Editing Ferroelectricity (section)

==Polarization==
[[Image:Dielectric polarisation.svg|right|frame|Linear dielectric polarization]]
[[File:Paraelectric polarisation DE.svg|frame|Paraelectric polarization]]
[[File:Ferroelectric polarisation DE.svg|frame|Ferroelectric polarization]]
When most materials are [[Polarization density|electrically polarized]], the polarization induced, ''P'', is almost exactly proportional to the applied external electric field ''E''; so the polarization is a linear function.  This is called linear dielectric polarization (see figure). Some materials, known as [[Paraelectricity|paraelectric]] materials,<ref>Chiang, Y. et al.: Physical Ceramics, ''[[John Wiley & Sons]]'' 1997, New York</ref> show a more enhanced nonlinear polarization (see figure). The electric [[permittivity]], corresponding to the slope of the polarization curve, is not constant as in linear dielectrics but is a function of the external electric field.

In addition to being nonlinear, ferroelectric materials demonstrate a spontaneous nonzero polarization (after [[entrainment (physics)|entrainment]], see figure) even when the applied field ''E'' is zero. The distinguishing feature of ferroelectrics is that the spontaneous polarization can be ''reversed'' by a suitably strong applied electric field in the opposite direction; the polarization is therefore dependent not only on the current electric field but also on its history, yielding a [[hysteresis]] loop.  They are called ferroelectrics by analogy to [[ferromagnetic]] materials, which have spontaneous [[magnetization]] and exhibit similar hysteresis loops.

Typically, materials demonstrate ferroelectricity only below a certain phase transition temperature, called the [[Curie temperature#Curie temperature in ferroelectric materials|Curie temperature]] (''T''<sub>C</sub>) and are paraelectric above this temperature: the spontaneous polarization vanishes, and the ferroelectric crystal transforms into the paraelectric state. Many ferroelectrics lose their pyroelectric properties above ''T''<sub>C</sub> completely, because their paraelectric phase has a centrosymmetric crystal structure.<ref>{{cite book|last1=Safari|first1=Ahmad|title=Piezoelectric and acoustic materials for transducer applications|date=2008|publisher=Springer Science & Business Media|isbn=978-0387765402|page=21|bibcode=2008pamt.book.....S}}</ref>