A general method of solution for the cluster variation method in ionic solids, with application to diffusionless transitions in yttria-stabilized zirconia

D. S. Mebane, J. H. Wang

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

A new, general method of solution for the cluster variation method using a reduced conjugate gradient approach with a truncated line-search algorithm is presented. The method is generally convergent. Additionally, the truncation of the line-search algorithm may increase the speed of convergence considerably, as the size of the problem is progressively reduced (especially for strongly ordered phases), opening up the possibility of a considerable increase in the size of maximal clusters. The method is successfully demonstrated for a single, eight-atom maximal cluster in the fluorite lattice. Using pairwise defect interaction energies calculated for cubic, yttria-doped zirconia and fixed defect concentrations, a pair of metastable states are found in a composition and temperature range which is experimentally characterized by metastable, diffusionless phase transitions.

Original languageEnglish
Pages (from-to)727-742
Number of pages16
JournalJournal of Statistical Physics
Volume139
Issue number4
DOIs
Publication statusPublished - 2010 May 1

Fingerprint

Cluster Variation Method
cluster variation method
yttria-stabilized zirconia
Line Search
Search Algorithm
defects
fluorite
Defects
zirconium oxides
metastable state
Metastable States
Conjugate Gradient
Speed of Convergence
Truncation
gradients
Pairwise
Phase Transition
approximation
atoms
interactions

Keywords

  • Cluster variation method
  • Diffusionless phase transition
  • Reduced gradient method
  • Yttria-stabilized zirconia

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

@article{3387efaca5e342a889901320ecb0cee5,
title = "A general method of solution for the cluster variation method in ionic solids, with application to diffusionless transitions in yttria-stabilized zirconia",
abstract = "A new, general method of solution for the cluster variation method using a reduced conjugate gradient approach with a truncated line-search algorithm is presented. The method is generally convergent. Additionally, the truncation of the line-search algorithm may increase the speed of convergence considerably, as the size of the problem is progressively reduced (especially for strongly ordered phases), opening up the possibility of a considerable increase in the size of maximal clusters. The method is successfully demonstrated for a single, eight-atom maximal cluster in the fluorite lattice. Using pairwise defect interaction energies calculated for cubic, yttria-doped zirconia and fixed defect concentrations, a pair of metastable states are found in a composition and temperature range which is experimentally characterized by metastable, diffusionless phase transitions.",
keywords = "Cluster variation method, Diffusionless phase transition, Reduced gradient method, Yttria-stabilized zirconia",
author = "Mebane, {D. S.} and Wang, {J. H.}",
year = "2010",
month = "5",
day = "1",
doi = "10.1007/s10955-010-9963-2",
language = "English",
volume = "139",
pages = "727--742",
journal = "Journal of Statistical Physics",
issn = "0022-4715",
publisher = "Springer New York",
number = "4",

}

TY - JOUR

T1 - A general method of solution for the cluster variation method in ionic solids, with application to diffusionless transitions in yttria-stabilized zirconia

AU - Mebane, D. S.

AU - Wang, J. H.

PY - 2010/5/1

Y1 - 2010/5/1

N2 - A new, general method of solution for the cluster variation method using a reduced conjugate gradient approach with a truncated line-search algorithm is presented. The method is generally convergent. Additionally, the truncation of the line-search algorithm may increase the speed of convergence considerably, as the size of the problem is progressively reduced (especially for strongly ordered phases), opening up the possibility of a considerable increase in the size of maximal clusters. The method is successfully demonstrated for a single, eight-atom maximal cluster in the fluorite lattice. Using pairwise defect interaction energies calculated for cubic, yttria-doped zirconia and fixed defect concentrations, a pair of metastable states are found in a composition and temperature range which is experimentally characterized by metastable, diffusionless phase transitions.

AB - A new, general method of solution for the cluster variation method using a reduced conjugate gradient approach with a truncated line-search algorithm is presented. The method is generally convergent. Additionally, the truncation of the line-search algorithm may increase the speed of convergence considerably, as the size of the problem is progressively reduced (especially for strongly ordered phases), opening up the possibility of a considerable increase in the size of maximal clusters. The method is successfully demonstrated for a single, eight-atom maximal cluster in the fluorite lattice. Using pairwise defect interaction energies calculated for cubic, yttria-doped zirconia and fixed defect concentrations, a pair of metastable states are found in a composition and temperature range which is experimentally characterized by metastable, diffusionless phase transitions.

KW - Cluster variation method

KW - Diffusionless phase transition

KW - Reduced gradient method

KW - Yttria-stabilized zirconia

UR - http://www.scopus.com/inward/record.url?scp=77951769103&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77951769103&partnerID=8YFLogxK

U2 - 10.1007/s10955-010-9963-2

DO - 10.1007/s10955-010-9963-2

M3 - Article

AN - SCOPUS:77951769103

VL - 139

SP - 727

EP - 742

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

SN - 0022-4715

IS - 4

ER -