Strain relaxation mechanisms of elastic softening and twin wall freezing associated with structural phase transitions in (Ca,Sr)TiO3 perovskites

Resonant ultrasound spectroscopy has been used to measure the bulk modulus (K), shear modulus (G) and acoustic dissipation of polycrystalline perovskite samples across the CaTiO3-SrTiO3 solid solution in the temperature range similar to 10-1350 K. A remarkable pattern of up to similar to 25% softening of G as a function of both temperature and composition is due to coupling of shear strain with order parameters for the Pm (3) over barm <-> I4/mcm, I4/mcm <-> Pnma and I4/mcm <-> Pbcm transitions. Anomalies in K associated with the phase transitions are small, consistent with only weak coupling of octahedral tilting order parameter(s) with volume strain. A change from tricritical character for the Pm (3) over barm <-> I4/mcm transition towards second order character at Sr-rich compositions appears to be due to changing properties of the soft optic mode rather than to changes in magnitude of strain/order parameter coupling coefficients. Precursor softening of G ahead of the Pm (3) over barm <-> I4/mcm transition, due to fluctuations or clustering, occurs over a temperature interval of up to similar to 200 K, and also changes character at the most Sr-rich compositions. The tetragonal structure with Sr-rich compositions is characterized by additional softening with falling temperature which is most likely related to the proximity of a ferroelectric instability. The I4/mcm <-> Pnma transition is accompanied by stiffening, which is attributed to the effects of strong coupling between order parameters for M-point and R-point tilting. The pattern of attenuation at RUS frequencies in the tetragonal phase can be understood in terms of the mobility of twin walls which become pinned below similar to 500 K, and the loss mechanism most likely involves local bowing of the walls by lateral motion of ledges rather than the advance and retraction of needle tips. Twin wall mobility is suppressed in the orthorhombic structure.