2-11-1 MATHEMATICAL THEORY OF VIBRATIONS OF ELASTIC PLATES R.D. Mindlin Department of Civil Engineering and Engineering Mechanics Columbia University, New York, NY This is a report of results of mathematical studies in the theory of vibrations of plates conducted during the past year by M. Medick, M. Onoe and R. D. Mindlin under Signal Corps Contract DA 36-039 SC-72831 with Columbia University. Except for a few degenerate cases, it is not possible to obtain closed solutions of the three-dimensional equations of elasticity for vibrations of plates with traction-free faces and edges. Approximate solutions of the exact equations or exact solutions of approximate equations are alternatives that are available. The latter technique has been employed in some of the studies made under this contract. The earliest examples of approximate equations of vibrations of plates are the Lagrange-Germain and Poisson equations governing low-frequency flexural and extensional modes of isotropic plates and their counterparts for crystal plates, as given by Cauchy. In the case of flexure, the next higher order of approximation accommodates the lowest thickness-shear and thickness-twist modes. These equations have been studied in some detail, during the past few years, under this contract. A further extension to higher frequencies has immediate applications to high frequency face-modes coupled with thickness stretch and thickness-shear. Some preliminary work along these lines was reported at the Symposium on Frequency Control last year. The completion of the formulation on the appropriate second order equations is described in Part A of the present report. The first test to which a new set of approximate equations must be put is a comparison of its predicted frequency spectrum for an infinite plate with the appropriate part of the exact frequency spectrum of an infinite plate, which may be obtained from the three-dimensional theory. The latter, in the case of an isotropic plate, is found in Rayleigh's solution. In fact, a new set of equations stands or falls on the basis of such a comparison. In the present case, the new equations reproduce very closely the known real and imaginary parts of the pertinent branches of Rayleigh's frequency equation. In addition, complex roots, associated with real frequencies appear in the approximate theory. Part B contains a summary of a study which establishes the existence of complex root, of Rayleigh's equation, corresponding to real frequencies. A detailed computation again shows a close correspondence with the corresponding complex pat of the approximate frequency spectrum. Furthermore, loci of complex roots are found to be associated with every point of zero slope in the Rayleigh spectrum of frequency vs. real or imaginary wave number. In view of this, it was necessary to gain a full understanding of the behavior of the real and imaginary roots of Rayleigh's equation. Such a study is described in some detail in Part C. While investigating the behavior of Rayleigh's solution in the neighborhood of zero wave-number, a new class of exact solutions for the infinite plate was encountered. These solutions comprise modes which have the same frequencies as the simple thickness-shear and thickness-stretch modes, but their mode-shapes are different. Typical examples are described in Part D. Analogous modes exist in crystal plates, and an example is given in Part E. 2-11-41 STRAIN PATTERNS IN THICKNESS-SHEAR RESONATORS K. S. Van Dyke Wesleyan University Models of the Strain Patterns The material of this report is largely to be found in the thesis of Ansel C. Anderson, and is given in much greater detail there. The electronic instrumentation used is discussed in the thesis of Paul E. Weston, as is also Weston's model of the thickness-shear strain distribution in a square AT-cut resonator of 13.94 dimensional ratio when vibrating in its fundamental mode of thickness shear. 1-11-62 THE ANELASTICITY OF NATURAL AND SYNTHETIC QUARTZ AT LOW TEMPERATURES J. C. King Bell Telephone Laboratories, Inc., Whippany, NJ In spite of the greater cost of the raw material, synthetic quartz is attractive to manufacturers of crystal resonators by virtue of: a. The high percentage of resonator grade material per pound of synthetic quartz. b. Ingenious use of seed plate orientation which provides maximum growth in a desired direction c. Morphological uniformity of synthetic crystals which greatly reduces the set-up time preparatory to cuttin resonator blanks. It is essential that studies be undertaken aimed at examining the fundamental differences between synthetic and natural quartz. Within recent years the acoustic spectrum has begun to assume a position comparable to that occupied by the optical spectrum in the theory of atomic and molecular structure. Investigations of the internal friction in metals and ionic crystals have clearly demonstrated the great value of this method for the definition and clearer understanding of processes which may occur in crystals. It is only natural that acoustical absorption be applied as a tool for the comparative study of natural and synthetic quartz. The present investigation is concerned with the anelasticity of synthetic quartz primarily as a function of temperature and frequency. 2-11-78 A STUDY OF VHF CRYSTAL UNITS Erich Hafner U.S. Army Signal Engineering Laboratories, Fort Monmouth, NJ With the use of ever higher frequencies for communication purposes, the need for very high frequency crystal units becomes more and more pressing. Although there are now crystals with a nominal frequency of 125 Mc available in production quantities, the question as to how the increasing admittance of the static capacity, formed by the electrodes, as well as the inductance of the wires holding the crystal blank affects the operating characteristic of the complete crystal unit has for some time been eyed with great concern. It was therefore deemed desirable to study the theoretical limitations for the satisfactory operation of a conventional type crystal unit and to identify the factors which are responsible for the deterioration of the frequency stabilizing characteristics. 1-11-90 SOME PROPERTIES OF DOPED AND UNDOPED SYNTHETIC QUARTZ CRYSTALS Joseph M. Stanley & Andrew R. Chi U.S. Army Signal Engineering Laboratories, Fort Monmouth, NJ Previous investigations in the U.S. Army Signal Engineering Laboratories have shown how the resonator properties, lattice spacing and diffraction pattern width are affected by the addition of certain impurities. More recent work in this field at these Laboratories has been concerned with the effect of these impurities on the alpha to beta inversion of synthetic quartz and the effect of x-ray irradiation and thermal bleaching on the frequency temperature characteristics of these doped materials. To determine the effect of X-ray irradiation and thermal bleaching on the frequency temperature characteristics of natural and synthetic quartz crystals, resonators prepared from natural, synthetic and doped synthetic crystals were subjected to varying periods of x-irradiation and heating. The resonators were all AT- cuts and vibrated in a thickness shear mode of 29 Mc/sec. 1-11-112 DEFECTS IN QUARTZ CRYSTALS George W. Arnold, Jr. U.S. Naval Research Laboratory While making routine investigations of polished quartz surfaces, it was observed that rather striking growth features could be seen when such surfaces were viewed by transmitted light and under low magnification. Hammond(1) has shown that sharply defined regions of colored and uncolored quartz appear when a section of Y-bar quartz is gamma irradiated. Figure 1 shows the typical appearance of such a section after a gamma-ray dose of the order of 10 to the 7th r. Figure 2 shows a section from the same Y-bar quartz which has not been irradiated. Although the contrast is not as great as in the gamma irradiated case, the same growth features are observed in the -X direction. The crystals discussed in this paper are those grown by the Y-bar method, but similar growth features have been observed for crystals grown on minor rhombohedral seeds. Figure 3 shows a crystal grown on a rhombohedral seed. The strained regions and growth layers are clearly evident. The layers are not exactly parallel to the seed surface. The growth layers in the +X direction for the non-irradiated Y-bar crystal cannot be seen in the photograph but can be seen during visual observation. 1-11-130 IMPROVING THE QUALITY OF CRYSTAL QUARTZ Frank Augustine Clevite Research Center Clevite Research Center, under contract with Signal Corps Engineering Laboratories, is concerned with the problem of how to improve the general overall quality of synthetic quartz - in particular how to improve its elastic properties. Bommel, Mason and Warner (1) have stated that the internal friction of quartz resonators is affected by the number of dislocations and to a lesser degree by impurity elements. Their findings were instrumental in promoting this work. The following aspects of the problem are being pursued: 1) growing synthetic quartz of very high quality; 2) a study of the topography and etch figures of synthetic quartz and their possible relation to dislocations in the crystal structure; 3) critical control of the quartz-growing process. 1-11-142 FACTORS GOVERNING THE HYDROTHERMAL FORMATION OF AND QUARTZ Richard G. Yalman Antioch College In 1946 the U.S. Army Signal Corps established a research contract at Antioch College to study the mechanism of the hydrothermal formation of quartz. The director of this project was the late Allyn Swinnerton. Associated with him were Drs. Owen of the Physics Department and Cerwin of the Chemistry Department, and the experimental work was carried out by undergraduate students as part of their cooperative job training program. Because of the varied interests of the senior staff the project was soon divided into several categories including the conductivity of water in the supercritical region, a mineralogical study of the diffusion of ions, and the chemistry of the hydrothermal formation of quartz. I would like to devote my time today to a review of the developments which have taken place in the chemistry section. 4-11-157 AGING STUDY OF QUARTZ RESONATORS Richard B. Belser and Walter H. Hicklin Engineering Experiment Station, George Institute of Technology Aging studies of over 200 quartz resonators fabricated and tested in 1955-1956 had pointed to gold, deposited by evaporation, as the most consistently dependable plating for quartz resonators of high stability. A need for a more precise frequency measuring technique was indicated, however, the effect of the container on resonator stability was still obscure. The use of a balanced bridge frequency measurement system, developed by Mr. Douglas W. Robertson of the Georgia Institute of Technology under Contract No. DA-36-039-SC-71191, solved the measurement problem. An apparatus adapted to preheating the resonator surface to approximately 450 degrees C, prior to evaporating gold simultaneously onto both faces of the crystal, has been constructed and used in the fabrication of 190 additional 16 mc AT-cut resonator units. Resonators mounted in evacuated glass containers gave upward frequency shifts of 0.0001 percent in 30 days. Changes of less than +/- 0.00005 percent were registered in the subsequent 200 days. Resonators similarly coated but mounted in HC-6/U cans of nickel-silver, double-electro cleaned; nickel- silver, hydrogen fired; copper, double-electro cleaned; copper, hydrogen-fired; and copper, enamel-lined, gave similarly stable frequencies with no initial departures. A high incidence of stability failures occurred only in the hydrogen-fired containers; leaking, related to solder flow and solder starvation at joints, and possible flux intrusion appeared to be the primary causes of instability. Meticulous fabrication procedures gave duplicably stable behavior for resonators in all container types. Few units showed drifts greater than 0.0001 percent in test periods of 6 months. The effect on resonator stability of overcoating to frequency remains to be studied. 4-11-189 HIGH TEMPERATURES AT CUT CRYSTAL UNITS Charles W. Mann Reeves-Hoffman Division The purpose of this project is to develop crystal units in the frequency range of 1000 to 3000 Kc. which will operate satisfactorily as oven units at 125 degrees C. Equipment was first constructed to facilitate the testing of crystal units over the range -60 to +135 degrees C and to enable the study of the aging characteristics at 125 degrees C. One-hundred-twenty-seven CR-19/U units were tested over the range -60 to 135 degrees C and aged at 125 degrees C. The major deficiency of these units was their poor coefficient at 125 degrees C. Units having various frequencies and various cutting angles were processed and measured. From the data obtained a curve of Cutting Angle vs Frequency was derived for crystal units operating at 125 degrees C. In order to study the effects of certain processing techniques on aging, 125 units were manufactured using different materials and techniques. These were aged 72 days at 125 degrees C. Results indicated that units having monolayer electrodes age less than any of the other crystals tested. Of the bimetal electrode units, nickel on gold aged least. Any of the techniques and materials studied could be used to produce crystal units in the 1000 to 3000 Kc. range capable of operating at 125 degrees C for 42 days and of passing a +/-.001% aging requirement. 