Acoustic Gain in Solids due to Piezoelectricity, Flexoelectricity, and Electrostriction

A quantitative discussion of the combined influence of three electromechanical effects: piezoelectricity, flexoelectricity, and electrostriction in solids is provided for acoustic absorption and gain. While piezoelectricity occurs in non-centrosymmetric materials only, flexoelectricity and electrostriction exist in all materials. Two important new results are demonstrated: 1) the possibility to realize acoustic gain in all materials (centrosymmetric and non-centrosymmetric) when the acoustic Cherenkov condition is fulfilled, and 2) realization of acoustic gain in the presence of a strong dc electric field, even when the Cherenkov condition is not fulfilled, in the case of strong cross-coupling between piezoelectricity, flexoelectricity, and electrostriction. A simple analytical expression for the acoustic dispersion relation is derived for the combined effect of piezoelectricity, flexoelectricity, and electrostriction. At lower frequencies, the piezoelectric effect dominates for inversion-asymmetric materials. At high frequencies (≈>1 MHz) flexoelectricity becomes increasingly important and eventually provides a major mechanism for gain and absorption in barium titanate (BaTiO3). In the presence of strong electric fields (≈>1 MV m−1), electrostriction provides a dominant isolated contribution to absorption/gain in BaTiO3. Strong coupling between the three electromechanical contributions determines the total absorption/gain coefficient.