Lithium niobate , piezoelectric

Of all the piezoelectric crystals that are available for use as shock-wave transducers, the two that have received the most attention are x-cut quartz and lithium-niobate crystals (Graham and Reed, 1978). They are the most accurately characterized stress-wave transducers available for stresses up to 4 GPa and 1.8 GPa, respectively, and they are widely used within their stress ranges. They are relatively simple, accurate gauges which require a minimum of data analysis to arrive at the observed pressure history. They are used in a thick gauge mode, in which the shock wave coming through the specimen is... 

The piezoelectric behavior of both quartz and lithium niobate has been studied in a series of careful, systematic investigations. (See Graham and coworkers [65G01, 70101, 75G04].) The experimental arrangement is shown Fig. 4.2. The impactor, preferably the same material as the piezoelectric sample (but perhaps another standard material), is accelerated to a preselected... 

Fig. 4.2. The technique used to study the piezoelectric behavior of the crystals quartz and lithium niobate used controlled, precise impact loading. The impact velocity can be measured to an accuracy of 0.1%, leading to the most precisely known condition in shock-compression science (after Davison and Graham [79D01]).

Fig. 4.3. Typical normalized piezoelectric current-versus-time responses are compared for x-cut quartz, z-cut lithium niobate, and y-cut lithium niobate. The y-cut response is distorted in time due to propagation of both longitudinal and shear components. In the other crystals, the increases of current in time can be described with finite strain, dielectric constant change, and electromechanical coupling as predicted by theory (after Davison and Graham [79D01]).

Fig. 4.4. The piezoelectric charge produced by elastic strain in x-cut quartz and z-cut lithium niobate is well represented by a quadratic relationship without a need for fourth-order contributions.

The measured relationships between piezoelectric polarization and strain for x-cut quartz and z-cut lithium niobate are found to be well fit by a quadratic relation as shown in Fig. 4.4. In both materials a significant nonlinear piezoelectric effect is indicated. The effect in lithium niobate is particularly notable because the measurements are limited to much smaller strains than those to which quartz can be subjected. The quadratic polynomial fits are used to determine the second- and third-order piezoelectric constants and are summarized in Table 4.1. Elastic constants determined in these investigations were shown in Chap. 2. 

The determination of piezoelectric constants from current pulses is based on interpretation of wave shapes in the weak-coupling approximation. It is of interest to use the wave shapes to evaluate the degree of approximation involved in the various models of piezoelectric response. Such an evaluation is shown in Fig. 4.5, in which normalized current-time wave forms calculated from various models are shown for x-cut quartz and z-cut lithium niobate. In both cases the differences between the fully coupled and weakly coupled solutions are observed to be about 1%, which is within the accuracy limits of the calculations. Hence, for both quartz and lithium niobate, weakly coupled solutions appear adequate for interpretation of observed current-time waveforms. On the other hand, the adequacy of the uncoupled solution is significantly different for the two materials. For x-cut quartz the maximum error of about 1%-1.5% for the nonlinear-uncoupled solution is suitable for all but the most precise interpretation. For z-cut lithium niobate the maximum error of about 8% for the nonlinear-uncoupled solution is greater than that considered acceptable for most cases. The linear-uncoupled solution is seriously in error in each case as it neglects both strain and coupling. 

The piezoelectric constant studies are perhaps the most unique of the shock studies in the elastic range. The various investigations on quartz and lithium niobate represent perhaps the most detailed investigation ever conducted on shock-compressed matter. The direct measurement of the piezoelectric polarization at large strain has resulted in perhaps the most precise determinations of the linear constants for quartz and lithium niobate by any technique. The direct nature of the shock measurements is in sharp contrast to the ultrasonic studies in which the piezoelectric constants are determined indirectly as changes in wavespeed for various electrical boundary conditions. 

The most distinctive aspect of the shock work is the determination of higher-order piezoelectric constants. The values determined for the constants are, by far, the most accurate available for quartz and lithium niobate, again due to the direct nature of the measurements. Unfortunately it has not been possible to determine the full set of constants. Given the expense and destructive nature of the shock experiment, it is unlikely that a full set of higher-order piezoelectric constants can be determined. A less expensive investigation of higher-order constants could be conducted with the ramp wave or acceleration wave loading experiment described in the chapter. 

In this book those ferroelectric solids that respond to shock compression in a purely piezoelectric mode such as lithium niobate and PVDF are considered piezoelectrics. As was the case for piezoelectrics, the pioneering work in this area was carried out by Neilson [57A01]. Unlike piezoelectrics, our knowledge of the response of ferroelectric solids to shock compression is in sharp contrast to that of piezoelectric solids. The electrical properties of several piezoelectric crystals are known in quantitative detail within the elastic range and semiquantitatively in the high stress range. The electrical responses of ferroelectrics are poorly characterized under shock compression and it is difficult to determine properties as such. It is not certain that the relative contributions of dominant physical phenomena have been correctly identified, and detailed, quantitative materials descriptions are not available. 

In this chapter studies of physical effects within the elastic deformation range were extended into stress regions where there are substantial contributions to physical processes from both elastic and inelastic deformation. Those studies include the piezoelectric responses of the piezoelectric crystals, quartz and lithium niobate, similar work on the piezoelectric polymer PVDF, ferroelectric solids, and ferromagnetic alloys which exhibit second- and first-order phase transformations. The resistance of metals has been investigated along with the distinctive shock phenomenon, shock-induced polarization. 

There are two principal types of materials that can function as piezoelectrics the ceramics and polymers. The piezoelectric materials most widely used are the piezoceramics based on the lead zirconate titanate, PZT, formations, mixed sodium and potassium niobates, lithium niobate, and quartz. The advantages of these piezoceramics are that they have a high piezoelectric activity and they can be fabricated in many different shapes. 

In general, the strains resulting from an applied field increase with the magnitude of the piezoelectric constants C/y 0 that lithium niobate, for example, exhibits larger strains than does gallium arsenide for a given electric field. However, die particular strain pattern found depends on the form of the piezoelectric matrix (and hence, on the crystal class involved) as well as the electric field direction. 

The most common SAW devices are based on quartz or lithium niobate. Eventually, piezoelectric LB films may be used to launch the surface waves. To date, however, the reported values of the piezoelectric coeflBcients in monolayers are too small (64). In SAW devices, input and output inter-digitated electrodes are defined with lithography. These electrodes perform... 

Two approaches are proposed to resolve this difficulty. The first is based on generation of a high-purity acoustic field in a spherical, unharmonic resonator, and the second is based on comparison of a set of transducers with limited but overlapping dynamic ranges. In the second approach, simultaneous measurement of a broadband signal produces an accurate characterization over the entire range. Candidates for sensor fabrication include solid dielectric capacitive sensors, piezoelectric transducers, and high-temperature lithium niobate or quartz transducers. 

Smith RT, Welsh FS (1971) Temperature dependence of the elastic, piezoelectric, and dielectric constants of lithium tantalate and lithium niobate. J Appl Phys 42 2219... 

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