A laser molecular-beam epitaxy (LMBE) system for the fabrication of atomically controlled oxides superlattices and an x-ray diffractometer that measures spatially resolved x-ray diffraction spectra have been developed based on the concept of combinatorial methodology. The LMBE chamber has two moving masks, an automated target stage, a substrate heating laser, and an in situ scanning reflection high-energy electron diffraction system. The x-ray diffractometer with a curved monochromator and two-dimensional detector is used for rapid concurrent x-ray diffraction intensity mapping with the two axes of the detector corresponding to the diffraction angle and a position in the sample.