Crystals - Introduction


last modified: Wednesday, 30-Nov-2016 22:17:26 CET

Quartz crystals occur in a great number of different shapes. Most rockhounds are familiar with their look and immediately recognize quartz crystals, so despite the great number of varieties and growth forms, all quartz crystals share some characteristics.

This chapter briefly introduces quartz crystal morphology and the basic terms used to describe crystals. If you want to know more about quartz crystals you should continue with the chapters listed under "Next Chapters" which are also accessible via the menu to the right.

Fig.1: Idealized Quartz Crystal
Figure 1 shows an idealized rendering of a quartz crystal with its most common shape. It is a six-sided prism with two six-sided pyramids at both ends. In most cases, the crystals are attached to a rock at one end, so they only show one six-sided pyramid.

Fig.2: Common Quartz Crystal Faces
Most real crystals will look as simple as this idealized crystal and will only show three types of crystal faces that are labeled with a single letter (Fig. 2, includes a top view at the bottom):

m: six faces belonging to the central six-sided prism with a typical horizontal striation

r: three, often roughly triangular faces at the crystal's tips. In well-developed crystals these faces are always present.

z: three, often triangular faces also at the crystal's tips, that sit between the r faces.

The basic shapes of most quartz crystals can be explained as variations of the relative sizes of these faces. The r faces are usually larger than the z faces, and are commonly presented that way in figures shown in mineralogy textbooks, but the size of each face depends much on the overall shape of the crystal, the growth conditions and the presence of other faces.

The top view shows that although the prism of the crystal is six-sided, it has a three-fold rotational symmetry. Quartz thus belongs to the trigonal crystal class.

Fig.3: Angles between Faces
Whatever the shape of a quartz crystal, the angles between the faces never change. Figure 3 shows the angles enclosed by the major crystal faces. You can see that although the z-faces are smaller, their position relative to the m-faces is identical to that of the r-faces: the r-m and the z-m angle is 142° in both cases.

Fig.4: Crystallographic Axes
To describe the geometry of crystals, so-called crystallographic axes are used. These axes define a three-dimensional coordinate system within the crystals' structure, and of course - as one would expect for describing three-dimensional bodies - there are 3 axes labeled a, b, and c. For example, one can describe a crystal face as part of a plane that lies parallel to the a- and the b-axis and cuts the c-axis.

This would work for quartz crystals as well, but for practical reasons and because of symmetry considerations, in quartz 4 axes defined in the hexagonal crystal system are used and labeled a1, a2, a3, and c (Fig. 4). The 3 a-axes intersect at an angle of 60° and lie on a plane (Fig. 4, light blue), and the c-axis runs perpendicular to the plane and intersects all a-axes at an angle of 90°. Often there is no need to distinguish between a1, a2 and a3 and one simply refers to the a-axis or a0-axis.

Quartz crystals lack mirror symmetry. The mirror image of a quartz crystal is different from the original image, no matter where the mirror plane lies.

Instead, quartz crystals show handedness: there are 2 types of crystals, left-handed and right-handed crystals. This is very similar to the human hand - you have a left and right hand. Each of them is a mirror image of the other, but the mirror image of the left hand is not a left hand, so each hand itself lacks internal mirror symmetry (unlike the human face, for example, which is roughly mirror symmetric).

Fig.5: Left-Handed Quartz
H.264-Movie, 256x256px, 367kb
You will note that it is very well possible to find 3 mirror planes in Fig.2 that give perfectly identical mirror images: they run centrally through the m-faces. And this seems to be true of many real crystals, too. But this mirror symmetry is only an apparent one, the internal molecular structure of the quartz crystal cannot be mirrored: the atoms in a quartz crystal are arranged in parallel, corkscrew-like chains or helices. A helix lacks mirror symmetry and is always either left- or right-handed (a more thorough discussion of the handedness of quartz on a structural can be found in the chapter Structure).

The handedness of quartz is only visible on quartz crystals that possess certain crystal faces. Figure 5 is a rendering of a left-handed quartz crystal (there is a link to an MPEG4/H.264-movie of a rotating crystal below).

There is no inherent tendency in quartz to prefer one direction, and left- and right-handed quartz crystals occur at the same frequency.

The additional faces on Fig.5 are the s-faces and the x-faces. The typical s-face is a rhomb, whereas an x-face is usually either a triangle or - when it is bordering an s-face - a trapezoid.

The rule of thumb to determine the handedness is:

Fig.6: s- and x-Faces on Left- and Right-Handed Quartzes
Figure 6 shows the s-faces (tinted blue) and x-faces (tinted orange) on both left- and right-handed quartzes and their relative position to the r-, z-, and m-faces.

Left and right quartz are mirror images of each other, but lack mirror symmetry themselves.

Double-terminated crystals with all s- and x-faces on them like those on the idealized renderings are extremely rare. Most crystals don't show s- and x-faces, and those that do often have only one or two of them, and either x- or s-faces, but rarely both of them.

Fig.7: A Twinned Quartz Crystal
Quite frequently one can find crystals that apparently do not obey the rules and show s- and x-crystal faces at unusual positions. For example, they show x-faces to the left and to the right of an r-face, making it impossible to classify the crystal as left- or right-handed. These crystals are twinned, that is, they consist of two or more crystals that are intergrown in a law-like manner. Quartz shows 3 types of twinning (twinning laws), and the 2 more common ones look very unsuspicious to the uninitiated. In contrast to many other minerals, most quartz crystal twins are not made of two clearly identifiable crystals, but simply a single crystal that ideally looks like the intersection of two crystals.

For example, in Fig.7 you see a rendering of a so-called Brazil twin, a crystal apparently formed by the superposition of a left- and a right-handed crystal. It is an apparent superposition because in fact different sections of the crystals are either left- or right-handed, and never both simultaneously.

Again, this is an idealized picture, and while natural crystals are twinned very often, they don't display the full range of crystal faces, making it difficult to recognize them. Brazil twins are common, but crystals that show a combination of faces like the one in the rendering are extremely rare.


Next Chapters

In the following chapters the various topics that have just been touched are discussed more thoroughly.

Basic Terms briefly introduces a few basic crystallographic terms necessary to understand quartz crystal morphology.

Forms introduces the most common crystal faces in quartz and their underlying crystallographic forms.

Habits explains common terms used when describing the overall shape of crystals.

Twinning introduces the 3 types of twins that are found in quartz and explains how to identify them.

Data and Renderings explains how I did the computer renderings on these pages and offers a few data sets for download.


Further Information, Literature, Links

If you are not familiar with basic terms of crystallography, I'd strongly recommend not only to read the section Basic Terms but also to look at other sources in the Internet. Certain notions used when describing quartz crystals remain incomprehensible without a minimal background in crystallography. A very nice introduction by Mike and Darcy Howard can be found at this website at Bob's Rock Shop: Introduction to Crystallography and Mineral Crystal Systems. It is definitely worth a visit.

Another page is discussing Crystals and Lattices, although the approach is rather mathematical.

Crystallographic terms can be quite confusing and I'd recommend to have a look at a good textbook of mineralogy to get more into it.

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