Elastic properties of SrTiO₃ crystals at ultralow frequencies

Abstract

The phase transition of SrTiO3 at 105 K has been examined by studying the temperature dependence of the Young's modulus of SrTiO3 crystals along various directions. Dynamic Mechanical Analysis (DMA) at 10-140K and 10-45 Hz has been used for the experiments. The elastic behaviour is interpreted in terms of Landau theory and the DMA results are compared with ultrasonic experiments. The striking differences between the two types of data are attributed to the Occurrence of domain wall motions at low frequencies. These motions are suppressed at high frequencies (ultrasonics). We have studied the temperature behaviour of the low-frequency elastic constants of SrTi03 as function of external stress. The data analysis shows that the domain wall contribution to the elastic constants is essentially suppressed with increasing of uniaxial compression.

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

“…However, the pattern of evolution of the shear modulus through T1 did not match that predicted using a Landau M a n u s c r i p t 4 free energy expansion which had been calibrated using the large amount of experimental data available for SrTiO 3 (Carpenter, 2007a,b). Furthermore, it is known that twin walls are mobile down to at least ~40 K in SrTiO 3 at low frequencies of applied stress (Schranz et al, 1999;Kityk et al, 2000a, b;Lemanov et al, 2002), and that the elastic properties of twinned samples measured at MHz frequencies are different from those obtained from within a single tetragonal twin domain by Brillouin scattering (as summarised in Carpenter, 2007a , though the actual values depends on the mass of the sample, the mass of the backloads, sample size and elastic stiffness, and the response of the small cross-section where the corner of the sample meets the driving piezoelectric crystal.…”

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

“…Some anelastic softening occurs in SrTiO 3 below the freezing temperature, however, as seen in published ultrasonic data obtained at MHz measuring frequencies (Figs. 6 and 7) and in Dynamical Mechanical Analysis (DMA) data collected at 1 350 Hz (Schranz et al, 1999;Kityk et al, 2000aKityk et al, , 2000b. Softening of the shear modulus of tetragonal CST beyond what is expected as a consequence of strain/order parameter coupling alone is also seen at room temperature in the pulse echo ultrasonic data shown in Figure 8c.…”

“…It was recognised from the early days of elastic constant measurements on SrTiO 3 that the displacement of transformation twin walls in response to an applied shear stress can give rise to additional softening and attenuation effects (Rehwald, 1971;Fossheim and Berre, 1972). These can be large in magnitude, giving rise to so called superelasticity (Schranz et al, 1999;Kityk et al, 2000aKityk et al, , 2000bBinder and Knorr, 2001;Lemanov et al, 2002;Harrison and Redfern, 2002;Harrison et al, 2003Harrison et al, , 2004aHarrison et al, , 2004bHarrison et al, , 2004c. Equivalent behaviour in silicate perovskites cannot be investigated directly because of the high confining pressure required to stabilise them, but a useful analogue system is the binary solid solution CaTiO 3 SrTiO 3 (CST).…”

“…The spontaneous strain orientation for one twin is different from that of an adjacent twin, so movement of the wall separating them can change the total macroscopic strain of the crystal. If the twin wall moves in response to an applied shear stress, the total resulting strain can become substantially greater than would occur by simple lattice bending and the crystal will be anomalously soft (Schranz et al, 1999;Kityk et al, 2000aKityk et al, , 2000bBinder and Knorr, 2001;Lemanov et al, 2002;Harrison and Redfern, 2002;Harrison et al, 2003Harrison et al, , 2004aHarrison et al, , 2004bHarrison et al, , 2004c. This mechanism of softening involves some dissipation of energy and is anelastic in character.…”

“…where S para is the compliance of the high symmetry form, ΔS L is the change in compliance described by Landau theory and ΔS W is the change in compliance due to movements of the twin walls (Schranz et al, 1999;Kityk et al, 2000aKityk et al, , 2000b. Given that the total strain accompanying twin wall movement scales with e t and, hence, with q 4 2 , the simplest model has ΔS W ∝ q 4 2 .…”