Editing Piezoelectricity (section)

==Crystal classes==

[[File:Capacitor schematic with dielectric.svg|thumb|Any spatially separated charge will result in an [[electric field]], and therefore an [[electric potential]]. Shown here is a standard dielectric in a [[capacitor]]. In a piezoelectric device, mechanical stress, instead of an externally applied voltage, causes the charge separation in the individual atoms of the material.]]

Of the 32 [[crystal class]]es, 21 are non-[[centrosymmetric]] (not having a centre of symmetry), and of these, 20 exhibit direct piezoelectricity<ref>{{cite web|title=Piezoelectric Crystal Classes|url=https://www.staff.ncl.ac.uk/j.p.goss/symmetry/PP_Piezo.html|publisher=Newcastle University, UK|access-date=8 March 2015|url-status=live|archive-url=https://web.archive.org/web/20150402160441/https://www.staff.ncl.ac.uk/j.p.goss/symmetry/PP_Piezo.html|archive-date=2 April 2015}}</ref> (the 21st is the cubic class 432). Ten of these represent the polar crystal classes,<ref>{{cite web|title=Pyroelectric Crystal Classes|url=https://www.staff.ncl.ac.uk/j.p.goss/symmetry/PP_Pyro.html|publisher=Newcastle University, UK|access-date=8 March 2015|url-status=live|archive-url=https://web.archive.org/web/20150402183459/https://www.staff.ncl.ac.uk/j.p.goss/symmetry/PP_Pyro.html|archive-date=2 April 2015}}</ref> which show a spontaneous polarization without mechanical stress due to a non-vanishing electric dipole moment associated with their unit cell, and which exhibit [[pyroelectricity]]. If the dipole moment can be reversed by applying an external electric field, the material is said to be [[ferroelectric]].
* The 10 polar (pyroelectric) crystal classes: 1, 2, m, mm2, 4, {{Not a typo|4mm}}, 3, 3m, 6, {{Not a typo|6mm}}.
* The other 10 piezoelectric crystal classes: 222, {{overline|4}}, 422, {{overline|4}}2m, 32, {{overline|6}}, 622, {{overline|6}}2m, 23, {{overline|4}}3m.

For polar crystals, for which '''''P'''''&nbsp;≠&nbsp;0 holds without applying a mechanical load, the piezoelectric effect manifests itself by changing the magnitude or the direction of '''''P''''' or both.

For the nonpolar but piezoelectric crystals, on the other hand, a polarization '''''P''''' different from zero is only elicited by applying a mechanical load. For them the stress can be imagined to transform the material from a nonpolar crystal class ('''''P'''''&nbsp;=&nbsp;0) to a polar one,<ref name="ZPB1995a"/> having '''''P'''''&nbsp;≠&nbsp;0.