skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Order parameters for symmetry-breaking structural transitions: The tetragonal-monoclinic transition in ZrO 2

Abstract

Group/subgroup structural phase transitions are exploited in a wide variety of technologies, including those that rely on shape-memory behavior and on transformation toughening. Here, we introduce an approach to identify symmetry-adapted strain and shuffle order parameters for any group/subgroup structural transition between a high-symmetry parent phase and its symmetrically equivalent low-symmetry product phases. We show that symmetry-adapted atomic shuffle order parameters can be determined by the diagonalization of an orbital covariance matrix, formed by taking the covariance among the atomic displacement vectors of all symmetrically equivalent product phase variants. We use this approach to analyze the technologically important tetragonal to monoclinic structural phase transformation of ZrO 2 . We explore the energy landscapes, as calculated with density functional theory, along distinct paths that connect m ZrO 2 to t ZrO 2 and to other m ZrO 2 variants. The calculations indicate favorable pairs of variants and reveal intermediate structures likely to exist at coherent twin boundaries and having relatively low deformation energy. We identify crystallographic features of the monoclinic ZrO 2 variant that make it very sensitive to shape changing strains.

Authors:
 [1];  [1]
  1. Univ. of California, Santa Barbara, CA (United States). Dept. of Materials
Publication Date:
Research Org.:
Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States). National Energy Research Scientific Computing Center (NERSC)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1544358
Alternate Identifier(s):
OSTI ID: 1405204
Grant/Contract Number:  
[AC05-00OR22725; AC02-05CH11231]
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review B
Additional Journal Information:
[ Journal Volume: 96; Journal Issue: 13]; Journal ID: ISSN 2469-9950
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY

Citation Formats

Thomas, John C., and Van der Ven, Anton. Order parameters for symmetry-breaking structural transitions: The tetragonal-monoclinic transition in ZrO2. United States: N. p., 2017. Web. doi:10.1103/PhysRevB.96.134121.
Thomas, John C., & Van der Ven, Anton. Order parameters for symmetry-breaking structural transitions: The tetragonal-monoclinic transition in ZrO2. United States. doi:10.1103/PhysRevB.96.134121.
Thomas, John C., and Van der Ven, Anton. Fri . "Order parameters for symmetry-breaking structural transitions: The tetragonal-monoclinic transition in ZrO2". United States. doi:10.1103/PhysRevB.96.134121. https://www.osti.gov/servlets/purl/1544358.
@article{osti_1544358,
title = {Order parameters for symmetry-breaking structural transitions: The tetragonal-monoclinic transition in ZrO2},
author = {Thomas, John C. and Van der Ven, Anton},
abstractNote = {Group/subgroup structural phase transitions are exploited in a wide variety of technologies, including those that rely on shape-memory behavior and on transformation toughening. Here, we introduce an approach to identify symmetry-adapted strain and shuffle order parameters for any group/subgroup structural transition between a high-symmetry parent phase and its symmetrically equivalent low-symmetry product phases. We show that symmetry-adapted atomic shuffle order parameters can be determined by the diagonalization of an orbital covariance matrix, formed by taking the covariance among the atomic displacement vectors of all symmetrically equivalent product phase variants. We use this approach to analyze the technologically important tetragonal to monoclinic structural phase transformation of ZrO2. We explore the energy landscapes, as calculated with density functional theory, along distinct paths that connect mZrO2 to tZrO2 and to other mZrO2 variants. The calculations indicate favorable pairs of variants and reveal intermediate structures likely to exist at coherent twin boundaries and having relatively low deformation energy. We identify crystallographic features of the monoclinic ZrO2 variant that make it very sensitive to shape changing strains.},
doi = {10.1103/PhysRevB.96.134121},
journal = {Physical Review B},
number = [13],
volume = [96],
place = {United States},
year = {2017},
month = {10}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 1 work
Citation information provided by
Web of Science

Figures / Tables:

FIG. 1 FIG. 1: Ball-and-stick illustrations of the 12-atom conventional cell of (a) cZrO2 and (b) tZrO2. Polyhedral models of the conventional cell of (c) tZrO2 and (d) mZrO2, viewed along the c axis. (e) Polyhedral models of the 8 equivalent variants of the mZrO2 structure depicted in (c), depicted as amore » 2 x 2 x 2 supercell of the conventional cell. Polyhedra are centered at tetrahedral O sites.« less

Save / Share:

Works referenced in this record:

REVIEW-Transformation Toughening in Ceramics: Martensitic Transformations in Crack-Tip Stress Fields
journal, May 1980


The O−Zr (Oxygen-Zirconium) system
journal, April 1986

  • Abriata, J. P.; Garcés, J.; Versaci, R.
  • Bulletin of Alloy Phase Diagrams, Vol. 7, Issue 2
  • DOI: 10.1007/BF02881546

Generalized Gradient Approximation Made Simple
journal, October 1996

  • Perdew, John P.; Burke, Kieron; Ernzerhof, Matthias
  • Physical Review Letters, Vol. 77, Issue 18, p. 3865-3868
  • DOI: 10.1103/PhysRevLett.77.3865

