Basic Concepts Piezo-, Pyro- and Ferroelectricity

Of the 32 crystal classes, 20 lack a center of symmetry. Materials built up by these crystals have, therefore, the potential for piezoelectric activity. 

The most useful piezoelectric constant is the tensor which relates electric polarization to the stress causing the polarisation. The d-constant is also identified to the derivative of the resulting strain with respect to the applied electric field [24]  

Among the 20 crystal classes lacking a center of symmetry ten of them contain a unique polar axis and exhibit pyroelectricity in addition to piezoelectricity, i.e. in the unstrained dipolar network of these crystals the dipole moment components remain and add to a resultant polar-axis moment. The term pyroelectricity is assigned because thermal expansion will expand or contract the dipole. The pyroelectric constant is defined by  

The length of the polar axis, and with it the polarization, varies with temperature hence crystals with a polar axis develop, as the temperature changes, a difference in potential Le. a pyroelectricity of opposite sign for heating and cooling [26]. 

Finally, ferroelectricity is manifest in asymmetrical crystals producing domains of spontaneous polarization whose polar axis direction can be reversed in an electric field directed opposite the total dipole moment of the lattice. The two (or more) directions can coexist in a crystal as domain structures comprising millions of unit cells which contain the same electric orientation. The symmetry elements are temperature sensitive in ferroelectric materials [27]. At a particular temperature called the Curie Point the values of the piezoelectric coefficients reach particularly high values. Above the Curie Point the crystal transformation is to a less polar form and the ferroelectric nature disappears. 

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