Anisotropic size broadening

An improved modelling of the average structure of ice Ic includes linear combination of stacking-probability driven structure models and anisotropic size broadening. It allows for a quantitative modelling of neutron diffraction data of different ice Ic samples. It will serve as well for the description of ice Ih samples with stacking faults. 

Layer-layer correlation probabilities. The analytical approach described by Berliner and Wemer is worth to be pursued further. From the four independent stacking probabilities corresponding to an interaction range of s=4, layer-layer correlation probabilities can be readily computed by a numerical approach for any finite crystallite size. It is then less trivial to compute the precise diffraction pattern corresponding to a correlation probability, and then to refine the parameters - the stacking probabilities - to fit an observed pattern. In principle, even the anisotropic size broadening can be taken into account in this approach as well as deviations from the layer positions. 

A second difficulty is the anisotropic size and strain broadening of the diffraction peaks, which is considerable as well, but highly correlated with the broadening due to stacking disorder. A de-convolution is not possible without determining the anisotropic size distribution, e.g., with electron microscopy, which is difficult to perform due to technical temperature and pressure constraints making it impossible to observe a stable sample of ice Ic. 

GRE 85] GREAVES C., Rietveld analysis of powder neutron diffraction data displaying anisotropic crystallite size broadening , J. Appl. Cryst, vol. 18, p. 48-50,1985. 

The diffraction lines due to the crystalline phases in the samples are modeled using the unit cell symmetry and size, in order to determine the Bragg peak positions 0q. Peak intensities (peak areas) are calculated according to the structure factors Fo (which depend on the unit cell composition, the atomic positions and the thermal factors). Peak shapes are described by some profile functions 0(2fi—2fio) (usually pseudo-Voigt and Pearson VII). Effects due to instrumental aberrations, uniform strain and preferred orientations and anisotropic broadening can be taken into account. 

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