Symmetry Limitations to Polarization of Polycrystalline Ferroelectrics

Abstract

The general integral for the determination of the average resultant polarization j5 in the direction of the applied polarizing electric field is evaluated under the assumption that the spontaneous polarization vector of each crystallite is limited to a highly symmetric set of directions. With the further assumption that a ferroelectric crystal has a structure which is a slight distortion of a nonpolar structure, expressions for j5 are given which may be applied to any set of allowed polarization directions which is likely to occur; each of the 22 nonpolar crystal classes yields one such expression. The special cases of interest for each of the 10 polar classes are evaluated. A general expression for j5 as a function of electric field strength is obtained and used to determine hysteresis curves for several commonly occurring special cases. The angular distribution of polarization vectors after complete polarization is also discussed for these special cases.

Microstructure, dielectric and piezoelectric properties of (Pb1−xSrx)Nb1.96Ti0.05O6 ceramics

“…Although the T c of the Sr 2þ ions-doped ceramics decreases, it is still higher than 570 C. The changes in T c can be attributed to the competing effects among internal stress, porosity and grain size, as reported in our previous work [8]. For the orthorhombic ferroelectric phase (mm2), polarization is confined to the aeb plane and b/a ratio can reflect a variation in internal stress [17]. With increasing the Sr 2þ content from 0, 0.02, 0.04, 0.06 to 0.08, the b/a ratio of the PNTSr/x ceramics changes from 1.018, 1.023, 1.015, 1.015 to 1.014, respectively.…”

Texture and Anisotropy of Polycrystalline Piezoelectrics

“…30,82 Switching by 901 and 1801 domains occurs between [100], ½ 100, [010], and ½0 10, such that four possible coplanar polarization directions exist. 83 Similar to orthorhombic bismuth titanate, polarization is confined to the aÀb plane of the crystal. When poled, polycrystalline ceramics of lead metaniobate exhibit a modest longitudinal piezoelectric coefficient, d 33 % 80 pC/N.…”

Fundamentals of Piezoelectric Sensorics

“…Number of permissible domains depends on the ferroelectric species (see Table 7.13 for the most common species used in perovskite ceramic systems). Assuming the random grain orientations and complete dipole line-up allowed by it, the fractions of the singlecrystal polarizations allowed for different perovskite species were calculated (Jaffe et al 1971;Redin et al 1963).…”

“…Structure of tensor material coefficients of ∞mm cylindrical polar symmetry is the same as for the hexagonal 6mm symmetry for dielectric, piezoelectric and elastic tensors. Table 7.13 Net polarization allowed by the symmetry as a fraction of the single-crystal polarization (Redin et al 1963;Jaffe et al 1971 …”