Temperature coefficients of crystalline-quartz elastic constants over the cryogenic range [4 K, 15 K]

TL;DR

This study measures the temperature coefficients of synthetic quartz elastic constants at cryogenic temperatures (4 K to 15 K) using resonance frequency data, aiding the design of ultra-low loss quartz devices.

Contribution

It provides new experimental data on quartz elastic constants at cryogenic temperatures, crucial for designing temperature-stable quartz devices.

Findings

Elastic constants vary with temperature in the cryogenic range.

Resonance frequency data can accurately determine elastic constant coefficients.

Results support improved design of quartz-based ultra-low loss systems.

Abstract

This paper brings out results of a measurement campaign aiming to determine the temperature coefficients of synthetic quartz elastic constants at liquid helium temperature. The method is based on the relationship between the resonance frequencies of a quartz acoustic cavity and the elastic constants of the material. The temperature coefficients of the elastic constants are extracted from experimental frequency-temperature data collected from a set of resonators of various cut angles, because of the anisotropy of quartz, measured on the very useful cryogenic range [4 K - 15 K]. The knowledge of these temperature coefficients would allow to further design either quartz temperature sensors or conversely frequency-temperature compensated quartz cuts. With extremely low losses, lower than $10^{-9}$ for the best ones, key applications of such devices are ultra-low loss mechanical systems used in many research areas including frequency control and fundamental measurements. The Eulerian formalism is used in this study to identify the temperature coefficients.