help for understand of spontaneous polarization in piezo

athosanian

dear all, I want to confirm whether there is spontaneous polarization in the piezo materials. I know the piezo materials need to be poled under high temperature and electric field before applications. So if there is spontaneous polarization, comes my following confusing.
Given a piezo disk with polarization along the thickness direction, with upper and bottom surface silver coated as electrodes. the spontaneous polarization of piezo disk is denoted as P0. When disk is in such a state, without any stress applied on it and the upper and bottom electrodes are connected. Then the stress and electric field in the piezo disk is zero. so from the constitutive equation:
　　　　　 D=ε*E+d*T
(where D is electric displacement, ε is electric permittivity, E is electric field, d is piezoelectric coefficient and T is stress.), the D is 0 in the piezo disk in such a state. However, because of spontaneous polarization in the piezo disk the D should not be 0, it should be P0 ! What is wrong with my thought? I hope some help. Thanks!

athosanian

Anyone could help?