Method of determining angle-of-cut

Details Method of determining angle-of-cut Method of determining angle-of-cut

2001-01-23

2003-02-11

Le, N. (Department: 2858)

Electricity: measuring and testing

Impedance, admittance or other quantities representative of...

Piezoelectric crystal testing

C324S076490, C310S360000, C378S081000

Reexamination Certificate

active

06518778

ABSTRACT:

FIELD OF THE INVENTION
This invention relates in general to the field of crystal resonators, and more particularly to methods of determining the angles-of-cut of doubly rotated crystal resonators.
BACKGROUND OF THE INVENTION
The frequency vs. temperature (“f vs. T”) characteristics of crystal resonators depend on the angles of cut of the quartz plate with respect to the crystallographic axes. In certain applications, an accuracy within seconds of arc is required. Due to imperfections in both the cutting techniques and the quartz, the angles of cut of each blank must be measured, the blanks must be sorted, and, if necessary, angle-corrected to achieve the required angles-of-cut precision.
X-ray diffraction is the standard technique for measuring angles-of-cut, and double-crystal X-ray diffraction is generally used to measure the angles between the major surface of a blank and a specified set of atomic planes. In this technique, X-rays are reflected from atomic planes in a crystal in accordance with Bragg's law: n&lgr;=2d sin &thgr;
&bgr;
, where &lgr; is the wavelength of the reflected X-rays and &thgr;
&bgr;
=the “Bragg angle,” the angle at which the peak of the reflection occurs. References on the X-ray techniques are J. L. Chambers, “An Instrument for Automated Measurement of the Angles of Cut of Doubly Rotated Quartz Crystals,” 37th Annual Symposium on Frequency Control, 1983, pp 275-283 and J. L. Chambers, et al., “An Instrument for Automated Measurement of the Angles of Cut of Doubly Rotated Quartz Crystals,” 35th Annual Symposium On FrequencyControl, 1981, pp. 60-70. In most X-ray orientation systems, the K
&agr;
radiation from a copper target is used because the wavelength of this radiation is near the typical atomic spacings.
Referring now to
FIG. 1
, which illustrates double-crystal X-ray diffraction, the monochromator crystal collimates the X-rays, allowing more accurate determination of the Bragg angle than is possible with single-crystal orientation systems. The goniometer allows varying the angle of incidence of the X-rays and determining the angle of maximum reflection. When a laser is used to define the plane of the blank, a measurement precision of ~2 seconds of arc is possible. Also, the X-ray and goniometer techniques can be combined in an X-ray goniometer as described in Knolmayer “X-Ray Goniometer of the Modified Doubly Rotated Cuts,” 35th Annual Symposium On Frequency Control, 1981, pp. 567. Other priors art techniques are based on an automated piezogonimeter described in Kobayashi, “Fully Automated Piezogoniometer (Automatic Quartz Plate Classifier),” 32nd Annual Symposium on Frequency Control, 1978: p 317-320.
The AT angle-of-cut presents a different problem not addressed by prior art techniques. The AT-cut is the most commonly used zero temperature coefficient (“ZTC”) thickness shear mode resonator. The AT-cut's angles of cut are about &thgr;=35°15′±30′ and &phgr;=0°, as depicted in FIG.
2
. The &thgr; angle is the primary determinant of the resonator's f vs. T characteristic. Therefore, it is intentionally adjusted to a precise value typically within the ±30′ range, depending on the application. The &phgr; angle is usually not measured during manufacturing operations for two reasons. First, a small error in the &phgr; angle generally has only small effects on the f vs. T characteristic of the resonator. Secondly, the equipment needed to measure both &thgr; and &phgr; angles is quite expensive, with an average cost exceeding $100,000 per instrument. The prior art X-ray diffraction and goniometer methods are particularly unsuitable for measuring errors in the &phgr; angle, because their errors are not always small, and even small &phgr; angle errors are not negligible for certain applications. For example, errors in the &phgr; angle can result in significant manufacturing yield problems. Such errors also effect properties such as the AT-cut's sensitivity to electric fields, i.e., when &phgr;=0°, the AT-cut is insensitive to electric fields, but when &phgr;≠0°, the AT-cut exhibits a finite sensitivity to electric fields. Prior art techniques are generally not satisfactory and are costly. There are no known inexpensive techniques for measuring the deviations from &phgr;=0°. Thus, there has been a long-felt need to determine inexpensively whether the &phgr; angle deviates from &phgr;=0°.
