SS01 Piezo-D meter
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Overview The piezoelectric test specimen and an NIST traceable force sensor form a part of the force head and are mounted mechanically in series. A force head is applied to them by the mechanical driver. The electronic console provides an excitation voltage with a fixed amplitude at 190Hz. The provided configuration faciitates the measurement of the piezoelectric charge coefficient for a wide range of element sizes and shapes. Specifications
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Piezoelectric Relations
The electrical condition of an unstressed medium placed under the influence of an electric field is defined by two quantities; the field strength (E) and the dielectric displacement (D). Their relationship is expressed as:
D = eE ....(3.1)
in which e is the permittivity of the medium.
The mechanical condition of the same medium at zero electric field strength is defined by two mechanical quantities; the applied stress (T) and the strain (S). The relationship between these two quantities is given in the following equation:
S = sT ....(3.2)
in which s denotes the compliance of the medium.
Piezoelectricity involves the interaction between the electrical and mechanical behavior of the medium. To a good approximation, this interaction can be described by a number of linear equations which relate the different electrical
and mechanical variables.
S = s E T + dE ....(3.3)
D = eT E + dT ....(3.4)
and E = [D/eT ] - gT ....(3.5)
The superscripts in the equations denote the quantity kept constant under boundary conditions. The superscript E denotes a constant electric field and superscript D indicates a constant dielectric displacement. It follows from the above equations that there are two ways of defining the piezoelectric constants d and g. These definitions are illustrated in Table 3.1.
From the above equations it is also possible to define a relationship between d and g:
d = e g ....(3.6)
The directional properties of these coefficients will be described in more detail in the following sub-section.
Directional Dependence
In piezoelectric materials, the constants depend on the directions of electric field, displacement, stress and strain. Hence, subscripts indicating directions are added to the symbols. For piezoelectric ceramics, the direction of positive polarization is usually taken to be that of the Z-axis of a right hand orthogonal crystallographic axes X, Y and Z which are represented by the subscripts 1,2 and 3 respectively; while the shear axes represented by the subscripts 4, 5 and 6, respectively. This is shown in the Table of Symbols and Terminology.
For the piezoelectric charge coefficients (d), two subscripts are required. The first subscript refers to the direction of electric field or displacement and the second subscript gives the direction of mechanical stress or strain. Using equation 3.3, d33 can be defined as the ratio of the strain in the 3-direction to the field applied in the 3-direction of the piezoelectric body being mechanically free and not subjected to fields in the 1 and 2 directions.
Alternatively, using equation 3.4, d33 also denotes the ratio of charge per unit area perpendicular to the 3-direction to the stress applied in the 3-direction when the electrodes are open circuited. In this case the expression for d 33 is given by the following expression:
d33 = [ dD3 /dT3 ]E .....(3.7)
where D is the electric displacement in the Z-direction and T is the applied stress also applied in the Z-direction.
Measurement of d33
The expression defined by Equation 3.7 can be rewritten as follows:
d33 = [ (Q/A)(F/A ] = (Q/F) = (CV/F) .....(3.8)
where A is the area stressed by a force F, C is the capacitance in the circuit and V is the voltage generated. In this form, it follows that the d33 coefficient of a sample of known capacitance can be determined by measuring the voltage induced across the piezoelectric test piece for a given applied force.
In the case of the SensorTech Piezo-d meter, an applied force is applied to the piezoelectric sample at a given frequency and the rms voltage generated across the piezoelectric ceramic is monitored in order to determine the d33 coefficient.
Definition of Piezoelectric Constants
| Direct Effect | Reverse Effect | |||||||
| Charge Constant: dij |
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| Units | Coulomb/Newton | meter/Volt | ||||||
| Voltage Constant: gij |
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| Units | Volt.meter/Newton | meter2/Coulomb |