Crystal Analysis and Point Sets

IT is customary in X-ray crystallography to regard a crystal as a continuous distribution of scattering matter, expressible in the form of the electron density function: Whereas X-ray techniques permit the determination of the amplitudes r, they do not determine the phases I±. This, as is well recognized, has been the essential limitation in X-ray analysis, not as a method of testing structures already proposed, but as a method of discovering the atomic structure of crystals. This difficulty prompted the introduction of the derived function1: where which is thus expressible in terms of the observed amplitudes and is independent of the unobserved phases. This function (representing the weighted distribution of density in the crystal about any point) can be used in conjunction with any structure already proposed, to pass it for further consideration or to reject it, according as its vector function does or does not tally with it.