Atomic Planes

Quartz Characteristics

Quartz is at position 7 on the Mohs scale, which means that it is one of the hardest common minerals. It crystallizes from the molten state at rather high temperatures but also can be deposited on the ocean floor at only a few degrees above zero. It forms very beautiful crystals that can be used as gemstones and is the source of crystals used for technical purposes. It is also the major ingredient in sand.  Some additional properties of quartz may be found here.

Quartz is piezoelectric. It can be observed when the crystal is squeezed slightly out of shape and then springs back. This shape change actually affects the crystal at the atomic level causing a movement of ions, with their attendant electric charges. This motion of the electrically charged particles constitutes flow of electrons, or electricity resulting in a charge difference across the crystal.

Types of Quartz

Probably the most familiar form of quartz is the clear, colorless form known as rock crystal. These crystals can range in size from the most minute to the gigantic; one from Brazil weighed in at 5.5 tons! 

Another form of quartz known and valued for its beauty is amethyst. This mineral is almost pure SiO2 with only a trace of iron. As the amount of iron increases, so does the intensity of the violet color, so it is believed to be the coloring agent. 

Smoky quartz does not differ from clear quartz in chemical composition. In fact when it is heated to very high temperatures the “smoky” color vanishes, and it looks identical to clear crystalline quartz. Treating the crystal with a beam of x-ray radiation can restore the color. Scientists believe that the color of smoky quartz is a result of natural radiation in the earth.

Agate is a common form of quartz, which does not have any external evidence of its crystal nature. The extremely tiny crystalline particles are so intergrown that they appear smoothly mixed. 

A form of quartz that is unique and appears to be most “un-quartz like” is the opal. It contains a rather large percentage of water, ranging from four to twenty percent. And a complex internal structure if microscopic silica fitted together in a lattice-pattern results in diffraction of the light hitting it, forming rainbows of brilliant color as the gem is rotated. Opal is a low-pressure and low-temperature mineral and is formed at the earth’s surface by deposition from ground water or by the evaporation of hydrothermal, or hot water, springs as they rise to the surface and cool leaving opal mineral behind. Because of the rather large amount of water present in opal, it tends to be relatively soft (5.5 to 6.5) and low in specific gravity. 

Synthetic or man made quartz is also made by a hydrothermal process. The difference is the process is done at high temperature and high pressure. It results in a crystal, which is very similar to rock crystal. Rock crystal is also called natural quartz.

Quartz Crystal Structure

Alpha quartz belongs to the crystallographic class 32.  It has a single axis of threefold symmetry (trigonal axis) and perpendicular to the three axes of twofold symmetry (digonal axes). The digonal axes are spaced 120 degrees 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 of symmetry and is a necessary condition for the existence of the piezoelectric effect. The digonal axes are known as the electric axes of quartz. The trigonal axis, also known as the optic axis or c-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 the optic axis. 

Since the values of coefficients describing the physical properties of the crystal are dependent upon direction, it is necessary to choose reference directions within the crystal to specify their values. These directions are called crystal axes and they refer to a direction within the crystal rather than a fixed line within the crystal.  

Usually these axial directions are chosen to make the description of the crystalline properties as simple as possible. An axis is always chosen with reference to some specific physical property of the crystal.  Different axial systems may be used to describe the same crystal.  For example , it is more convenient to use the Bravais-Miller axial system to specify the natural faces and atomic planes in quartz, whereas it is more convenient to use an orthogonal coordinate system for purposes of computations involving the piezoelectric and mechanical properties of the crystal. 

It is obvious one can pick a set of orthogonal axes at any of three different 120^o rotations because  quartz exhibits three fold symmetry about the Z' axis.  One may arbitrarily select the X and Y axis since it is impossible to tell the difference between any rotation chosen.  The positive sense of the X-axis is defined by IEEE standards. The positive X direction is chosen to be the direction in which a positive strain produces a positive charge.  A positive strain is defined to be the extension resulting from tension. By this definition, that end of the X-axis is positive where a negative charge is developed by compression.  Using this definition, a lumbered quartz bar can be placed between two metal electrodes in an arbor press. A high impedance charge measuring device can then be used to determine which electrode becomes positive when the bar is squeezed. The opposite side it the plus X direction.  

