Direct and Reciprocal Lattices
Nevill Gonzalez Szwacki, Teresa Szwacka · 2016
A three-dimensional Bravais lattice may be seen as a set of two- dimensional lattices, whose planes are parallel to each other and equally spaced. Each of these planes represents a lattice plane of the three-dimensional Bravais lattice. The way of seeing a three- dimensional lattice as a set of two-dimensional lattices is not unique. A set of parallel, equally spaced lattice planes is known as a family of lattice planes. The orientation of the planes belonging to each family is given by the so-called Miller indices. We will show in this chapter that the Miller indices represent the components of a translation vector of the reciprocal lattice which is orthogonal to the family of the lattice planes labeled with these indices. In the next section, we will learn how to obtain the Miller indices.