Truncation in diffraction pattern analysis. I. Concept of a diffraction line profile and its range

An evaluation of the concept of a line profile is provoked by truncation of the range of intensity measurement in practice. The measured truncated line profile can be considered either as part of the total intensity distribution which peaks at or near the reciprocal-lattice points (approach 1), or as part of a component line profile which is confined to a single reciprocal-lattice point (approach 2). Some false conceptions in line-profile analysis can then be avoided and recipes can be developed for the extrapolation of the tails of the truncated line profile. Fourier analysis of line profiles, according to the first approach, implies a Fourier series development of the total intensity distribution defined within [l − ½, l + ½] (l indicates the node considered in reciprocal space); the second approach implies a Fourier transformation of the component line profile defined within [− ∞, + ∞]. Exact descriptions of size broadening are provided by both approaches, whereas combined size and strain broadening can only be evaluated adequately within the first approach. Straightforward methods are given for obtaining truncation-corrected values for the average crystallite size.