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Elastic anomalies accompanying phase transitions in (Ca,Sr)TiO3 perovskites: Part I. Landau theory and a calibration for SrTiO3

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Published/Copyright: April 1, 2015
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American Mineralogist
From the journal American Mineralogist Volume 92 Issue 2-3

Abstract

Landau theory has been used to develop expressions for the elastic anomalies that accompany octahedral tilting transitions in perovskites that are associated with the M and R points of the Brillouin zone. The master equation is a 246 Landau potential with saturation terms that provides phenomenological descriptions of transition sequences from a parent cubic structure through tetragonal or rhombohedral intermediates to orthorhombic or monoclinic product structures. Data from the literature have been used to determine values for all the coefficients required to generate a quantitative description of the Pm3̄ m ↔ I4/mcm transition in SrTiO3, which is taken as a model system. Solutions to the Landau expansion have been adapted to include the general influence of hydrostatic pressure and non-hydrostatic stress on transition temperature and the evolution of the order parameter. Critical examination of elastic constant data from the literature reveals inconsistencies between the results of measurements on tetragonal samples using ultrasonic rather than Brillouin scattering methods. An internally consistent data set has, nevertheless, been assembled. Good qualitative agreement was obtained between the general pattern of calculated and observed variations of all the single crystal elastic constants, and semi-quantitative agreement was obtained for C11, C33, C12, and C13. Some inconsistencies remain in relation to the temperature dependence of the square of the soft mode frequencies in the tetragonal phase, which follow the square of the order parameter rather than its inverse susceptibility, but the 246 potential seems to provide a good description of the structural evolution of SrTiO3 over a wide temperature interval up to the cubic-tetragonal transition point.

Keywords : Phase transitions; Landau theory; perovskite; SrTiO3
Received: 2006-4-27
Accepted: 2006-9-28
Published Online: 2015-4-1
Published in Print: 2007-2-1

© 2015 by Walter de Gruyter Berlin/Boston

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  8. Elastic anomalies accompanying phase transitions in (Ca,Sr)TiO3 perovskites: Part I. Landau theory and a calibration for SrTiO3
  9. Elastic anomalies accompanying phase transitions in (Ca,Sr)TiO3 perovskites: Part II. Calibration for the effects of composition and pressur
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  12. Effect of variable carbonate concentration on the solidus of mantle peridotite
  13. Time-resolved structural analysis of K- and Ba-exchange reactions with synthetic Na-birnessite using synchrotron X-ray diffraction
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  15. Organic anions in layered double hydroxides: An experimental investigation of citrate hydrotalcite
  16. The 6H-SiC structure model: Further refinement from SCXRD data from a terrestrial moissanite
  17. Cobalt incorporation in mullite
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  19. Armbrusterite, K5Na6Mn3+Mn2+14[Si9O22]4(OH)10·4H2O, a new Mn hydrous heterophyllosilicate from the Khibiny alkaline massif, Kola Peninsula, Russia
  20. Letter. An empirical scaling model for averaging elastic properties including interfacial effects
  21. Letter. Optical absorption spectra of ferropericlase to 84 GPa
  22. Letter. The acoustic emissions signature of a pressure-induced polytypic transformation in chlorite
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https://doi.org/10.2138/am.2007.2295
Keywords for this article
Phase transitions; Landau theory; perovskite; SrTiO3

Articles in the same Issue

  1. Combined cathodoluminescence hyperspectral imaging and wavelength dispersive X-ray analysis of minerals
  2. Identification of cathodoluminescence activators in zoned alkali feldspars by hyperspectral imaging and electron-probe microanalysis
  3. Ionoluminescence of leucophanite
  4. Digital near-infrared (NIR) cathodoluminescence (CL) imaging and image processing
  5. Significance of aluminum phosphate-sulfate minerals associated with U unconformity-type deposits: The Athabasca basin, Canada
  6. Hardness, toughness, and modulus of some common metamorphic minerals
  7. Diffusion compensation for argon, hydrogen, lead, and strontium in minerals: Empirical relationships to crystal chemistry
  8. Elastic anomalies accompanying phase transitions in (Ca,Sr)TiO3 perovskites: Part I. Landau theory and a calibration for SrTiO3
  9. Elastic anomalies accompanying phase transitions in (Ca,Sr)TiO3 perovskites: Part II. Calibration for the effects of composition and pressur
  10. Elastic anomalies accompanying phase transitions in (Ca,Sr)TiO3 perovskites: Part III. Experimental investigation of polycrystalline samples
  11. Patterns in the compositions of oxysalt and sulfosalt minerals, and the paradoxical nature of quartz
  12. Effect of variable carbonate concentration on the solidus of mantle peridotite
  13. Time-resolved structural analysis of K- and Ba-exchange reactions with synthetic Na-birnessite using synchrotron X-ray diffraction
  14. Heat capacity of synthetic hydrous Mg-cordierite at low temperatures: Thermodynamic properties and the behavior of the H2O molecule in selected hydrous micro and nanoporous silicates
  15. Organic anions in layered double hydroxides: An experimental investigation of citrate hydrotalcite
  16. The 6H-SiC structure model: Further refinement from SCXRD data from a terrestrial moissanite
  17. Cobalt incorporation in mullite
  18. Thermal expansion between 480 and 940 °C of Cr-doped mullites derived from single-phase precursors
  19. Armbrusterite, K5Na6Mn3+Mn2+14[Si9O22]4(OH)10·4H2O, a new Mn hydrous heterophyllosilicate from the Khibiny alkaline massif, Kola Peninsula, Russia
  20. Letter. An empirical scaling model for averaging elastic properties including interfacial effects
  21. Letter. Optical absorption spectra of ferropericlase to 84 GPa
  22. Letter. The acoustic emissions signature of a pressure-induced polytypic transformation in chlorite
  23. Letter. A new high-pressure CaGe2O5 polymorph with 5- and 6-coordinated germanium
  24. Letter. Terrestrial analogs of martian jarosites: Major, minor element systematics and Na-K zoning in selected samples
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