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Joint structure refinement of x-ray and neutron diffraction data on disordered materials: application to liquid water

X-ray diffraction data on liquids and disordered solids often provide useful complementary structural information to neutron diffraction data. Interpretation of the x-ray diffraction pattern, which is produced by scattering from the atomic electrons rather than from the atomic nuclei as in the case of neutron diffraction, is, however, complicated by the Q-dependent electronic form factors, which cause the x-ray diffraction signal to decline rapidly with increasing Q, where Q is the wave vector change in the diffraction experiment. The problem is particularly important in cases such as water where there is a significant molecular polarization caused by charge transfer within the molecule. This means that the electron form factors applicable to the molecule in the condensed environment often deviate from their free atom values. The technique of empirical potential structure refinement (EPSR) is used here to focus on the problem of forming a single atomistic structural model which is simultaneously consistent with both x-ray and neutron diffraction data. The case of liquid water is treated explicitly. It is found that x-ray data for water do indeed provide a powerful constraint on possible structural models, but that the Q-range of the different x-ray data sets (maximum Q ranges from 10.8 to ∼17.0 Å−1 for different x-ray experiments), combined with variations between different data sets, means that it is not possible to rigorously define the precise position and height of the first peak in the OO radial distribution function. Equally, it is found that two different neutron datasets on water, although measured to a maximum Q of at least 30 Å−1, give rise to further small uncertainties in the position of the hydrogen bond peaks. One general conclusion from the combined use of neutron and x-ray data is that many of the classical water potentials may have a core which is too repulsive at short distances. This produces too sharp a peak in r-space at too short a distance. A softer core potential is proposed here.