A profile-fitting procedure for analysis of broadened X-ray diffraction peaks. I. Methodology

A convolutive profile-fitting procedure is described for analysing X-ray diffraction peak profiles broadened by microstructural factors (crystallite size and lattice disorder). The method requires, in a first stage, an accurate determination of the instrumental function, which is subsequently convoluted with a parametric function adjusted to fit the diffraction profile intensities of the specimen investigated. In the calibration of the instrument function throughout the angular range 20–145° in 2θ, 58 peaks of a well crystallized α-quartz specimen are examined. Provision is made to include in the instrument function an exponential function containing an angle-dependent asymmetry parameter. In the present methodology, a pseudo-Voigt function is suggested to obtain the shape factors (integral breadth, peak width at half maximum, Gaussian content) that contain useful information related to the microstructural properties in the frame of the so-called 'simplified methods' of line broadening analysis. Furthermore, if the optimized profile functions in the Fourier analysis of the broadened peaks are used directly, many relationships follow straightforwardly in the real-space domain. In this way it is easy to apply the formalisms currently used to derive physical information (e.g. the Warren & Averbach and Vogel, Haase & Hosemann methods).