4-11-214 HIGH TEMPERATURE-LOW FREQUENCY CRYSTAL UNITS J.M. Wolfskill Bliley Electric Co. The difficulty of making low frequency wire mounted crystal units to operate at high temperatures, that is, much above 90 degrees C has plagued the crystal industry for a long time. For missile and other high temperature applications most of the current designs will not meet these requirements. The basic problem is primarily one of supporting the crystal blank proper, so the supporting method is unaffected by temperature variations. By using higher temperature solders and the new epoxy cements some improvements have been made but the limitations were always determined by the soldering or cementing method. This meant that if much progress was to be made to extend the temperature range beyond 90 or 95 degrees C. an entirely new approach would be required. Such an approach was proposed by Bliley Electric Company, and early in 1956 the Bu-Ships awarded Bliley Electric a contract to develop a crystal unit that would operate at 125 degrees C both as a oven controlled unit holding a stability of +\-.0025% in an oven maintaining 125 +\- 5 degrees C. Also to be capable of operating over a temperature range of - 40 to +125 degrees C. with recommended tolerances that could be maintained over this range. The development was to cover a frequency range of 80 Kc. to 500 Kc. 4-11-240 HIGH PRECISION CRYSTAL UNITS Louis Dick James Knights Company In 1954 the James Knights Company introduced a non oven controlled crystal, type G-12A, designed to be used in broadcast transmitters. For broadcast transmitter use this crystal was successful. Shortly after its introduction, one of our customers encouraged us to modify this design for use in a precision oscillator. At that time, we did not foresee the measurement problems that lay ahead. We approached the specifications in Table I with a "fools-rush-in" attitude. In particular, we overlooked the importance of shock specification. During the course of the next year the specifications of Table I were changed to include a short term stability of 0.2 PPB/20 min. and a more stringent secular stability of 2 PPB/day. We also minimized the short term stability requirement. Later events showed that shock and short term stability's could be measured and they proved to be the greatest problem. About this time, the Signal Corps, having anticipated the problem of precision frequency control, had engaged the Bell Laboratories to develop a portable precision oscillator. The heart of their oscillator was a 5 mc 5th mode crystal. We were one of the crystal companies fortunate to be awarded a resulting I.P.S. Contract. Shortly thereafter, another customer having received a similar contract on the complete standard, placed a sample order with us for the 5 mc crystal. This placed us in a favorable position, with two good precision crystal designs and an opportunity to work with the end user. During this period, our precision G-12A customer list had grown to include many critical users. With the introduction of our own 1 mc frequency standard we became our most critical customer. By now, we had gained a keen appreciation of the problems involved in the production of precision crystals. One problem that stood out above all others, as reports came back from our customers, was instability due to shock and vibration. Following these reports a standard test of a 20 g impact was instituted. Table II shows permanent changes in frequency as great as 63 PPB due to a 20 g impact on the initial design of our 1 mc precision crystal. This led us into further development from which we emerged some two years later with a current design of the 1 mc crystal, type G-12AS. Progress on shocks stability during this two year period is shown in Fig. 1. From this graph we see that the latest design shows a permanent frequency change of less than 1 PPB due to several 20 g impacts. These findings led us into study of shock stability on the 5 mc crystal. The results are shown in Fig. 2. We were pleased to find that the same techniques learned on the 1 mc crystal are equally successful on the 5 mc unit. 4-11-256 STABILITY OF QUARTZ RESONATORS AT VERY LOW TEMPERATURES F.P. Phelps National Bureau of Standards Quartz crystals serve as the frequency determining elements in the more precise types of frequency standards, oscillators and like equipment where precise control of frequency is required. In fact, the best way at present for controlling frequency to a high degree of precision, for any protracted period of time is by means of Quartz Crystals. Atomic and molecular standards will probably be used as spot checking devices while the Quartz Crystal is used as the flywheel to carry on between checks. However, all quartz crystal units designed for frequency control are subject to the defect of "aging" i.e., the resonance frequency of the crystal changes as time elapses. For crystals fabricated with the utmost skill and care, or such as those used to control the frequency of the Standard Frequency and Time Broadcast Stations of the NBS, WWV at Washington, D.C., and WWVH at Hawaii, the residual drift is very small, being less than 1 part in 10 to the 9th per day and after several years this may decrease to about a part in 10 to the 10th. To give a concrete idea of what this means, let us suppose that the crystal is used to drive a clock. Since there are approximately 10 to the 9th seconds in 30 years, a precision of one part in 10 to the 9th corresponds to about one second in 30 years while a precision of 1 part in 10 to the 10th corresponds to about one second in 300 years. However, these changes, as small as they are, need to be reduced as there are military and other applications requiring a precision of frequency measurement of about this order of magnitude (1 part in 10 to the 9th) or about that of the present primary standard of frequency. Since it is axiomatic that a primary standard should be more precise, preferably by one or more orders of magnitude, than that which is to be measured by the Standard, it has become increasingly clear that the present standard of frequency must be improved; and obviously this also means improved measuring techniques and equipment since these go hand in hand with the standard. Work with this end in view is now under way at the Boulder Laboratories of the NBS along several avenues of approach including development of atomic and molecular frequency standards as well as improvements in the performance of Quartz Crystals. This report concerns only a small part of this work. 4-11-277 FUNDAMENTAL STUDIES ON AN IMPROVED CRYSTAL CONTROLLED FREQUENCY STANDARD M.D. Fagen & W.L. Smith Bell Telephone Laboratories, Inc. The purpose of the work to be described is the development of a crystal controlled frequency standard improved by at lest one order of magnitude beyond the best designs presently available. Of these, the Ground Station of the Navarho System, with an aging requirement of less than 5 ppb per month, is representative of the present state of the art. To do this, studies are being made of quartz resonator design and performance at very low temperatures where frequency aging and temperature coefficients are expected to be materially reduced. With the resulting higher Q and increased stability, the ultimate performance will depend upon variation of circuit parameters. Consequently, studies are being made of these effects to compare existing circuits and to develop new circuitry for decoupling the driving and measuring functions from the crystal unit. Thus far, the work on crystal units has been modification of existing highly stable designs utilizing AT, GT and -18 degrees X-cut quartz plates for operation at very low ambient temperatures; the work on circuits has been in investigating the effects on frequency due to variation in circuit reactance's and tube-gain characteristics of the Meacham Bridge, Rome III and other types of oscillators with a view to evaluating the optimum circuit conditions for maximum stability. We are now far enough along in this first phase of the program to have submitted models of 100 and 200 KC GT units, 100 KC -18 degrees X-cut units, and 5 mc AT units to the Bureau of Standards for studies of long-term aging and stability at liquid nitrogen and liquid helium temperatures. These units and their characteristics will be described later. Our continuing work on resonators will include studies of combinations of quartz blank size, frequency, and temperature to yield the highest Q, studies of thin quartz blanks to reduce the effect of small temperature effects on frequency, studies of polishing, dimensions, and crystal current level to obtain an extremely low frequency versus crystal current characteristic, and finally, investigation of methods of adjustment and sealing to materially reduce the frequency adjustment tolerance. The first portion of this paper will be a description of the resonator development being done at the Bell Laboratories by J.P. Griffin, D.L. White and A.W. Warner. The second portion of this paper will cover the circuit studies by W.L. Smith. Details of the instrumentation for obtaining low temperatures and for the precision frequency measurements may be found in the quarterly reports under contract DA-36-039-SC-73078. 7-11-307 RUBIDIUM OSCILLATOR EXPERIMENTS T.R. Carver Princeton University Preliminary experimental data obtained with a Rubidium 97 gas cell frequency standard will be described. Line widths of several hundred cycles per second have been obtained with the use of optical pumping and Doppler-reduction. Questions of wall collision and buffer gas pressure effects in shifting and broadening the line will be mentioned. 7-11-318 OPTICAL PUMPING, BUFFER GASES, AND WALLS W.B. Hawkins Yale University There are a number of purposes for which it would be desirable to increase the amount of orientation of atoms which can be produced by optical pumping. Optical pumping is intrinsically one of the simplest means of orienting atoms, but it suffers from two defects. The first is an intrinsic part of the method, which consists of allowing circularly polarized light at the natural frequency of the atom to be oriented to interact with a group of such atoms. The atoms absorb the light and along with it the angular momentum carried by it due to its circular polarization. They then re-radiate the light, but the re-radiated light is nearly unpolarized and therefore carries little angular momentum, which is left with the atoms. A group of atoms having a net total angular momentum is just what we mean by a group of oriented atoms. Now is it plain that no atoms can be oriented which are not reached by the light, and when sufficient atoms are introduced into the group that those in front shade those behind, a limit to the number of atoms which can be oriented is reached. the cross-section for absorption of resonance radiation is so large that this limit is 10 to the 10th atoms per cm squared, or if these are assumed to occupy a depth of about 1 cm, a pressure of about 10 to the -7th mm of Hg. this is not a dense sample! This limitation is independent of light intensity, and cannot be evaded by using atoms with a smaller absorption cross-section, for these are harder to orient. To achieve large orientation, one needs as large a cross-section as possible. 7-11-324 HOT SOURCES FOR MASER M.W.P. Strandberg Dept. of Physics & Research Laboratory of Electronics Massachusetts Institute of Technology, Cambridge, MA Ammonia has been used for most MASER work for the very good reason that with it an operating device of this kind is most easily obtained. The partition sum of this molecule is small compared with that of most molecules. Ammonia loses only a minor amount of its intensity of interaction with electromagnetic fields because of fine structure that arises from quadripole and magnetic interaction. The interaction of ammonia with reasonably high electric fields, its Stark effect, is given by second-order perturbation theory that is adequate for the calculation of state selectors and focusers. This simple Stark effect is essentially unique among molecules, and how unique it is will be realized from the fact that all other symmetric-top molecules have a first-order Stark effect, while ammonia has only a second-order Stark effect within the usually available electric fields. However, ammonia has a number of disadvantages for engineering an optimum time- and frequency-standard. For example, the molecules presents a rather awkward pumping problem when it is used in making a sealed-off device, or even a room-temperature device. Then, too, the ammonia resonance, like the cesium resonance's, appear effectively in only a narrow part of the microwave spectrum. This prevents the use of the operating frequencies as a design parameter in designing an optimum system. 7-11-335 PROGRESS IN PHASE LOCK TECHNIQUES Dr. Gernot M.R. Winkler U.S. Army Signal Engineering Laboratories The purpose of a phase lock system is to transfer the inherent stability of a weak microwave frequency standard signal (i.e. a MASER signal) to an oscillator operating at a higher power level with zero frequency error. Principle: The weak MASER signal and the klystron power are fed into the E and H arm of a magic tee (see Lit.). Crystal detectors in the other arms deliver signals to a broad band DC differential amplifier whose output is applied to the klystron repeller. The large DC component in the crystal outputs due to the high power of the klystron is canceled by the differential amplifier. 