Atomic-scale visualization of surfaces with x rays

A solution to the phase problem for the case of surface crystallography is presented. By oversampling a surface diffraction pattern along the continuous crystal-truncation rods, we can iteratively recover the phases of the complex structure factors of an unknown surface atomic geometry. Simple Fourier inversion of these structure factors directly yields a three-dimensional map of the electron density in the surface region with similar to angstrom resolution. This model-independent determination of atomic positions can then be used as a starting point for quantitative refinement using conventional means.