Erwin Kittinger

Fundamentals of Piezoelectric Sensorics

The first € price and the £ and

Nonlinear piezoelectricity and electrostriction of alpha quartz

price are net prices, subject to local VAT. Prices indicated with * include VAT for books; the €(D) includes 7% for Germany, the €(A) includes 10% for Austria. Prices indicated with ** include VAT for electronic products; 19% for Germany, 20% for Austria. All prices exclusive of carriage charges. Prices and other details are subject to change without notice. All errors and omissions excepted. J. Tichý, J. Erhart, E. Kittinger, J. Prívratská Fundamentals of Piezoelectric Sensorics

Electroelastic effect in alpha quartz

Starting from the rotationally invariant nonlinear equations of electroelasticity the initial derivative of the propagation velocity of elastic waves with respect to the magnitude of an electric biasing field is derived. This derivative is given by an expression which is linear in third‐order material constants. From propagation measurements of ultrasonic waves under the application of a constant electric field, values for the eight independent components of the nonlinear piezoelectric tensor eKABCD and for the eight independent components of the electrostriction tensor lKLAB for alpha quartz are obtained. While some of the electrostriction constants remain rather uncertain, the nonlinear piezoelectric constants are determined with good accuracy.

Ferrobielastic hysteresis in α‐quartz

The electroelastic effect of α quartz is investigated by means of high‐resolution measurements of ultrasonic transit times as a function of a superimposed biasing field. Experimental results are reported for 25 different configurations of wave normal, displacement, and electric field vectors. It is shown that these results may consistently by expressed in terms of an effective fifth‐rank tensor with eight independent components.

The different sets of electrical, mechanical, and electromechanical third‐order constants for quartz

The ferrobielastic behavior of α‐quartz crystals under compressive stress has been investigated making use of the piezoelectric and piezo‐optic effects. The direction of mechanical stress was so chosen that secondary twinning is favored. Above a threshold of approximately 0.5 GPa, ferrobielastic switching results in a complete orientation reversal. Unexpectedly the mere removal of the mechanical constraint leads to a complete restoration of the original orientation. This retrotransition occurs between 0.1 and 0.025 GPa. This effect is discussed in terms of a simple thermodynamical model.

Elastic Properties of Crystals

Any combination of one mechanic, one electric, and one thermal variable may serve as a basis for the phenomenological characterization of piezoelectric crystals by material constants. According to this choice different, but interrelated, sets of constants arise. Based on a proper thermodynamic formulation, relations between the different sets of electrical, mechanical, and electromechanical third‐order constants of piezoelectric crystals are given and applied to experimental data on quartz. In this way four complete sets of these constants are obtained.

Relations between isothermal and adiabatic third‐order material constants of piezoelectric and pyroelectric crystals

The objective of present day physics is to describe and explain the properties of solid materials, in particular of crystals, on the basis of their atomic structure. In this chapter we will not pursue this aim. The treatment of matter here will be confined to the continuum model. In this model a body consists of a compact continuous set of material points. The boundary of this set of points is called the surface of the body. Frequently it is convenient to consider a body as a material element cut out of the surrounding continuum. The surface then separates the body under consideration from its surroundings.

Comments on ‘‘Material nonlinear piezoelectric coefficients for quartz’’

Depending on measurement conditions different choices of independent variables are used in the phenomenological description of piezo‐ and pyroelectricity. Eight different sets of material constants arise in this way on the basis of the commonly employed field variables resulting in a vast number of different but related third‐order constants. To cope with this fact a generalized notation is introduced for them. Starting from the proper rotationally invariant form of the electric Gibbs function and the electric enthalpy, the relations between isothermal and adiabatic third‐order material constants are derived. A numerical estimate for the nonlinear piezoelectric constants of α‐quartz is presented.

Correction procedure for measurements of the electroelastic effect in transverse fields

True material nonlinear piezoelectric coefficients must be applicable to the piezoelectric response of a crystal under static as well as under dynamic conditions. Experiments involving the static compression of quartz crystals in suitable geometries indicate that some of the nonlinear piezoelectric constants are considerably smaller than those given by R. Brendel [J. Appl. Phys. 54, 5339 (1983), 55, 608 (1984)].

Dependence of ultrasonic propagation velocities and transit times on an electric biasing field in alpha quartz

The determination of the dependence of the elastic stiffnesses of an applied dc field (electroelastic effect) by means of ultrasonic velocity measurements presents difficulties when electric fields perpendicular to the propagation direction are applied. In such a geometry the field is disturbed by the transducer. The magnitude of the field therefore varies along the path of the ultrasonic pulses. A simple method, based on the variation of the size of the field generating electrodes, to correct the measured field effect is described.