A method for denoting planes in crystal lattices relies on a set of three integers, known as Miller indices. These indices are inversely proportional to the intercepts of the crystal plane with the crystallographic axes. For instance, if a plane intersects the x-axis at unit length ‘a’, the y-axis at ‘2a’, and is parallel to the z-axis (intersecting at infinity), the reciprocals of these intercepts are 1, 1/2, and 0. Clearing the fractions to obtain the smallest set of integers yields the Miller indices (2 1 0).
This notation simplifies the analysis of diffraction patterns in crystalline materials. Accurate determination of these indices allows researchers and engineers to understand and predict material properties, crucial in fields like materials science, solid-state physics, and crystallography. The ability to identify crystal orientations through this method has historically been instrumental in developing new materials with tailored properties, enhancing efficiency in various applications ranging from semiconductors to structural alloys.
