2) ◽  
Author(s):  
Mirjana Milić
Keyword(s):  
Ising Model ◽  
Probability Distribution ◽  
Chain Length ◽  
Nearest Neighbor ◽  
Cluster Variation Method ◽  
Variation Method ◽  
Ising Chain ◽  
High Tc ◽  
One Dimensional ◽  
Cluster Variation

AbstractAn expression for the chain length probability distribution p(l) of a one dimensional Ising chain was derived using the cluster variation method formalism, the p(l) being expressed through the pair cluster probabilities. It was shown numerically that the same expression also applies in the case of one dimensional chains formed along one of the next-nearest neighbor interactions included in the two dimensional ASYNNNI (Asymmetric Next-Nearest Neighbor Ising) model, widely used to describe the statistics of oxygen ordering in the basal CuOx planes of the YBa2Cu3O6+x type high-Tc superconducting materials. Equivalency between ASYNNNI and 1d Ising model is discussed.

Sign in / Sign up

Export Citation Format

Share Document