Nonlinear elastic behaviour of SrTiO ₃ crystals in the quantum paraelectric regime

Abstract

The ultra-low-frequency (Hz region) elastic behaviour of SrTiO3 has been examined over a wide temperature range including the cubic-tetragonal transition at Tc = 105 K and the quantum paraelectric region (T < 40 K) using a three-point-bending method. A giant elastic softening has been found in the tetragonal phase. It is explained by a model, which takes into account the motion of ferroelastic domain walls in response to the applied dynamic stress. In the quantum paraelectric regime we have detected nonlinear elastic anomalies in the real and imaginary parts of the complex Young's modulus. Our data can be consistently described if we assume that ferroelectric order is induced by the applied strain gradient, which due to flexoelectric coupling is equivalent to a homogeneous electric field. Below 25 K the induced ordered polarization clusters are frozen on the experimental timescale (11 Hz).

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.…”

“…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 . This provides an effective description of softening in single crystals of SrTiO 3 (Schranz et al, 1999;Kityk et al, 2000aKityk et al, , 2000b. A different empirical relationship appears to provide a better description of the softening of G for polycrystalline samples of tetragonal CST, however.…”

“…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 .…”