Interpretation of Patterson Diagrams

Abstract

THE direct F² Fourier series of Patterson¹ is one of the most powerful methods in modern crystal analysis, and many of its applications have been described from time to time in NATURE². Patterson's original result was derived as an extension of the application to crystals of the theory of scattering of X-rays in liquids made by Gingrich and Warren³. Patterson computes the weighted average distribution of electron density ; about a point in the crystal, cell-size abc, volume v, by the relation which gives the distribution about the point as a function of the parameters uvw. Making use of the usual expression for the electron density in terms of the structure amplitudes F(hkl), namely, the function A (uvw) is obtained as The importance of A(uvw) arises because it will only be large when there are high values in ;(xyz) both at (xyz) and at (x+u, y+v, z+w). Thus a peak in the function A(uvw) at (u₁v₁w₁) corresponds to an interatomic distance in the crystal defined by a vector the components of which are (u₁v₁w₁).