Piezoelectric Quartz Plate Research Articles

Forced vibration analysis of piezoelectric quartz plates in resonance

Quartz is a widely used piezoelectric material and quartz resonators are the primary components in many industrial applications due to the piezoelectric effect. To have a thorough understanding on the vibration characteristics of quartz plates, the experimental measurement of resonant frequencies and mode shapes is indispensable. In this paper, two experimental techniques, amplitude-fluctuation electronic speckle pattern interferometry (AF-ESPI) and laser Doppler vibrometer (LDV), which are, respectively, full-field and point-wise displacement measurement methods, are used to obtain the out-of-plane vibration characteristics of AT-Cut quartz in real time. The resonant frequencies and the corresponding vibration mode shapes are successfully obtained at the same time from AF-ESPI method. However, only the resonant frequencies of the out-of-plane vibration modes are determined by the LDV. The cantilever and completely free quartz plates are used in this study and the experimental results are verified by the finite element method (FEM) analysis. The cantilever quartz plates are excited from applying voltage and acoustic waves. Furthermore, three designs of electrode for a quartz plate with free-boundary condition are studied. Excellent agreement between the measured data from the optical method and the numerical results predicted by FEM are found for both resonant frequencies and mode shapes.

Measurement of the Detachment of LB Films from a Piezoelectric Quartz Plate at the Air-Water Interface

Abstract Langmuir-Blodgett (LB) films were found to detach partially from a substrate passed through the air-water interface. When a piezoelectric quartz plate (quartz-crystal microbalance, QCM) was employed as a substrate, the detached amount could be obtained in nanogram level from the frequency change of the QCM substrate. The removal of LB films mainly occurred when the substrate was lowered slowly into a pure water surface, but not when it was raised. The detachment was largely reduced when the substrate was lowered quickly through a water surface having a low surface tension at low temperature. The detachment was also reduced when well-oriented and defect-free LB films were prepared from long chain amphiphiles or polymerized monolayers.

特集「高機能両親媒性化合物の合成とその高次構造」 ポリイミド前駆体ＬＢ膜の累積挙動とそのイミド化過程の水晶振動子マイクロバランス法による研究

The processes of deposition of precursor LB films and imidization to polyimide LB films were monitored by weight change using a piezoelectric quartz plate as a microbalance. N-Octadecylpyrrolidine was better than N, N-dimethyloctadecylamine as a long alkyl amine to obtain the Y-type multilayer. Although imidizaion using the solution of acetic anhydride and pyridine was performed within several hyndred seconds in benzene, it did not complete in hexane, whereas initial imidization speed was faster in hexane. Swelling would be important factor for imidization process, because benzene make the LB film swell more than other solvents.

In situ weighing of water-deposited Langmuir–Blodgett films on a piezoelectric quartz plate

Monolayers of cadmium stearate were deposited on a piezoelectric crystal plate by the Langmuir–Blodgett (LB) technique, and it was found from frequency changes of the crystal that the LB films were deposited on the crystal with water which gradually evaporated through the layers of the films when exposed to air.

Holographische Untersuchung von schwingenden piezoelektrischen Quarzplatten

Abstract The application of holography to the analysis of the vibrations of piezo-electric quartz plates is demonstrated. A series of interference patterns appeared on the vibrating quartz plates as reconstructed by holograms. These patterns were photographed, and the amplitudes of vibration were determined. It is shown that the amplitude of vibration is increased as higher voltages are applied to the quartz. These results are compared with the experimental results of authors using interferometer techniques.

Piezo-electric Oscillations of Quartz Plates at Even and Half-odd Harmonics

IT is well known that a piezo-electric quartz plate can be excited into strong oscillations at its fundamental frequency, mainly determined by its thickness, or at any of its odd multiples, the even multiples being ruled out on theoretical considerations1. Parthasarathy2 first observed that a quartz plate can vibrate at its 5/2 and 7/2 harmonics. Afterwards, Parthasarathy, Pande and Pancholy3 showed that an X-cut quartz plate could also be made to oscillate, though with a lower intensity, at its even harmonics and such frequencies as ½, 3/2, 5/2, etc., of its fundamentals. This observation was later confirmed by Tsien and Chu4 and Ozdogan5. The former also reported that, besides the even and half of odd multiples of the fundamental frequency, the plate would oscillate continuously, though with less intensity, at any intermediate frequency.

Chapter XIII*: The Mounting and Fabrication of Plated Quartz Crystal Units

THIS paper is one of a series on piezoelectric quartz plates and deals primarily with the methods employed in mounting crystal plates operating up to approximately one megacycle for practical utilization in communication equipment. The theoretical aspects of mounting crystals have been covered in Chapter VII. The discussion is confined to plates <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> having definite nodal lines or points, such as +5° and −18° 25′ X cuts, GT, CT, DT, MT and NT cuts. The mounting of high-frequency crystal plates such as AT and BT cuts, which vibrate in thickness shear modes, is not included. It should also be noted that the subject matter is treated descriptively and that no attempt is made to go into the more intricate details of design or to give performance characteristics. These matters will be dealt with fully in a later paper. The designs and methods outlined are up to date for each type of unit, the results of many years of development on the part of Bell System engineers to evolve practical designs for commercial manufacture and use. Expanding on the contributions of the early investigators mentioned by W. P. Mason in Chapter I, <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> these engineers had, in the ten years prior to 1939, worked out practical designs and developed suitable tools and processes for wide commercialization in telephone applications. In the last five years, under the impetus of war, further improvements have been made in the design and manufacture of crystal units, particularly those for use by the Armed Forces.

