Abstract

A new solution to the problem of controllable focusing of ultrasonic beams is given. It consists in that the application of a nonuniform electric field of special configuration in piezoelectrics and ferroelectric ceramics causes a quadratic change of the velocity in the cross-section of an ultrasonic beam A new type of a controllable device for acoustic beams focusing - an electroacoustic lens - has been made. The dependence has been established of the focal length on the lens length and aperture as well as on the control voltage value and electroacoustic parameters of the material.

Table of contents

1. Introduction
2. Electroacoustic lenses made of electrostrictional ferroelectric ceramics
3. Electroacoustic lenses based on piezoelectric crystals
4. Experimental results and discussion
5. References

1 Introduction

The action of an external electric field on solids leads to a change in the phase velocity of the acoustic waves traveling in them In piezoelectric crystals the relative change in velocity ( AV/V ~ E)is proportional to the first power of the applied field. The linear electroacoustic effect exerts a weak action on the phase velocity and polarization state of acoustic waves traveling in a piezoelectric medium (dV/V ~ 10^-3 / 10^-2 % with E ~ 1 / 10 kV/cm).

To control the ultrasonic waves parameters under the action of an electric field, centrosymmetric paraelectrics with a strong deformation dependence of permittivity [1] are used in addition to piezoelectric crystal. In centrosymmetric paraelectrics and ferroelectric ceramics, the relative change in the acoustic wave velocity is proportional to the square of the electric field applied (dV/V~E²). In strongly electrostrictional ceramic materials relative change in velocity may reach a few percents [2] at field strength E ~ 1 / 10 kV/cm. Of special interest are the electrically induced acoustic effects in nonuniform electric fields. The application of such fields permits creating controllable devices for acoustic beams focusing - electroacoustic lenses.

2 Electroacoustic lenses made of electrostrictional ferroelectric ceramics

Figure 1: Focusing acoustic lens The possible designs of ferroelectric ceramic lenses for controllable focusing of longitudinally polarized ultrasonic waves are represented schematically in Fig. 1. To create a nonuniform electric field in the acoustic line one uses hyperbolic electrodes in the form of straight cylinders which guides are parallel to the z- axis. When a controllable external voltage is applied, the electric potential distribution is set inside the acoustic line:

(1)

where ₀ is the potential difference between the electrodes, 2R is the distance between the electrodes peaks.

The arising electric field with components causes, due to the electrostriction effect, a quadratic change in the velocity of acoustic waves in the section perpendicular to the direction of ultrasonic waves propagation. Let the longitudinal ultrasonic wave propagate along the z-axis (Fig. 1). In this case the focal length F of the spherical acoustic lens of length I is defined by the formula:

(2)

where d₁₁₁ is the component of the quadratic electrostriction tensor in the matrix representation, c₁₁ - modul of elasticity and n=V_akV_o - the ratio between the velocities V_ak in the external medium and V_o in the material of the acoustic line.

For example the values of the required parameters of BaTiO₃ are: d₁₂₂=10⁶ c₁₁=17*10¹⁰ H/m, =6,8*10³. If the spherical lens of length 1=5 cm and aperture 2R=2*10^-2 m is placed in water, then with the control potential ₀ =5*10³ V the focal length will be F=10 cm.

3 Electroacoustic lenses based on piezoelectric crystals

It is also possible to induce a quadratic change in acoustic waves velocity at cross-section of an ultrasonic beam propagating in piezoelectrics having a linear in field E electroacoustic effect. In this case the electrodes elements are described by the equation: 3x²y- y³ = +-R³, where 2R is the distance between the electrodes peaks in the direction of the y-axis.

When the electrodes are connected to the voltage source, the following potential distribution settles in the acoustic line:

(3)

Due to the linear electroelastic effect, at the electroacoustic lens section normal to the z-direction a linear in field and quadratic in (x,y)-coordinates change in ultrasound phase velocity arises.

In this case the longitudinally polarized acoustic beam is focused to form a line located at the distance from the output face of the device:

(4)
where Q is the electric nonlinear parameter.

Let us estimate the focal length of a lens having an aperture 2R = 1 cm and length L = 10 cm. This lens was made from a piezoelectric of the type of lithium niobate or bismuth germanate for which the electric nonlinear parameter has the value Q = 10 - s cm/V. At control voltage =10⁴ V the minimum focal length of this lens placed in water has the value F ~ 200 cm

4 Experimental results and discussion The spherical lens, shown in Fig. 1, was designed for experimental study. The working medium of the electroacoustic lens was made of ferroelectric ceramics based on solid solution of lead zirconate-niobate (PbZn1/3Nd1/3O3). The lens had geometrical dimensions 22 x 22 x 50 mm at the working aperture of ~ 17mm. A beam of longitudinally polarized ultrasonic waves with a frequency of 10 MHz was excited by plate 20 mm in diameter made of barium titanate piezoceramics and injected into the lens through the glass buffer. After passing through the lens, the ultrasonic beam was introduced through the glass buffer into a cell with distilled water. In experiments we measured the amplitude distribution of the acoustic field over the beam section at various distances from the output surface of the lens with various values of the control voltage. For example, Fig. 2 give the result of successive measurement of the acoustic field distribution over the beam section at distances 15 cm from the lens with control voltage values 0 (a) and 5kV (b). The spatial coordinates over the beam section are plotted on the axis x,y, and the ultrasound intensity is plotted along the vertical axis. For a given beam section the ultrasound intensity is normalized to the maximum value of the series dimensions obtained at different values of the control voltage. During the process of distribution measurement the acoustic beam power was held constant for the fixed section. It is seen from Fig. 2 that the cross-sectional dimension of the ultrasonic beam and its spatial distribution depend on the bias voltage value. Thus, with increasing control voltage the acoustic field power increases in the central part of the beam and there is a decrease in its diameter as to distribution half-height, which is indicative of controlled spherical focusing. For this type of ceramics and geometric dimensions of the electroacoustic lens, the focal length measured at 5kV is F=15 cm, and the beam intensity at the distribution maximum increases by more than three times compared to the zero control voltage.

Figure 2: The acoustic field distribution over the beam section at distances 15cm from the lens with control voltage values O (a) and 5 kV (b).

5 References

1. Belyi V.N. and Seuryk, B.B. Electric-field-induced acoustic anisotropy in centrosyrnmetric crystals with high dielectric perrnittivity, Sov.Phys.Crystallog., 1983, 28, 925-931.
2. Yushin,N.K, Dorogovtsev,S.N., Gulyamov,G. and Smirnov,S.I. Nonlinear electroacoustic effect in ferroelectrics with a diffuse phase transition, Solid State Physics, 1990, 32, 512-520.

Authors

International Conference "Computer Methods and Inverse Problems in
Nondestructive Testing and Diagnostics", 21-24 November 1995, Minsk, Belarus
Contact for the proceedings: DGZfP Deutsche Gesellschaft für Zerstörungsfreie Prüfung e.V.
Motardstraße 54 , 13629 Berlin, Germany
Telephone: + 49 (030) 386 29 911, Fax:.. /29 918,
Email: mail@dgzfp.de