Because a piezoelectric ceramic is anisotropic, physical constants relate to both the direction of the applied mechanical or electric force and the directions perpendicular to the applied force. Consequently, each constant generally has two subscripts that indicate the directions of the two related quantities, such as stress (force on the ceramic element / surface area of the element) and strain (change in length of element / original length of element) for elasticity. The direction of positive polarization usually is made to coincide with the Z-axis of a rectangular system of X, Y, and Z axes ( | ||||||||||||||||||

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Piezoelectric Charge Constant | ||||||||||||||||||

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Piezoelectric Voltage Constant | ||||||||||||||||||

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Permittivity | ||||||||||||||||||

The permittivity, or dielectric constant,
, for a piezoelectric ceramic material is the dielectric displacement per unit electric field.
^{T} is the permittivity at constant stress,
^{S} is the permittivity at constant strain. The first subscript to
indicates the direction of the dielectric displacement; the second is the direction of the electric field.The relative dielectric constant, K, is the ratio of
, the amount of charge that an element constructed from the ceramic material can store, relative to the absolute dielectric constant,
_{0} , the charge that can be stored by the same electrodes when separated by a vacuum, at equal voltage (
_{0} = 8.85 x 10^{-12} farad / meter). | ||||||||||||||||||

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Electromechanical Coupling Factor | ||||||||||||||||||

The electromechanical coupling factor, k, is an indicator of the effectiveness with which a piezoelectric material converts electrical energy into mechanical energy, or converts mechanical energy into electrical energy. The first subscript to k denotes the direction along which the electrodes are applied; the second denotes the direction along which the mechanical energy is applied, or developed.k values quoted in ceramic suppliers' specifications typically are theoretical maximum values. At low input frequencies, a typical piezoelectric ceramic can convert 30 - 75% of the energy delivered to it in one form into the other form, depending on the formulation of the ceramic and the directions of the forces involved. A high k usually is desirable for efficient energy conversion, but k does not account for dielectric losses or mechanical losses, nor for recovery of unconverted energy. The accurate measure of efficiency is the ratio of converted, useable energy delivered by the piezoelectric element to the total energy taken up by the element. By this measure, piezoelectric ceramic elements in well designed systems can exhibit efficiencies that exceed 90%. The dimensions of a ceramic element can dictate unique expressions of k. For a thin disc of piezoelectric ceramic the planar coupling factor, k _{p} , expresses radial coupling - the coupling between an electric field parallel to the direction in which the ceramic element is polarized (direction 3) and mechanical effects that produce radial vibrations, relative to the direction of polarization (direction 1 and direction 2). For a disc or plate of material whose surface dimensions are large relative to its thickness, the thickness coupling factor, k_{t} , a unique expression of k_{33} , expresses the coupling between an electric field in direction 3 and mechanical vibrations in the same direction. The resonance frequency for the thickness dimension of an element of this shape is much higher than the resonance frequency for the transverse dimensions. At the same time, strongly attenuated transverse vibrations at this higher resonance frequency, a result of the transverse contraction / expansion that accompanies the expansion / contraction in thickness, make k_{t} lower than k_{33} , the corresponding factor for longitudinal vibrations of a thin rod of the same material, for which a much lower longitudinal resonance frequency more closely matches the transverse resonance frequency. | ||||||||||||||||||

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Dielectric Dissipation Factor | ||||||||||||||||||

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Frequency Constant | ||||||||||||||||||

When an unrestrained piezoelectric ceramic element is exposed to a high frequency alternating electric field, an impedance minimum, the planar or radial resonance frequency, coincides with the series resonance frequency, f | ||||||||||||||||||

Curie temperature | ||||||||||||||||||

Temperature at which the permittivity of ferroelectric ceramics reaches its peak. Above this temperature the ceramic material will not exhibit piezoelectric properties. | ||||||||||||||||||

Mechanical quality factor | ||||||||||||||||||

Amplitude magnification of oscillating piezoelectric parts in a resonant state. This is a non-dimensional factor indicating the mechanical loss of the component under dynamic operating conditions. |