Projector augmented-wave method
journal, December 1994


Phase-Field Models for Microstructure Evolution
journal, August 2002


The martensitic transformation in ceramics — its role in transformation toughening
journal, January 2002


Thermal diffusivity and conductivity of Zr 1−x Y x O 2−x/2 ( x =0, 0.084 and 0.179) single crystals
journal, September 2004


Microstructural evolution of ZrO 2 –HfO 2 nanolaminate structures grown by atomic layer deposition
journal, February 2004

  • Kim, Hyoungsub; McIntyre, Paul C.; Saraswat, Krishna C.
  • Journal of Materials Research, Vol. 19, Issue 2
  • DOI: 10.1557/jmr.2004.19.2.643

Systematic approach for determination of equilibrium atomic surface structure
journal, October 2010

  • Thomas, John C.; Modine, Normand A.; Millunchick, Joanna Mirecki
  • Physical Review B, Vol. 82, Issue 16
  • DOI: 10.1103/PhysRevB.82.165434

On a martensitic phase transformation in zirconia (ZrO2)—II. Crystallographic aspects
journal, April 1974


Modeling transformation paths of multiphase materials: The triple point of zirconia
journal, March 2009


Twin Boundaries in Monoclinic ZrO 2 Particles Confined in a Mullite Matrix
journal, February 1983


From ultrasoft pseudopotentials to the projector augmented-wave method
journal, January 1999


Twin Boundaries in Ferroelastic Media without Interface Dislocations
journal, September 1984


The crystal structure of baddeleyite (monoclinic ZrO 2 ) and its relation to the polymorphism of ZrO 2
journal, June 1965


Beyond Space Groups: the Arithmetic Symmetry of Deformable Multilattices
journal, July 1998

  • Pitteri, M.; Zanzotto, G.
  • Acta Crystallographica Section A Foundations of Crystallography, Vol. 54, Issue 4
  • DOI: 10.1107/S010876739701667X

Mechanochemical spinodal decomposition: a phenomenological theory of phase transformations in multi-component, crystalline solids
journal, June 2016


Some phase transitions in crystals
journal, January 1980

  • Ericksen, J. L.
  • Archive for Rational Mechanics and Analysis, Vol. 73, Issue 2
  • DOI: 10.1007/BF00258233

Possibility of Spinodal Decomposition in ZrO2-Y2O3 Alloys: A Theoretical Investigation
journal, June 1995


Nonhydrostatic stabilization of an orthorhombic phase of zirconia
journal, October 2003


High-temperature stability of δ′-ZrO
journal, December 2015


Graphite to Diamond: Origin for Kinetics Selectivity
journal, February 2017

  • Xie, Yao-Ping; Zhang, Xiao-Jie; Liu, Zhi-Pan
  • Journal of the American Chemical Society, Vol. 139, Issue 7
  • DOI: 10.1021/jacs.6b11193

A climbing image nudged elastic band method for finding saddle points and minimum energy paths
journal, December 2000

  • Henkelman, Graeme; Uberuaga, Blas P.; Jónsson, Hannes
  • The Journal of Chemical Physics, Vol. 113, Issue 22, p. 9901-9904
  • DOI: 10.1063/1.1329672

Effects of strain on the stability of tetragonal ZrO 2
journal, August 2016


High temperature aging of YSZ coatings and subsequent transformation at low temperature
journal, November 2005


Elastic properties and stress-temperature phase diagrams of high-temperature phases with low-temperature lattice instabilities
journal, December 2014


Reconciliation of local and global symmetries of crystals
journal, June 1984


Energy Landscape of Zirconia Phase Transitions
journal, June 2015

  • Guan, Shu-Hui; Zhang, Xiao-Jie; Liu, Zhi-Pan
  • Journal of the American Chemical Society, Vol. 137, Issue 25
  • DOI: 10.1021/jacs.5b04528

A phase field model for the formation and evolution of martensitic laminate microstructure at finite strains
journal, December 2012


Thermodynamics of the Zr-O system from first-principles calculations
journal, September 2013


Shape Evolution of a Coherent Tetragonal Precipitate in Partially Stabilized Cubic ZrO2: A Computer Simulation
journal, December 1993


A microscopic theory for antiphase boundary motion and its application to antiphase domain coarsening
journal, June 1979


Stress-Induced Transformation of Tetragonal ZrO2 Particles in Ceramic Matrices
journal, January 1978


Three-dimensional field model and computer modeling of martensitic transformations
journal, February 1997


Crystal symmetry and the reversibility of martensitic transformations
journal, March 2004

  • Bhattacharya, Kaushik; Conti, Sergio; Zanzotto, Giovanni
  • Nature, Vol. 428, Issue 6978
  • DOI: 10.1038/nature02378

Electrical Resistivity of Stabilized Zirconia at Elevated Temperatures
journal, January 1963

