Crystallography Today

Abstract

It is the task of the structural crystallographer to find the positions of the atoms in a crystal. An X-ray diffraction pattern contains this information but since there is no X-ray lens the process of combining the diffracted beams to form an image must be done mathematically. This requires a knowledge of the relative phases of the beams, which is not given directly by the observed data. The last two decades has seen the rise of direct methods by which phases are estimated by mathematical procedures from the intensities of the diffracted beams. The most important tools used in these methods are the triple-phase relationship and the tangent formula. Examples are given of methods employing these ideas and of structures solved by their use. In particular there is described the computer package MULTAN which accounts for nearly one-half of all equal-atom structures solved at the present time.