7-11-352 MASER ENGINEERING Walter H. Higa Jet Propulsion Laboratory This paper is concerned with some of the practical aspects of the ammonia-beam maser (see ref. 1) as a frequency standard. The excellence of the molecular-beam maser as a stable frequency generator arises from the fact that the molecules sustaining oscillations in a resonant cavity are isolated particles with extremely high Q. An additional factor is that the oscillations are sustained with a minimum of man-made electronics. Somewhere along, however, one is forced to employ electronics to utilize the frequency-stable signal. One of the problems to be dealt with here is, therefore, that of frequency reduction from K-band to some lower frequency where electronic amplifiers are readily available. A second problem to be discussed is that of designing a portable sealed-off oscillator for limited time (approximately 1 hour) applications. The details of a satisfactory arrangement using liquid nitrogen trapping to "pump" the ammonia will be given. Finally, the possibility of designing a continuously pumped maser (without liquid nitrogen cold traps) will be discussed. 7-11-373 PRECISION ATOMIC BEAM TECHNIQUES P. Kusch Dept. of Physics, Columbia University, New York, NY Certain factors that determine the precision with which the frequency of a hyperfine structure line may be established and measured are evaluated with reference to the use of such a line as a frequency standard. To exemplify the discussion the hfs of both cesium and thallium is discussed. It appears that the use of thallium nay lead to smaller uncertainties in the determination of a line frequency that the use of cesium. Certain technical problems in the use of thallium are discussed. 7-11-385 PERFORMANCE OF A CS-BEAM FREQUENCY STANDARD AND FCB's FUTURE R&D PLANS F.H. Reder and S. Roth, FCB U.S. Army Signal Engineering Laboratories It is a great satisfaction to us that we have at least a working model of an Atomic Frequency Standard on whose performance we can report to you. But before I give you this evaluation report, let me briefly go over some general remarks. 11-11-402 STANDARDIZATION IN THE FIELD OF QUARTZ OSCILLATOR CRYSTAL UNITS William J. Young Standard Telephones and Cables Ltd, England At the present time in many countries, there are no generally accepted Standard Specifications for quartz crystal units intended for commercial use. The Services, of course, have their own specifications, but in all other cases, arrangements have to be made between individual companies and their customers for specifying and testing crystal units according to particular requirements. As a result of this individual approach, a very large number of different types of units has to be designed and produced, and frequently the differences between many of them are so slight, that a preliminary guidance in restricting choice would have meant similar performance from the units and fewer types to products. Standardization in the field of quartz crystals can assist materially in a number of ways. First, it can go right to the source of the difficulties stated above by restricting the number of universally accepted types of units. In this way, the user's attention is much more closely devoted to adjusting his requirements to fit an available crystal, than by making the crystal fit a more or less arbitrary set of conditions. Of course, calling on crystal units to satisfy such arbitrary conditions may be very satisfactory in some ways for the user, but generally speaking, to find a crystal unit of standard specification which will in fact give adequate performance, is not a serious problem. Naturally, as time goes on, the user will find difficulty in getting all he wants from available standardized crystals, and this will result in a number of new types becoming available from various sources, all having essential features in common. It is then that standardization steps in, and defines new crystal units according to the latest requirements, by ironing out any differences amongst the newly available types. 6-11-426 CRYSTAL OVEN DEVELOPMENTS Maynard D. McFarlane Robertshaw-Fulton Controls Company Control of a crystal oven at the melting point of a selected material establishes an invariant oven temperature and prevents drift, and use of proportional control avoids cyclic heater variations. A new medium-precision crystal oven uses the volume change which accompanies the melting of the material to exert pressure on a carbon pile, thus controlling the resistance of the pile. Current passing through the pile dissipates heat into the device, so that no heater winding is required to maintain the oven at its pre-determined temperature. Tests with prototype models of this oven show a stability and accuracy of control closer than other self-contained crystal ovens. 11-11-441 EQUIPMENT FOR DETECTING UNWANTED MODES IN OSCILLATOR CRYSTALS Joseph Loos Applied Research Department, Motorola, Inc. The basic purpose of this study is to develop a test instrument which will determine the acceptability of oscillator crystals in the range of 1 to 100 mc from the standpoint of their spurious responses. This instrument will consist of one or more crystal oscillators which are more susceptible to operating on a spurious mode than any presently used oscillator. The requirements of simplicity, high gain and extreme selectivity have narrowed the choice of oscillators to two types, the Butler and the Series Mode Hartley. These circuits are analyzed to determine the highest values of crystal spurious resistance's allowing sustained oscillations. Two oscillators developed for use between 6 and 7 mc are described. The data obtained from testing a quantity of crystals in these oscillators is given. The relationship between the selectivity and gain of a circuit and its ability to detect spurious responses is illustrated. A method of simulating spurious responses by the use of crystals in series with resistance's is described. Data obtained by the use of this method is given. The problems encountered in trying to maintain the required gain, selectivity and simplicity while covering the required frequency range with a minimum number of oscillators are discussed. Methods of compensating for the effect of the crystal shunt capacity over a wide frequency range in the Butler and Hartley circuits are described. 11-11-457 LOW FREQUENCY C.I. METER AN/TSM-14 E. A. Gilbert Radio Frequency Laboratories, Inc. During 1955-56 our laboratories were under contract with the Signal Corps Engineering Laboratories to develop a sensitive C.I. Meter for the testing of low frequency crystals. This development work has resulted in the Crystal Unit Test Set AN/TSM-14. The AN/TSM-14 consists essentially of the basic circuitry of the old Crystal Impedance Meter TS-710 with additional instrumentation circuits added for measuring the voltage across the crystal, the current through the crystal, and the absorbed crystal power at resonance. The Test Set is intended for both laboratory and production testing of crystal units in the frequency range of 10-1100 kilocycles. The Test Set allows the following measurements to be made on low frequency crystals. 1. Effective series resonance and anti-resonance crystal resistance between 100 ohms and 500,000 ohms with extreme limits depending somewhat on the frequency and type of crystal. The substitution method of measuring the quartz crystal impedance is used and an internal ohmmeter is provided for measurement of the substitution resistor. 2. The crystal current between 2 micro amperes and 3.16 milli amperes in five ranges. 3. The voltage across the crystal from .02 volts to 10 volts in four ranges. 4. The power dissipated in the crystal unit is directly measured at resonance between .002 and 31.6 milliwatts in 20 ranges. 11-11-463 VHF CRYSTAL IMPEDANCE METER AN/TSM-15 Dennis Pochmerski U.S. Army Signal Engineering Laboratories Development of a new crystal impedance meter has been recently completed by Frequency Control Branch. It will measure VHF overtone crystals having resistance's of 10 to 100 ohms, at power levels of 0.4 to 4.0 mw in the frequency range 75 to 200 mc/sec. This instrument has been nomenclatured as the AN/TSM-15 Quartz Crystal Test Set and service test models are presently being fabricated by Radio Frequency Laboratories. A few years ago, Frequency Control Branch initiated a study and investigation program on crystal measurement techniques and methods to improve existing crystal instrumentation with respect to accuracy and frequency range. Detailed results were previously presented by Georgia Institute of Technology and by Dr. Guttwein of Frequency Control Branch in the 1955 and 1956 Frequency Control Symposia and are also available in Engineering Report entitled, "Extension of the Upper Frequency Limit of Crystal Impedance Meters." The results of this program indicated the necessity of several requirements for a VHF C.I. meter in order to develop an accurate instrument and one suitable for production testing of crystals. The capability of a circuit to oscillate to 200 mc/sec is an obvious requirement. However, this is not sufficient for a precision measurement instrument and additional requirements considered necessary are listed in Figure No. 1. At present, I will briefly comment on each requirement. Following this, a more detailed discussion will be presented and how each requirement was fulfilled will be indicated. 11-11-479 CRYSTAL MEASURING TECHNIQUES ABOVE 200 MC/SEC Samuel N. Witt, Jr Engineering Experiment Station, Georgia Institute of Technology Numerous methods have been developed and are in current use to determine the equivalent electrical parameters of quartz crystal resonators.(1,2,3) Various instruments and methods are used to measure one or more of the many fundamental and derived parameters. At frequencies below about 200 mc/sec these instruments are capable of providing useful information concerning the crystals as an aid in determining their quality as well as providing information useful in designing crystal controlled oscillators. Within the past few years and even months the progress in crystal manufacturing techniques has permitted the fabrication of crystals capable of useful operation at frequencies well above 200 mc/sec. Efforts at Georgia Tech under the sponsorship of the U.S. Army Signal Engineering Laboratories have, for the past year, been directed toward the development of methods and techniques for the measurement of quartz crystal parameters in the frequency range of 150 to 300 mc/sec. The efforts have actually been two fold: (1) the development of a simple instrument or system capable of moderately accurate routine crystal measurements, and (2) the development of a laboratory standard system of measurements capable of precision determination of quartz crystal equivalent electrical parameters. 6-11-502 DESIGN CRITERIA FOR VACUUM TUBE CRYSTAL OSCILLATORS H.E. Gruen Armour Research Foundation Results of a study of crystal oscillators in the 0.8 to 200 mc region are described. The study, directed toward the development of usable circuits and sound operating techniques, has resulted in the choice of two series resonant circuits for use at frequencies from 10 to 150 mcs. A method for design of these circuits, the Grounded Grid and Cathode Coupled, is outlined and previously developed design criteria for the Colpitts and electron coupled Colpitts circuits is extended to 20 mcs. The design information, based on circuit analysis and measurements, consists of a series of graphs and tables showing circuit performance obtained for a wide range of operating conditions. Reference circuits providing near optimum performance throughout the frequency range have been established, output and crystal drive is plotted as a function of frequency, and effects of component value changes are presented in curves normalized with respect to the reference circuit performance and component value. Design variables include all bias and load parameters as well as tube characteristics and crystal parameters. Accuracy of performance prediction is 10 to 20 percent for output and 20 to 30 percent for crystal drive. 6-11-518 STUDIES OF TRANSISTOR CRYSTAL OSCILLATORS Everett Eberhard & W.R. McSpadden Motorola, Inc. The design methods presented here are the result of work done on Contract No. DA-36-039-SC-72337, Project 3-24-02-072 SC Project 867B. The work was done at Motorola Research Laboratories, Phoenix, AZ during the period from 1 July 1956 to the present. The purpose of this contract is to investigate practical analytical approaches to transistor crystal oscillator design and to evolve design data sheets enabling rapid step-by- step design. An ideal design method should have the following characteristics: (1) the method of analysis should be simple and straightforward; (2) it should be reasonably accurate, yet capable of considerable simplification for approximate checks; (3) the design should depend upon well known and measurable characteristics of transistors and networks; (4) the method should be applicable to a wide range of transistor characteristics; (5) the procedure would permit design with a minimum of theory and mathematics for the applications engineer. The two design procedures presented here are an attempt to satisfy these ideal requirements. However, the scope of this paper is such that a detailed theoretical analysis is not possible. Therefore the theory will merely be outlined and the design procedures presented. 