Compound phases often display properties that are symmetry-forbidden relative to their nominal, average crystallographic symmetry, even if extrinsic reasons (defects, strain, imperfections) are not apparent. Specifically, breaking the macroscopic inversion-symmetry of a centrosymmetric phase can dominate or significantly change its observed properties while the detailed mechanisms and magnitudes of the deviations of symmetry-breaking are often obscure. Here, we choose piezoelectricity as a tool to investigate macroscopic inversion symmetry breaking in nominally centrosymmetric materials as a prominent example and measure Resonant Piezoelectric Spectroscopy (RPS) and Resonant Ultrasound Spectroscopy (RUS) in 15 compounds, 18 samples, and 21 different phases, including unpoled ferroelectrics, paraelectrics, relaxors, ferroelastics, incipient ferroelectrics, and isotropic materials with low defect concentrations, i.e. NaCl, fused silica, and CaF 2 . We exclude the flexoelectric effect as a source of the observed piezoelectricity yet observe piezoelectricity in all nominally cubic phases of these samples. By scaling the RPS intensities with those of RUS, we calibrate the effective piezoelectric coefficients using single crystal quartz as standard.Using this scaling we determine the effective piezoelectric modulus in nominally non-piezoelectric phases, finding that the 'symmetry forbidden' piezoelectric effect ranges from ∼ 1 pm/V to 10 −5 pm/V (∼ 0.5% to ∼ 2 × 10 −7 % of the piezoelectric coefficient of poled ferroelectric lead zirconate titanate). The values for the unpoled ferroelectric phase are only slightly higher than those in the paraelectric phase. The extremely low coefficients are well below the detection limit of conventional piezoelectric measurements and demonstrate RPS as a convenient and ultra-highly sensitive method to measure piezoelectricity. We suggest that symmetry-breaking piezoelectricity in nominally centrosymmetric materials and disordered, unpoled ferroelectrics is ubiquitous.
I. INTRODUCTIONAlong with chiral dichroism, second harmonic generation and the Rashba spin splitting, the classic effects of piezoelectricity and pyroelectricity belong to a group of functionalities enabled by specific crystal class (CC) symmetries. Both effects require an absence of inversion center, i.e. belonging to a non-centrosymmetric (NCS) crystal class. In addition, whereas pyroelectricity is restricted exclusively to polar crystal classes, piezoelectricity is allowed both in polar symmetries