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All crystals fall into one of seven crystal systems, based on their symmetry. In crystal drawings, by convention, the c-axis usually is orientated vertically, in the plane of the paper. All crystals except those in the cubic (or isometric) crystal system have a c-axis. Cubic system crystals, like diamond, garnet and spinel, have no c-axis because all three crystallographic axes are necessarily the same length. In the other crystal systems the c-axis can be longer or shorter than the other crystallographic axes. In many minerals, particularly those in the tetragonal, hexagonal and trigonal crystal systems, the c-axis is associated with unique optical properties. These are useful to know if you are a gem cutter. Here are some examples.

Star ruby and sapphire gemstones are corundum, crystallising in the trigonal crystal system. The c-axis here has three-fold rotational symmetry. Fine, needle-like rutile inclusions in three sets form perpendicular to the c-axis and intersect at 120°. If the c-axis is orientated vertically in a cabochon stone, light reflected from these rutile fibres results in a 6-rayed bright star in the stone.

Zircon crystallises in the tetragonal crystal system, often forming elongated crystals with a square cross-section at right angles the c-axis. The strong facet edge doubling due to the high birefringence of zircon is not visible if the stone if viewed parallel or perpendicular the c-axis. So if the table facet of the stone is orientated perpendicular or parallel to the c-axis, the fuzzy doubling effect will be minimised in a zircon gem.

Topaz crystallises in the orthorhombic system, with the same symmetry as a matchbox. The c-axis runs down the length of the crystal, and is perpendicular to the easy cleavage planes. When faceting a topaz, it is important to avoid having the c-axis either perpendicular or parallel to the table facet. If the table is perpendicular to the c-axis, it will be very difficult to polish it, as it will tend to cleave. If the table is parallel to the c-axis, two opposite girdle facets will be difficult to polish and will be prone to vertical cracking because of the cleavage.

Tourmaline crystallises in the trigonal system, often in elongated crystals with striations along the length. The c-axis is then the long axis of the crystal. Gem cutters describe tourmaline as having an ‘open’ or ‘closed’ c-axis. The absorption of colour may be very strong in the direction of the c-axis, in which case the crystal has a ‘closed’ c-axis. If the colour is light when viewed along the length of the crystal, or parallel to the c-axis, it is ‘open’. Open c-axis tourmalines tend to produce better gems, without the darkening effect of the intense light absorption of the ‘closed’ c-axis stones.

Scapolite and spodumene often have more intense, better colour when viewed parallel to the c-axis. They also have two directions of easy cleavage parallel to the c-axis. This means stones need to be orientated carefully with respect to the c-axis, in order to optimise the colour and at the same time to avoid having cleavage planes parallel to any major facets.

So, how does one recognise the c-axis in rough gemstones? Sometimes it is easy. In elongated tourmaline crystals, for instance, the c-axis is parallel to the length and any striations there may be. It is perpendicular to the bulging triangular cross-section. In ‘closed’ c-axis specimens the colour will be very dark or even black when viewed in the c-axis direction. In ruby and sapphire the c-axis runs down the length of the elongated barrel-shaped crystals, or perpendicular to the flat ends of squat six-sided crystals. Quartz is trigonal, but often forms six-sided crystals terminated by a point made up of two sets of three triangular faces. The c-axis runs along the length of the crystal from the point. Beryl also forms six-sided crystals, but belongs to the hexagonal crystal system. Here the c-axis also is parallel to the length. In tetragonal scapolite and zircon crystals, the c-axis runs from the pyramidal point, parallel to the rectangular side faces. Topaz crystals usually show their cleavage as a flat ‘base’ or as parallel fractures in the crystal. This plane is perpendicular to the c-axis.

But what if you are looking at irregular gem rough, with no convenient crystal faces to guide you? In some cases, careful inspection of the rough stone will reveal traces of cleavage. This can be seen as regularly flat-stepped fractures on broken surfaces, or as reflective internal cleavage planes. These are best seen in oblique or dark-field lighting. A convenient was to achieve this is by holding the stone just below the rim of a desk lamp, with the lamp shading your eyes. Knowing the crystallographic orientation of any particular mineral’s cleavage should enable you to identify the c-axis direction and orientate the stone crystallographically.

But what if there is no visible cleavage? In the case of star ruby or sapphire, reflection from the crystallographically orientated rutile inclusions may help. The c-axis is perpendicular to the intersection of the six arms of the star. In strongly birefringent stones like zircon, the direction in which you see least doubling of the image of fractures on the far side of the rough will be either the c-axis direction, or perpendicular to it. So, how does one tell the difference?

Here, and with weakly birefringent stones with no easy cleavage, like quartz and beryl, a polariscope is very useful. A polariscope consists of a light source and two polarising filters. This can be a commercially available piece of optical equipment, or something homemade. You can use two pieces of Polaroid sheet or even the lenses from a pair of 3D movie spectacles. A flat computer screen can act as a source of plane polarised light. In this case you only need one polarising filter. The technique for finding the c-axis in gems with only one optic axis (which includes quartz, beryl, scapolite and zircon) is to cross the polars or rotate a single polarising filter to the dark position, effectively cutting out all the light. Then holding them steady, rotate the stone between them in a variety of orientations, until the stone stays uniformly dark (or in some cases, uniformly light). In this position, when the transmitted light through the stone does not fluctuate from light to dark as you rotate it, you are looking in the c-axis direction. A spot of marker pen ink on the surfaces nearest and furthest from you will define the c-axis orientation. Having found the c-axis direction, all you now have to do is orientate the gem design appropriately for the mineral species in question, and cut your stone.

For those wanting a bit more adventure, once you have found the c-axis of an optically uniaxial crystal using a polariscope, try inserting a lens (a 10× loupe will do) between the stone and the upper polarising filter. With a bit of jiggling, you will see an interference figure consisting of coloured rings and a dark central cross. There are all sorts of useful gemmological things you can do with polarised light. A good place to learn is from ‘How to play with polarised light’, downloadable from Olaf Medenbach’s superb website <http://homepage.ruhr-uni-bochum.de/Olaf.Medenbach/eng.html>.