Order parameters for symmetry-breaking structural transitions: The tetragonal-monoclinic transition in
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 . We explore the energy landscapes, as calculated with density functional theory, along distinct paths that connect to and to other 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 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 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. https://doi.org/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. https://doi.org/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 = {Fri Oct 27 00:00:00 EDT 2017},
month = {Fri Oct 27 00:00:00 EDT 2017}
}
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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 »
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