Law of Rational Indices in Crystal Systems
Crystalline solids exhibit different toms depending on the relative sizes of the ions or atoms, type of binding force, nature of stacking etc. any of the six or sometimes seven main groups into which crystals are commonly classified according to the relative lengths and inclinations of their axes or according to their respective symmetries.
The law of rational indices
The faces of crystals and also planes within crystals can be characterized by means of a suitable set of co-ordinates. Let consider the three axes OX, OY, OZ (Figure) which are cut by a crystal face ABC at distances OA, OB and OC from the origin. These distances at 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).