Piezoelectric measurement

Piezoelectric coefficients need to be measured accurately over a wide range of temperature, drive field amplitude, and frequency, in order to predict device performance appropriately. There are multiple methods available for such characterization in bulk materials and thin films. This paper overviews some of the standard characterization tools, with an emphasis on the methods utilized in the ieee Standard on Piezoelectricity. In addition, several of the evolving methods for making accurate piezoelectric coefficient measurements on thin films are reviewed. Some of the common artifacts in piezoelectric measurements, as well as means of avoiding them, are discussed. 

Piezoelectric measurements in bulk samples can also be made by applying an alternating stress and measuring the charge developed. Recent work in this area has been reported by Damjanovic and co-workers using a dynamic press apparatus [17]. In that work, the importance of measurement frequency and stress amplitude was also clearly pointed out. 

Temperature dependent piezoelectric measurements are difficult to carry out using interferometric optical techniques, although recently some progress has been made in this direction [13]. 

In this paper we shall try to demonstrate how these two techniques can be used not only for routine piezoelectric measurements, but to give a deeper insight into different processes operating in ferroelectric materials. 

In summary, we can conclude that the optical interferometry can be a useful technique not only for routine piezoelectric measurements but that it can reveal crucial information on different mechanisms operating in the material. 

Moldenhauer, H., Htinerbein, B., and Kala, H. (1972), Recording of pressure-path diagrams from an eccentric press using piezoelectric measurement, Pharmazie, 27, 417—418. 

Piezoelectric measurements have also been made on-line with supercritical extraction by using an FI interface such as that of Fig. 7.18C, which allowed the determination of fat in foods using the procedure described in Section 7.6.2 [120]. 

Both molecular and atomic detectors have been used in combination with SCF extractors for monitoring purposes. Thus, the techniques used in combination with SFE are infrared spectroscopy, spectrophotometry, fluorescence spectrometry, thermal lens spectrometry, atomic absorption and atomic emission spectroscopies, mass spectrometry, nuclear magnetic resonance spectroscopy, voltammetry, and piezoelectric measurements. 

Figure 6 shows a simulated binding curve in a piezoelectric measurement. A normal experiment is stopped by switching back to buffer flow and thus starting the dissociation phase. It is also obvious from Fig. 6 that at least a three times longer injection of analyte is required to reach a A/near the equilibrium. 

Piezoelectric effect is of fundamental importance for the piezoelectric measurements technology. General thermodynamic theory of a piezoelectric effect will be described more in details in this paragraph. Temperature or entropy a is held constant in the diagram according to Fig. 4.1. Hence the diagram is reduced just to the relationship between mechanical quantities or (stress or strain) and electrical quantities Ek or Dk (electric field or electric displacement). No special superscript for isothermal or adiabatic option is further used in linear piezoelectric equations of state. Omitting abovementioned thermal quantities, the system of 24 equations of state in Table 4.1 is reduced just to 8 equations - see Fig. 5.1 and Eqs. (5.1), (5.2), (5.3), (5.4), (5.5), (5.6), (5.7), and (5.8). 

Independent variables Ek and 7 belong to the free mechanical and electrical conditions. Piezoelectric effect is characterized by the coefficient dif in this case. Such situation is especially important for piezoelectric measurements technology. It is more or less fulfilled or at least assumed as fulfilled. Direct piezoelectric effect is described by... 

The piezoelectric measuring methods can be roughly divided in two groups, corresponding to the fact of whether the sensor works with a passive or an active principle. 

In case of the inverse contrast, the field oriented ferroelectric domains are looking as areas charged by electric current from the tip and only a comparison with piezoelectric measurements may finally show whether a ferroelectric has been switched or has not. Below we present the results of such a comparison (note, for all images below the tip is grounded, i.e. has a zero potential). 

The < 33 strain constant may be determined on bulk samples through converse piezoelectric measurements. As noted earlier, the strain constant is expressed in units of mA that are equivalent to C/N. Converse piezoelectric measurements are more experimentally difficult compared with the direct measurements, but provide greater accuracy. The converse measurements use an optical technique in order to measure the small strains in the sample caused by the application of a voltage. The experimental system is composed of a high voltage amplifier and interface as well as an optical... 

Figure 1.11 Butterfly loop observed in converse piezoelectric measurements. Reprinted with permission from Ok et al., Chem. Soc. Rev., 35, 710 (2006). Copyright (2006) Royal Society of Chemistry...

The sample preparation for a bulk pyroelectric measurement is very similar to what is required for a bulk piezoelectric measurement, namely a well-sintered ceramic disc that has been electrically poled. Determining the pyroelectric coefficient may be divided into two groups - the measurement of the pyroelectric current and the measurement of the charge. We will describe measurement techniques for both groups. In addition, the pyroelectric effect can be subdivided into primary and secondary effects. The primary effect is observed when the material is rigidly clamped under a constant strain to prevent any thermal expansion or contraction. Secondary effects occur when the material is permitted to deform, i.e. the material is under constant stress. Thermal expansion results in a strain that changes the spontaneous polarisation, attributable to the piezoelectric effect. Thus the secondary pyroelectric effect includes contributions caused by piezoelectricity. Exclusively measuring the pyroelectric coefficient under constant strain is experimentally very difficult. What is usually experimentally measured is the total pyroelectric effect exhibited by the material - the sum of the primary and secondary effects. 

A pressure sensor which is well suited to measure dynamic pressure changes is a quartz crystal (piezoelectric measurement). A charge across the crystal is proportional to the force on the crystal. This force results in a deformation which causes a subsequent short lasting change in flow of electric charge. These sensors ate therefore not suited to measure static pressures. 

Wu et al. [24) studied the effects of anisotropy and absorbed water on piezoelectric properties of nylon-9 and nylon-11. The piezoelectric measurements on polymorphs of nylon-ll and nylon-9 were carried out at various poling fields and temperatures. Piezoelectric constant for uniaxially stretched and poled a-nylon-9 was measured as a funetkw of angle between the orientation axis and applied tensile stress. The maximum piezoelectric constant dji was recorded when the tensile stress was applied in the extended direction, whereas the minimum ds was obtained when the stress was ap dicd to the film perpendicular to the extended duection. The d),/dj3 have a ratio of 10. Nylon-ll showed similar results. The angle dependence of the piezoelectiic constants and the ratio of djt/ dn were similar to the oriented form 1 PVDF film. 

Piezoelectric measurements use the appearance of an electrical polarization, or a variation in an existing polarization, in certain anisotropic dielectric materials, for example, quartz. This polarization appears when a force is applied in the appropriate direction. The piezoelectric effect is reversible because the material can deform or vibrate when an electric field is applied in the appropriate direction. Piezoelectric devices are used at their resonance frequencies for the determination of small variations in mass. These variations may result firom biological reactions that involve association or coupling, for example, enzyme-inhibitor associations or antigen-antibody coupling. 

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