Calculation of diffuse scattering from simulated disordered crystals: a comparison with optical transforms

An investigation is carried out on the feasibility of calculating the diffuse scattering from computer simulations of crystals containing substitutional and displacement disorder which have hitherto been used in conjunction with optical transform methods to aid in the interpretation of observed X-ray diffraction patterns. A straightforward method of calculation based on direct Fourier summation of the simulated lattice is used instead of fast Fourier transform (FFT) techniques, which are not in general suited to this type of calculation. This computational method provides a number of advantages over the optical method. It allows calculation in three dimensions, more flexibility in the assignment of atomic positions and scattering power of the individual atoms involved and the computation can be made in absolute units allowing for direct comparison with data scaled to electron units. Comparison of the two techniques is presented using, as an example, a simulation of planar disorder in a synthetic mullite. It is found that calculated patterns of comparable quality to ones obtained optically are feasible using the current generation of computers. Nevertheless, the transforms can still consume considerable computational resources particularly when the extension to three dimensions is required.