Description and peak-position determination of a single X-ray diffraction profile for high-accuracy lattice-parameter measurements by the Bond method. II. Testing and choice of description

Abstract

The reliability of the results of the peak-position determination by means of various approximating functions – the polynomials and shape functions considered in paper I [Gatdecka (1993). Acta Cryst. A49, 106–115] – was examined based on test calculations in which both measurement data and computer-simulated data were used. It was found that accurate peak-position determination must be based on a reasonable physical and statistical model of the diffraction profile. The statistical model is required to provide an objective criterion of the goodness of fit. The goodness of fit is a necessary but not sufficient requirement for obtaining accurate results. To provide unbiased and stable enough (independent of scanning range) results, the function to be used must, in addition, be continuous and give a good approximation to known physical models of the diffraction profile. It was proved that the use of a reasonable shape function – here, a pseudo-Voigt function with a linear (or exponential) asymmetric factor, the best of the functions considered – leads to accurate enough and highly stable results. Results obtained using polynomials, even when the goodness of fit is being carefully checked, are no more precise and are less stable and so less accurate than those obtained using the carefully selected shape function. Only in the case of a parabola – the simplest and the most preferred among polynomials – there is a possibility of reducing the bias of outcomes by an extrapolation of results obtained for various scanning ranges. However, the improvement also requires a reasonable model (here, the shape function mentioned above).