The Nature of Hysteresis

Strain upon poling
Three kinds of strain occur in a “fresh” ferroelectric ceramic sample during poling (curve a: the so-called ‘virginal’ curve). At low electric field strength, 180° domain switching occurs, which does not involve strain. Domain realignment by angles other than 180°, depending on the allowed dipole axes within a unit cell, is responsible for the first, large magnitude, kind of strain.
Accompanying this, as orientation proceeds, is a second kind of strain: a piezoelectric effect within the aligned domains. Contrary to the piezoelectric strain, being truly linear, the third kind of strain varies quadratically with the applied electric field. The latter phenomenon, termed electrostriction, is present in any dielectric material and is often considered to be of negligible magnitude.

Once saturated, a somewhat non-linear and hysteretic, but reversible path is followed in subsequent field excursions in the same direction (loop b: the typical hysteresis loop shown by piezoelectric ceramic actuators). Strains here involve piezoelectric deflection plus some residual dipole reorientation effects that come and go during each excursion. The latter effects cause the difference between the maximum polarisation at saturation Ps and the remnant polarisation Pr.

For fields in the opposite direction, behaviour is considerably different and more complex, because depoling starts to take effect. In this context, it should be remembered that large excursions in both directions generate the “butterfly” loop of strain versus field. In practice this implies that piezoelectric ceramics may not be exposed to highly negative electric fields.

In order to obtain reasonable expansion out of a piezoelectric ceramic actuator, the material is exercised through a significant fraction of the hysteresis loop (loop b). Piezoelectric actuators, when controlled by application of a voltage to the electrodes, therefore suffer from a considerable amount of hysteresis, which may be as large as 15% of the commanded motion.

Just like the non-linear and hysteretic behaviour indicated above, creep in piezoelectric ceramics is related to the effect of the applied voltage on the remnant polarisation. Creep is the expression of the slow realignment of the crystal domains in a constant electric field over time. If the operating voltage of a PZT is changed, after the voltage change is complete, the remnant polarisation continues to change, manifesting itself in a slow creep. The rate of creep decreases logarithmically with time.

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