5-11-535 LATEST DEVELOPMENTS IN MECHANICAL FILTERS J.C. Hathaway Collins Radio Co. I. Current State of the Art Mechanical filters have found wide use in communications equipment where narrowband selectivity, small size, and stable characteristics are desired. In the development of mechanical filters a number of improved techniques are being employed. These techniques will permit the design of models with new characteristics, thereby extending their range of applications. To illustrate typical filters being produced at the current state of the art, a pair of single sideband filters has been selected at 250 Kc. Frequency response curves for these filters are illustrated in Fig. 1. The passband of each filter is sufficient to pass audio frequencies from 350 cps to 3.2 Kc, while the carrier at 250 Kc is rejected by at least 20 db. This characteristic is obtained with ten resonant sections in the design. The filter with a passband above 250 Kc is designed to accept the upper sideband while rejecting the carrier and adjacent channel on the low side; while the filter below 250 Kc is designed to accept the lower sideband, and reject the carrier and upper sideband. 5-11-556 HIGH-FREQUENCY QUARTZ CRYSTAL BANDPASS FILTERS Leo Storch Hughes Aircraft Co., Culver City, CA Quartz crystals possess several very attractive properties, such as very accurate series-resonant frequencies, very high Q's, a high degree of temperature stability, and a small volume at the higher frequencies, which explain their importance as circuit elements in many applications. In high-frequency bandpass filter applications, their high Q's are of particular importance. It is usually taken for granted in network design that the Q's of the components must exceed by a substantial margin the reciprocal of the desired fractional bandwidth of the filter.(1) Consequently, quartz crystals can be employed to achieve bandpass characteristics with fractional bandwidths (i.e. ratios of the 3 db or 6 db bandwidth to the center frequency) which are inaccessible to LC filters, because of the relatively substantial dissipative components which are always associated with inductance's in actual construction. However, the well-known equivalent circuit of quartz crystals (Slide 1) imposes certain limitations in the design of bandpass filters which employ quartz crystals as the principal resonators. In the past, one has had to differentiate between three separate regions of fractional bandwidth on this account. In the first or Class (a) region, quartz crystals and capacitors constituted the effective circuit elements. The maximum fractional bandwidth could not exceed a value of 1/r, where "r" signifies the ratio of the holder capacitance to the crystal capacitance for the specific crystal cut being used. 9-11-574 LOW FREQUENCY STANDARDS TRANSMISSIONS W.D. George National Bureau of Standards Boulder Laboratories The standard frequency broadcast services have required improvement at a rate of greater than one order increase in accuracy per decade since they were commenced by the National Bureau of Standards in 1923. The accuracy as transmitted is now plus or minus 1 part in 10 to the 8th and may be increased to plus or minus 1 part in 10 to the 9th or better by reference to the ephemeris second or by adoption of atomic frequency standards. An expanding science and technology requires higher accuracy and worldwide distribution of standards. The immediate problem is to distribute the basic standard of frequency with less loss of accuracy. Investigation has not uncovered a practical way of realizing an improvement in the high-frequency part of the radio spectrum; however, recent measurements in the USA, Europe and New Zealand on 16 kc and 60 kc have shown that it is possible to operate at VLF and obtain a great improvement in received accuracy. In the 1930's the NBS considered VLF before adoption of the plan to broadcast several high frequencies simultaneously. The principal reason for adopting the high-frequency system was the existence, at that time, of suitable receiving equipment in the hands of the public for the high frequencies and the lack of it for the low frequencies. It was recognized that the principal advantage of the low frequency would be freedom from transmission vagaries and that two outstanding disadvantages would be high antenna cost and possible interference from natural noise. 6-11-586 A PORTABLE FREQUENCY STANDARD R.L. Craiglow Collins Radio Company A portable frequency standard consisting of a 5 Mc, 5th overtone crystal unit in a change of state oven, a transistor Pierce oscillator, transistor buffer amplifiers, and an internal mercury cell supply is being developed for the Signal Corps on contract DA36-039-SC-73030. The early work on this project involved the analysis and experimental investigation of several series resonant type oscillators and the Pierce oscillator. The Pierce oscillator demonstrated better frequency stability in all respects to the series resonant oscillators and therefore was selected for further experimental and theoretical investigation. The simplified and equivalent circuit shown in figure 1 were analyzed in terms of the input impedance looking into the oscillator circuit from the crystal terminals with the crystal removed. The input impedance is given by Z sub in = e sub x over i sub x where e sub x is the voltage of a test generator placed across the crystal terminals and i sub x is the current flowing through the test generator. This impedance consists of a negative resistance (R sub x) in series with a capacitance (C sub x) which is the input or load capacitance. For oscillation to build up the negative resistance must be greater than the crystal resistance and for operation to be on the proper frequency the input capacitance must be equal to that for which the crystal was designed. It will be noted that the transistor equivalent circuit used is the low frequency "T". 11-11-597 PRECISION MEASUREMENT OF SHORT TERM INTERVALS F.K. Priebe, D. Schwab, & H. Tansman U.S. Army Signal Engineering Laboratories Methods for measuring time intervals with an accuracy of plus or minus 1/10 microsecond are very well known. Several counter type time interval meters are commercially available. The problem that was given to the Frequency Control Branch was to measure the time interval between two electrical pulses with the greatest accuracy. The system should be restricted only to two pulses and not accept any other signal. In the first attempt of a solution for this problem, some of the commercially available time interval meters were used. This first system was quite successful; it was described in SCEL Engineering Memorandum 1665 and subsequently in "Instruments and Automation," October 1956. However, the accuracy and resolution of this system was limited since the inherent error of the 10-mc counter type time interval meter is plus or minus .1 microsecond. A 100-mc counter type time interval meter was considered as the obvious remedy for increasing the resolution to plus or minus 1/100 microsecond. Unfortunately, no such equipment is available and its development would be quite time consuming and expensive since none of the vital components have been developed. Gates for a direct reading 100-mc time interval meter must operate with a precision of better than 1/200 microsecond and high speed flip- flop circuits are required. As an alternate to the direct-reading time measurement, a vernier time measurement system was used. This reduced the rate at which the counter in the time interval meter has to operate from 100 mc to 1 mc according to the vernier ratio used. The gates were operated in such a manner that they do not affect the accuracy of the system. 6-11-614 FREQUENCY TRANSLATOR FOR MASER S. Schneider Polarad Electronics Corp. The Frequency Translator is designed for the Signal Corps to operate with the MASER to provide output frequencies in more convenient and desirable frequency ranges, however, with a minimum degradation of stability as compared to the reference MASER signal. These output frequencies are to be integer numbers such as 100 kc, 1 mc, 100 mc, etc. A separate output of the translator will be provided at 1 kc for the purpose of driving a chronometer. The chronometer can then be used to determine the long time stability of the MASER itself against astronomical standards. 2-12-2 MATHEMATICAL THEORY OF VIBRATIONS OF ELASTIC PLATES AND BARS R.D. Mindlin Columbia University This is a report of results of mathematical studies in the theory of vibrations of elastic plates and bars conducted, in whole or in part, under Signal Corps Contract DA-36-039 SC- 72831 with Columbia University. E.A. Fox (Rensselaer Polytechnic Institute), D.C. Gazis (General Motors Research Laboratory), R.K. Kaul (University of California), R.D. Mindlin, M. Onoe (on leave from University of Tokyo) and Y.H. Pao participated in the investigations. 2-12-9 FREQUENCY SPECTRA IN QUARTZ RESONATORS C.R. Mingins, R.W. Perry, & D.W. MacLeod Lowell Technological Institute Research Foundation, Lowell, MA Experiments have been carried out on fully plated, flat, circular AT-cut piezoids in order to trace the curves of normalized frequency as a function of normalized diameter. Experimental curves are shown for the intermediate range of d/h (between 20 and 50). The curves are compared with the Mindlin first order asymmetric curves for the same region obtained from theory. The comparison is complicated by the fact that orders other than the first appear on the experimental plots, as do modes of different azimuthal index not comprised in the approximate theory. Mode identification is extremely important and involves an investigation of the amplitude distribution pattern in the stationary wave system of the mode. The methods we most use for this purpose are (1) mechanical probing over the surfaces, (2) schemes of selective plating precisely applied to enhance the probable mode, and (3) the application of powder or liquid to form patterns on a vibrating surface. The precisely designed plating are applied by a photographic method, using jigs for exact alignment. Flat plates are used both as a concession to theory and to encourage the proliferation of possible modes. 4-12-37 EFFECT OF PLATING TO FREQUENCY ON THE STABILITY OF QUARTZ RESONATORS Richard B. Belser & Walter H. Hicklin Engineering Experiment Station, Georgia Institute of Technology In order to determine the effect of the frequency adjustment step on the stability's of 16.5 mc AT-Cut quartz resonators, 175 resonators have been fabricated and tested. The frequencies of these have been measured at a constant temperature of 85 degrees C over period of 60 to 180 days. Among the resonators fabricated were 30 plated with a single coat of evaporated gold and mounted in the HC-6/U cans by methods known to give high stability, 71 similarly mounted but overcoated to frequency subsequently with a second coat of evaporated gold, and 20 frequency adjusted by partially deplating the single layer plating by positive ion bombardment or by using the Tesla discharge technique. Similarly fabricated specimens (29), except for the deplating adjustment, were mounted in glass containers. The use of reclaimed resonator blanks and containers for the first 79 units fabricated contributed to a greater variation in data than was expected. However, data obtained subsequently with new blanks and containers verified, in general, the results obtained from the earlier data. Over-plating a gold plated resonator with a second coat of gold for frequency adjustment did not appreciably degrade the frequency stability of the original resonator. In the limited number of tests conducted, adjustment by ion bombardment for a range of several thousand cycles did degrade the frequency stability's of the original units. Of thirty resonators plated by evaporation of a single coat of aluminum on the hot (450 degree C) quartz substrate a number exhibited frequency drops of 0.0002 to 0.0006 percent in 60 days and thereafter stabilized at slopes of less than 0.00005 percent per month. The bulk of those that did not stabilize proved to be leakers. Increases in the R subscript s of a few resonators, apparently as a result of oxidation of the thin aluminum film, impressed an upward drift on a few resonators. Consideration of this factor is necessary in the analysis of the aging behavior of aluminum coated resonators. Ten resonators plated by evaporation of a single coat of silver on the hot (200 degree C) quartz substrate mounted in the HC-6/U container exhibited stability's nearly equivalent to the gold plated resonators. Unexpected downward drifts of a large number of gold plated resonators led to the examination of all units for leaks by a vacuum leak test. Cracks of the glass type bases of the HC-6/U containers were found in a high percentage of units. These developed upon the act of inserting the resonators in tight sockets of the constant temperature oven and vitiated much of the collected stability data. Different rates of drift appeared to be proportional to different sizes of micro-leaks. Leaks in the HC-6/U containers produced in this innocuous manner appear to be responsible for much of the loss of stability of units mounted in that container. The value of the glass containers for both experimental studies and practical use is that it is not subject to the development of micropores with time; the development of these appears to be an intrinsic weakness of the HC-6/U containers as now designed and sealed. 