1. Introduction

Quartz is a piezoelectric material. A thin wafer of quartz, with electrodes attached to opposing surfaces, vibrates mechanically when voltage is applied to the two electrodes. Frequency of vibration is primarily a function of wafer dimensions. The wafers, called crystal resonators when suitably mounted with electrodes attached, have long been used for controlling frequency of radio transmitters, and it has been an essential component in telecommunication communication equipment where its piezoelectric properties are used in filters, oscillators and other devices. Now quartz crystals time and coordinate signals for microprocessors, computers, programmable controllers, watches, and other digital equipment such as various DSP.

Quartz is a crystalline form of silicon dioxide (SiO₂). It is a hard, brittle, transparent material with a density of 2649 kg/m³ and a melting point of 1750° C. Quartz is insoluble in ordinary acids, but soluble in hydrofluoric acid and in hot alkalis. When quartz is heated to 573° C, its crystalline form changes. The stable form above this transition temperature is known as high-quartz or beta-quartz, while the stable form below 573° C is known as low-quartz or alpha-quartz. For resonator applications, only alpha-quartz is of interest and unless stated otherwise the term quartz in the sequel always refers to alpha-quartz. Quartz is an abundant natural material, but considerable labor is required to separate good quality from poor-quality natural quartz. Although silicon (mainly in the form of dioxide, and generally as small quartz crystallites) comprises approximately one third of earth’s crust, natural quartz of size and quality suitable for use in devices employing its piezoelectric properties, has been found principally in Brazil. Natural quartz is also costly to process because it occurs in random shapes and sizes. Moreover, some segments of poor-quality quartz are discovered only after partial processing. And widespread impurities in natural quartz often make cutting of small wafers impractical. The first major step in the development of cultured quartz was in 1936 when the US Army Signal Corps gave a contract to Brush Laboratories under the direction of Drs. Jaffe, Hale, and Sawyer. This was done due to the pending scarcity of natural quartz with good piezoelectric quality, customarily purchased from Brazil.

Today, quartz is now grown artificially to specified dimensions. Crystal orientation is controlled, and purity is uniformly high. Standard sizes reduce the cost of cutting wafers, and impurities are widely dispersed, making possible small resonators requiring low driving power.

2. The Basic Process of Growing Cultured Quartz

Cultured quartz is grown in a large pressure vessel known as an autoclave (see the following schematic drawing). The autoclave is a metal cylinder, closed at one end, capable of withstanding pressures up to 30,000 pounds per square inch with internal temperature of 700 to 800° F. It usually stands from 12 to 20 feet high and 2 to 3 feet in diameter.

Small chips of pure but un-faced quartz (1 to 1.5 inch in size), called "lascas or nutrient", are placed in a wire mesh basket and lowered into the bottom half of the vessel. A steel plate with prearranged holes, called a "baffle", is set on top of the basket. The baffle is used to separate the growth (seed) region and the nutrient region, and to help establish a temperature differential between the two regions. Suitably oriented single crystal plates (either natural or cultured), called "seed", are mounted on a rack and suspended on top of the baffle in the upper half of the vessel. The autoclave is then filled with an aqueous alkaline solution (Sodium Carbonate or Sodium Hydroxide) to approximately 80% of its free volume to allow for future liquid expansion, and it is sealed with a high-pressure closure. The autoclave is then brought to operating temperature by a series of resistive heaters attached to the exterior circumference of the cylinder. As the temperature increases, the pressure begins to build within the autoclave. A temperature of 700 to 800° F is attained in the lower half of the vessel while the top half is maintained at 70 to 80° F cooler than the bottom half.

At operating pressure and temperature, the lascas dissolves in the heated solution in the lower half of the vessel, which then rises. As it reaches the cooler temperature of the upper part of the vessel, the solution becomes supersaturated, causing the dissolved quartz within the lascas to re-crystallize onto the seed. The cooled spent solution then returns to the lower half of the vessel to repeat the cycle until the lascas is depleted and the cultured quartz stones have reached the desired size. This so-called "Hydrothermal Process" time ranges from 25 to 365 days, depending upon the desired stone size, properties, and the process type – Sodium Hydroxide or Sodium Carbonate.

3. Symmetry, Twinning and Size of Quartz Crystal

Alpha-quartz belongs to the crystallographic class 32, and it is a hexagonal prism with six cap faces at each end. The prism faces are designated m-faces and the cap faces are designated R and r-faces. The R-faces are often called major rhomb faces and the r-faces are minor rhomb faces.  Both left-hand and right-hand crystals occur naturally and can be distinguished by the position of the S and X faces.

As shown in the above schematic drawing, alpha-quartz crystal has a single axis of three-fold symmetry (trigonal axis), and it has three axes of two-fold symmetry (digonal axes) that is perpendicular to that trigonal axis. The digonal axes are spaced 120° apart and are polar axes, that is, a definite sense can be assigned to them. The presence of polar axes implies the lack of a center symmetry and is necessary condition for the existence of the piezoelectric effect. The digonal axes are also known as the electric axes of quartz (x-, y-axis). In crystal with fully developed natural faces, the two ends of each polar axis can be differentiated by the presence or absence of the S and X faces. When pressure is applied in the direction of the electric axis, a negative charge is developed at that end of the axis modified by these faces. The trigonal axis, also known as the optic axis (z axis), is not polar, since the presence of digonal axes normal to it implies that the two ends of the trigonal axis are equivalent. Thus no piezoelectric polarization can be produced along optic axis.  In the rectangular coordinate systems, the z-axis is parallel to the m prism faces. A plate of quartz cut with its major surface perpendicular to the x-axis is called an X-cut plate. Rotating the cut 90 degrees about the z-axis gives a Y-cut plate with the y-axis now perpendicular to the major surface. Since a quartz crystal has six prism faces, three choices exist for the x- and y-axis. The selection is arbitrary; each behaves identically.

