Law of Rational Indices

The Law of rational indices is a fundamental principle in the field of crystallography. According to this law, the intercepts of a crystal face along the crystallographic axes (the three-dimensional axes along which a crystal is measured) can be expressed as either equivalent to the unit intercepts (a, b, c) or simple whole number multiples of them. These multiples are typically denoted as na, n'b, and n''c, where n, n', and n'' are simple whole numbers.

To illustrate, consider a crystal with three crystallographic axes labeled OX, OY, and OZ. The unit plane within this crystal is denoted as PQR. The unit intercepts in this system would be a, b, and c.

Applying the law of rational indices, the intercept of any other plane within the crystal, such as KLM, on these three axes can be expressed as simple whole number multiples of a, b, and c, respectively.

In essence, this law helps to describe the geometric arrangement of atoms within a crystal systematically and mathematically. This law is crucial in developing crystallography as a scientific discipline, enabling researchers to predict and understand the properties of crystals based on their internal atomic structures.