Negative piezoelectric phase

Order parameters may also refer to underlying atomic structure or symmetry. For example, a piezoelectric material cannot have a symmetry that includes an inversion center. To model piezoelectric phase transitions, an order parameter, r], could be associated with the displacement of an atom in a fixed direction away from a crystalline inversion center. Below the transition temperature Tc, the molar Gibbs free energy of a crystal can be modeled as a Landau expansion in even powers of r (because negative and positive displacements, 77, must have the same contribution to molar energy) with coefficients that are functions of fixed temperature and pressure,... 

Figure 19.11 Phase maps f(x, y) of a 6x4/um region of a fatigued FeCap (108 cycles) after negative (left) and positive (right) poling and evolution map of the piezoelectric phase signal f(x, E) (central picture) under varying (triangular shape) electric field E of the horizontal line indicated by the horizontal arrows. PI, P2, LI and L2 are discussed in detail later.

The PEM is made of a piezoelectric transducer that is glued to a ZnSe crystal. The piezoelement converts a periodic voltage to a periodic mechanical (acoustic) wave, which compresses or expands the crystal. This movement changes the refractive index in the x direction and imposes a periodic retardation (or acceleration) of the fix component of the incident linearly polarized wave. The fiy component remains unchanged. The PEM is operated at its resonant frequency (50 kHz). If the optical element is at rest, the polarization of the radiation remains unchanged. If the optical element undergoes compression or expansion, the component fix has a positive (retardation) or negative (acceleration) phase shift relative to the phase component of the component fiy. 

Figure 19.20 Piezoelectric vibration maps of phase ((a), (c)) and amplitude ((b), (d)) (3x3 /um2) of a fatigued Pt-PZT-Pt structure after positive ((a), (b)) and negative ((c), (d)) poling. Bright and dark phase areas correspond to bottom-to-top and top-to-bottom polarization orientations, respectively.

An important group of piezoelectric ceramics are solid solutions of PbZrOj and PbTiOs represented as Pb(Zr, Ti)03 (and commonly referred to as PZT). At high temperature these compounds have the cubic perovskite structure (Fig. 1). In the ferroelectric phase, which is stable at room temperature, the lattice is distorted, and the asymmetry of the positive and negative ions results in a net dipole moment. Spontaneous polarization is the dipole moment per unit volume. 

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