Electric Polarization in Dielectric Materials

Polarization and susceptibility can be determined by measuring and comparing the capacities C of a capacitor with a dielectric (C) and an empty capacitor (Co, in vacuum). The ratio C/Cq determines the relative dielectric permittivity e, = e/ b, where e is the permittivity of the dielectric and Eq is the absolute dielectric constant of the vacuum. For the isotropic case, the susceptibili1y f and the relative dielectric permittivity e, are related by 

both e, and e are second rank tensors and link the vector of the electric field strength E and the dielectric displacement vector D by 

From Fq. (8.3a) it follows that the dielectric displacement D and hence the polarization P both reduce to zero when the electric field disappears. However, there are crystals that display a so-called spontaneous polarization Pj already in the absence of an electric field, caused by the presence of singular (polar) directions in their crystal structures. This happens in the ten symmetry groups 1, m, 2, mm2, 3, 3m, 4, 4mm, 6, and 6mm (Table 8.3). It is important for any further 

Polarity Centro symmetry No. of point groups Cubic Hexagonal Tetragonal Rhombohedral Orthorhombic Monoclinic Triclinic 

On the other hand, all point groups without a center of symmetry show the piezoelectric effect, with the exception of 432, the high overall symmetry of which appears to prevent charge delocahzation. The 20 piezoelectric point groups are enclosed by a soHd hne (see Table 8.3). 

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