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

Department of Earth Sciences, University of Cambridge, Downing Street, Cambridge CB2 3EQ, U.K.

Correspondence: ^* E-mail: mc43{at}esc.cam.ac.uk

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 PmmI4/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.

Key Words: Phase transitions • Landau theory • perovskite • SrTiO₃

This article has been cited by other articles:

				M. A. Carpenter Elastic anomalies accompanying phase transitions in (Ca,Sr)TiO3 perovskites: Part II. Calibration for the effects of composition and pressure American Mineralogist, February 1, 2007; 92(2-3): 328 - 343. [Abstract] [Full Text] [PDF]

				M. A. Carpenter, B. Li, and R. C. Liebermann Elastic anomalies accompanying phase transitions in (Ca,Sr)TiO3 perovskites: Part III. Experimental investigation of polycrystalline samples American Mineralogist, February 1, 2007; 92(2-3): 344 - 355. [Abstract] [Full Text] [PDF]