1-12-67 IMPROVING THE QUALITY OF SYNTHETIC QUARTZ D.R. Hale & Frank Augustine Clevite Research Center At the last symposium qualitative observations on X- irradiated synthetic quartz were presented and the greater darkening of specimens grown in the presence of added aluminum was shown. Absorption spectra have now been taken. Z-growth quartz containing added aluminum shows the now well-known band at 475 mu, sometimes called the A-band. It also seems to show a peak at about 210 mu. Plus X-growth shows much greater absorption than the Z-growth at the same wavelength with rather little difference in shape depending on whether aluminum was added to the hydrothermal solution or not. Minus X-growth normally shows the 475 mu band and a hump at about 310 mu; when aluminum is added, the 475 mu peak has become a hump and a sharp absorption peak appears at 290 mu. Germanium-doped minor r-growth develops an absorption peak at 285 mu believed to be the same peak shown by the minus X-grown quartz doped with germanium. This peak is absent from minor r-growth quartz when free from germanium. Several specimens of synthetic quartz were examined with a double crystal X-ray monochrometer. They show a broad range of relative structural perfection in terms of reflection versus rocking angle. Fissure flaws in quartz grown in small autoclaves are believed to be caused by poor diffusion of the reacting species; they may be eliminated by decreasing the crystallizing temperature. 1-12-84 X-RAY IRRADIATION ON THE ANELASTICITY OF NATURAL AND SYNTHETIC QUARTZ J.C. King Bell Telephone Laboratories Various samples of natural quartz, and synthetic quartz, grown from Z-cut, and z-minor rhombohedron seed faces have been used to fabricate 5 mc AT-cut precision crystal resonators. Measurements of the Q of these crystal units between liquid helium temperature and 100 degrees C, before and after x irradiation, have been carried out. Within this temperature range the loss curves for the unirradiated samples are dominated by the anelastic absorption centered about 50 degrees K. This is especially apparent in synthetic quartz where Q to the -1 in some specimens is observed to be as large as 8 x 10 to the -4. X-irradiation is found to have a profound effect upon the anelasticity of quartz. In all samples so far investigated, the crystal defect responsible for the relaxation absorption at 50 degrees K is all but eliminated. In addition, the ionizing radiation induces another structural relaxation process of considerable strength in some samples. The induced relaxation is manifested in part by an absorption peak at 100 degrees K which is computed to have an activation energy of 3000 cal/gm mole and a relaxation time of approximately 10 to the -14 sec. Since structural relaxation contributes a plastic component to the elastic strain, the quartz vibrators suffer a change in their resonant frequency whenever a process of stress relaxation is either induced or removed. Differences between the frequency-temperature behavior of crystal samples with and without relaxing elements can be associated with change in the temperature coefficient of the elastic modulus, attributable to stress relaxation. 3-12-101 PILE IRRADIATION OF QUARTZ CRYSTAL UNITS F.E. Graham & A.F. Donovan Admiral Corporation Because of the radiation from nuclear reactors used for the propulsion of military vehicles, an additional environmental requirement - nuclear radiation - is imposed upon electronic components. For this reason an investigation was made of radiation effects on the resonance characteristics of fourteen types of quartz crystal units. The elements studied were of the AT, DT, NT and GT variety. All pile irradiation's took place in the CP-5 research reactor of Argonne National Laboratory; here the crystal units were subjected to a total integrated thermal neutron flux of approximately 10 to the 18th neutrons/cm squared/sec. The total gamma dose was approximately 2 x 10 to the 8th roentgens. Measurements were made before, during, and after irradiation. Selected crystal units were also irradiated in the 20 kilo- curie cobalt 60 facility of Admiral Corporation. Here an attempt was made to distinguish between damage due to neutron bombardment and that due to gamma irradiation. The major results of the investigation are as follows: 1. Most structural materials currently used in the fabrication of military crystal units are unsatisfactory for use in a nuclear environment. 2. The change in resonance characteristics of crystal units operating in thickness-shear vibrational modes is much greater than that of crystal units operating in either flexural or face-shear modes of vibration. 3. The performance of crystal units in a nuclear environment is dependent on: a) the techniques employed by the various manufacturers; b) the past history of the crystal unit; and c) the various other materials used in their construction. 4 .Recommendations can be made for the improvement of reliability and performance of crystal units intended for use in a nuclear environment. 5. Recommendations can be made concerning the methods of conducting future investigations. 6-12-131 FUNDAMENTAL STUDIES ON AN IMPROVED CRYSTAL-CONTROLLED STANDARD W.L. Smith & A.W. Warner Bell Telephone Laboratories, Inc., Whippany, NJ The purpose of the work to be described is the development of a quartz crystal frequency standard for USASEL improved by at least one order of magnitude beyond the best designs presently available. This goal has been interpreted to be a frequency aging rate of 1 part in 10 to the 10th per month or better and a frequency stability from second to second of 1 part in 10 to the 10th. That is, the frequency averaged over any one second period will not differ from that of any other one second period by more than 1 pp 10 to the 10th. We have two principal schemes to accomplish this, both using an AT-cut crystal unit. The first uses a relatively simple crystal unit in a liquid helium bath at about 4 degrees K. The second uses a more precise crystal and a well regulated oven operating near room temperature. 4-12-162 RESEARCH AT NBS BOULDER LABORATORIES ON QUARTZ CRYSTAL RESONATORS AND OSCILLATORS AT LOW TEMPERATURES F.P. Phelps & A.H. Morgan National Bureau of Standards Measurements performed at NBS Boulder Laboratories on the short term and long term frequency stability of crystal controlled oscillators and quartz resonators, temperature stabilized by cryogenic fluid, are described. Included are some details on the cryogenic temperature ovens used, some of the troubles encountered with them, as well as their long term and short term performance characteristics. Effects of vibration, filling the cryogenic ovens, temperature inversion occurring in the liquid, and ambient temperature changes on the resonators and oscillators are discussed. Some information on the frequency measuring systems will also be given. 10-12-193 A FREQUENCY STANDARD FOR USE IN MISSILES H. Paul Brower Collins Radio Company Under contract with the U.S. Army Signal Engineering Laboratories, the Collins Radio Company has under development a frequency standard whose environmental characteristics will allow its satisfactory use in a missile. The environmental characteristics of this unit include a preliminary stability of 1 part in 10 to the 6th and an ultimate stability of 1 part in 10 to the 8th for one hour under vibrations of up to 10 g's over the range of 10 to 2000 cycles per second, static accelerations up to 60 g's along one axis and an operating temperature range of +15 to +50 degrees C. The frequency standard is to be completely transistorized with an output power of 5 milliwatts into 50 ohms at 99.92 megacycles and is not to exceed 30 pounds in a maximum allowable volume of one- half cubic foot. The first half of this project is nearly completed and the units already delivered weigh eight pounds in one-sixth cubic foot and have a frequency stability of better than 1 part in 10 to the 6th under all conditions. Work is progressing satisfactorily toward the ultimate goal but in the final analysis the attainment of the 1 part in 10 to the 8th will depend on the performance of commercially available crystal units under the vibration and acceleration conditions. 4-12-211 RUGGEDIZATION OF LOW FREQUENCY CRYSTAL UNITS J.M. Wolfskill Bliley Electric Company Shock and vibration requirements on electronic equipment and components today presents probably the largest single mechanical problem in the design of quartz crystal units, particularly in the low frequency range where the mass of the crystal varies greatly with oscillation frequency. Since the crystal blank must be supported in such a way that its electrical characteristics are not disturbed and still be capable of giving dynamic performance under high shock, and mechanical vibration frequencies of 20 to 2000 cps at 10 G's, the support mechanism presents a real problem. The purpose of this paper is to present a method of supporting crystals in the low frequency range from 200 to 500 kc, which will provide standard CR-26/U crystal performance both during and before and after the shock and vibration requirements of 100 G and 20 to 2000 cps at 10 G respectively. The design of the support is based on complete symmetry around the central axis of the crystal in which the support wire length, diameter and termination weights for a given mass of crystal have been calculated to take the "Rotational" and "Translational" mechanical response frequency in all planes outside of the shock and frequency range of interest. 4-12-241 PHASE STABLE QUARTZ CRYSTAL UNITS Louis A. Dick The James Knights Co. The report of the analytical and experimental studies of crystallographic orientations and crystal plate mountings leading to an improved phase stable crystal unit under mechanical shock and vibration is made. An hypothesis will be advanced which suggests that a neutral axis (or axes) exists in the plane of an AT plate and if the blank is mounted at the ends of this axis (or axes), the frequency (or phase) of the crystal unit will not be changed by any stress applied through the mounting points. Evidence will be given showing the importance of oscillator design on the problem of phase (or frequency) stability as a result of mechanical shock and vibration. 4-12-260 MODERATE PRECISION CRYSTAL UNITS Donald L. Hammond Scientific Radio Products, Inc. Moderate precision crystal units fulfill the need for frequency control elements in the range between normal crystal units which are produced at standard tolerances and in large quantities, and the high precision crystal units which are produced at comparatively high cost with extremely tight tolerances and in relatively small quantities. The greatest need for the moderate precision crystal lies in the application to single side band communication systems. A study has been conducted to develop moderate precision fundamental mode crystal units in the frequency range from 1.0 to 20.0 MC. The primary requirements are: an aging stability greater than 2 x 10 to the -7/wk, a temperature coefficient less than 2 x 10 to the -7/degrees C, and a tolerance on nominal frequency at the operating temperature (85 degrees C) of 10 to the -5. The unit is sealed in the metal HC-6/U holder. The design procedures employed in obtaining a near optimum resonator, established optimum designs, and the performance characteristics obtained are described. Special processing techniques which have been developed to improve the temperature coefficient and aging characteristics are discussed in detail. The precise measurement of the frequency temperature characteristics and the measurement of the stability of the moderate precision crystal units with respect to time require special equipment. These are discussed in detail. 4-12-281 LOW FREQUENCY XY' FLEXURE CRYSTAL UNITS A.S. Matistic Bulova Watch Company, Electronics Division The XY' flexure crystal is a single crystal element, bar shaped and approximately square in cross section. Four electrodes plated on the major surfaces are suitably paired to provide a two terminal crystal unit capable of excitation in a flexure mode; the generated frequency is approximately one-half the value of a comparable NT crystal having the same length. The crystal length reduction resulting from utilization of the XY' flexure crystal was exploited for downward extension of the frequency range encompassed by MIL TYPE crystal units CR-50/U and CR- 38/U. Crystal bars for frequencies as low as 8 kc were suitably mounted in HC-13/U holders; further extension to 2.4 kc was attained using the same crystal holder configuration except for increased holder length. Limited production and favorable results have been achieved in the frequency range 2 kc to 46 kc; approximately 12 different frequencies have been fabricated in this range. Both evacuated glass bulbs and metal holders containing relatively inert atmospheres were employed for mounting. Related dimensions, methods of fabrication, crystal parameters and temperature vs. frequency characteristics are discussed. Comparisons with similar crystal types are cited, significant differences are noted and recommendations for effective utilization are offered. 