Pulse echo and combined resonance techniques: a full set of LGT acoustic wave constants and temperature coefficients

Abstract

This work reports on the determination of langatate elastic and piezoelectric constants and their associated temperature coefficients employing 2 independent methods, the pulse echo overlap (PEO) and a combined resonance technique (CRT) to measure bulk acoustic wave (BAW) phase velocities. Details on the measurement techniques are provided and discussed, including the analysis of the couplant material in the PEO technique used to couple signal to the sample, which showed to be an order of magnitude more relevant than the experimental errors involved in the data extraction. At room temperature, elastic and piezoelectric constants were extracted by the PEO and the CRT methods and showed results consistent to within a few percent for the elastic constants. Both raw acquired data and optimized constants, based on minimization routines applied to all the modes involved in the measurements, are provided and discussed. Comparison between the elastic constants and their temperature behavior with the literature reveals the recent efforts toward the consistent growth and characterization of LGT, in spite of significant variations (between 1 and 30%) among the constants extracted by different groups at room temperature. The density, dielectric permittivity constants, and respective temperature coefficients used in this work have also been independently determined based on samples from the same crystal boule. The temperature behavior of the BAW modes was extracted using the CRT technique, which has the advantage of not relying on temperature dependent acoustic couplants. Finally, the extracted temperature coefficients for the elastic and piezoelectric constants between room temperature and 120 degrees C are reported and discussed in this work.

Evaluation of the transmission line model for couplant layer corrections in pulse-echo measurements

“…2) was used to model the acoustic coupling layer [4], [10]. When comparing the buffer rod reflection with the first sample reflection (labeled B and c in Fig.…”

“…The precision of a v p extracted through PE measurements is typically ~10 −3 for samples of a few millimeters in size and is usually limited by measurement precision of the physical length of the sample, assuming that the ToF can be measured to at least an order of magnitude better in precision [4]. If the physical dimensions of the sample can be measured without bias, the accuracy of the determined phase velocity is limited entirely by the accuracy with which one can determine the ToF in the sample.…”

“…The phase shifts acquired by the acoustic waves upon reflection from and transmission through interfaces combine to lead to a difference between measured time delay (the delay between the arrival of echoes B and c in Fig. 1) and the actual transit time in the sample at any given frequency, f [4], [7]- [11]:…”

“…1 by the acoustic wave. The need to account for this phase shift in determining the correct ToF in the sample has been recognized for many years [9] and has been addressed by several authors [4], [7]- [11]. It is interesting to note that the effects of the couplant can be avoided altogether through use of an immersion ToF technique such as is described in [12].…”

Measurements of elastic properties of langatate at liquid helium temperatures for design of ultra low loss mechanical systems

“…Since all these coefficients are temperature dependent, the knowledge of this dependence is essential for predicting resonance frequency sensitivity to temperature and corresponding stability. Various methods have been used to determine such coefficients from phase velocity measurement by a pulse echo overlap method, or resonant ultrasound spectroscopy and combined resonance techniques [14,15], or by means of laser ultrasonic techniques [16,17]. Although application of these methods at low temperatures is associated with technical problems.…”