Assessment of parameter accuracies in profile analysis of white-beam neutron powder diffraction experiments

Abstract

One of the problems arising in profile analyses of white-beam powder diffraction experiments is that in order to assess the reliability of the refined structure parameters allowance must be made not only for errors in the actual powder data but also for uncertainties in the various wavelength-dependent corrections involved. As a means for such assessments the present work provides a general method in which the incident white neutron flux spectrum is assumed to be measured and combined with the other wavelength-dependent factors to form a set of effective incident intensities with known statistical properties for the diffraction peaks. Given that appropriate models are used for both the powder spectrum and the effective fluxes, the unknown model parameters and their accuracies can be estimated optimally through a single least-squares fit of the available experimental data. By applying the formalism to a real nickel powder measurement, it was shown that the precision of the parameter estimates may depend considerably on the errors of the wavelength-dependent corrections, unless these are known with much higher accuracies than the diffraction pattern. In the example this proved true especially for the scale factor and the temperature factor.

The distinction of frame overlap and the cohesion of time-of-flight diffraction patterns collected at various scattering angles

“…Firstly, the range of accessible d spacings for a given neutron source is greater and, secondly, the analysis is considerably less susceptible to systematic and statistical errors in the instrument calibration. This last point may be rather important since it has recently been suggested that such errors probably outweigh the counting statistics of TOF diffraction patterns (Poyry & Tilli, 1983). When the TOF method is used in conjunction with several diffraction angles, each Bragg peak is convoluted with much of the incident intensity profile such that random irregularities and some systematic errors of this profile lose significance.…”