Use of Punched Card Tabulating Machines for Crystallographic Fourier Syntheses

Abstract

THE use of 2-dimensional Fourier syntheses in the determination of crystal structures from X-ray data has been well established for some years ; but it is becoming increasingly recognized that for detailed determinations these alone are not enough, and that 3-dimensional syntheses are also necessary. The methods of summation which have been used for 2-dimensional work¹, and which employ no other mechanical aids than adding machines, can be applied to 3-dimensional problems, but are then comparatively slow and impose a considerable strain on the computer. Moreover, with rising standards of accuracy, some improvement is desirable on the existing Beevers-Lipson strips which have so far been most commonly used for 3-dimensional work ; the 'rounding-off' errors arising from the use of the strips, with their 2-figure accuracy and 6° intervals of computation, may in unfavourable cases lead to displacements of atomic centres by 0.01 A., which is now no longer small compared with the accuracy theoretically attainable².