An Ultrasonic Source of Improved Design: Optical Studies of Ultrasonic Waves in Liquids

After discussing the production of sound radiation suitable for ultrasonic interferometry in liquid media, a source is described in which a piezoelectric quartz plate mounted at a nodal plane for its principal vibration mode has one vibrating face exposed directly to the liquid media so that its motion may approximate that of a piston radiating into a semi-infinite medium. A review is given of some of the optical methods using continuous illumination that can be used in the investigation of ultrasonic radiation fields in liquids. Both progressive and standing sound wave systems are used with plane and divergent light. Photographs are included and bring out in a striking manner phenomena discussed in optics and acoustics.

Acoustic Absorption and Reflection Coefficients in Gases by Supersonic Interferometry

The necessary experimental requirements of acoustic interferometry in gases have been examined by optical and electrical methods with the object of evaluating the influence of the boundary of the acoustic field, and the effect of departure from parallelism of the reflector with the source upon the experimentally determined attenuation and reflection coefficients. The results show that the requirements of parallelism of the reflector are as rigorous as in optical interferometry and are best met by adjustment for maximum height of peaks rather than by optical or mechanical methods. Recently determined values of reflection coefficients at 1237 kc are found to be in much better agreement among themselves and with the theoretical predictions of the theory (in press) of K. F. Herzfeld for dissipative reflection coefficients than most of those heretofore obtained with the resonator interferometer. Schlieren photographs of modes of vibration of X-cut piezoelectric quartz plates and of the acoustic radiation from them will be shown.

MEASUREMENT OF THE VELOCITY OF SOUND IN LOW TEMPERATURE LIQUIDS AT ULTRASONIC FREQUENCIES

An ultrasonic interferometer apparatus has been developed for the measurement of the velocity of sound in low temperature liquids. The method follows in general the conventional manner of producing sound waves in a liquid, i.e., by the vibrations of a piezoelectric quartz plate driven at a high frequency. The velocity of sound in liquid oxygen and hydrogen at an ultrasonic frequency of 427 kilocycles per sec. was found to be:—oxygen, 912 metres per sec. (temp., − 182.9 °C); hydrogen, 1127 metres per sec. (temp., − 252.7 °C).

An X-Ray Examination of the Harmonic Thickness Vibration of Piezoelectric Quartz Plates

An X-Ray Examination of the Harmonic Thickness Vibration of Piezoelectric Quartz Plates

Experimental Study of Parallel-Cut Piezoelectric Quartz Plates

Y-cut piezoelectric quartz plates were studied with respect to the charges developed on the plates when oscillating near their resonant frequencies. The attractive force between crystal and electrodes was measured. Two methods for determining the piezoelectric voltage developed across the crystal are suggested. It is concluded from a study of crystal breakage that fracture is due to intense mechanical vibration.

A Visual Method for Studying Modes of Vibration of Quartz Plates

A large number of beautiful patterns formed on the surface of a piezo-electric quartz plate by the glow discharge at low pressures of gas were observed at various radio frequencies of the exciting oscillator. They are caused by different modes of vibration of the plate of which there seems to be a great number. Evidence in support of the theory that the bright spots in the pattern occur at the antinodes of standing waves in the plate is presented from which it appears that the value of Young’s modulus is the same for directions at angles of from 0 to 78 degrees from the optic axis. These patterns explain the multitude of frequencies at which a piezo-electric quartz plate will vibrate observed by Cady and others.Water vapor was found to condense on the crystal in the configuration of the pattern corresponding to the last mode of vibration of the crystal and a thin spark was produced about 13 mm long between the electrodes and over the surface of the vibrating crystal at a pressure of 5 mm.

Piezo-Electric Resonance and Oscillatory Phenomena with Flexural Vibrations in Quartz Plates

A method of obtaining flexural vibrations from piezo-electric quartz plates together with the equations for flexural vibrations in quartz is given. Crystal mountings for obtaining best results with the first, second, and higher modes of flexural vibration are developed. The use of the crystal at flexural frequencies in the oscillator circuits of Cady and Pierce, and the luminous phenomena obtained when resonating in a partially evacuated chamber with different types of mountings, are also described. Without using unusually long plates the range of frequencies obtainable is extended into the audible range. Among the problems still to be solved are the temperature coefficient of frequency and logarithmic decrement for the various modes of flexural vibration as well as constancy of frequency under variations of load and constants of the electric circuit. Investigations are still in progress, of which a report will be communicated later.