Acoustic Second-Harmonic Generation in Piezoelectric Crystals

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Abstract
The treatment of acoustic second‐harmonic generation has been extended to piezoelectric crystals. This extension shows that the third‐order elastic constants measured by means of second‐harmonic generation are not equal to the field‐free third‐order elastic constants. It is shown that the size of the effective third‐order elastic constants depends on all of the material constants of the crystal free energy that are third order in strain and electric field. Estimates of the relative sizes of the material constants contributing to the effective third‐order elastic constants have been made for longitudinal waves propagating along the z axis in LiNbO 3 . A comparison of these estimates with the measured value of the effective elastic constant C 333 in LiNbO 3 shows that indirect piezoelectric coupling may produce a large fractional difference between the field‐free third‐order elastic constant and the effective third‐order elastic constant.