Page 12 - Spring 2010

Fig. 3. A polyvinylidene fluoride (PVDF) based cell for measurement of the reso- nances of very small, fragile samples.
and eigenfunctions of a matrix with a size as large as 20,000 x 20,000 elements.
Thermoelectric rattlers
Anybody regularly filling the gas tank of a car has most likely wondered how to increase the number of miles the car travels on a gallon of gas. Realizing that two-thirds of a car’s fuel is emitted unused in the form of heat, makes one wonder if a significant portion of this waste-heat could be recovered and improve the car’s mileage. A generator using thermo- electric materials could, in principle, accomplish this feat. Thermoelectric materials, that are also found in the portable cooler that is powered from your car battery, generate electric currents when heat is applied and induce a change in tem- perature when an electric current passes through them. Not only could these materials lead to a noticeable reduction in fuel consumption, they could also replace today’s refrigera- tor-compressors with systems that have no moving parts and are ozone-layer friendly. So why is not every car and kitchen equipped with thermoelectric generators and refrigerators? There is a catch-22—the greatest thermoelectric efficiency comes from materials that have very good electrical conduc- tivity, but poor heat conductivity. Unfortunately, only a hand- ful of materials fit in this category, and thermoelectric research is focusing on increasingly complex materials that can reconcile these requirements. One set of materials that have promising thermoelectric properties are semiconduct- ing structures (hosts) that contain large, open voids. The abil- ity to populate these voids with other atoms (guests) makes them useful thermoelectrics. The guests tend to “rattle” in the oversized structure, which leads to a dramatic decrease in the thermal conductivity, while good electronic conductivity is maintained by the host.
Before looking into the elastic properties of these novel thermoelectric materials, it might be useful to briefly display “normal” elastic behavior. Such “normal” behavior is typified in Fig. 4—the elastic moduli gradually increase with decreas- ing temperature, and level off at low temperatures. The rattling guest atoms in the structures discussed in this section provide an elastic system of slightly more complex behavior, and the
specks of dust. The major difficulty for such small samples arises from the notion that for resonance, “the part that is being measured is the part that is storing the energy.” Thus a small sample requires small transducers—if one is to meas- ure the properties (e.g., temperature dependence) of the sam- ple, rather than those of the transducers, then the transduc- ers must be sufficiently smaller than the sample. In a similar fashion, reducing the transducer loading of a small sample requires small transducers. Another requirement for the transducers occurs because the small samples have high nat- ural frequencies, and this necessitates that the transducers be broadband. These restrictions led to the use of transducers made of thin piezoelectric film, polyvinylidene fluoride (PVDF), with dimensions of only 500 x 500 x 9 microns (Fig. 3).
A second potential problem is that some new materials are intended for applications for which the material must be in the form of a thin film on a substrate. The lattice mismatch between the substrate and the film produces strain and a shifted potential energy field for the new material. This results in modified (and presumably improved) properties for the new material. The strain mechanism causing the altered properties is readily probed by measuring the elastic properties of the film. The difficulty is that to measure the elastic constants of a film on a substrate, the film must occu- py a sufficient fraction of the whole sample. Roughly, if one can measure resonant frequencies to about ten parts per mil- lion, then the sample should be about 1/1000 of the whole sample. A film of a few hundred nanometers should be on a substrate with a thickness of a few hundred microns. Such samples are readily measured with the small sample RUS described above.
A third problem that may occur with new materials is that samples may be fragile or chemically reactive so that pol- ishing into a suitable shape for RUS is too risky. Such samples must be used “as is,” and the RUS’s theory must be modified to apply to an arbitrary shape. For such samples the Visscher
9 RUS analysis is replaced with a finite element method. For
the analysis, the shape of the sample as well as the acoustic field inside is fit with “isoparametric shape functions,” and a sophisticated computer code is used to find the eigenvalues
Fig. 4. Temperature
dependence of elastic constants for “normal” solids.
8 Acoustics Today, April 2010