4-12-296 DESIGN DATA FOR HF AT CRYSTAL UNITS L. Tyler and C. Rutkowski Union Thermoelectric Corporation From the standpoint of resonator design, the 4 to 20 mc range can be subdivided into three frequency ranges, each with its own particular problems. From 8 to 20 mc, uncontoured, circular plates are satisfactory provided the diameter- thickness ratio is kept within suitable limits. From 4 to 6 mc very good results are obtained with a plano-convex shape, the curvature of the convex surface depending upon the frequency. In the range 6 to 8 mc satisfactory results can be obtained using modifications of the plano-convex design, or plates having a circular edge bevel, dimensions again depending upon the frequency. Studies have been made to determine the ZZ' orientation angle for minimum frequency deviation over several temperature ranges, including -55 to +90 degrees C, for both uncontoured and contoured plates. The curves for optimum angle vs. diameter/thickness ratio are independent for contoured and uncontoured plates. ZZ' angle tolerances for frequency deviations of + or - .005% and + or -.003% have been determined. The study of frequency plate-back with aluminum vs. resistance show a marked difference in the rate of frequency change between contoured and uncontoured plates. 4-12-316 DESIGN PARAMETERS FOR VHF CRYSTAL UNITS D. McKeown U.S. Army Signal Engineering Laboratories A study has been made to determine the effects of various blank sizes, plating areas and thickness' on the quality of VHF crystal units. Two groups of AT cut quartz crystals, having fundamental frequencies of 25 and 35 mc were used. The crystals were resonated as passive elements on overtones which fell in the 75-175 mc frequency range and their impedance's were measured on a bridge set-up. The motional arm parameters were measured to accuracy's of + or - 3% by correcting for the shunting effects of the spurious modes and keeping the crystal's drive constant. The results of the study can be summarized as follows. For wide variations in the design parameter, the 25 mc crystals had Q's of 85,000 + or - 3% for the third, 70,000 + or - 20% for the fifth and 60,000 + or - 10% for the seventh overtone, and the 35 mc had Q's of 75,000 + or - 20% for the third and 50,000 + or - 10% for the fifth overtone. At any particular overtone the Q was found to be the lest affected motional arm parameter with changes in the design parameters. In general, the crystals having the larger motional arm resistance had the larger motional arm inductance so that comparing crystals on the merits of the motional arm resistance had little meaning. At 175 mc where a direct comparison between 35 and 25 mc crystals could be made, this was especially true. It was found that, although the 35 mc crystals had lower motional arm resistance's, they did not have higher Q's which indicates that the best VHF crystals are obtained from low fundamental frequency crystals. The study also includes an analysis of the mounting losses encountered when a crystal is placed in a wire holder and how these losses were reduced by modifying this holder. 11-12-334 INVESTIGATION OF NEW TECHNIQUES FOR MEASURING CRYSTAL UNITS A.O. Plait, H.G. Tobinski & H.E. Gruen Armour Research Foundation Current work on an investigation of methods and techniques for accurate measurement of crystal resonant frequency and power dissipation is reported. Resonance measurement by indication of both phase angle and voltage or current level are investigated. Several forms of crystal driving circuits including transmission and bridge circuits are analyzed to determine their sensitivity as related to phase and amplitude indication. Comparison of available phase indicating systems to the requirements of the analyzed circuits shows insufficient sensitivity to assure resonance indication to the desired one part in 10 to the 8th for typical crystals. The most promising method is shown to be the use of a bridge associated with the crystal network. Resolution and repeatability of one part in 10 to the 7th are readily obtained, however, considerable care in test procedure and close temperature control of the crystal are required to evaluate the method further. Repeatability of crystal resonance measurements also requires a reproducible indication of crystal drive. Voltage measurements must be repeated within one-half percent for typical crystals at drive levels of one- half milliwatt to assure frequency repeatability to one part in 10 to the 8th. Evaluation of voltage measuring methods and design of an r-f voltage reference source for use in this evaluation are described. 11-12-359 AN INSTRUMENT FOR DETECTING UNWANTED MODES IN OSCILLATOR CRYSTALS Joseph Loos Motorola, Inc. The basic purpose of this study is to develop a test instrument which will determine the acceptability of oscillator crystals in the range of 1 to 125 mc from the standpoint of their spurious responses. This instrument consists of two units, one covering 1 to 40 mc and the other covering 40 to 125 mc. The lower frequency unit covers its range in two bands. Circuits used for each band are illustrated and described. Functions of all variable controls are discussed. Metering circuits are also explained. The panel layout of both unit is illustrated. The controls are described in detail. The operating procedure of testing a crystal for unwanted spurious modes is outlined. The benefits of using an "Interrupter" to momentarily disconnect B+ from the detector at short periodic intervals are explained. Methods employed to nullify the effect of the crystal shunt capacity are described. The sensitivity of the detector units is sufficient to detect spurious modes in a major portion of manufactured crystals. The method used to determine the setting of the sensitivity control at any particular frequency is discussed. 11-12-383 VHF CRYSTAL PARAMETER MEASUREMENTS Samuel N. Witt, Jr. Georgia Institute of Technology For some time, Crystal Impedance Meters have been available for measuring the parameters of quartz crystals at frequencies as high as 200 mc. The accuracy's obtainable are generally sufficient only for quality checking and not for precise laboratory analysis. Also, the instruments do not permit evaluation of al of the crystal parameters. No instruments are currently available for either quality checks or laboratory measurements of crystals at frequencies above 200 mc. Systems are under development at Georgia Tech for both Crystal Impedance Meter applications and laboratory investigations of quartz crystals at frequencies from 175 to 300 mc. The eventual goal for the CI Meter type of instrument is to be able to make effective resistance measurements to within + or - 5%. The Laboratory Standard Measurements System is to be able to measure impedance magnitude and phase angle within + or- 1% and + or - 1 degree respectively. Both systems must be able to measure frequency with great precision and to control the crystal drive level to within + or - 20%. The Laboratory Standard System, which consists primarily of commercially available instruments, is presently capable of measuring all of the quartz crystal parameters with less than 4% error and controlling the crystal drive level to within about 10%. Primary sources of measurement error have been evaluated and are discussed in some detail. The drive level measurement system is also discussed in detail. Methods of interpreting the laboratory data by using an electronic digital computer are described. Several design principles for instruments requiring lesser accuracy's have been investigated. The conventional CI Meter method has been temporarily abandoned at frequencies above 200 mc. A method using a specially designed bridge has been developed but not yet perfected. Another method using a novel circuit approach looks promising as a very simple means of measuring the crystal Q and effective resistance. Suitable instrumentation for use with this latter method has not yet been perfected, however, in its current form the method has other useful applications such as the locate and quantitative measurement of all spurious crystal responses. Applications and measurements of quartz crystal at frequencies above 300 mc are also discussed briefly. 6-12-406 A PRECISION DELAYED PULSE GENERATOR AS A VARIABLE TIME INTERVAL STANDARD Dexter Hartke, Marvin Willrodt, & Donald Broderick Hewlett-Packard Company A high speed multiple preset counter and a pulsed crystal oscillator, which can be synchronized in constant phase with respect to a random time reference pulse, comprise the basis of a new precision delayed pulse generator. The range of delay times is continuously adjustable from 1 to 10,000 microseconds and the maximum error is less than: (+ or - 0.1) microseconds plus (+ or 0.001%) of delay. Output pulses of various characteristics are available and the device can also function in a variety of other capacities which include a multiple preset one megacycle counter, a gate function generator, and a pulse rate or frequency divider. 6-12-420 FREQUENCY MULTIPLICATION WITH PHASE-LOCKED OSCILLATORS Harold T. McAleer General Radio Company The uses of phase-locked oscillators in frequency multiplication are briefly reviewed. A simple automatic-phase- control (APC) system is analyzed as a servomechanism analog. Three major characteristics of the system are considered: the lock range, the capture range, and the bandwidth. The lock range is the total drift in the unlocked oscillator frequency which can be exactly compensated by the locked system. The capture range is the largest unlocked frequency difference at which synchronization, or lock in, will occur. The bandwidth of the system expresses the performance of the system as a low- pass filter with respect to noise components existing in the input to the system and as a high-pass filter with respect to noise components generated within the output oscillator. The mutual interdependence of these characteristics and the various quantities affecting each one are discussed. The conditions for stable operation of the system are established. The unlocked, locking in, and locked conditions of operation are discussed. Simple design criteria are established. 5-12-437 FILTER CRYSTALS R. Bechmann U.S. Army Signal Research & Development Laboratory The requirement for crystals used in filter networks are considered. An essential requirement for filter crystals is that the excited resonance frequency be sufficiently isolated from other responses. For low frequency crystals, this requirement is normally fulfilled except in the case of a few dimensional ratios. Thickness modes, in particular the thickness-shear type, usually have a variety of modes in the vicinity of the main response rather than a single mode. The methods for suppressing unwanted thickness-shear modes of circular quartz plates in the frequency range 0.5 to 10 mc are discussed. For high frequency quartz filter crystals in the range 7 to 30 mc, a triangular plate shape has been found to form boundaries resulting in a satisfactory reduction of unwanted modes. 5-12-475 HIGH FREQUENCY CRYSTAL FILTERS R.A. Sykes Bell Telephone Laboratories The problems peculiar to the performance and design of high frequency crystal filters are presented and discussed. The derivation of design equations for lattice and ladder type sections are shown which allow a quick appraisal of the feasibility for a given set of filter requirements. Finally, specific designs for single side band transmission and reception are presented for frequencies in the vicinity of 9 mc. One of these is shown to have a minimum discrimination of 60 db at a frequency 750 cycles from the edge of a pass band 3700 cycles in width. The in-band loss is of the order of 1 db. 5-12-501 TYPE NB BANDPASS CRYSTAL FILTERS Leo Storch Hughes Products, Division of Hughes Aircraft Co., Los Angeles, CA In a paper entitled "High Frequency Crystal Filters" and presented at last year's Symposium, a general discussion was given of Type NB bandpass crystal filter design and of the flexibility it offers in developing high-frequency filters that overcome many of the limitations which are normally caused by the relatively narrow range of motional crystal capacitance and the rather inflexible crystal capacitance ratio. In this paper, the principles basic to the Type NB design procedure are dealt with in greater detail, and the essential analytical aspects are covered. Furthermore, measured attenuation characteristics are presented for Type NB filters with (a) center frequency 10.7 mc and 6 db bandwidth 70 kc; (b) center frequency 20 mc and 3 db bandwidth 150 kc. In both of these cases the passband ripple does not exceed + or - 0.25 db, although effective coil Q's are kept in the vicinity of 40. 7-12-517 PROGRESS OF MASER WORK AT FREQUENCY CONTROL DIVISION, USASRDL F.H. Reder Fort Monmouth, NJ 1. MASER versus other Molecular or Atomic F-Standards -- The MASER's advantages are its high short-time stability and its relatively simple design. It seems, therefore, particularly suitable for applications calling for utmost mobility, as in missiles and satellites, and for applications requiring highest short-time stability, in some cases even under severe environmental conditions. It is also conceivable that, eventually, a combination of an atomic beam device driven by a MASER will result in an ideal frequency standard combining in one device the short-time stability of its MASER flywheel and the long-time stability of the atomic beam component. A basic disadvantage of the MASER over passive atomic standards is the strong frequency pulling effect of the cavity. For appreciation of the general progress in the MASER art, let us first take a look at Fig. 1, showing the original MASER built at Columbia University by Townes and Gordon in 1954/55. 