Advanced Piezoceramics, Ultrasonic Transducers & Devices
Piezoceramics
Home > Basic Material Testing
Basic Material Testing
Typical laboratory equipment can be used to measure dielectric, elastic, and piezoelectric constants for piezoceramics. MIL-STD (military standard) 1376B, ANSI/IEEE Standard 176-1987, and European Standard EN 50324:2002, as well as IRE Standards on Piezoelectric Crystals (1961), all describe their preferred methods for taking measurements. Some of those step-by-step procedures are described here for the familiar constants listed below.
Coupling Factors k33 k3 kp
Free Relative Dielectric Constant K3T
Dissipation Factor (Low field) D or tan δ
Elastic-Compliances SD33 SE33 SD11 SE11
Piezoelectric d and g constants d33 g33 d31 g31
Mechanical Q Qm
Test Specimens
Samples of various specific shapes are used to avoid large errors in determining some of the constants. Determining different constants require the use of various different shapes. These shapes often do not include the practical shapes found in transducers, because they are not appropriate for measuring many of the constants. Three different shape configurations (as shown in Fig. 1) are required to measure all the above listed constants.
The measurements that must be performed on the test specimens are:
Weight – or Density
Free capacitance and dissipation factor – (low field)
Frequency of minimum impedance and frequency of maximum impedance
The magnitude of the minimum impedance.
The data obtained from these measurements are used to calculate the various constants.
To perform these measurements, the following equipment is required:
Laboratory balance capable of weighing to accuracy of about 1 milligram.
Micrometer(s) with range(s) to measure all dimensions of the test specimens.
Capacitance (and dissipation) bridge capable of covering the range of about 10 pf to 10,000 pf with accuracy of better than 1%.
Impedance analyzer capable of covering the frequency range of about 100 KHz to 10 MHz with an accuracy of about 1%.
Quasi-static d33 meter such as a 'Berlincourt' meter.
Measurement Procedure
The steps necessary to determine the constants are as follows:
From Fig. 1, select specimen shape or shapes required for the constants to be determined.
Make the measurements indicated below. See the following paragraphs for detailed instructions.
Calculate the constants from the measured data as explained in detail later in this report.
Measurement of Weight
Weigh the test specimen in air. This is required, together with dimensions, for determination of density. If preferred, the density may be determined by weighing the specimen in air and then in water by the method of Archimedes.
Measurement of Dimensions
Measure the dimensions of the test specimen with a micrometer. It is advisable to measure at several points and use the averages of these measurements.
Measurement of Capacitance and Dissipation
Measure the capacitance C and the dissipation factor D at 1 KHz. Keep the test voltage across the specimen below: 100 x (distance between electrodes measured in inches) volts.
Measurement of Frequencies of Minimum and Maximum Impedances
Sweep frequency over the expected resonant frequency of the part geometry being tested. Choose a range of approximately +/- 20% around this frequency. Determine the frequency at which the impedance is at a minimum and where it is at a maximum over this range.
Measurement of Magnitude of Minimum Impedance
The set up for this measurement is the same as for the measurement of frequencies of minimum impedance. Measure the value at the minimum point and record this value as Zm.
Calculation of Density
The density in Kilograms/cubic meter is required in later calculations.
Calculation of Free Relative Dielectric Constant KT33
This is calculated from the measured values of capacitance and physical dimensions of the specimen.
Calculation of Coupling
Coupling is calculated from the frequencies of minimum and maximum impedances. The applicable formula depends on the vibration mode as shown below. The frequencies of minimum and maximum impedances are not the exact frequencies required for these calculations, and a small correction theoretically should be made as described in the IRE Standards. However, when dealing with Lead Zirconate-Lead Titanate compositions, the error resulting from omitting the correction is not significant. Accordingly, the corrections generally are not made and will not be included here.
Calculation of Coupling k33
This is applicable only to length poled rods as shown in Fig. 1.
This is applicable only to long, slim thickness Poled specimens as shown in Fig. 1.
Calculation of Coupling kp
This is applicable only to thin discs as shown in Fig. 1.
Calculate: (fn – fm) / fm
Use the curve Fig. 8 to determine kp. Fig. 8 is valid only for piezoelectric ceramic having Poisson's ratio near 0.3. Presently available Lead Titanate-Lead Zirconate compositions meet this requirement.
Calculation of Elastic Constants
Elastic constants are calculated from the frequency controlling dimension, density, and the frequencies of minimum or maximum Impedance as shown below. Physical dimensions must be in meters.
Calculation of Coupling SD33
Calculation of Coupling SE33
This is applicable only to long, slim, thickness poled specimens as shown in Fig. 1.
Calculation of Piezoelectric Constants
The d and g constants are calculated from values of coupling, dielectric constant, and elastic constant previously calculated.
Calculation of Piezoelectric Constant d33
Calculation of Piezoelectric Constant g33
Calculation of Mechanical Q
This is calculated from the frequencies on minimum and maximum impedance, the magnitude of the minimum impedance, and capacitance.
Piezo Basics
Origin of the Piezo Effect
Material Families
Tolerances and Capabilities
Modes of Vibration (PDF)
Back to Ultrasonic Basics Main Page
Piezoelectric Ceramics
Materials Chart
Modified Bismuth Titanate (K-15)
Modified Lead Metaniobate (K-81, 83, 85, 91)
Modified Lead Zirconate Titanate (K-181, 182, 183, 270, 278, 300, 320, 340, 350, 500, 600, 740)
Modified Lead Titanate (Nova 3B)
Ultrasonic Transducers
Air-In-Line (AIL)
Contact Transducers
Downhole Transducers
Dual Element
High Power Transducers
Immersion Transducers
Medical / HIFU
Assembly Process / NHA
Quality / Certifications
Ultrasonic Basics
Piezo Technologies – Headquarters, Manufacturing & Product Development
8431 Georgetown Road, Suite 300 - Indianapolis, IN 46268 - Ph: +1.317.876.4670
At Amphenol-ASTG, we make Quality, Safety and Environmental Protection a top priority. We believe that making sustainable choices in the way we conduct our business creates short-term and long-term value for our stakeholders. We do not create long-term value by merely complying with regulations, but we go beyond compliance to find ways to green our operations and our products to ensure continuity of the material and human resources that we need to operate the business.
Serving the United States, including California, Los Angeles, San Francisco, San Diego, Colorado, Denver, Connecticut, Delaware, Florida, Georgia, Atlanta, Illinois, Chicago, Springfield, Indiana, Terre Haute, Lafayette, Evansville, Bloomington, Columbus, Muncie, Fort Wayne, South Bend, Kokomo, Kentucky, Louisville, Lexington, Maryland, Massachusetts, Michigan, Detroit, Lansing, Grand Rapids, Minnesota, Minneapolis, Missouri, St. Louis, Nevada, New Hampshire, New Jersey, New York, North Carolina, Ohio, Cincinnati, Columbus, Dayton, Toledo, Cleveland, Oregon, Pennsylvania, Rhode Island, Texas, Houston, Dallas, Utah, Vermont, Washington, Wisconsin, as well as Canada and Mexico, and more.
© 2022 Piezo Technologies. All Rights Reserved.
Privacy | Terms of Sale
We are using cookies to give you the best experience on our website. Our Privacy Policy has been updated.
You can find out more about which cookies we are using or switch them off by changing your browser settings.