Structural evolution, strain and elasticity of perovskites at high pressures and temperatures

Abstract

Octahedral tilting transitions in perovskites are usually identified by the significant lattice distortions which accompany them. The underlying mechanism of coupling between the tilts and the macroscopic strain also gives rise to large anomalies in single crystal and bulk elastic moduli. Landau theory provides an effective framework for describing these different changes in properties and relating them, quantitatively, to the evolution of the driving order parameter for the transition. This approach has been used to analyse the overall elastic behaviour of perovskites belonging to the CaTiO 3 SrTiO 3 (CST) solid solution, which is expected to be closely analogous to the behaviour of silicate perovskites at higher pressures and temperatures. Pm3 m ↔ I4/mcm and I4/mcm ↔ Pnma transitions in CST perovskites are marked by changes in the shear modulus of ~ 10 30%. The evolution of the order parameter and, hence, of the octahedral tilt angles through these can be followed through the variations of spontaneous strains extracted from high resolution lattice parameter data. Contributions to the elastic softening which are due to strain/octahedral tilt coupling have been calculated using a fully parameterised Landau model of the Pm3 m ↔ I4/mcm transition as a function of temperature, pressure and composition. Differences between calculated elastic constants and experimental data from Dynamical Mechanical Analysis, pulse echo ultrasonics and Resonant Ultrasound Spectroscopy suggest that a proportion of the total softening in tetragonal samples may be due to anelastic effects. The anelastic contributions are observed at frequencies of both a few Hz and 10's of MHz, and can be understood in terms of strain contributions arising from movements of transformation twin walls in response to an externally applied shear stress. Similar transitions in other perovskites are likely to display small anomalies in the bulk modulus, due to weak coupling between octahedral tilts and volume strain, but much larger anomalies in the shear modulus. The elastic properties of tetragonal and orthorhombic structures are likely to be quite different due to different anelastic contributions from twin wall displacements.

Trapping of oxygen vacancies in the twin walls of perovskite

“…29 The elastic properties were less well determined in this model so that a new parameter set ͑M2͒ was fitted here as an extension of M1 by including elastic moduli [30][31][32] and phonon frequency modes 33 for the fit. The reliability of these models was first tested with small relaxations of variable unit cells ͑20 at-oms͒, which were performed using static calculations with GULP.…”

Characterizing the nonlinear interaction of S- and P-waves in a rock sample

“…The curious decorrelation inb between days 2 and 6 probably involves other experimental parameters such as the humidity and pressure that are also known to perturb the nonlinear response. 51,52 Another unexplained feature of this experiment is the first measurement ofb after half a day with no pump on day 7 which is 50% smaller than subsequent points. This bias was noted for all the experiments and for this reason the first measurement is excluded when an average is performed.…”

Anelasticity maps for acoustic dissipation associated with phase transitions in minerals

“…2001; Jackson et al . 2002; Webb & Jackson 2003; Faul & Jackson 2005; Jackson 2007, Salje 2008) or transformation microstructures (Harrison & Redfern 2002; Harrison et al 2003, 2004a,b,c; Carpenter et al . 2006a; Daraktchiev et al .…”

“…). This has become a topical issue, as evidenced by a flurry of papers on the variation of mechanical quality factor, Q, with depth in the Earth (Selby & Woodhouse 2002;Gung & Romanowicz 2004;Resovsky et al 2005;Dalton & Ekström 2006;Lawrence & Wysession 2006;Matas & Bukowinski 2007;Romanowicz & Mitchell 2007), and on acoustic dissipation mechanisms associated with grain boundaries (Tan et al 2001;Jackson et al 2002;Webb & Jackson 2003;Faul & Jackson 2005;Jackson 2007, Salje 2008 or transformation microstructures (Harrison & Redfern 2002;Harrison et al 2003Harrison et al , 2004aCarpenter et al 2006a;Daraktchiev et al 2006Daraktchiev et al , 2007Walsh et al 2008;McKnight et al 2009a,b).…”

“…Carpenter & Salje 1998;Benoit 2001;, while microstructures such as ferroelastic transformation twins can be mobile under the influence of an applied stress and hence provide a mechanism for acoustic losses across wide temperature intervals in the stability field of the low symmetry phases (e.g. Schranz et al 1999Schranz et al , 2003Kityk et al 2000a,b;Wang et al 2000Wang et al , 2006Bourim et al 2002;Harrison & Redfern 2002;Lemanov et al 2002;Harrison et al 2003Harrison et al , 2004aCarpenter et al 2006a;Daraktchiev et al 2006Daraktchiev et al , 2007Schranz & Kityk 2008;Walsh et al 2008;McKnight et al 2009a,b;Zhang et al 2010a,b). The possibility of steep variations in anelastic loss with depth has not yet been incorporated into seismological models and may represent challenges to current possibilities in relation to resolution (e.g.…”