Combined X-ray and neutron Rietveld refinement

Abstract As is noted in Chapter 1, a neutron or X-ray powder diffraction pattern can be modelled from descriptions of the crystal structure of the sample, both instrumental and sample contributions to peak broadening, intensity effects such as absorption and extinction, and a background contribution. Also noted is that a Rietveld (1969) refinement performs a least-squares minimization of the weighted differences between this calculated pattern and observed data by computing the shifts in the adjustable parameters for the model. Since the problem is non-linear, several cycles of least-squares refinement are needed to complete the minimization. However, because both the complex nature of the structure factors and much of the directional character of reciprocal space are lost in a powder diffraction experiment, there is a larger question of uniqueness for the result of a Rietveld refinement of a single powder pattern than for the result of a single crystal refinement.