Theoretical calculation of the resonant frequency temperature dependence for domain-engineered piezoelectric resonators

Material properties of ferroelectric single-domain crystal are temperature dependent. In multi-domain ferroelectric crystal, different domains might contribute in a different way to the effective temperature dependence, due to the crystallographic orientation. Calculations of the effective temperature dependence of the resonant frequency for the piezoelectric resonator were performed for the ferroelectric species m3¯m→4mm, for all possible combinations of domain twins. Temperature dependence is presented for the resonant frequency of the length-extensional vibrations for (0 0 1), (1 1 0) and (1 1 1) BaTiO3 thin bar resonator. Temperature dependence of the resonant frequency for the piezoelectric resonator is suppressed with respect to the single-domain crystal resonator of the same crystallographic orientation. Different twin-domain systems for the same resonator orientation are discussed on the basis of practical applicability for the resonator (orientation, available domain states and external fields to create such twinned system).