Mineralogy

There are certain conventions with regard to the lettering and order of the crystallographic axes. In the most general case, that in which the unit form cuts all three axes at unequal lengths and in which none of the axes is at right angles to any other, the crystallographic axis which is taken as the vertical axis is called c, that running from right to left is b, and that running from front to back is a. One end of each axis is positive, and the other end is negative, and the rule with regard to this is illustrated in Fig. 17. The angle between + a and + b is called y, that between + b and + c is called a, and that between + c and + a is B.

In this most general case, the unit form cuts the three axes at unequal lengths from the origin, and this fact is often indicated loosely by stating that the crystallographic axes of this type of crystal are of unequal lengths.

In some crystals the unit form cuts two axes at an equal distance and the third at a different distance. In this case, the axes cut at equal distances are both called a and the third, placed vertical, is called c. It is customary to say here that the two axes are equal and the third different.

Again, in other crystals, the unit form cuts all three axes at the same distance, so that all the axes are interchangeable; in this case the axes are all called a, and are loosely said to be equal.

The position in space of the faces of a great number of crystals can be referred to three crystallographic axes, but in one group four axes are used.

The planes in which two of the crystallographic axes lie are called the axial planes.

Crystallographic Notation

Crystallographic notation is a concise method of writing down the relation of any crystal face to the crystallographic axes. The most widely used systems depend upon either parameters or indices Of these systems of notation, the chief are two,-the Parameter System of Weiss, and the Index System of Miller (modified by Bravais).

Parameter System of Weiss

In this system of crystallographic notation, the axes are taken in the order explained above,-that is, a, b , c, for unequal axes, a, a, c, for two axes equal, and a, a, a, for three axes equal. The intercept that the crystal face under discussion makes on the a-axis is then written before a, the intercept on the b-axis before b, and the intercept on the c-axis before c. These intercepts are of course measured in terms of the intercepts made by the unit form on the corresponding crystallographic axes.

The most general expression for a crystal face in the Weiss notation is

na, mb, pc,

where n, m, p are the lengths cut off by. the face on the a, b , c axes as compared with the corresponding lengths cut off by the unit form. It is usual to reduce either n or m to unity.

If a crystal face is parallel to an axis, it can be imagined as cutting that axis at an infinite distance, and accordingly the sign of infinity, 00, is placed as its parameter before the corresponding axial letter . Thus a face cutting the a-axis at a distance 1 unit,-that is at the same distance as the unit form cuts this same axis,-and cutting the b-axis at a distance 2 units or twice the distance cut off by the unit form along the b-axis, and running parallel to the c-axis has the Weiss symbol

a, 2b, c.

A face cutting the a-axis and parallel to the b-axis and c-axis obviously has the symbol

a, b, c.