Higher-Order Temperature Coefficients of the Elastic Stiffinesses and Compliances of Alpha-Quartz

Bechmann, R.; Ballato, A.; Lukaszek, T.

doi:10.1109/jrproc.1962.288222

Cited by 335 publications

(41 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…The material constants of the quartz and their temperature coefficients used for the analysis are shown in Tables I and II, which are taken from Reference [8].…”

Section: Time Keeping Devicesmentioning

confidence: 99%

Temperature‐frequency characteristics simulation of piezoelectric resonators and their equivalent circuits based on three‐dimensional finite element modelling

Wakatsuki¹,

Kagawa²,

Suzuki³

et al. 2003

Int J Numerical Modelling

View full text Add to dashboard Cite

SUMMARYThe electromechanical resonators made of piezoelectric crystals such as a quartz crystal are widely used for electronic devices. Their frequency-temperature characteristics are of primary importance for their applications to the frequency control devices. The present paper demonstrates numerical simulation for several types of resonators using 3-D Finite Element Modelling. The results are compared with the theoretical values whenever they are available. As they are electronic devices, the equivalent circuit representation is often favourable for describing the admittance at the electrical terminals which enables the circuit analysis including the effect of the temperature change by using commercially available circuit simulators.

show abstract

“…The material constants of the quartz and their temperature coefficients used for the analysis are shown in Tables I and II, which are taken from Reference [8].…”

Section: Time Keeping Devicesmentioning

confidence: 99%

Temperature‐frequency characteristics simulation of piezoelectric resonators and their equivalent circuits based on three‐dimensional finite element modelling

Wakatsuki¹,

Kagawa²,

Suzuki³

et al. 2003

Int J Numerical Modelling

View full text Add to dashboard Cite

show abstract

“…A difficulty arises in Eq. (14) because the left-hand side is a matrL and it is not clear how to apply the near-resonance condition.…”

Section: Lnsjmentioning

confidence: 99%

“…This gives the clue for decoupling the amplitudes aL and a,s on the left-hand side of Eq. (14), thereby allowing the coupled wave approximation to be implemented. Under SAW -resonance' conditions for the m space harmonic the matrix on the left-hand side …”

Section: Lnsjmentioning

confidence: 99%

Temperature Compensation of Surface Transverse Waves for Stable Oscillator Applications

Auld

Thompson

1987

IEEE 1987 Ultrasonics Symposium

View full text Add to dashboard Cite

“…Although application of these methods at low temperatures is associated with technical problems. Alternatively, elastic coefficients can be accurately identified from the frequency-temperature measurements of plate resonators based on corresponding material [18,19]. This technique has been used to determine LGT coefficients at room temperatures [20].…”

mentioning

confidence: 99%

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

Goryachev

Abbé

Dulmet

et al. 2014

Applied Physics Letters

View full text Add to dashboard Cite

We present full characterisation of acoustic wave devices based on the fully synthetic crystalline material at the liquid helium temperature range required for the design of ultra low loss mechanical systems in many areas of research including frequency control and fundamental measurements. Temperature coefficients of the effective elastic tensor of Langatate (LGT) in Lagrangian representation are determined for the temperature range 3.8 − 15K. The Lagrangian formalism is mandatory in the analysed situation since the expansion coefficients of the LGT are still unknown at these temperatures. The measurement method involves a set of high-quality resonators of various cut angles, and uses measurements of frequency-temperature relations to extract the temperature coefficients of the elastic tensor. In addition, power sensitivity of LGT resonators at cryogenic temperatures is determined and dominant loss mechanism is identified.Recently low temperature applications of piezoelectric Bulk Acoustic Wave (BAW) devices has drawn serious attention due to their extraordinary quality factors [1][2][3]. Such applications include but not limited to frequency control systems [4], quantum hybrid devices[2, 5, 6] and atomic force spectroscopy. It is demonstrated [7,8] that in most of these applications, and in frequency control in particular [9], thermal response of such devices is critical and requires further improvement. For this purpose, thermal coefficient of the utilised material have to be identified at the liquid helium temperature range.Although langasite-type materials were initially developed as laser crystals, some of their properties make them very good candidates for frequency control applications. Like other compounds of this crystal family, Lanthanum gallium tantalite (La 3 Ga 5.5 Ta 0.5 O 14 ) or Langatate (LGT) belongs to the same trigonal crystal class 32 as quartz, and as a consequence exhibits similar properties. First, it is piezoelectric with an electromechanical coupling coefficient two to three times greater than that of quartz. These properties make Langatate ideal for variety of frequency-control applications including BAW and surface acoustic wave (SAW) resonators and filters [10]. BAW LGT resonators have already demonstrated their efficiency as master resonators in very stable oscillators [11]. Since LGT-based devices exhibit similar low phase noise and high Q regimes as quartz devices, they can also be classified as a low-loss material [12]. Nevertheless, such applications require careful selection of the material in terms of crystal quality. It should also be pointed out that LGT crystal can be made according to a purely synthetic process of growth whereas quartz crystal cannot be reproduce infinitely from synthetic seeds. Indeed, the crystalline quartz quality de-

show abstract

Higher-Order Temperature Coefficients of the Elastic Stiffinesses and Compliances of Alpha-Quartz

Cited by 335 publications

References 12 publications

Temperature‐frequency characteristics simulation of piezoelectric resonators and their equivalent circuits based on three‐dimensional finite element modelling

Temperature‐frequency characteristics simulation of piezoelectric resonators and their equivalent circuits based on three‐dimensional finite element modelling

Temperature Compensation of Surface Transverse Waves for Stable Oscillator Applications

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

Contact Info

Product

Resources

About