Abstract: A method for observing the arrangement of atoms in a thin layer on a surface and an apparatus for employing the method are disclosed. According to the method, a finely converged electron beam is directed to a surface of a sample and the X-ray emitted from the surface is detected at a take-off angle equivalent to, or in the vicinity of, the total reflection angle, thereby avoiding interference from X-rays emitted beneath the surface. The apparatus includes an electron gun, a sample holding means, one or more detectors and devices for storing, processing and displaying the output signal from the detectors. The apparatus also provides for two-dimensional scanning of a surface and for adjustment of the position of the sample and of the detectors.