Crystal Notation and
Crystallographic Axes

A system of notation has been developed by which we can describe the different crystal classes and the crystal forms found in each. One of the important conceptions to this end is that of crystallographic axes.

Crystallographic Axes
Crystallographic axes are imaginary lines or directions within a crystal to which the crystal face are referred and in terms of which they are described. In the different systems the axes vary in number (three of four), in their relative lengths and in the angles of inclination to each other. As a general case we will consider the crystallographic axes of the Orthorhombic System. They are three in number, at right angles to each other, and each has a characteristic relative length. Figure 8 represents such axes for the orthorhombic mineral sulfur. When placed in the proper position for description, or “orientated” as it is termed, one axis called a is horizontal and perpendicular to the observer, another axis, called b, is horizontal and parallel to the observer, while the third axis, called c, is vertical. The ends of each axis are designated by either a plus or a minus sign, the front end of a, the right-hand end of b and the upper end of c being positive, while in each case the opposite end is negative. When, as in the Orthorhombic System, the three axes have different relative lengths, these values have to be determined experimental by making the necessary measurements on crystals of each mineral. Figure 9 would represent a crystal of sulfur in which each face of the crystal form, known as a pyramid, intercepts each axis at what is considered as its unit length. From the values obtained by measuring the angles between the different faces of this crystal an expression of the relative lengths of the three axes can be obtained by calculation. The length of the b axis is taken as unity and the lengths of a and c axes are expressed in terms of it. The axial ratio for sulfur is a : b : c = 0.813 : 1.00 : 1.903. It must be borne in mind that these lengths are only relative in their value. They do not represent any actual distances. A sulfur crystal may be of microscopic size or several inches in diameter, but in either case the above ratio would hold true.