Inequality of direct and converse piezoelectric coefficients

It is demonstrated theoretically and experimentally that the direct and converse piezoelectric coefficients. ∂P/∂σ and ∂ε/∂E, are not equal as is generally believed. The correct relationship between these coefficients is derived, and it is shown that the experimentally measured quantities analogous to the piezoelectric coefficients are equal. Similar considerations apply to the relationship between the pyroelectric and electrocaloric coefficients.