Quartz crystal resonators can exhibit huge quality factors (in excess of 1 billion) at liquid-helium temperature. However, they must satisfy a set of conditions to meet this high level of performance. With the help of experimentation, the main conditions are identified, such as the material quality, the energy trapping due to the vibrational mode structure, as well as the corresponding influence of the support mechanism and the effects of the electrodes.
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Galliou et al. (2015) studied this question.
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