Quantitative X-ray powder diffraction analysis applied to transmission diffraction

Reference intensity ratios (RIR or k_i) may be used with powder diffraction intensities obtained from convergent-beam transmission scattering once the intensities have been corrected for irradiated volume variations that are a function of the angle (ω) between the mean beam direction and the normal to the sample plane. For a given ω setting this volume does not vary with 2θ. The fundamental absorption relationship giving the beam attenuation as a function of sample mass absorption coefficient, sample specific mass and ω and 2θ angles has been derived. Attenuation of the beam through thin samples is nearly constant below 90° 2θ scattering angle, and hence quantitative analysis using RIR values can be performed in this region with little error by converting the integrated intensities to those equivalent to Bragg–Brentano scattering using the appropriate Lorentz factor. Ambient air particulate samples or those artificially prepared using aerosol suspension or liquid filtration and collected on membrane filters can be scanned in transmission while spinning at a moderate speed without particle loss or layer fragmentation in a horizontal goniometer. Mass absorption coefficient measurements may be made with such an instrument by two methods: (1) the sample can be positioned eccentrically for spinning direct-beam transmission measurements, or (2) by substrate diffraction using the θ–2θ Bragg–Brentano stage.