Crystal Structure Analysis

Abstract

In crystallography, finding the spatial arrangement of the average unit cell contents requires solution of the phase problem. As described in Chapter 1, the Fourier transform relationship between an image and its diffraction pattern can be experimentally realized in one direction if only intensity data are recorded. Since the image intensity is linearly proportional to the crystal potential, when the weak phase object approximation is valid, the directly computed transform finds the crystallographic phases (the Fourier transform of relative mass shifts). Structure factor magnitudes are all that one can obtain from recorded diffraction intensities, on the other hand, and the phase interactions of the scattered beams are lost. (However, an intensity transform, assuming all-zero phases, can also be useful, as will be shown.) Using high-resolution electron micrographs as an independent source of crystallographic phase information, therefore, demonstrates a potential advantage of electron crystallography over x-ray crystallography. On the other hand, great care must be taken to ensure that all measured data are adequately near the single scattering approximation to guarantee the success of ab initio structure analyses (see Chapter 5).