Beta Phase: Square45 is currently in beta testing. Expect some features or content to be incomplete or missing.
45

Miller Indices

A system of notation used to identify crystallographic planes in a crystal lattice, defined by their intercepts with the crystallographic axes.
📜

The statement of the theorem

Given a crystal lattice defined by basis vectors a,b,c\mathbf{a}, \mathbf{b}, \mathbf{c} and a plane intersecting the crystallographic axes at intercepts (p,q,r)(p, q, r), the Miller indices (h,k,l)(h, k, l) are defined by the reciprocal relationship:\n[hkl]=[1/p1/q1/r]\left[\begin{array}{c} h \\ k \\ l \end{array}\right] = \left[\begin{array}{c} 1/p \\ 1/q \\ 1/r \end{array}\right]\nThese indices are typically reduced to the smallest set of co-prime integers by multiplying by the least common multiple of the denominators.
Source: Wikipedia