Order parameters for symmetrybreaking structural transitions: The tetragonalmonoclinic transition in ${\mathrm{ZrO}}_{2}$
Abstract
Group/subgroup structural phase transitions are exploited in a wide variety of technologies, including those that rely on shapememory behavior and on transformation toughening. Here, we introduce an approach to identify symmetryadapted strain and shuffle order parameters for any group/subgroup structural transition between a highsymmetry parent phase and its symmetrically equivalent lowsymmetry product phases. We show that symmetryadapted 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 ${\mathrm{ZrO}}_{2}$. We explore the energy landscapes, as calculated with density functional theory, along distinct paths that connect $m{\mathrm{ZrO}}_{2}$ to $t{\mathrm{ZrO}}_{2}$ and to other $m{\mathrm{ZrO}}_{2}$ 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 ${\mathrm{ZrO}}_{2}$ variant that make it very sensitive to shape changing strains.
 Authors:

 Univ. of California, Santa Barbara, CA (United States). Dept. of Materials
 Publication Date:
 Research Org.:
 Lawrence Berkeley National Lab. (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:
 AC0500OR22725; AC0205CH11231
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Physical Review B
 Additional Journal Information:
 Journal Volume: 96; Journal Issue: 13; Journal ID: ISSN 24699950
 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 symmetrybreaking structural transitions: The tetragonalmonoclinic 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 symmetrybreaking structural transitions: The tetragonalmonoclinic transition in ZrO2. United States. https://doi.org/10.1103/PhysRevB.96.134121
Thomas, John C., and Van der Ven, Anton. Fri .
"Order parameters for symmetrybreaking structural transitions: The tetragonalmonoclinic transition in ZrO2". United States. https://doi.org/10.1103/PhysRevB.96.134121. https://www.osti.gov/servlets/purl/1544358.
@article{osti_1544358,
title = {Order parameters for symmetrybreaking structural transitions: The tetragonalmonoclinic 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 shapememory behavior and on transformation toughening. Here, we introduce an approach to identify symmetryadapted strain and shuffle order parameters for any group/subgroup structural transition between a highsymmetry parent phase and its symmetrically equivalent lowsymmetry product phases. We show that symmetryadapted 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}
}
Web of Science
Figures / Tables:
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