History of the reciprocal lattice

Abstract

History of the development of the reciprocal lattice is reviewed. The reciprocal lattice as an essential tool for the study of diffraction experiments by ordered structures and characterization of their structural properties is widely taught in any text of solid state or chemistry, but usually without discussion of its history. This article aims to give a coherent historical perspective on the reciprocal lattice. First, a basic introduction to the reciprocal lattice concept, its mathematical foundation and physical origin, and its relationship with the direct lattice is provided. Then a detailed chronicle of ideas leading to the concept of the reciprocal lattice is presented, including a review of the contributions of Gibbs, Ewald, and others. The polar lattice concept, the great ancestor of the reciprocal lattice, is presented.