Machine for the rapid summation of Fourier series: an X-ray investigation of sulphuric acid monohydrate

Abstract

PART I. A MACHINE FOR THE RAPID SUMMATION OF FOURIER SERIES

The machine about to be described has been specially designed with a view to its use in X-ray crystallographic laboratories. In the elucidation of structures from measured intensities of scattering of X-rays, the performance of Fourier syntheses is probably the best way of obtaining atomic parameters, although this method is limited by the fact that the phases of most, at any rate, of the F-values must be known beforehand. However, the introduction of the Patterson (1) method enables the measured intensities to be used directly to give a diagram which, properly interpreted., can give valuable information about the atomic parameters. Nevertheless, for complicated structures, a TWO- DIMENSIONAL PATTERSON PROJECTION (obtained from the F² (h, k, o), F² (o, k, l), or F² (h, o, l) values) becomes very difficult to interpret due to the large number of interatomic vectors involved; this is particularly true for organic compounds, due to the fact that the commonly occurring atoms (C, O, and N) have very similar scattering powers for X-rays. In such circumstances, the maximum of information can be obtained from a three dimensional Patterson summation, using the general F² (h, k, l) values. The fact that such summations have not hitherto been used is due, not merely to difficulty in getting values for the general intensities, but to the great labour involved in calculating the series. The present machine, by greatly reducing that labour, should make possible the general use of the very powerful three-dimensional Patterson method. It will also, of course, greatly facilitate the method of approximation to the true structure by successive Fourier syntheses, already largely used.

There are of course existing machines which are capable of performing the process of Fourier synthesis, but these are all very expensive, and not particularly fast. There is therefore a real need for a machine, such as the present, which is sufficiently inexpensive to be acquired permanently by most crystallographic laboratories, and which is very fast in operation, while giving all the accuracy necessary for X -ray crystallographic work (and no more).

PART II. AN X-RAY INVESTIGATION OF SULPHURIC ACID MONOHYDRATE

On the basis of oscillation and Weissenberg photographs of Sulphuric Acid Lonohydrate (H₂SO₄.H₂0 ) crystals, the unit cell and space group have been 'determined, and a Fourier Synthesis of the (h k 0) reflections has been carried out. Based on this synthesis, on considerations of interatomic distances, and on the observed general (h k 1) reflections, a structure has been suggested.

Powder photographs have been taken of the monohydrate at temperatures varying from just below its melting point to liquid oxygen temperature, and it has been confirmed that the monohydrate has the above structure throughout this range of temperature.