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It is shown that piezoelectric effects can be easily derived from bulk properties and are expressible in terms of linear and quadrupole moments of variations in charge density induced by atomic displacements. The linear-moment contribution is determined by optic macroscopic effective charges and internal-strain parameters. The remaining terms measure directly the induced quadrupole moment, and hence provide insight into the nature of interatomic forces and chemical bonding. Special attention is focussed upon the zinc-blende structure. An important step in the derivation is the use of translation and rotation invariance to transform the basic equations to eliminate convergence difficulties and give expressions manifestly independent of surface configurations.
Richard M. Martin (Tue,) studied this question.