The Y-axis is not a polar axis in quartz and no electric polarization results from an extensional strain in the Y-direction.  If a shear stress is applied to a Y-cut quartz plate does result in electric polarization. This relationship form the basis for a number of important types of quartz piezoids.

Inversion Temperature

Quartz is the most stable and most common form of silica.  At the inversion temperature of 573ºC it undergoes a transition from Alpha quartz to Beta quartz. Beta quartz cannot exist below the inversion point. It is only stable at temperatures above 1063º F (573º C). Thus, all quartz specimens we see are alpha quartz. Once a sample of beta quartz is lowered below the above-mentioned temperature, it automatically transforms back into alpha quartz.  However, it may transition back to either right or left handed quartz.  

Enantiomorphism - Right and Left Handed Quartz

Crystallography and "Handness" of Quartz

      Way back in 1816, a naturalist/crystallographer by the name of Weiss discovered a property of crystal forms called enantiomorphism. This word is a mouth full, but pretty easy to understand.

Enantiomorphism has to do with the internal structure of the mineral.  Quartz is composed of silica, SiO2, which occurs in the crystal structure as a tetrahedral form. Tetrahedrons are 4-sided closed geometric figures which are composed of equilateral triangles. You can think of it as a 3-sided pyramid sitting on the 4th side -- its base. All 4 sides are equal in area. Now, to grow a quartz crystal, these tetrahedra link together in chains which are parallel to the C axis, but the chains will have a rotational twist. They may either rotate clockwise along the length of the crystal or counterclockwise. The odds are 50-50 as to which direction they rotate. However, once they begin to form, the crystal's handedness has been locked in.

Alpha 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 polarizations occurs, the amount of the rotation depending upon the distance traversed. The sense of rotation can be used to tell the sense of the twist and thus the difference between two naturally occurring forms of alpha quartz.  

Most of the cultured quartz produced in the world is right handed quartz.  One company in England specializes in producing left handed quartz.  Claims that left handed quartz is superior to right handed quartz are not valid. The properties of the two types of quartz are exactly the same.  Either form of alpha quartz can be used to produce resonators.   

Twining

It is possible to have a quartz stone that has areas of left and right handed material.  One of the ways this can happen is to heat a quartz stone above the inversion temperature of  573º C and then cool it below this temperature.  This will cause the stone to have both left and right handed areas. When this condition exists the quartz is said to be "twined".  The twining may be either optical twining  or electrical twining.  Material in which contains left and right forms cannot be used. 

One can intuitively understand why twining degrades resonator performance by considering the fact that the motion of the crystal resonator will have a different direction either side a a twined boundary. On an AT-cut crystal the thickness shear mode would be driven in opposite directions on either side of the boundary.  This clearly is counter productive resulting in a degradation of resonator Q other electrical characteristics of the resonator. 

While twining can be produced by simply heating a quartz crystal above it's inversion temperature of 573^oC there are other ways to twin the material.  A common example is demonstrated when quartz crystal blanks are rounded on a grinding machine called a rounder. A diamond wheel is applied to a stack of quartz wafers to give them a specific diameter. It the feed and speed of the wheel is too great, the pressure and friction of grinding will produce an edge on the crystal blanks that is extensively twinned. Twining can also be observed on blanks that have been lapped on a lapping machine.  If pieces of quartz are dragged across the surface of the lapped quartz wafer, the pressure and friction will cause a line of small areas of twinning.  Both of these forms of damage can be observed by deep etching the quartz blanks. 

Copyright ©  2001 thru 2013  by Theodore Lind