|Engineering Bulletin E-6:
Frequency Control with Quartz Crystals
Certain crystalline substances, such as quartz, Rochelle Salts and tourmaline, exhibit a most interesting property. In brief, if any one of these substances is distorted mechanically an electric charge will be developed; and, conversely, mechanical distortion will result if the substance is placed in an electric field. This property, the Piezoelectric Effect, makes possible precision frequency-control of radio transmitting equipment.
There are a surprisingly large number of crystalline substances which do exhibit piezoelectric properties but, out of the entire group, quartz is the only material which is truly satisfactory for frequency control purposes. Rochelle Salts exhibits the most intense piezoelectric properties but is not a suitable material for it is too unstable both physically and electrically. Tourmaline, a gem material, has been employed but due to its relatively high cost and the superior qualities of quartz, it is no longer in general use.
Quartz is silica (silicon dioxide) and is found throughout the world in many different forms. It appears most commonly in the sands and sandstones of the earth and occurs in various rocks of igneous origin such as granite. Some varieties of quartz, including amethyst and rose quartz, are cut into gems and ornaments. Amongst its many commercial applications, quartz is used in the manufacture of piezoelectric devices, lenses, balance weights, chemical ware and abrasives. Because of its extremely low internal friction and small thermal expansion coefficient, quartz, fused and drawn into very Pine threads, is highly valued for suspensions in scientific apparatus.
Quartz is an exceptionally hard material having a rating of 7 in Moh's Scale of Hardness where the diamond is rated at 10. It is very stable both physically and chemically; it is not affected by common acids and can be fused only with considerable difficulty. For general scientific and piezoelectric applications, comparatively large natural crystals of high purity are required. Although natural crystals can be found in many different parts of the world, including the U. S. A., Brazil, at present, has the only suitable source of supply.
To take advantage of the piezoelectric effect of quartz, it is necessary to cut small "plates" from the raw natural crystals. These plates must be cut in certain definite directions with respect to the axes of the raw crystals, they must be free from mechanical and electrical flaws, and each must be carefully ground such that its major faces are essentially plane and parallel. If one of these plates is placed in an oscillating electric field, it will vibrate mechanically and produce a counter-voltage at the frequency of the applied field. The magnitude of this action will be quite small, but, should the frequency of the applied field be adjusted to correspond with a natural vibrating period of the plate, the vibrations will become vigorous and have appreciable amplitude. In fact, should the strength of the applied field be sufficiently great, the vibrations can easily become so strong that the plate will be physically ruptured.
This same plate, if distorted by physical force, will develop an electric charge. If the plate is X-cut (that is, the planes of its faces perpendicular to the direction of one of the side faces of the natural crystal and parallel to the axis of the crystal along its length and through the peak) and the force is normal to the major faces, the charge developed will be very nearly 10E-11 coulombs per pound (6.36 X 10E-8 e.s.u. / dyne). This charge will be essentially independent of crystal face area or thickness and of temperature for any value up to about 550°C.; at 573°C., piezoelectric action will cease. For pressure measurement purposes, the amount of charge, or the voltage resulting from the charge, can be determined. The voltage is, of course, proportional to the charge divided by the circuit capacity (Q = CE).
It is most important that a finished quartz plate be entirely free from mechanical or electrical flaws if best results are to be obtained. If flaws are present, the crystal cannot vibrate freely and, as a result, it may oscillate very weakly or not at all. Should the crystal be intended for measuring pressures or forces, flaws can greatly decrease the developed charge and can cause the crystal to fracture under a relatively light mechanical load.
Flaws which commonly appear in the raw quartz are bubbles, needles, veils, strains, fractures, phantoms and twinning, Bubbles are a physical defect in the quartz material and appear in random sizes and formations. Veils and needles are small bubbles and striations occurring in groupings which suggest the descriptive terms given to them . Strains are permanent internal stresses which cannot be relieved. Fractures are definite cracks caused during formation of the crystals or by physical breakage during mining and handling. Phantoms are a variation in cross sectional appearance of the quartz such that, to the eye, one crystal appears to have grown inside another; they are apparently the result of a change in growth of the crystal during formation. Twins are the definite result of one crystal growing within another, either totally or partially.
Practically all natural quartz has at least some of the possible flaws outlined. To prevent the appearance of these flaws in the final product, the raw quartz must be very carefully selected and then only the sound portions used.
Finished quartz plates are popularly termed crystals' and will be so designated throughout this book. The greatest practical value of quartz crystals is derived from the unusual fact that they can be produced as mechanical vibrators having electrical characteristics not fully attainable by any ordinary electrical circuit or component. In radio-frequency oscillatory systems, the quartz crystal has no peer for determining and maintaining circuit frequency. In filter circuits, where it is desired to pass only a relatively narrow band of frequencies, great simplification and better results can be obtained through the use of quartz crystals.
The electrical action of an oscillating quartz crystal may be most readily analyzed by reference to its equivalent electrical network as shown in Figure 2. This equivalent network, while theoretical in nature, can be used to exactly define the electrical behavior of a crystal. As a matter of fact, it provides the basis for mathematically designing certain types of crystals prior to their manufacture. The inductance, L, represents the mass of the crystal, the capacity, C, the resilience, and the resistance, R, the frictional losses. C1, is the capacity due to the crystal electrodes with the crystal as the dielectric while C2 represents the series capacity between the crystal and its electrodes.
Neglecting C2, it should be noticed that the equivalent electrical network made up of L, C, C1, and R has the properties of either a series or a parallel resonant circuit. At some definite frequency, for a given crystal, the reactances of L and C will be numerically equal. This is the requirement for a series resonant circuit and the frequency at which this resonance occurs is the series resonant or natural frequency of the crystal. At a slightly higher frequency, the effective reactance of L and C combined will be inductive and numerically equal to the reactance of C1. At this frequency anti-resonance occurs and the crystal acts as a parallel or anti-resonant electrical circuit. C2 is only effective when the crystal electrodes are not in intimate contact with the crystal faces. As the value of C2 is decreased, the resonant frequency will increase.
The inductance, L, of quartz crystals is very large; it varies from 0.1 henry to 100 henries with individual crystals and depends on the manner in which the crystal is cut from the raw quartz, its physical proportions, and the frequency, Because the inductive reactance, XL, is many times greater than the resistance, R, quartz crystals have a very high Q factor [Q = (2FL) ÷ R]. Commercially produced crystals have Q factors ranging from about 6000 to about 30,000 while, under laboratory control, crystals with Q factors up to 400,000 have been reported.
In an oscillator circuit operating at radio frequencies, the frequency stability is largely determined by the Q of the frequency determining "tank". The Q of quartz crystals is many times greater than can be obtained with conventional inductance-capacity tanks, and it follows, therefore, that crystal frequency-control offers the highest degree of frequency stability. In explanation, it may be pointed out that the oscillating frequency of a conventional oscillator circuit is that frequency at which the total circuit reactance reduces to zero. Any circuit changes caused by varying voltages, aging of the tube or circuit components, or other causes, necessitates a change in frequency to again bring the net circuit reactance to zero. Because quartz crystals have a very steep resonance curve, a large change in reactance can be brought about with only a small shift in circuit frequency.