The Angular Dependence of Piezoelectric Plate Frequencies and Their Temperature Coefficients

Abstract

Doubly rotated plate vibrators of quartz are hewn t o possess a locus of zero f i r s t o r d e r temperature coe f f i c i e n t of frequency f o r a l l v a l u e s of the azimuthal angle. Along t h i s l o c u s a number of cuts (V, FC, I T , SC/TS, RT) have been used f o r p a r t i c u l a r purposes but, by and large, past applications have been r e l a t i v e l y few. Consequently, l i t t l e i n t h e way of detailed information has been published regarding the general properties of arbitrary cuts on the locus. I n this paper we consider the problem o f plane wave propagation i n doubly rotated piezoelectric crystals and compute the quantities of importance, such a s frequency, coupling factor and t h e i r temperature coefficients, as function of orientation for plates along the zero temperature coefficient locus i n q u a r t z . Included are graphs of the angle gradients of these quant i t i e s from which the orientation sensitivities may be obtained.The results are applied to misorientation comctions also. For example, it i s shown t h a t rotated-Ycuts are unaffected to f i r s t order by misorientations i n azimuth angle, and the second-order corrections are determined.Although we concentrate on quartz applications because of t h e i r immediate i n t e r e s t , t h e methods we use are valid in general and may be applied to any c r y s t a l f o r which the material constants are known, such as aluminum phosphate and lithium t a n t a l a t e . A s e r i e s of temperature coefficient calculations for aluminum graphs present typical frequency constant, coupling and phosphate.

A new method of highly accurate orientation of single crystals on a standard powder diffractometer

“…For example, the frequency-temperature characteristics of quartz resonators depend primarily on the cut orientation of the quartz plate, as presented by Ballato & Iafrate (1976).…”

Electronic Activity Dip Measurement

“…Doubly rotated cuts generally could be expected to have even more problems in this regard than AT-cuts since they exhibit less symmetry and have, therefore, a more complicated mode spectrum when lateral boundaries are taken into account. An exception appears to be the SC/TTC orientation [7]- [10] for which activity dips have yet to be encountered [11].…”

The Temperature Sensitivity of Doubly Rotated Quartz Resonators.

“…We apply these boundary conditions to our general solution which is a linear combination of the modal eigenvectors. (wk/vn (Ballato & Iafrate [1976]). …”