Measuring and testing – Gas content of a liquid or a solid – By vibration
Reexamination Certificate
2001-02-16
2002-04-16
Williams, Hezron (Department: 2856)
Measuring and testing
Gas content of a liquid or a solid
By vibration
C073S024060, C073S030040, C073S031060, C073S03200R, C073S054410, C073S061490, C073S061750, C073S061790, C073S064530, C374S031000, C374S142000, C374S043000
Reexamination Certificate
active
06370939
ABSTRACT:
FIELD OF THE INVENTION
The present invention pertains generally to the field of sensors for the measurement of changes in mass and heat flow. More particularly, the present invention pertains to multiple microresonator mass and heat flow sensors which may provide simultaneous and continuous measurement of the changes in mass and heat flow at a gas-solid interface. The present invention also pertains to an apparatus comprising such sensors as sample and reference sensors, and to methods of measuring the mass and heat flow of a gas, liquid, or solid sample by utilizing such apparatus.
BACKGROUND OF THE INVENTION
Although the piezoelectric effect has been known since the 19th century, the development of quartz crystal devices which oscillate at precisely defined resonant frequencies and which can be incorporated as passive elements into electronic instruments began in the 1920's. Like much of our modem electronic technology, their development received a massive push during World War II, when over 30 million quartz crystal oscillators were produced for use in military communications equipment. Today there is widespread use of quartz crystal oscillators and of new types of microresonators in electronics wherever precise control of frequency is needed as, for example, in radio frequency communications, in frequency meters and timepieces, in scientific instrumentation, and in computers and cellular telephones.
There are several useful books which describe the physics of quartz crystal oscillators and other microresonators and their use in electronic circuits. For example, Introduction to Quartz Crystal Unit Design by Bottom, Van Nostrand Reinhold, New York, 1982, discusses the physical crystallography of quartz, mechanic vibrations and stress/strain relationships, the piezoelectric effect, the equivalent circuit of the quartz resonator and its use as a circuit component, the temperature stability of quartz oscillators, and other topics of importance in the application of these devices.
Science
, Vol. 249, pages 1000-1007 (1990), by Ward et al., describes the converse piezoelectric effect and its use in in-situ interfacial mass detection, such as in thickness monitors for thin-film preparation and in chemical sensors for trace gases.
Analytical Chemistry
, Vol. 65, pages 940A-948A and 987A-996A (1993), by Grate et al., compares the acoustical and electrical properties of five acoustic wave devices used as microsensors and transducers, including quartz crystal oscillators.
Any crystalline solid can undergo mechanical vibrations with minimum energy input at a series of resonant frequencies, determined by the shape and size of the crystal and by its elastic constants. In quartz, such vibrations can be induced by the application of a radio frequency voltage at the mechanical resonant frequency across electrodes attached to the crystal. This is termed the inverse piezoelectric effect. The thickness shear mode is the most common mechanical vibration used in quartz crystal oscillators. A typical commercially available quartz crystal oscillator is a thin circular quartz plate, cut from a single crystal at an angle of 37.25° with respect to the crystal's z axis (the so-called “AT cut”). This angle is chosen so that the temperature coefficient of the change in frequency is, to the first approximation, zero at 25° C., thus minimizing the drift in resonant frequency with ambient temperature change. A slight change in the cut angle produces crystals with zero temperature coefficients at elevated temperatures. The AT-cut plate has thin film electrodes on most of the top and bottom surfaces of the crystal, and is supported in various ways at its circumference or perimeter. Both the fundamental and the first few overtones of the thickness shear mode have been utilized in crystal oscillators. A typical AT-cut quartz disk piezoid operating at a 10.8 MHz fundamental has the following dimensions, according to page 99 of the above-mentioned reference by Bottom:
diameter:
8.0
mm
electrode diameter:
2.5
mm
blank thickness:
0.154
mm
The quality factor, Q, defined for any resonant circuit incorporating quartz crystal oscillators is usually not less than 10
5
and may be as high as 10
7
. With careful attention to the control of temperature in a vacuum environment, a short-term frequency stability of one part in 10
10
can be obtained, although the stated short-term stability for commercial units is ±3 ppm.
The resonant frequency of a quartz crystal oscillator is inversely proportional to the thickness, e, of the plate. For a circular disk,
f=nK/e
where n=1, 3, 5, . . . and K is the frequency constant (for example, see page 134ff of the above-mentioned reference by Bottom). For an AT-cut disk, K=1664 kHz mm, so that a disk of a thickness of 1 mm will oscillate at 1,664 MHz. If this thickness is increased by the deposition of material on the surface of the quartz crystal oscillator, then its frequency will decrease.
In 1957, Sauerbrey in
Z. Physik
, Vol. 155, 206 (1959), derived the fractional decrease in frequency f of a circular disk quartz crystal oscillator upon deposition of a mass, m, of material on its surface. The derivation relies on the assumption that a deposited foreign material exists entirely at the anti-node of the standing wave propagating across the thickness of the quartz crystal, so that the foreign deposit can be treated as an extension of the crystal, as, for example, described in
Applications of Piezoelectric Quartz Crystal Microbalances
by Lu et al., Elsevier, New York, 1984. Sauerbrey's result for the fundamental vibrational mode is as follows:
&Dgr;ƒ/ƒ
0
=−&Dgr;e/e
0
=−2ƒ
0
&Dgr;m/A{square root over (&rgr;&mgr;)}
Here, &Dgr;e is the change in the original thickness e
0
, A is the piezoelectrically active area, &rgr; is the density of quartz, and &mgr; is the shear modulus of quartz. By measuring the decrease in frequency, one thus can determine the mass of material deposited on the crystal. This is the principle of the quartz crystal microbalance. In practice, the assumptions underlying the Sauerbrey equation are valid for deposits up to about 10% of the crystal mass, although the sensitivity to mass has been shown experimentally to decrease from the center of the electrode to its edge.
Torres et al. in
J. Chem
. Ed., Vol. 72, pages 67-70 (1995), describe the use of a quartz crystal microbalance to measure the mass effusing from Knudsen effusion cells at varying temperatures, in order to determine the enthalpies of sublimation. They reported a sensitivity of about 10
8
g/sec in the mass deposition rate. The application of the quartz crystal microbalance in chemistry for the sensitive detection of gases adsorbed on solid absorbing surfaces has been reviewed by Alder et al., in
Analyst
, Vol. 108, pages 1169-1189 (1983) and by McCallum in
Analyst
, Vol. 114, pages 1173-1189 (1989). The quartz crystal microbalance principle has been applied to the development of thickness monitors in the production of thin films by vacuum evaporation, as, for example, described in the above-mentioned reference by Lu et al. Quartz crystal oscillators of various sizes and modes of vibration are commonly used currently in research efforts in sensor development.
Throughout this application, various publications and patents are referred to by an identifying citation. The disclosures of the publications and patents referenced in this application are hereby incorporated by reference into the present disclosure to more fully describe the state of the art to which this invention pertains.
U.S. Pat. No. 5,339,051 to Koehler et al. describes resonator-oscillators for use as sensors in a variety of applications. U.S. Pat. No. 4,596,697 to Ballato and U.S. Pat. No. 5,151,110 to Bein et al. describe coated resonators for use as chemical sensors.
To overcome the influences of temperature changes on the microresonators, U.S. Pat. No. 4,561,286 to Sekler et al. and U.S. Pat. No. 5,476,002 to Bower et al. describe active temperatur
Smith Allan L.
Wadso Ingemar
Miller Rose M.
Sampson & Associates
Williams Hezron
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