Why is SrTiO3 much stronger at nanometer than at centimeter scale?

Controlling Piezoelectric Responses in Pb(Zr0.52Ti0.48)O3 Films through Deposition Conditions and Nanosheet Buffer Layers on Glass

“…It was found that the larger d 33f value of the PZT film on CNOns/glass than those on CNOns/Si and STO. For these relatively thin films a large fraction of the clamping is due to the substrate, that is expected to be proportional to the Young’s modulus ( Y s ) of the substrate ( Y s = 238 GPa for STO substrate, 44 which is much higher than that of Si ( Y s = 150 GPa) 45 and glass ( Y s = 67.6 GPa) 42 substrates). Thus, one may expect with decreasing Y s the effective piezoelectric coefficient of the film increases, as is observed.…”

A New Material for High‐Temperature Lead‐Free Actuators

“…For our case, where the film is much thinner than the substrate ( t f ≪ t s )30–32 and the electrode/film covers the whole active area, a simple formula is valid: where L is the distance from the anchoring point, E f and E s , are Young's moduli of the substrate and the film respectively and t s is thicknesses of the substrate. In the d 31 calculations, the Young's modulus of the substrate (Nb doped bulk STO) is E s = 238 GPa 33. Equation (1) is applicable for all samples studied in this work.…”

Electric field mediated switching of mechanical properties of strontium titanate at room temperature

“…Experiments of Paufler et al [18] for different crystal orientations resulted in a hardness ranging from H = 11.5 GPa to 12.2 GPa. Young's modulus can also be derived from single crystal data of the elastic compliance [19] giving E <100> = 1/s 11 = (265 ± 2) GPa for the <100> direction of SrTiO 3 .…”

“…This is related to an increasing possibility of encountering material defects or a surface layer hardened by polishing [21]. Paufler et al [18] gave the similar argument that mobile dislocations are only available in macroscopic indentation depths, so that SrTiO 3 is stronger at the nanometer scale. We observed a maximum hardness at a depth of about 135 nm nearly independent of the applied electric field.…”