Reciprocal Space and Reciprocal Lattice

The reciprocal lattice concept was introduced by Ewald in 1913 [1]. He applied it some years later in the interpretation x-ray diffraction photographs [2], although the procedure was conceived independently a year earlier by Bernal [3]. In reciprocal space a lattice, the reciprocal lattice, is defined for each of the fourteen real space Bravais lattices; it is derived here first by the following construction, as applied to a monoclinic lattice in projection on the x, z plane. A primitive unit cell is outlined by vectors a and c, with three families of planes indicated by their Miller indices; b is normal to the plane of projection. Lines are constructed from the origin O that are normal to the families of Bravais lattice planes (hkl) shown (Fig. A20.1a). Along each of these lines, reciprocal lattice points hkl are defined...