High Electromechanical Coupling Piezoelectrics - How High Energy Conversion Rate is Possible
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(Stored mechanical energy / Input electrical energy)
(1)
(Stored electrical energy / Input mechanical energy).
(2)
=
or =
When an electric field E is applied to a piezoelectric actuator, since the input electrical energy is (1/2) &j)e E2 per unit volume and the stored mechanical energy per unit volume under zero external stress is given by (1/2) x 2 / s = (1/2) (d E) 2 / s, k2 can be calculated as 2 k2= [(1/2) (d E) / s] I [(1/2) =d2 / poc-s.
c0s E 2]
3 Mat. Res. Soc. Symp. Proc. Vol. 459 ©1997 Materials Research Society
(3)
On the other hand, the efficiency 1j is defined as 'l = (Output mechanical energy) / (Consumed electrical energy)
(4)
= (Output electrical energy) / (Consumed mechanical energy).
(5)
or In a work cycle (e. g. an electric field cycle), the input electrical energy is transformed partially into mechanical energy and the remaining is stored as electrical energy (electrostatic energy like a capacitor) in an actuator. Then, this ineffective energy can be returned to the power source, leading to near 100 % efficiency, if the loss is small. Typical values of dielectric loss in PZT are
about 1 - 3 %. The electromechanical coupling factor is different according to the sample geometry. Figure 1 shows two sample geometries corresponding to k33 and k31, which we will discuss later. In some particular applications such as Non-Destructive Testing, large piezoelectric anisotropy, i. e. a large value of the ratio k33/k3 1, is required to improve the image quality in addition to a large value of k33 itself. However, the empirical rule suggests that these two requirements are contradictory to each other. In Figure 2 we plotted the k33 versus k31 relation for various perovskite oxide piezoelectric polycrystal and single crystal samples such as Pb(Zr,Ti)03, PbTiO3, Pb(Znl/3Nb2/3)03 and Pb(Mgl/3Nb2/3)03 based compositions [4]. It is obvious from this convex tendency that the piezoelectricity becomes isotropic (i. e. the k33/k31 ratio approaches to 1) with increasing the electromechanical coupling factor (i. e. the k33 value).
Polarization DirectionDieto
Electrode
Dirpaetint
(b) k31 (a) k33 Fig. I Typical vibration modes of piezoelectric devices. 10
08'
06-
G4--* Y
"i6
0z'Cr.t"fl-
0.2
0
02
04
06
08
-k31
Fig.2 Relation between k33 and k31 for various perovskite oxide piezoelectrics.
HIGH ELECTROMECHANICAL COUPLING MATERIALS Morphotropic Phase Boundary Composition Conventionally, Pb(Zr,Ti)03 (PZT), PbTiO3 (PT) and PZT based ternary ceramics with a small amount of a relaxor ferroelectric have been utilized for piezoelectric applications. Figure 3 shows the composition dependence of permittivity and electromechanical coupling factor kp in the PZT system. It is notable that the morphotropic phase boundary (MPB) composition between the rhombohedral and tetragonal phases exhibits the maximum enhancement in dielectric and piezoelectric properties; this is explained in terms of a phenomenological theory [5]. The physical properties of a perovskite solid solution between A and B, (l-x) A - x
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