Surface x-ray crystallography with alternating constraints in real and reciprocal space: the case of mixed domains

A recently developed recursive algorithm for the direct recovery of the electron density of a surface unit cell from scattered x-ray intensities is adapted to crystal surfaces that may consist of mutually rotated domains. We examine the cases of both mutually coherent scattering from the domains and the more common case of mutually incoherent scattering. In each case we test the algorithms on simulated data calculated from a standard surface x-ray diffraction computer program. In both cases the iterative algorithm depends on satisfying data constraints in reciprocal space and non-negativity constraints on the electron density in real space. (author)