Structural modeling total scattering

All of the studies published so far have been aiming at the reconstruction of the total electron density in the crystal by redistribution of all electrons, under the constraints imposed by the MaxEnt requirement and the experimental data. After the acceptance of this paper, the authors became aware of valence-only MaxEnt reconstructions contained in the doctoral thesis of Garry Smith [58], The authors usually invoke the MaxEnt principle of Jaynes [23-26], although the underlying connection with the structural model, known under the name of random scatterer model, is seldom explicitly mentioned. 

The presence of a minor second phase impurity can be added either in the form of the actual structural model of Ni or as a Le Bail s phase, where only the unit cell and peak shape parameters are taken into account. The latter option has been chosen since we are not interested in the crystal structure of this minor impurity, and it may be a difficult task given its small contribution to the total scattered intensity. 

It is shown that both the Bragg and the diffuse scattering parts of neutron powder diffraction data on ice Ih can be interpreted simultaneously by constructing large models of the structure that are consistent with the measured total scattering functions within errors. The RMCPOW algorithm proved to be readily applicable for the purpose. 

The Rayleigh-Debye-Gans model of scattering predicts that for N particles in a scattering volume V, each particle will occupy a volume Vp and the total scattered intensity L from a beam of vertically polarized incident light is the summation of the individual scattering intensities, modified by an additional term that contains a structure factor S (rij) that accounts for the inter-particle interaction as shown in Eq. 2.35. 

In practice, one can use Eq. (6.24) to model the scattering intensity to obtain information about the inhomogeneity size (R, total volume or contrast (G), and surface or structure (fi. Pi). In certain cases, parameters obtained from Eq. (6.24) can be used to provide information about agglomerates [53], size distribution [54], or a two-phase system [55]. 

The amplitude of the elastic scattering, Ao(Q), is called the elastic incoherent structure factor (EISF) and is determined experimentally as the ratio of the elastic intensity to the total integrated intensity. The EISF provides information on the geometry of the motions, and the linewidths are related to the time scales (broader lines correspond to shorter times). The Q and ft) dependences of these spectral parameters are commonly fitted to dynamic models for which analytical expressions for Sf (Q, ft)) have been derived, affording diffusion constants, jump lengths, residence times, and so on that characterize the motion described by the models [62]. 

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