# Crystallographic Notations

We can describe the slope of crystal faces with reference to the intercepts they make on the crystallographic axes. The methods that are commonly used for expressing the intercepts of crystal faces are : (a) Weiss Parameter System, (b) Index System of Miller. These two are the most common parameters used to determine the slopes of crystal faces.

### (1). Wiess’s Parameter System:

As per Weiss Parameter System, the parameters of the crystal face system are written along with the notation of crystallographic axes. For example, a face that cuts the a-axis at unit distance, b-axis at a distance of 2 units and lies parallel to the c-axis, its Weiss symbol is written as follows.

a,2b,∞c

### (2). Miller’s Index System: As per Miller’s index system, the notations of crystal faces are known as ”Miller indices”. The Miller Indices of a face consist of a series of the whole numbers that have been derived from the parameters by taking their reciprocals and then by clearing of fractions. The numbers of the Miller indices are always written in the axial order a,b and c. For example, let us consider the crystal face PQR shown in the following figure. Its Miller indices are determined as follows.

1. For the face PQR, which cuts the positive ends of the crystallographic axes, the parameters are 3a, 3b, and 2c respectively. Since the intercepts are always written the axial order a, b, and c, the letters themselves are omitted and the parameters are written as: 3, 3, 2.
2. The reciprocal of the parameters are taken which leads to 1/3, 1/3, and 1/2 respectively.
3. The fractions are cleared by multiplying all by 6 and the Miller symbol for the face QPR is obtained, which is ”223”. The Miller indices of the octahedron are shown in the following figure.