## What is Law of Rational Indices?

## Law of Rational Indices

The law of rational indices was deduced by Hauy.*The law of rational indices states that the intercepts of any face of a crystal along the crystallographic axes are either equal to the unit intercepts or some simple whole number multiples of them.*

The faces of crystals and also planes within crystals can be characterized by means of a suitable set of coordinates.

Let consider the three axes OX, OY, OZ which are cut by a crystal face ABC at distances OA, OB, and OC from the origin. Let OX, OY, and OZ represent the three crystallographic axes and let ABC be a unit plane. The unit intercepts will then be a, b and c.

According to the above law, the intercepts of any face such as KLM, on the same three Axes will be simple whole number multiples of a,b and c respectively. These distances are called intercepts. It is found that if the axes are suitably chosen, the intercepts of different faces upon them bear a simple ratio to each other or a given face may cut an axis at infinity. This is called the law of rational intercepts or indices.

### Miller Indices

### Weiss Indices

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