7-12-534 MEASUREMENT OF MASER FREQUENCY IN TERMS OF CS BEAM STANDARD Gernot M.R. Winkler U.S. Army Signal R&D Laboratory It is obvious that for every suitable MASER it is desirable to know the frequency-time behavior of an operating MASER. In order to get a better understanding of the influence of various characteristics, as cavity mode, focuser voltage, temperature stabilization of the cavity, varying nozzle pressure, etc. on the MASER output frequency, it was deemed most suitable to design an automatic frequency measurement system which refers the MASER frequency to a standard frequency. Due to the very high accuracy's involved (resolution 1.10 to the -10th) the use of a cesium beam frequency standard is advantageous and allows a drift free absolute measurement. Due to the availability of the "Atomichron", this type of frequency standard was used in the circuit indicated in Fig. 1. The circuit makes use of a phase locked klystron, oscillating at exactly 23,840 Mc/s. The necessary offset secondary standard frequency is supplied by a Rhode and Schwarz synthesizer. 7-12-538 MASER RESEARCH AT NEUCHATEL UNIVERSITY, SWITZERLAND J.A. Bonanomi Laboratoire Suisse de Recherches Horlogeres, Neuchatel Several Ammonia-masers have been built, the frequencies of which are resettable within one part in 10 to the 10th. The difficulty due to the pulling of the frequency by the cavity has been overcome in several ways. The effects due to state selector voltage and other parameters are nearly absent for the 3,2-line; this suggests the construction of a maser oscillating on the 3, 3 line of N to the 15th-enriched ammonia. 7-12-551 BEAM MASER TECHNIQUES W.H. Higa Jet Propulsion Laboratory, Cal Tech, Pasadena, CA Recent progress in beam-maser techniques is described. The design of beam sources and focusers has been improved sufficiently that liquid nitrogen is no longer needed for the masers under development at the Jet Propulsion Laboratory. The feasibility of designing a "dry" sealed-off maser, which uses titanium gettering to dispose of the spent ammonia gas, has been verified. Also, some experiments have been carried out with a two-cavity maser, in an attempt to resolve the line structure of the main 3-3 inversion line of ammonia. Details of this experiment are described. 7-12-569 A SEALED-OFF MASER S. Johnson Polytechnic Research & Development Co. The paper will describe the development effort on a sealed-off MASER and will deal in detail with the sealing off problem, the stabilization of molecular flow, the reduction in time of the rejuvenation procedure, and the tuning of the MASER cavity. Special techniques which are essential in the all-metal construction of the MASER will be described and the initial test data on the performance of two MASERS will be given. 7-12-577 REALIZATION AND MEASUREMENT OF LONG FREE ATOM SPIN STATE LIFETIMES A.G. Dehmelt University of Washington When alkali atoms in a magnetic field are irradiated with their suitably circularly polarized and filtered resonance radiation introduced parallel to the field, or Z-direction, only the atoms pointing toward the positive Z-axes absorb while the atoms pointing towards the negative Z-axes are transparent to the radiation. The absorption and re-emission cycles can now cause a sizable orientation, with most of the atoms collecting in the transparent direction provided the experimental conditions insure a long lifetime against disorientation. Since the transparency of the atom sample is a measure for its degree of orientation we have now a convenient tool for the measurement of spin state lifetime. It has been applied to sodium atoms diffusing in an argon buffer and rubidium and cesium atom contained in inert wall cells. In both instances relaxation time approaching a second have been observed, which corresponds to the order of a billion alkali-buffer gas and thousand alkali-inert wall collisions without disorientation. This indicates that ultimately resonance signal with a width of the order of a cycle should be obtainable. Results on low field paramagnetic rubidium and cesium resonance experiments employing inert wall cells and consideration for the choice of a suitable coating material will be discussed. 7-12-593 OPTICAL DETECTION OF THE CESIUM HYPERFINE TRANSITION Peter L. Bender & Earl C. Beaty, National Bureau of Standards Andrew R. Chi, U.S. Naval Research Laboratory The argon spectral line at 8521.4A has been used in the detection of the cesium hyperfine transition at 9192.63 mc. The argon line was Zeeman split to overlap one hyperfine component of the cesium resonance line at 8521A. A glass bulb containing cesium vapor diffusing in a buffer gas was illuminated by the argon light source and the scattered light was observed. Transitions from the upper ground state hyperfine sublevel to the excited state were produced, and the atoms then returned by spontaneous emission to both ground state sublevels. There was thus a pumping of atoms out of the upper hyperfine level and into the lower one. This depletion of the population of the upper level caused a decrease in the amount of scattered light. Microwaves were then applied to the bulb by a horn antenna. At resonance the difference in population of the hyperfine levels was reduced and an increase in the scattered light was seen. Shifts in the resonance frequency of the (4,0) to (3,0) line with buffer gas pressure were observed for He, N sub 2, Ne, Ar and Kr, the smallest being -200 cycles/mm for argon and +580 cycles/mm for Ne. An upper limit of 10 cycles/cm of argon was found for the expected pressure-dependent line breadth caused by cesium argon collisions. The microwave frequencies were obtained from an Atomichron by feeding in an accurately known variable frequency at the 6.315920 mc stage in the synthesizer. The basic 5 mc frequency for the multiplication chain was supplied by the 5 mc output from another Atomichron which was operating normally. 17-12-606 GAS CELL "ATOMIC CLOCKS" USING BUFFER GASES AND OPTICAL ORIENTATION M. Arditi ITT Laboratories The need for a small size "atomic clock" compatible with airborne operation has led to the development of a gas cell simpler in construction than the atomic beam apparatus. Following a suggestion by R.H. Dicke(1) for an atomic sodium clock employing buffer gas reduction of the Doppler width and following recent approaches to increasing useful population differences and detection sensitivity by employing optical orientation methods, we have investigated the hyperfine transitions in the ground state of Na to the 23rd and Cs to the 133rd (delta F = 1, delta m sub F = 0). The effect of various buffer gases in sodium and cesium vapors will be discussed and preliminary results on sodium and cesium "gas cell clocks" will be described. 10-12-623 THE VELOCITY OF LIGHT J.R. Zacharias Massachusetts Institute of Technology The velocity of light and its measurement will be discussed from a general point of view. The precision of such measurements may be improved through the use of accurate frequency standards. 10-12-624 EXPERIMENTAL TESTS OF SPECIAL AND GENERAL RELATIVITY BY ACCURATE TIMING DEVICES C.H. Townes Columbia University The accuracy of timing devices is advancing to the point where they may be used for detecting a number of very small effects connected with general and special relativity, and thereby afford critical tests of these theories. Possible experiments of this type will be discussed, including those which may test for ether drift, gravitational red shift, and transverse doppler effects. The use of satellites for some of these experiments will be considered. 7-12-625 DISCUSSION OF SOME LIMITS OF ATOMIC FREQUENCY CONTROL T.R. Carver Princeton University Principally to stimulate discussion, some remarks will be made about limits of accuracy of atomic clocks, considering such questions as averaging time, minimum volume, mass, atomic cross section, and type of detection. Practical reasons for present failure to reach such limits will be rechecked. If time permits, some fundamental limitations involved in the physical notion of time will be mentioned. 7-12-632 DESIGN CONSIDERATIONS OF ATOMIC BEAM FREQUENCY STANDARDS FOR MISSILE ENVIRONMENT R.T Daly TRG Inc. The effect of both external and internal corrupting forces on the performance of an atomic beam frequency standard has been analyzed. Forces which vary rapidly in time are represented as statistical quantities and a minimum root-mean- square error criterion is applied. Quantitative expressions are obtained for the effect of forces acting at two points in the system: the controlled crystal oscillator and the atomic beam tube. In the former case and in the range of interest, the important parameters are found to be the crystal sensitivity to the applied force and, more importantly, to the quantity f sub c tau which is the product (servo gain crossover frequency) x (measuring time interval). As an example of this result, the consequence of vibration isolator resonance is evaluated. In the case of the beam tube a "figure-of-merit" expression is derived which determines the significant design parameters and operating levels in terms of the r.m.s. deviation and measuring time allowed. Numerical evaluation of the "figure-of-merit" for a new beam tube configuration has been carried out. The results will be presented. A separate parameter is found to represent a limitation in both cases above, viz., the beam transport time delay, the flight time of the particles from the midpoint of the r.f. excitation cavity to the detector. This quantity also appears in the tolerance of the tube to transverse acceleration. Both considerations indicate that optimum design lies in the direction of broad resonance lines. 9-12-648 RESULTS OF COMPARISON: ATOMICHRON - BRITISH CESIUM BEAM STANDARD A.O. McCoubrey National Company, Inc., Malden, MA During March of this year, two Atomichrons were compared to the cesium atomic beam frequency standard at the National Physical Laboratory, Teddington, England. The tests included systematic measurement of frequency differences following repetitive misalignment of the Atomichrons and re-alignment according to a procedure established for field use. In addition, tests were carried out to establish the origin of the small frequency difference which was found. Analysis of the data indicated the Atomichrons to be within one part in 10 to the 10th of each other and about 3.5 parts in 10 to the 10th high with respect to the N.P.L. standard. The standard deviation associated with the measurements was about + or - 5 parts in 10 to the 11th. The methods used in making the measurements, the results of the comparison and the probable sources of the residual frequency difference will be discussed. The comparison program was a cooperative effort including contributions by the following organizations and persons: U.S. Army Signal Corps -- F. Reder & G. Winkler National Physical Laboratory of England -- L. Essen & J.V.L. Parry National Company-- J. Holloway & W. Mainberger It is a pleasure to acknowledge the support of the program as well as the equipment provided by the Signal Corps. 9-12-665 COMPARISON OF ATOMIC AND ASTRONOMICAL TIME Wm. Markowitz U.S. Naval Observatory The unit of time, the second, was redefined by the International Committee of Weights and Measures in 1956 so as to be a constant unit of time, identical with the second of Ephemeris Time. The second of Universal Time which was formerly the unit, is a variable unit of time. Obviously, it is desirable that the frequencies of atomic standards be referred to the second of Ephemeris Time. The National Physical Laboratory, Teddington, and the U.S. Naval Observatory, Washington, have been engaged since June 1955 in a joint program for the determination of V sub E, the frequency of cesium in terms of the second of E.T. E.T. has been determined at the U.S. Naval Observatory with the dual-rate moon position camera since June 1952. The program of reduction for the IBM 650 has recently been completed and most of the plates taken have now been reduced. As an intermediate step, V sub U, the frequency of cesium in terms of the second of U.T. was determined at monthly internals from June 1955 to January 1958. The mean value of V sub U for this period is 9,192,631,880 cycles per second of U.T. The reductions of the moon observations made thus far indicate that V sub E is less than 9,192,631,800 cycles per second of E.T. 1-13-1 DISLOCATION AND IMPURITY INDUCED DEFECTS IN QUARTZ W. C. King Bell Telephone Laboratories, Inc. Whippany, N. J. I. INTRODUCTION The acoustic absorption spectra in crystals is proving of considerable value in the study of imperfections. Defects such as dislocations, interstitialcies, and impurity induced lattice distortions often reveal themselves in terms of specific stress induced relaxation processes. Studies of the effects of ionizing radiation, temperature annealing, doping agents, cold- work and knock-on radiation on a given relaxation process assist in defining the underlying defect. The investigation of the acoustic absorption in natural and synthetic quartz (ref. 1) has done much to account for differences in the room temperature behavior of resonators fabricated from the two materials. It has been shown, for example, that differences in the frequency-temperature characteristic between natural and synthetic AT-cut resonators, operating over the range -60 to 100 C, derive from an alteration of the shearing modulus in synthetic quartz which is attributable to the 50 K deformation defect. Also, the effect of x-irradiation on the resonant frequency of AT- and BT-cut resonators is now known to derive from the irradiation induced "100 K" deformation defect. Thus far it is apparent that differences in the room temperature behavior of various kinds of quartz are not closely related to the concentration of dislocations in the crystal. This is inferred from the rather uniform amplitude of the dislocation relaxation absorption from one sample to another. In the present discussion we will dwell not so much on the phenomenological association of defect induced relaxation processes with resonator behavior but rather concern ourselves at this time with a) a more detailed study of the dislocation relaxation process in quartz, b) an interpretation of the 100 K (x-irradiation-induced) absorption, and c) a preliminary account of the effect of electrolytic purification on the Q of synthetic quartz. 