X-ray diffraction on the X cut of a langasite crystal (La3Ga5SiO14) modulated by a Λ=12 μm Rayleigh surface acoustic wave (SAW) has been studied at the ESRF synchrotron radiation source. Due to the sinusoidal modulation of the crystal lattice involved by the SAW diffraction satellites appear on the rocking curve, with their number, angular positions, and intensities depending on the amplitude and wavelength of the ultrasonic superlattice. Full extinction of a specific satellite could be performed by adjusting the acoustic amplitude. It is shown that x-ray diffraction can be used to study surface acoustic wave field distributions in crystals.

X-ray Bragg diffraction from langasite crystal modulated by surface acoustic wave

This paper reports on a set of langatate (LGT) elastic constants extracted from room temperature to 1100°C using resonant ultrasound spectroscopy techniques and an accompanying assessment of these constants at high temperature. The evaluation of the constants employed SAW device measurements from room temperature to 900°C along 6 different LGT wafer orientations. Langatate parallelepipeds and wafers were aligned, cut, ground, and polished, and acoustic wave devices were fabricated at the University of Maine facilities along specific orientations for elastic constant extraction and validation. SAW delay lines were fabricated on LGT wafers prepared at the University of Maine using 100-nm platinum rhodium- zirconia electrodes capable of withstanding temperatures up to 1000°C. The numerical predictions based on the resonant ultrasound spectroscopy high-temperature constants were compared with SAW phase velocity, fractional frequency variation, and temperature coefficients of delay extracted from SAW delay line frequency response measurements. In particular, the difference between measured and predicted fractional frequency variation is less than 2% over the 25°C to 900°C temperature range and within the calculated and measured discrepancies. Multiple temperature-compensated orientations at high temperature were predicted and verified in this paper: 4 of the measured orientations had turnover temperatures (temperature coefficient of delay = 0) between 200 and 420°C, and 2 had turnover temperatures below 100°C. In summary, this work reports on extracted high-temperature elastic constants for LGT up to 1100°C, confirmed the validity of those constants by high-temperature SAW device measurements up to 900°C, and predicted and identified temperature-compensated LGT orientations at high temperature.

High-temperature langatate elastic constants and experimental validation up to 900°C

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 120degC are reported and discussed in this work.

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

Low hysteresis relative humidity sensing characteristics of graphene oxide–gold nanocomposite coated langasite crystal microbalance

This paper reports on the assessment of LGT acoustic material constants and temperature coefficients by surface acoustic wave (SAW) delay line measurements up to 130 °C. Based upon a full set of material constants recently reported by the authors, seven orientations in the LGT plane with Euler angles (90°, 23°, Ψ°) were identified for testing. Each of the seven selected orientations exhibited predicted coupling coefficients (K2) between 0.2% and 0.75% and also showed a large range of predicted temperature coefficient of delay (TCD) values around room temperature. Additionally, methods for estimating the uncertainty in predicted SAW propagation properties were developed and applied to SAW phase velocity and temperature coefficient of delay calculations. Starting from a purchased LGT boule, the SAW wafers used in this work were aligned, cut, ground, and polished at University of Maine facilities, followed by device fabrication and testing. Using repeated measurements of two devices on separate wafers for each of the seven orientations, the room temperature SAW phase velocities were extracted with a precision of 0.1% and found to be in agreement with the predicted values. The normalized frequency change and the temperature coefficient of delay for all seven orientations agreed with predictions within the uncertainty of the measurement and the predictions over the entire 120 °C temperature range measured. Two orientations, with Euler angles (90°, 23°, 123°) and (90°, 23°, 119°), were found to have high predicted coupling for LGT (K2 ≫ 0.5%) and were shown experimentally to exhibit temperature compensation in the vicinity of room temperature, with turnover temperatures at 50 and 60 °C, respectively.

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Assessment of langatate material constants and temperature coefficients using SAW delay line measurements

We have determined the elastic constants of langasite-type crystals (La3Ga5SiO14, La3Ga5.5Nb0.5O14, and La3Ga5.5Ta0.5O14) from measurements of the sound velocity of acoustic waves. Starting with the elastic tensor determined from bulk acoustic waves, we optimized the data set by investigating the influence of the elastic tensor components on the angular dispersion of surface guided waves. This procedure is particularly useful for accurate determination of the nondiagonal elements of the elastic tensor. Phase velocity calculations based on the new set of constants show an increased agreement with experimental data compared to the data set derived from bulk waves and previously published material data.

E. Chilla

Papers

Elastic properties of langasite-type crystals determined by bulk and surface acoustic waves