The document discusses Miller indices, which are used to uniquely identify crystallographic planes and directions in a crystal lattice. It provides the following key points: - Miller indices were introduced in 1839 and assign integers to the intercepts of a plane or direction with the crystallographic axes. - To determine Miller indices, the intercepts are taken, reciprocals are calculated, fractions are cleared, and results are written in parentheses with negative numbers denoted by bars. - Miller indices provide information about the orientation of a plane or direction relative to the crystal axes. A zero index means parallel, smaller numbers mean more parallel, and larger numbers mean more perpendicular. - Families of equivalent planes related