Isothermal study
Authier, A.,

International Tables for Crystallography
(2013).
Vol. D,
Section 1.1.5.1,
p.

[ doi:10.1107/97809553602060000900 ]
Remark . The piezoelectric effect, namely the existence of an electric polarization P under an applied stress, is always measured at zero applied electric field and at constant temperature. The second equation of (

**1.1.5.1**) becomes under ...

Relation between the pyroelectric coefficients at constant stress and at constant strain
Authier, A.,

International Tables for Crystallography
(2013).
Vol. D,
Section 1.1.5.3,
p.

[ doi:10.1107/97809553602060000900 ]
to the properties of tensors
By combining relations (

**1.1.5.1**) and (

**1.1.5.2**), it is possible to obtain relations between the pyroelectric coefficients at constant stress,, and the pyroelectric coefficients at constant strain,, also ...

Other forms of the piezoelectric constants
Authier, A.,

International Tables for Crystallography
(2013).
Vol. D,
Section 1.1.5.2,
p.

[ doi:10.1107/97809553602060000900 ]
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 ...

Thermodynamic functions and physical property tensors
Authier, A.,

International Tables for Crystallography
(2013).
Vol. D,
Section 1.1.5,
p.

[ doi:10.1107/97809553602060000900 ]
: 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 ...

Adiabatic study
Authier, A.,

International Tables for Crystallography
(2013).
Vol. D,
Section 1.1.5.4,
p.

[ doi:10.1107/97809553602060000900 ]
to the properties of tensors
Piezoelectric resonators usually operate at a high frequency where there are no heat exchanges, and therefore in an adiabatic regime . From the third equation of (

**1.1.5.1**), we obtain a relation between ...