On the numerical corrections of time-of-flight neutron powder diffraction data

Time-of-flight neutron powder diffraction data for NIST Standard Reference Materials have been used to study the adequacy of the peak profile model obtained from a convolution of back-to-back exponentials with a pseudo-Voigt function that is widely used in Rietveld refinement. It is shown that, while the empirical models for d-spacing (wavelength) dependence of Gaussian and Lorentzian components of the pseudo-Voigt function and rise exponent are satisfactory, the behavior of the decay exponent and peak positions demonstrate significant deviations, which can be corrected by numerical methods. The practical side of this process as implemented in GSAS and FULLPROF and the effect of the corrections on the Rietveld analysis results are discussed.