  • Dixon, J. M.; LaGrange, L. D.; Merten, U.
  • Journal of The Electrochemical Society, Vol. 110, Issue 4
  • DOI: 10.1149/1.2425731

Low-temperature transformation kinetics of electron-beam deposited 5wt.% yttria-stabilized zirconia
journal, April 2007


The Tetragonal-Monoclinic Transformation in Zirconia: Lessons Learned and Future Trends
journal, September 2009


First Principles Phase Diagram Calculations for the Octahedral-Interstitial System ZrO X , 0 ≤ X ≤1/2
journal, January 2012

  • Paul Burton, Benjamin; van de Walle, Axel; T. Stokes, Harold
  • Journal of the Physical Society of Japan, Vol. 81, Issue 1
  • DOI: 10.1143/JPSJ.81.014004

Materials Design for the Next Generation Thermal Barrier Coatings
journal, August 2003


First-principles theory of ferroelectric phase transitions for perovskites: The case of BaTiO 3
journal, September 1995


Ceramic steel?
journal, December 1975

  • Garvie, R. C.; Hannink, R. H.; Pascoe, R. T.
  • Nature, Vol. 258, Issue 5537
  • DOI: 10.1038/258703a0

On Landau theory and symmetric energy landscapes for phase transitions
journal, July 2007


Special points for Brillouin-zone integrations
journal, June 1976

  • Monkhorst, Hendrik J.; Pack, James D.
  • Physical Review B, Vol. 13, Issue 12, p. 5188-5192
  • DOI: 10.1103/PhysRevB.13.5188

Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set
journal, October 1996


Phase field methods: Microstructures, mechanical properties and complexity
journal, April 2010


State of the art of zirconia for dental applications
journal, March 2008


The continuum field approach to modeling microstructural evolution
journal, December 1996


Thermodynamic modeling of the ZrO system
journal, March 2002


Deposition and characterization of ZrO 2 thin films on silicon substrate by MOCVD
journal, June 1993

  • Hwang, Cheol Seong; Kim, Hyeong Joon
  • Journal of Materials Research, Vol. 8, Issue 6
  • DOI: 10.1557/JMR.1993.1361

Unified Landau description of the tetragonal, orthorhombic, and monoclinic phases of zirconia
journal, November 2002


Group theory description of transformation pathway degeneracy in structural phase transformations
journal, May 2016


Improved tangent estimate in the nudged elastic band method for finding minimum energy paths and saddle points
journal, December 2000

  • Henkelman, Graeme; Jónsson, Hannes
  • The Journal of Chemical Physics, Vol. 113, Issue 22
  • DOI: 10.1063/1.1323224

Finite-temperature properties of strongly anharmonic and mechanically unstable crystal phases from first principles
journal, December 2013


The phenomenological theory of martensite crystallography: Interrelationships
journal, September 1994

  • Wayman, C. M.
  • Metallurgical and Materials Transactions A, Vol. 25, Issue 9
  • DOI: 10.1007/BF02649029

Electrolytes for solid oxide fuel cells
journal, November 2006


Computer Simulation of Twin Formation during the Displacive c t' Phase Transformation in the Zirconia-Yttria System
journal, March 1995


Local epitaxial growth of ZrO2 on Ge (100) substrates by atomic layer epitaxy
journal, September 2003

  • Kim, Hyoungsub; Chui, Chi On; Saraswat, Krishna C.
  • Applied Physics Letters, Vol. 83, Issue 13
  • DOI: 10.1063/1.1613031

Microstructural Development of Coherent Tetragonal Precipitates in Magnesium-Partially-Stabilized Zirconia: A Computer Simulation
journal, March 1995


The exploration of nonlinear elasticity and its efficient parameterization for crystalline materials
journal, October 2017


Atomic Layer Deposition of ZrO2 Thin Films with High Dielectric Constant on TiN Substrates
journal, January 2008

  • Kim, Seong Keun; Hwang, Cheol Seong
  • Electrochemical and Solid-State Letters, Vol. 11, Issue 3
  • DOI: 10.1149/1.2825763

A generalized solid-state nudged elastic band method
journal, February 2012

  • Sheppard, Daniel; Xiao, Penghao; Chemelewski, William
  • The Journal of Chemical Physics, Vol. 136, Issue 7
  • DOI: 10.1063/1.3684549

Considerations for surface reconstruction stability prediction on GaAs(001)
journal, February 2013

  • Thomas, John C.; Van der Ven, Anton; Millunchick, Joanna Mirecki
  • Physical Review B, Vol. 87, Issue 7
  • DOI: 10.1103/PhysRevB.87.075320

The influence of oxides on the performance of advanced gas turbines
journal, January 2008


Local minimizers and planar interfaces in a phase-transition model with interfacial energy
journal, July 2010

  • Ball, J. M.; Crooks, E. C. M.
  • Calculus of Variations and Partial Differential Equations, Vol. 40, Issue 3-4
  • DOI: 10.1007/s00526-010-0349-8