The quantitative interpretation of X-ray fluorescence (XRF) data is often difficult because of matrix effects. The intensity of fluorescence measured for a given element is not only dependent on the element's concentration, but also on the mass absorption coefficients of the sample for the excitation and fluorescence radiation. Also, there are interelement effects in which high-energy fluorescence from heavier elements is absorbed by ligher elements, with a resulting enhancement of their fluorescence. Recent theoretical treatments of this problem have shown that X-ray fluorescence data can be corrected for these matrix effects by calculations based on first principles. Fundamental constants, available in atomic physics data tables, are the only parameters needed. It is not necessary to make empirical calibrations. In this paper we report the application of this correctional procedure to alloys and alumina-supported catalysts. We also discuss how it may be applied to other matrices. A description is given of a low-background spectrometer which uses monochromatic AgKα radiation for excitation. Matrix corrections by first principles can be easily applied to data from instruments of this type because fluorescence excitation cross-sections and mass absorption coefficients can be accurately defined for monochromatic radiation.