Recovery of concentration spectra of binary solids from diffraction profiles by means of band matrices

A method for the retrieval of concentration spectra of crystalline mixtures from x-ray diffraction profiles is described. Both spectra are associated with an integral equation which can be simplified to yield a set of linear equations. Solutions are readily obtained by triangular decomposition since the equations are typically described by band matrices. The method has been tested with simulated diffraction profiles to allow for a variety of options concerning the concentration spectra. The procedure is well suited for binary alloys containing crystals of different structure and lattice parameters. The time consumption of the calculations is significantly reduced as compared to hitherto available methods.