The inventors have observed that the effects of c-modes' displacement ratio i.e. the ratio of out-of-plane to in-plane displacement, variations with &phgr; angle can be used to determine deviations from &phgr;=0°. They have observed a direct relationship between deviation from &phgr;=0° and the c-mode displacement ratio, so that the larger the deviation from &phgr;=0°, then the larger is the change in the normalized frequency of the c-mode upon immersion in, or contact with, a fluid. Thus, &phgr; angle deviations are determined by measuring &thgr; and &phgr; angles of standard resonators with different small &phgr; angles, i.e. less than or equal to 7°, and their quasi-pure mode frequencies in ambient air and a test fluid, calculating the normalized frequency changes between the air and fluid measurements, measuring the test resonator in air and then in fluid, and then comparing the results. Accordingly, this invention fulfills the long-felt need to determine inexpensively &phgr; angle deviation by providing methods of determining the &phgr; angle-of-cut, which do not suffer from the disadvantages, shortcomings and limitations of the current expensive, time-consuming and cumbersome testing equipment. Other useful prior art references are:
J. Clastre et al. “Goniometric Measurements of the Angles of Cut of Doubly Rotated Quartz Plates,” Proc. 32 th Ann. Symposium on Frequency Control, pp. 310-316, 1978;
J. F. Darces et al., “Final X-Ray Control of the Orientation of Round or Rectangular Quartz Slides for Industrial Purposes,” Proc. 32 th Ann. Symposium on Frequency Control, pp. 304-309, 1978;
V. E. Bottom,
Introduction to Quartz Crystal Unit Design,
Van Nostrand Reinhold Company, Chapter 11, 1982;.
J. A. Kusters, “Resonator and Device Technology,” in E. A. Gerber and A. Ballato;
Precision Frequency Control,
Vol. 1, pp.161-183, Academic Press, 1985;
C. A. Adams et al., “X-Ray Technology—A Review,” Proc. 41 st Ann. Symposium on Frequency Control, pp. 249-257, 1987; and
H. Bradaczek, “Automated X-Ray Sorting Machine For Round Quartz Blanks,” Proc. 45 th Ann. Symposium on Frequency Control, pp. 114-116, 1991.
SUMMARY OF THE INVENTION
It is therefore one object of the present invention to provide methods and techniques to determine whether the &phgr; angle deviates from &phgr;=0° based on the quasi-pure modes' displacement ratio variations with the &phgr; angle.
It is another object of the present invention to provide methods and techniques to determine whether the &phgr; angle deviates from &phgr;=0° based on the c-modes' displacement ratio variations with the &phgr; angle.
It is still another object of this invention to provide methods and techniques to determine whether the &phgr; angle in a near AT angle-of-cut deviates from &phgr;=0° based on the c-modes' displacement ratio variations with the &phgr; angle.
It is yet another object of this invention to provide methods and techniques to determine whether the &phgr; angle in a near BT angle-of-cut deviates from &phgr;=0° based on the b-modes' displacement ratio variations with the &phgr; angle.
It is still a further object of this invention to provide methods and techniques to determine whether the &phgr; angle in the LGX family of rotated-y-cut ZTC crystal resonators deviates from &phgr;=0° based on the quasi-shear modes' displacement ratio variations with the &phgr; angle. The term “LGX” is well-known to those skilled in the art as a shorthand expression for a family of piezoelectric crystals, including the langasite (LGS), langan

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