Page 20 - Winter 2008

Fig. 1. An RUS probe used to 290mK and 15T. The small metallic sample is just resting on the lower transducer, while the upper transducer is also only making contact with its own weight.
Recently, full utilization of digitally generated and acquired signals has made possible advances in measurement techniques for both PE and RUS that are not possible with purely analog systems. We describe here two key processes, one for PE, and one for RUS, that address the speed and noise issues in acquiring resonance data for RUS, and the ambigu- ity in determining the exact timing of an echoed pulse for PE.
Fast acquisition of swept-frequency RUS scans using digital signal processing
It is amusing to realize that all our laboratory work can be described as an analog to digital conversion because we begin with the analog processes to be studied and end with a file on a computer. Before we write a paper though, there is often an electronic conversion of some analog signal to a dig- ital approximation of it (A/D). This process is necessarily constrained in many ways, not the least of which is that we must use commercially available A/D converters that are lim- ited in speed, number of bits of precision, and have noise above the thermodynamic Johnson limit because of the com-
Fig. 2. Shown are: a) raw echoes from sample (S) and buffer rod (BR); b) the sam- ple echo; and c) the convoluted echoes as described in the text.
are accessible to everyone. Also both methods have deep sim- ilarities based on the most precisely measured quantities in all of science. Those quantities—frequency and time—are used by both PE and RUS. For PE, the time of flight of an acoustic pulse is measured by counting the number of cycles of a stable oscillator that pass during transit of the pulse through the specimen. For RUS, the frequency at maximum response of a specimen resonance is measured by subdividing the frequency of a precision oscillator, effectively a timing measurement. In Fig. 1 we show an RUS probe for use at low temperatures, and in Fig. 2 we show typical echoes from a PE system.
Let us compare the applicability of the two methods. For both methods, the specimen must have very accurate geom- etry and crystallographic orientation. For PE, transducers must be carefully bonded. This permits measurements at high pressure because the specimen and transducer can be a pressure vessel. For RUS, only weak contact is needed but is also required, making it easy to make a simple measurement but essentially impossible to use at other than pressures. RUS obtains the entire elastic tensor in one measurement, while PE requires a separate measurement and transducer location for each modulus. PE almost always gives a correct result that can be analyzed using a pocket calculator while RUS can give spurious results and requires a complex computer code9 for analysis.
18 Acoustics Today, January 2008