Direct structure determination of systems with two-dimensional periodicity

We describe a new x-ray method for the direct measurement of structures whi ch have two-dimensional (2D) periodicity, and are positionally correlated w ith an underlying substrate crystal. Examples include reconstructed crystal structures at interfaces, layered heterostructures, crystalline-amorphous interfaces, and self-assembled structures on crystalline substrates. The st ructure is obtained by determining the complex scattering factors along the Bragg rods and Fourier back-transforming them into real space. The method for determining the complex scattering factors has two variations. The firs t is generally applicable. It involves the measurement of the derivative of the diffraction phase along the Bragg rods and the subsequent determinatio n of the diffraction phase using the known structure of the substrate, The second is applicable to 2D systems, with an unknown structure, that are bur ied within a crystal with a known structure, In this case the diffraction p hase is determined without me need to measure its derivative first. We expe rimentally demonstrate both variations by determining the diffraction phase alone one Bragg rod of a GaAs sample with four buried AlAs monolayers. Usi ng simulated data along the Bragg rods within a volume in reciprocal space, we show that the method yields the three-dimensional structure of 2D syste ms with atomic resolution.