Question

what is law of rational indices

Answer 1

Definition - The law of rational indicesstates that the intercepts, OP, OQ, OR, of the natural faces of a crystal form with the unit-cell axes a, b, c are inversely proportional to prime integers, h, k, l. They are called the Miller indices of the face.

Answer 2

The Rational Indices Law in Crystal Systems

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 rational indices law

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, according to the law of rational indices. A suitable set of coordinates can be used to characterize the faces of crystals as well as planes within crystals. Consider the three axes OP, OQ, and OR (Figure), which are cut by a crystal face ABC at OA, OB, and OC distances from the origin. Consider OP, OQ, and OR to be the three crystallographic axes, and ABC to be a unit plane. The unit intercepts are a, b, and c. The intercepts of any face, such as KLM, on the same three Axes will be simple whole number multiples of a, b, and c, according to the above law. These distances are known as intercepts. It is discovered that if the axes are chosen properly, the intercepts of different faces on them have a simple ratio to each other, or that a given face may cut an axis at infinity. This is referred to as the law of rational intercepts (or indices).