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Piezo Engineering Tutorial
between the final device package size and stiffness because the stiffness of the device decreases with the
square of the lever amplification ratio used. Aerotech's piezo nanopositioning stages are optimized to
provide superior mechanical performance in a compact stage package.
C.3.2 Hysteresis Effects
Piezoelectric materials are a subset of a larger class of materials known as ferroelectrics. Ferroelectricity is
a property of certain materials that have a spontaneous electric polarization that can be reversed by the
application of an electric field. Like the magnetic equivalent (ferromagnetic materials), ferroelectric materials
exhibit hysteresis loops based on the applied electric field and the history of that applied electric field.
C-1
shows an illustration of a strain (X) versus electric field (E) "butterfly" curve for a PZT material driven to
its excitation limits.
Figure C-1:
Strain (displacement) behavior of a ferroelectric material like PZT with an applied
As the electric field is cycled from positive to negative to positive, the following transformations occur in the
piezo actuator:
A. Initially, strain increases with electric field and is only slightly nonlinear. As the electric field is
increased, the dipoles of all the grains will eventually align to the electric field as optimally as is
possible and the distortion of the grains will approach a physical limit.
B. When the field is reversed, strain decreases more slowly due to the reoriented dipoles. As the field gets
smaller, the dipoles relax into less ideal orientations and strain decreases at a faster rate.
C. As the field becomes negative the dipoles are forced away from their original orientation. At a critical
point they completely reverse direction and the piezo actuator becomes polarized in the opposite
direction. The electric field at the point of polarization reversal is known as the coercive field (E
D. After polarization reversal, the piezo expands again until it reaches its physical strain limit.
E. The electric field is reversed again and the same hysteretic behavior that occurred along curve B
occurs as strain decreases.
44
electric field driven to its excitation limits
Appendix C
QNP3 Hardware Manual
www.aerotech.com
Figure
).
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