International
Tables for
Crystallography
Volume D
Physical properties of crystals
Edited by A. Authier

International Tables for Crystallography (2013). Vol. D, ch. 1.1, p. 32

## Section 1.1.5.2. Other forms of the piezoelectric constants

A. Authiera*

aInstitut de Minéralogie et de Physique des Milieux Condensés, 4 Place Jussieu, 75005 Paris, France

#### 1.1.5.2. Other forms of the piezoelectric constants

| top | pdf |

We use here another Gibbs function, the electric Gibbs function, , defined by

Differentiation of givesIt follows thatand a set of relations analogous to (1.1.5.1):where the components are the isothermal elastic stiffnesses at constant field and constant temperature, are the piezoelectric stress coefficients at constant strain and constant temperature,are the temperature-stress constants andare the components of the pyroelectric effect at constant strain.

The relations between these coefficients and the usual coefficients are easily obtained:

 (i) At constant temperature and strain: if one puts and in the first equation of (1.1.5.1) and (1.1.5.2), one obtains, respectively, from which it follows that at constant temperature and strain. (ii) At constant temperature and stress: if one puts and , one obtains in a similar way from which it follows that at constant temperature and stress.