Strain analysis of phase transitions in (Ca,Sr)TiO₃perovskites

Abstract

A single Landau free energy expansion is used to describe phase transitions in perovskites, from a cubic parent structure to tetragonal and orthorhombic structures with space groups related to the M 3 and R 25 points of the Pm3 -m reciprocal lattice. This expansion permits relationships between symmetry-adapted forms of the spontaneous strain and individual order parameter components to be predicted. Data from the literature for (Ca,Sr)TiO 3 perovskites are analyzed in the light of these predictions. Shear strains for I4/mcm, Pnma, and Cmcm structures tend to conform to the predicted pattern. The Pm3 -m ↔ I4/mcm transition has nearly tricritical character as a function of temperature in CaTiO 3 and more nearly second-order character as a function of composition at the Sr-rich end of the solid solution. Coupling with the volume strain appears to be both temperature and composition dependent, which may be a general feature of phase transitions in perovskites. Renormalization of fourth-order terms by changing the volume coupling coefficients could be responsible for the unusual order parameter evolution shown by CaTiO 3 and for changes in thermodynamic character of the phase transitions as a function of composition. The pattern of strain variations also correlates closely with patterns of variations in heat capacity from the literature, suggesting revisions to the subsolidus phase diagram for the (Ca,Sr)TiO 3 solid solution above room temperature.

Elastic and anelastic anomalies in (Ca,Sr)TiO3 perovskites: Analogue behaviour for silicate perovskites

“…In this context, perhaps there is some significance in the variation of high temperature lattice parameter data given by Kennedy et al (1999) for CaTiO 3 , in that the tetragonal strain which is close to zero between T2 and ~800 K becomes larger in magnitude below ~800 K (see Fig. 5 of Carpenter et al, 2001). Once there is a finite tetragonal strain, there will be a resolved shear stress on the twin walls for most orientations of an externally applied stress.…”

“…This is because the coupling of volume strains with the order parameter for octahedral tilting transitions in perovskites is generally weak. Carpenter (2007a) used the strain analysis approach of Carpenter et al (2001) to show that the bulk modulus might reduce by a few %, at most, for…”

“…Harrison et al (2003) found that Pnma CST samples show no obvious signs of anelastic behaviour and concluded that the twin walls do not move under an externally applied stress once the symmetry is reduced below tetragonal. They commented on the fact that Pnma samples at intermediate compositions in the CST solid solution have pseudocubic lattice geometry (Carpenter et al 2001), which means that there will be no resolved shear stress on the twin walls (see, also, discussion in Carpenter et al, 2007). It is not universally the case that twin walls are immobile in Pnma perovskites, however, since Daraktchiev et al A c c e p t e d M a n u s c r i p t 15 in Q below ~800 K in CaTiO 3 (Fig.…”

“…Page 9 of 34 A c c e p t e d M a n u s c r i p t 3 attracted interest as a potential analogue system for the structure, properties and behaviour of (Mg,Fe)SiO 3 and CaSiO 3 perovskites at high pressures and temperatures (Qin et al, 2000(Qin et al, , 2002Carpenter et al, 2001Carpenter et al, , 2007Harrison et al, 2003;Carpenter, 2007a,b). In this context, the most significant issues relate to how the elastic properties vary with pressure, temperature and structure type and, in particular, to whether there are any anomalies in elastic constants or mechanical quality factor, Q, which might lead to a better understanding of the seismic properties of the lower mantle.…”

Group-theoretical analysis of octahedral tilting in ferroelectric perovskites

“…Also, Howard & Stokes (1998) obtained the group±subgroup relationships between the different tilt systems. This systematic treatment of tilt systems has already proved useful, to varying degrees, in guiding the correct determination of various distorted perovskite structures, for example, CaFe x Ti 1Àx O 3Àxa2 (Becerro et al, 2000), SrZrO 3 (Howard et al, 2000), PrAlO 3 (Moussa, Kennedy, Hunter et al, 2001), CaTiO 3 (Kennedy, Howard & Chakoumakos, 1999), LaGaO 3 , NaTaO 3 (Kennedy, Prodjosantoso & Howard, 1999), (Ca,Sr)TiO 3 (Carpenter et al, 2001), Sr 1Àx Ba x ZrO 3 , Pb(Zr 0X65 Ti 0X35 )O 3 (Liu et al, 2001), SrTi x Zr 1Àx O 3 (Kam-Yuen et al, 2001) and BaPbO 3 .…”