Proton disordering

Both clusters in Fig. 5.31 exhibit considerable cooperative proton-ordering that distinguishes them from many alternative proton-disordered (and destabilized) isomeric forms that could be imagined. For example, the 24-mer (Fig. 5.31 (a)) has two fully cooperative W6C-like caps as well as a fully cooperative 12-ring girdle, ... 

There is some form of hydrogen disorder in nearly all polymorphs, just as in ice(Ih). However the rhombohedral ice(II) is an exception. Its protons are ordered. As was suggested by Whalley (1967), this may have profound significance. Were ice(II) proton-disordered, it would have a higher entropy. A possible consequence would be that this polymorph would become thermodynamically stable under conditions that might arise on Earth. As ice(II) has a density 1.2 g cm-3, it would then accumulate at the bottom of lakes or seas, so that Earth s waters would freeze from the depths upwards. Life, as we know it, could hardly have developed, or survived, in such circumstances. 

FIGURE 2.2 (a) Two-dimensional proton-disordered ice lattice (Bjerrum defect illustrated... 

We have published some papers concerning some less common heterocycles such as 1,2,4-diazaphospholes 257 and 258 [203], Using X-ray crystallography, CPMAS NMR, and GIAO-type calculations we have found that 257 is a cyclic dimer with localized N-H protons (similar to pyrazole dimers) while 258 is probably a tetramer (similar to pyrazole tetramers) showing ISSPT (intramolelecular solid state proton transfer). This prediction was only partly true because 258 crystallizes in two cyclic dimers, both presenting proton disorder [204] (Fig. 8). 

H. Nada and Y. Furukawa, Anisotropy in growth kinetics at interfaces between proton-disordered hexagonal ice and water, A molecular dynamics study using the six-site model of H20, J. Crystal Growth, Article in press (2005). 

Here we should note that the dispersion curve calculation has provided all the information required to obtain the response from a single crystal sample aligned along a specific direction in Q. Indeed, if such an experiment were realistically feasible it would be the preferred technique. This is because the dispersion curves would be measured directly and the detailed information about the force field could be extracted. However, this is often not practical, at least for the exotic phases of ice and powdered samples were used. For ice Ih, single crystals are widely available (but a large crystal of ice Ic has not been obtained), after many attempts [49,55], reliable dispersion curves have yet to be obtained. This is due to the proton disordering in the structure of ice Ih and hence all the optic modes are localised. 

As an example of the information lost by exploring the DOS of powdered samples we compare the calculated dispersion curves of ice Ih and Ic. They have quite different dispersion curves in the translational region due to their different symmetries, but these are inaccessible to neutron dispersion measurements due to the proton disorder in the structures. Only the DOS can be measured. As a result, the detail of the information in the dispersion curves is lost, or at least degraded, by comparing only the DOS. From both experiments [22,55] and calculations, we have found that the two ices share an identical spectrum as shown in Fig. 3. This is because they share the same local structure in their lattices (the tetrahedral symmetry) and the same local force field. If the integration over the first BZ is incomplete (i.e. if too few q-points were used), there would be a considerable difference between calculation and observation spectra. 

Fig. 20. A plot shows a series of LD results using the different sizes of the ice Ih lattice to represents the proton disordering (a) for a lattice cell with 4 molecules (b) for 8 molecules (c) for 16 molecules and (d) for 32 molecules.

From this series of calculations, we have demonstrated that proton disordering in the lattice can generate the common triangular shapes seen for the two optic... 

At high pressure, there are many kinds of ice polymorphs and the phase diagram of water is complicated. In ice VlII and XI, protons are ordered while most of ice phases have proton disordered forms. In ambient condition, satisfied is the ice rule water exists as an H2O molecule and a proton sits between two adjacent oxygens. In ice Ih, the number of configurations arising from the proton-disordering is approximately (3/2) " for Nw molecule system[16. This is also true for ice Ic and some other ices except for proton-ordered forms. 

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