where Ge(E) represents the background-free XRF spectrum of pure element e, B(E) is the non-element-specific background in the spectrum and Se (xi , ωk) represents the weight of the contribution of element e to spectrum (i, k). The latter weights are determined by least-squares fitting of the individual XRF spectra. For reduction of the raw XRD data, the XRDUA program was employed. In a similar manner as for the XRF data, each individual diffractogram IXRD(x, ω, 2θ) was expressed as a linear combination of crystal phase-specific contributions: