A capacitive displacement system for studying the piezoelectric strain and its temperature variation

A capacitive displacement system was constructed to measure the electric-field-induced piezoelectric strain in the simple form of either a bulk or thin film. The system can determine an AC displacement of 2 pm precisely by using a lock-in detection and can measure the large displacement within the range of ± 25 μ m with a sub-nanometer resolution. The system can also be used to measure the variation in strain within the temperature range of 210–450 K, allowing the evaluation of the temperature coefficient of a piezoelectric constant and the studies on the effects of a phase transition on the piezoelectric response. Experimental results on quartz, Pb ( Zr 1 − x Ti x ) TiO 3 ceramics and thin films, and BaTiO 3 confirm the capabilities of the developed system.