Methods for measuring piezoelectric, elastic, and dielectric coefficients of crystals and ceramics

I. INTRODUCTION T HE FUNDAMENTAL PROPERTIES of interest in a piezoelectric crystal or electrostrictive ceramic are the piezoelectric or "equivalent" piezoelectric constant of the material, the dielectric constant and dielectric loss of the material, the elastic constants and elastic losses of the materials, and the variations of these properties with temperature, humidity and pressure, as well as frequency and amplitude of signal. Dependence on the latter two is of significance primarily in ferroelectric materials, whose properties moreover may show marked dependence on previous history. A number of methods have been used to measure these properties and it is the purpose of this paper to describe the advantages and disadvantages of these methods and to recommend certain preferred methods. By using such methods as fundamental standards it is the hope that the measured properties of new crystals and electrostrictive ceramics made by different investigators will be more comparable and reliable.
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PROCEEDINGS OF THE I-R-E
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III. MEASUREMENTS ON LARGE-SIZED CRYSTALS A. Capacitance Measurements at Low and High Fre-
II. METHODS FOR INVESTIGATING SMALL SIZE SPECIMENS time and effort necessary to measure and Since the grow large-sized piezoelectric crystals are very considerable, and since special growing techniques are often re-quired for specific crystals, it is a matter of some importance to obtain methods for eliminating nonpromising crystals in the small-grain size state, since these are rather easily grown in beakers by spontaneous seeding. Two methods have been used for this purpose, the click oscillator and a balanced capacity bridge method.
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For the click oscillator,' a number of grains of the substance are inserted between two electrodes which are placed across the plates of the oscillator as shown by Fig. 1. The frequency of the oscillator is changed by varying the tuning condenser C, and if a resonance of one of the piezoelectric crystals occurs near the oscillator frequency, the frequency of the oscillator will be briefly controlled by the crystal resonances. As the condenser is turned further, the frequency jumps from the crystal frequency to that determined by the condenser.
1 This method was first discovered by W. G. Cady ("The piezoelectric resonator," PROC. I.R.E., vol. 10, pp. 83-114; 1922) and has been applied systematically by E. Giebe and A. Scheibe ("A simple method for qualitative indication of piezoelectricity in crystals," Zs. Ph., vol. 33, pp. 760-766; 1925) to obtain a qualitative indication of piezoelectric properties. 2 "Piezoelectric Crystals and Their Application to Ultrasonics," W. P. Mason, D. Van Nostrand & Co., New York, N. Y., pp. 49-50;
Summary-This paper considers methods for measuring the piezoelectric, dielectric, and elastic coefficients of crystals and ceramics and recommends certain preferred methods of measurement. Static measurements are not considered to be as satisfactory as dynamic measurements. Of the dynamic methods, measurements of the resonant and anti-resonant frequencies, the low frequency capacitance and the resistance at resonance appear to be the simplest and most accurate method, provided that the ratio of Qlr is high. Quasi-static methods are useful for crystals having a low ratio of Qlr, for determining the sign of the piezoelectric coefficients, and for production checks. Hydrostatic methods are useful for complicated crystals such as monoclinic types and for measuring a sum of two of the coefficients of electrostrictive ceramics. This measurement can be carried out for odd-shaped samillator circuit.
This jump in frequency is accompanied by a change in the plate current, so that a pair of head phones or a loud speaker attached to the plate circuit of the oscillator will produce an acoustic click. By following the tube with an audio amplifier, weaker clicks can be heard. By changing the oscillator frequency over a wide range, a number of possible resonances will be determined. This is a qualitative method since the loudness of the clicks cannot be related to the electromechanical coupling in the crystal or the crystal's Q. The bridge method, (Fig. 2, p. 922) consists in placing a number of crystal grains between two electrodes which are in one arm of a capacitance bridge. An oscillator is connected to the input and a sensitive detector to the output of the bridge. The capacitance Ci is balanced outside the crystal-resonance range so that a minimum of current occurs in the detector. As the frequency is changed, the bridge becomes unbalanced as a crystal resonance is approached and the amount of unbalance can be shown2 to be determined by the ratio of