Measurement of Material Constants

Measurement of Material Constants
The properties of ceramics are strongly dependent on the process route and show systematic and statistical fluctuations within a given batch. The fluctuations are caused by inhomogeneous chemical composition, mechanical differences in the forming process, chemical modification during sintering, and the polarization method. The maximum variance of properties is as follows:

Elastic: 5%
Piezoelectric: 10%
Dielectric: 20%

It is also necessary to pay special attention to the specimen holders during measurements. The ceramics must generally be held at the nodal points of vibration so that the clamp will not change the measured properties. The high values of permittivity and the low QM encountered with the ceramics put less stringent requirements on stray capacitance etc. The high piezoelectric coupling factors generally require that approximations in the calculation of coupling coefficients must be used with caution.
 

Test Specimens:
The piezoelectric material constants re expressed in rationalized mks units. To make accurate measurments of various constants, it is necessary to perform experiments on test specimens which are dimensioned to provide appropriate boundary conditions for the specific piezolectric modes. These are listed in Table-2.

Table 2:

Mode Specimen Size(mm)

Material Constants
to be determined
Planar 1.0 x 16.0
(h x Df)		 kp, K3T, Tan δ, ρ, QM
Thickness
(33 Mode)		 16.0 x 6.35
(h x Df)		 kp, K3T, Tan δ, ρ, QM

d33, g33,S33D, S33E

Shear
(15 Mode)

 12 x 10 x 0.2
(l x w x h)		 kp, K3T, Tan δ, ρ, QM

d31, g31,S11D, S11E

 

Measurement of Density:
Density can be measured using a balance and a micrometer. A buoyancy technique (please see reference 7) provides a better accuracy and has the advantage that measurements can be made on any shape. The density ρ can be calculated as follows:

Measurement of Dielectric Constant and Dissipation Factor:
The dielectric contact (K) and dissipation factor (Tan d) can be measured using a standard impedance bridge or an impedance analyzer, both of which provide a direct reading. Measurements are generally carried out at 1 kHz to measure static (away from mechanical resonance) parameters at low applied electric field.

Equivalent Circuit:
A piezoelectric element operating at or near its resonance frequency can be characterized by an equivalent circuit shown in Figure 6. The series and parallel resonant frequencies, Fr and Fa respectively, are given by the following equations:

 

 Figure 6: Resonator


 

 

Measurement of Resonant Frequencies
The resonant frequencies can be measured using constant voltage and constant current circuits show respectively in Figure 7-1 and 7-2. The variation of impedance and admittance of the piezoelectric ceramic element as a function of the frequency are also shown in Figure 8-1 and 8-2 respectively. The piezoelectric material behaves capacitively below Fr and above Fa. Between Fr and Fa, it behaves inductively. The phase angle of the element also undergoes a sign change at both the resonance frequencies, and is often used in the measurement of resonant frequencies. This is shown in Figure 8-3.
 
 
     
 


STANDARDS

  1. IEEE Standard on Piezoelectricity (IEEE Standard 176-1978); Institute of Electrical and Electronic Engineers Inc., 345 East 47th St, New York, NY 10017. 55 Pages.
  2. IRE standards on Piezoelectric Crystals: Measurements of Piezoelectric Ceramics; 1961 (IEEE Standard 179-1961). Proceedings of the IRE, 1961, pp1161-1169.
  3. Methods for Measuring Piezoelectric, Elastic and Dielectric Coefficients of Crystals and Ceramics; W.P. Mason, H. Jaffe., (IEE Standard 178-1958). Proceedings of the IRE, 42, 1954, pp921-930.
  4. Piezoelectric Ceramic Materials and Measurement Guidelines for Sonar Transducers DOD-STD-1376A, 25 August 1985.
  5. IEC Standard Publication 642, 1979. Piezoelectric Ceramic Resonators and Resonator Circuits for Frequency Control and Selection. Bureau Central de la Commission Electrotechnique Internationale, 1 rue de Vexembé, Gen ève, Swisse. 48 Pages.
  6. Tentative Method of Testing for D-C Volume Resistivity of Glass, ASTM Designation: C657- 70T.
  7. Tentative Method of Testing for Density of Glass by Buoyancy, ASTM Designation: C693-71T.