Many modern devices such as resonators for radio frequency filtering, medical ultrasound, fuel injectors, sonar, and vibration-powered electronics rely on the piezoelectric property of materials that can convert mechanical to electrical energy and vice versa. The piezoelectric coefficients d ij and e ij , quantify the strength of the piezo-response. Usually the longitudinal strain piezocoefficient, d 33 of common piezoelectrics, e.g. PbTiO 3 , is positive as the material expands along the polar axis under an applied electric field in the same direction.