Calculation of x-ray intensity from a rough sample based on a statistical model

An x‐ray intensity correction is developed which begins with a roughness model that is often used to describe real surfaces. This is based upon a normal distribution of surface asperities relative to a mean plane. Pair correlation between absorbing elements along x‐ray paths either entering or leaving the sample with respect to the signal producing element is accomplished by means of an exponential autocorrelation function. This allows the degree of roughness to be varied on a local scale to fit specific surfaces using statistical data. Equations are developed to describe x‐ray fluorescence and diffraction signals for symmetric and asymmetric beam optics. Theory is compared with experiment using a roughened, fully stabilized zirconia sample.