Piezoelectricity and flexoelectricity in crystalline dielectrics

Piezoelectricity in pyroelectrics and the linear response of polarization to a strain gradient?lexoelectricity) are discussed in the framework of the unified approach. It was pointed out by Born and Huang and by Martin, that there was a difference between the piezoelectric response for the cases of a sound wave and of a uniform strain in a finite crystal, and that only the ``proper'' parts of piezoelectric constants coincided for these cases. It is shown in this paper that there is no such difference if an accurate definition of piezoelectricity is applied. The theory of flexoelectricity in solid crystalline dielectrics is developed. It is shown that the general properties of flexoelectric response strongly differ from those of piezoelectric response: (1) there is an appreciable surface contribution to the flexoelectric response and (2) the bulk flexoelectric responses for the case of a propagating sound wave and for that of a static uniform strain gradient are considerably different. It is proposed to use flexoelectric effect as a method of crystal surface investigation.