1-13-17 FACTORS INFLUENCING THE RATE OF GROWTH OF SYNTHETIC QUARTZ CRYSTALS R. A. Laudise Bell Telephone Laboratories, Inc. Summary A systematic study of the growth rates of quartz under hydrothermal conditions in NaOH is described. It was found that: (1) The rate was a linear function of At, the temperature difference between the dissolving and growth zones. (2) The log of the rate was a linear function of the reciprocal of the absolute temperature of the growth zone. (3) The rate was dependent on the per cent of fill in a roughly linear way which probably can be explained from solubility considerations. (4) The rate was linearly dependent on the super- saturation. The rate was found to be dependent on seed orientation, concentration of NaOH, and per cent of baffle left open in a manner generally consistent with previous investigations. Methods for determining the solubility of quartz under hydrothermal conditions are mentioned and the systematic dependence of solubility on per cent fill and temperature is described. The mechanism of crystallization is examined, a rate equation is developed, and thermodynamic data for the activated state are calculated and discussed. The problem of crevice flawing is considered. The resultant study lead to means of achieving rates in excess of l/4"/da in the z direction and these experiments are discussed as is the process whereby the laboratory findings were transferred to a pilot plant. Some comparisons with lower pressure kinetics in carbonate solutions are made and the implications of rate studies for the preparation of high Q quartz are drawn. 3-13-37 DEFECTS OF THE QUARTZ SYSTEM PRODUCED BY NEUTRON IRRADIATION R. A. Weeks Solid State Division, Oak Ridge National Laboratory Summary A comparative study of the electron spin resonance (ESR) spectra of neutron irradiated high purity silica and quartz single crystals confirms the presence of three or probably four defects of the quartz system which are paramagnetic. In quartz y-ray irradiation not only ionizes defects of the lattice already present, but also impurities. The saturation concentration of the lattice defects is of the same order as the impurities. prolonged neutron irradiation (> 5 x 10 exp18 fast neutrons/cm2) increases the concentration of the lattice defects at least an order of magnitude over the impurity concentration, thereby separating the two kinds of defects. Annealing of the paramagnetic lattice defects indicate the probable existence of at least two other defects of the lattice. The defect models suggested by the ESR spectra are as follows: The single line, g = 2.0006, is due to an electron trapped at an oxygen ion vacancy in agreement with the g <0. The large increase observed for this line upon annealing (300 C 30 min.) a specimen irradiated at low temperatures suggests two electrons may be trapped at such a vacancy and that this center is then stable at room temperature (although annealing has been observed in a specimen held at room temperature for several months). The anisotropy of a double line centered on the g = 2.0006 line, separation ~ 0.4 oersted, suggests a Si with three 0 and a trapped electron. The line, g = 2.0065, also increases with this anneal. Although confirmatory evidence from the anisotropy of the line is lacking, the only available hole traps (g >0) excluding impurities, are interstitial oxygen ions. A defect model for the neutron specific line, g = 2.0020, has not been devised. The anisotropy of this line indicates that it is a hole (g>0). 2-13-53 SOME NEW RESULTS IN THE MATHEMATICAL THEORY OF VIBRATIONS OF CRYSTAL PLATES R. D. Mindlin Columbia University 1. The Cauchy-Voigt equations of extensional vibrations of thin crystal plates have been examined with a view to converting them to equations of the form exp2 _ + nexp2 _ =0 so that general solutions, analogous to those available for isotropic plates, may be found. The conversion can be achieved by linear transformations if two relations exist among the constants of elasticity. The relations hold for four cuts of quartz: the Z- cut, a rotated Y-cut and two double rotation cuts. 2. Ekstein's frequency equation (Phys. Rev. 68, 11, 1945) for an infinite crystal plate with monoclinic symmetry has been a subject of study for a number of years because it is a possible basis of approximate solutions for bounded, rotated Y-cut, quartz plates. The analysis has now advanced to the stage where the intricate behavior of the branches at the cut-off frequencies can be expressed explicitly by simple formulas. This information, along with the network of bounds established previously (Newman and Mindlin, J. Acoust- Soc. Am. 29, 1206, 1957) facilitates the construction of a major portion of the branches for all frequencies and real and imaginary propagation constants. 3. Approximate equations of motion have been established which take into account the coupling of thickness-shear and flexural modes with extensional and face-shear modes. 2-13-54 MODES OF VIBRATION OF QUARTZ CRYSTAL RESONATORS INVESTIGATED BY MEANS OF THE PROBE METHOD I. Koga, University of Tokyo H. Fukuyo and J.E. Rhodes, Georgia Institute of Tech. SUMMARY Dr. Issac Koga and Dr. H. Fukuyo at Tokyo Institute of Technology developed equipment for studying strain distribution patterns of vibrating quartz crystal. The high resolution automatic recording equipment developed by Dr. Fukuyo has been brought to this country by him. He is studying circular quartz AT-cut blanks at the Georgia Tech Engineering Experiment Station. This equipment and its utilization is described in detail. Polarization patterns for the (3,1,1) and the (5,1,1) enharmonic modes will be shown (digits refer to distributions along coordinate axes x, y, and z where y is the thickness of the blank). 4-13-71 STABILITY STUDIES OF INDUSTRIALLY AND LABORATORY FABRICATED AT- CUT QUARTZ RESONATORS OF 16.25 MC FUNDAMENTAL FREQUENCY Richard B. Belser and Walter H. Hicklin Engineering Experiment Station, Georgia Institute of Technology SUMMARY One hundred quartz crystal 16.25 mc resonators of type CR l9-U have been obtained from each of six manufacturers. One third of each group were stored 25 C, 85 C, and 125 C respectively. The frequencies of those stored at 85 C were measured periodically at that temperature whereas those stored at 25 C and 125 C were brought to 55 C every 14 days for measurement. The better units exhibited both positive and negative drifts of 1 ppm in periods of 60 to 150 days at 25 C 2 ppm at 85 C and 5 ppm at 125 C; however, the bulk of the units exhibited far greater drifts than these. Fifty-four of the units stored at 85 C were leak tested. Six were shown to leak by a helium leak test but 49 were shown to leak by the vacuum oil technique. Leaks through the metal to glass seals of the base were the predominant type of leak. The results of the vacuum oil leak test were more nearly in agreement with aging data. Positive frequency drifts observed appeared to be associated with stressed electroplated nickel films or inadherence; and negative drifts with leaking, corrosion, or bimetal diffusion of the nickel and silver films commonly used for plating. One hundred 16.25 mc aluminum plated resonators have been fabricated in glass containers and stored at 85 C. Conditions of fabrication changed were substrate temperature during deposition, post deposition heating, vacuum bake-out and the atmosphere of the container--either vacuum or dry argon. The better units, 40 of the 100, exhibited only small random shifts of 0.5 ppm. The aluminum plating of the better units was deposited on the quartz surface after the surface was heated to 450 C and cooled to 250 C in vacuo. Subsequently the units were vacuum baked at 180 C for three hours before sealing in vacuo. 4-13-109 AGING CHARACTERISTICS OF QUARTZ CRYSTAL UNITS P.E. MULVIHILL U. S. Army Signal Research and Development Laboratory Hundreds of quartz crystal units were evaluated and the data from several types of test was analyzed with a view to obtaining an aging prediction formula from the correlation of (a) short and long term aging rates, (b) heat cycling and subsequent frequency change, and (c) leak rates and aging rates. During previous aging investigations, a "rule-of-thumb" for predicting frequency drifts with time was formulated as follows: A unit, stored at 83 C, which did not drift more than one-half ppm in five days, would not drift more than five ppm in six months. The data was analyzed in terms of this criterium. Noting the erratic behavior of some groups of units during the first five days the daily measurements were extended to ten days. The data is broken down into the following four categories as shown in Figure 1. The vertical axis is short term aging in terms 0.5 ppm in 5.0 days; the horizontal axis is the long term aging in terms of 5.0 ppm in six months. A Go-No-Go" description is shown in each quadrant. "In-In" describes those units which drifted less than 0.5 ppm in five days and remained within the 5.0 ppm criterium for six months; "In-Out" describes those units which were within 0.5 ppm in five days but drifted beyond 5.0 ppm in six months; "Out-In" is the group of those units which aged but less than 0.5 ppm in five days but less than 5.0 ppm in six months; the last quadrant includes those units which met neither requirement. Figure 2 shows the distribution for several types of units. The sum of the units below the horizontal dotted lines is the percent yield for the short term acceptance test. For the CR-5 4/U, this is 51%; for the CR- 53/U, 40%; and for the glass holder units, it is 67%. However only 2% of the plated, metal holder units, 25% of the pressure mounted units and 58% of the glass enclosed units also meet the long term aging requirement of 5.0 ppm in six months. The following is observed also from this figure. 1. Extending the short term period to ten days does not materially affect the acceptance or rejection rates. 2. The superiority of the glass enclosed units over other types is evident. It is seen that rates of acceptance of units that remain within the six month limit are comparatively high; this represents a high yield for the fabrication process. Rates of acceptance of units which later drift beyond the six month limit are Low -- a high reliability of the aging formula; and the number of units which were initially not acceptable but which remained within the six month limit is low-- low loss o! good units. This high degree of correlation between short and long term aging is very apparent for the glass enclosed units. This is true also for the pressure mounted units but not to the same extent. It is interesting to note here that the oscillator plate in a pressure mount has neither plated surfaces nor bonding cement associated with it; it is also partially shielded by the quartz electrodes from contaminants which may evolve from the inner wall of the metal can. Which structure is responsible for the relatively low aging rates is not yet discernible. 11-13-123 MEASUREMENT OF HIGH FREQUENCY CRYSTAL UNITS WITH INCREASED ACCURACY D. Pochmerski and C. L. Shibla U. S. Army Signal Research and Development Laboratory Military crystal units are generally classified as standard units, high precision units, and the recently developed moderate precision units. Figure 1 presents the general characteristics of the three classes. Of particular interest are the moderate precision requirements on accuracy, 1 to 2 parts in 10exp 5; temperature coefficient, 2 parts in 10 exp 7 per degree; and aging, 1 to 2 parts in 10 exp 7 per week. The development of these units has created a need for test sets of comparable accuracy. The present test set in the frequency range of interest is the TS-330/TSM with both an accuracy and repeatability of setting of parts in 10 exp 6. Required is a test set with an agreement between instruments of a part in 10 exp 6. for accuracy and a repeatability of setting to a part in 10 exp 8 for temperature coefficient and aging measurements. This paper will pertain chiefly to the repeatability aspect of setting oscillatory conditions and will present findings of various organizations and our internal investigations which are considered significant in the development of a moderate precision test set. Laboratory techniques and systems are considered as a logical approach to the problem. A passive laboratory technique using servo control has been considered and developed by Frequency Control Division for use as a research tool. This system will produce a repeatability of a part in 10 exp 8 to over 100 mc. Our goal, however, is the development of a field instrument for use by Government inspectors and depot personnel, visualized as a single integral test set, appropriate for operation by semi-