Single crystals, piezoelectric materials

Finkelmann, H and Eckert. T., Piezoelectricity of Sf- -liquid single crystal elastomers, Material Research Society 1996 Spring Meeting, San Franci.sco, April 8-12, 1996, Abstracts, 18.6. 

In contrast to polycrystaUine ceramic materials with ferroic properties, there exist nonferroic single crystal piezoelectrics such as a-quartz or materials with a calcium gaUium germanate (CGG) structure, as well as single crystal pyroelectrics with perovskite structure such as lithium tantalate (IiTa03). 

Various crystalline materials with desired properties have been synthesized, and this has driven the utilization of single crystals in the production of semiconductor, opto-electronic, piezoelectric, and pyroelectric materials. 

More recently methods have also been developed to measure the adsorbed amount on single surfaces and not onto powders. Adsorption to isolated surfaces can, for instance, be measured with a quartz crystal microbalance (QCM) [383]. The quartz crystal microbalance consists of a thin quartz crystal that is plated with electrodes on the top and bottom (Fig. 9.11). Since quartz is a piezoelectric material, the crystal can be deformed by an external voltage. By applying an AC voltage across the electrodes, the crystal can be excited to oscillate in a transverse shear mode at its resonance frequency. This resonance frequency is highly sensitive to the total oscillating mass. For an adsorption measurement, the surface is mounted on such a quartz crystal microbalance. Upon adsorption, the mass increases, which lowers the resonance frequency. This reduction of the resonance frequency is measured and the mass increase is calculated [384-387],... 

In many ferroelectric materials, the net piezoelectric effect is a result of both intrinsic and extrinsic responses. Here, intrinsic refers to the response that would result from an appropriately oriented single crystal (or ensemble thereof, in a polycrystalline sample). The extrinsic response is typically the result of motion of non-180° domain walls. The principle of these... 

Figure 2.4 Strain-field curves for < 001 > oriented 0.91PbZn1/3Nb2/303-0.09PbTi03 single crystals. The sample in (a) was poled at room temperature, where the resulting domain state is unstable (due to induction of tetragonal material associated with the curved morphotropic phase boundary), yielding substantial hysteresis. In (b) the crystal was poled at low temperatures to keep it in the rhombohedral phase. When measured at room temperature, the piezoelectric response is much more linear and non-hysteretic, due to the improved stability of the ferroelectric domain state. Data courtesy of S. E. Park.

In such a measurement, the sample is clamped as lightly as possible, and the displacement of the surface in monitored. The amount of sample clamping is important, because the mechanical constraints can impact the ferroelastic response of the sample. That is, in samples where the mechanical coercive stress is low, it is possible to change the domain state of the material by improperly clamping it in the sample fixture. This is especially important in elastically soft piezoelectrics, such as many of the relaxor ferroelectric PbTiC>3 single crystals. 

Lithium tantalate is a single-crystal material that is produced in quantity by the Czochralski method (see Section 3.11) for piezoelectric applications and is therefore readily available. It is stable in a hard vacuum to temperatures that allow outgassing procedures. It is insensitive to humidity. It is widely used where precise measurements are to be made. 

An example of a one-port device is the bulk resonator shown in Figure 6.1, which has a single, planar electrode on each side of a slab of piezoelectric material (these two electrodes together comprise a single port). Most often, the material takes the form of a disk and the electrodes are circular, covering less than the entire surface of the disk. Connection to an external circuit is typically made via a coaxial cable, with one of the two electrodes connected to the shield and the other to the center conductor. This device is known as a resonator because an external circuit (see Section 6.3.3.2) excites the piezoelectric substrate in such a way that a standing wave is set up in the crystal, which thus resonates. 

In the gravimetric method, the adsorbent (usually in the form of powder) is placed into a bulb, which is mounted on a sensitive balance and the bulb is then evacuated. Next, the weight increase of the adsorbent solid as a function of the absorptive gas pressure is monitored at constant temperature. More recently, the quartz crystal microbalance (QCM) technique has been applied this is very sensitive to mass increases. Quartz is a piezoelectric material and the thin crystal can be excited to oscillate in a traverse shear mode at its resonance frequency when a.c. voltage is applied across the metal (usually gold) electrodes, which are layered on two faces of the crystal. When the mass on the crystal increases upon adsorption, its resonance frequency decreases. The increase in the mass is calculated from the reduction in resonance frequency. On the other hand, adsorption on single flat surfaces can also be measured by ellipsometry, which measures the film thickness of transparent films optically using the difference between light reflection from bare and adsorbed surfaces. 

To understand why ceramics have particular structures and why certain defects form in these structures, it is really important to understand Pauling s rules. These rules require you to visualize a tetrahedron and an octahedron and to see how they fit together. To understand properties such as piezoelectricity or the mechanisms of phase transformations, you must be able to visualize the crystal structure of the material. This is particularly important when we want to predict the properties of single crystals. We summarize the features of crystallography that we use throughout the text and give references to more specialized resources for rigorous proof of theorems and more detailed discussion. 

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