Frequency-temperature relations of novel cuts of quartz crystals for thickness-shear resonators

TL;DR

This study identifies novel quartz crystal cuts with cubic frequency-temperature relations, enabling the fabrication of resonators with stable frequencies near operating temperatures, thus improving thermal stability.

Contribution

The paper introduces new quartz crystal cuts exhibiting cubic frequency-temperature relations, expanding beyond traditional AT- and SC-cuts, and confirms their superior thermal stability through theoretical analysis.

Findings

New cuts exhibit cubic frequency-temperature relations.

Resonators with new cuts achieve comparable stability to traditional cuts.

Theoretical analysis confirms improved frequency stability.

Abstract

In a recent study, we have reported that there are many novel cuts of quartz crystal exhibiting the highly treasured cubic frequency-temperature relations which are currently shown only with the AT- and SC-cut. Through setting the first- and second-order derivatives of the frequency respect to temperature to zeroes, a family of quartz crystal cuts with different temperatures of zero frequency (turnover temperatures) has been found and examined. It is now possible to fabricate quartz crystal resonators with turnover temperature near its operating temperature to keep the resonator functioning in a lean and more natural state. By selecting a few cuts based on orientations from our study, we analyzed the thickness-shear vibrations of quartz crystal plates to confirm the superior frequency-temperature relations with the theory of incremental thermal field and Mindlin plate equations and presenting comparisons with known AT- and SC-cut to demonstrate that resonators with newly found cuts can also achieve exceptional frequency stability as demanded.