Quartz is an optically active material. When a beam of plane-polarized light is transmitted along the optic axis, a rotation of the plane of polarization occurs, and the amount the rotation depends on the distance traversed in the material. The sense of the rotation can be used to differentiate between the two naturally occurring forms of alpha-quartz known as left quartz and right quartz. In left quartz the plane of polarization rotates anti-clockwise when seen by an observer looking towards the source of light, and in right quartz it rotates clockwise. Most cultured quartz produced is right quartz, whereas in natural left- and right- quartz are about equally distributed. Either form can equally well be used in the manufacture of resonators, but material in which left and right forms are mixed, which is called optically twinned material, can not be used. On the other hand, electrically twinned material is all of the same hand, but contains regions where the sense of the electric axis is reversed, thus reducing the overall piezoelectric effect. Such material is also not suitable for resonator application. The presence of twinning and other defects in natural quartz crystal is the major reason for the shortage of suitable natural material, and the absence of significant twinning in cultured quartz constitutes one of its main advantages. When alpha-quartz is heated to above 573° C, the crystalline form changes to that of beta-quartz, which has hexagonal rather than trigonal symmetry. On cooling down through 573° C, the material reverts to alpha-quartz, but in general will be found to electrically twinned. By the same token, the application of large thermal or mechanical stresses can induce twinning, so it is necessary in resonator processing to avoid any such thermal or mechanical shocks.

After being removed from an autoclave in which they were produced, cultured quartz crystals are converted, by grinding, into so-called lumbered bars. These are long, rectangular bars, suitable for subsequent cutting into wafers for resonators. Lumbered bars are typically 6 to 8 inch long, but usable length is about 5 to 6 inch because material near the ends is unusable. Longer bars can be grown, but these require longer seeds, the cost of which increases rapidly with length. Height of lumbered bars generally is approximately twice the width because two wafers are normally cut from each slice. Numerous standard-sized lumbered bar are available, and quartz can also be grown and ground to specified dimensions.

4. Chemical Impurities in Quartz Crystal

Both cultured and natural quartz contain chemical impurities that can affect resonator performance. Chemical impurities are those that form chemical bonds with silicon and oxygen in quartz. Aluminum, iron, hydrogen and fluorine are typical chemical impurities. They are held to a much lower level in cultured quartz than that often found in natural quartz. However, chemical impurities are not evenly distributed in cultured quartz. The +x , - x, z regions, and so-called s regions that occasionally form, contain different levels of chemical impurities. The two z regions contain the least amount of impurities. The +x region contains more impurities that the z region, and the - x region has yet more impurities. Density of impurities in the s regions, which are generally small, is between that in the z regions and that in the +x region. When wide seeds are used for culturing, the z regions of a lumbered bar are large and the +x and - x regions are small. When narrow, less expensive seeds are used, the z regions are smaller and the +x and - x regions larger. In general, the chemical impurities can result in degrade in the resonator performance such as radiation hardness, susceptibility to twining, oscillator short term and long term stability, and filter loss.

5. Resonator Q and Crystal Q

The Q value of a crystal resonator is the ratio of energy stored to energy lost during a cycle:

Q º 2p Energy stored during a cycle / Energy lost during a cycle

The value is important because it is a measure of the power required to drive the resonator. The Q is primarily a function of the atmosphere in which a resonator operates, surface imperfection, mechanical attachments and other factors resulting from processing and mounting the resonators.

Quartz lumbered bars also are assigned a Q value, but the Q for a quartz bar is not based on a direct measurement of energy stored and energy lost. Instead, the Q of a quartz bar is a figure of merit based on impurities in the bar. Chemical impurities in cultured quartz are measured by directing an infrared light through the z regions in a cross-section slice of a lumbered bar. The difference in transmittance at two specific wavelengths (3,500 nm and 3,800 nm) is measured, and Q value is calculated from these data. Quartz having a high Q contains less impurity than those with low Q, and "Infrared Q" measurements, per EIA Standard 477-1, are routinely used by quartz growers and users as an indicator of quartz quality.

The value of Q for a resonator generally is not identical to that for the quartz bar from which the resonator was cut. However, the Q of a resonator can be affected when Q of the quartz bar is below a critical level. A Q value of 1.8 million or higher for cultured quartz is an indication that chemical impurities will not be a factor in the final Q of a resonator for most applications. Quartz having such values for Q is generally called electronic grade (Grade C). Premium grade quartz has a Q of 2.2 million (Grade B), and special premium has a Q of 3.0 million (Grade A). It is important to be aware of that the Q value for cultured quartz is based on impurities in the z region only. Therefore, even where crystal Q is adequate for an application, resonator Q and frequency vs. temperature behavior can be adversely affected where the active portion (between the electrodes) of a resonator includes +x, - x, or s region material.

Quartz crystal wafers containing only z-region material can be successfully cut only from bars grown from wide seeds, which are relatively expensive. Fortunately, electrodes rarely cover the entire surface area of a resonator wafer, and impurities contained in +x, - x, or s region does not adversely affect resonator operation when these impurity material lie outside the active portion. Thus, resonators for most applications can use quartz grown from a relatively cheap narrow seed.

6. Summary

Piezoelectric quartz crystal, discovered in 1880 by the famous Curie couple and once obtained at high cost from rough-hewn natural crystal, is now grown artificially by a process that produces crystals of specified size and purity. This cultured quartz has lowered the cost and reduced the size of resonators critical to the timing of today’s digital circuits.