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low-temperature form of ice until the 1980s, when calorimetry experiments on
samples doped with impurities, particularly potassium hydroxide (KOH), exhibited
a clear signature of a proton-ordering transition at 72 K [8-10]. The transition
temperature was independent of the KOH concentration, indicating that KOH acts
like a catalyst. This proton-ordered structure suggested by subsequent diffraction
experiments [10-15] is called ice XI. It is structure (a) of space group symmetry
Cmc 2 1 in Fig. 2, where ice XI can be seen to be ferroelectric on account of the
ordered c -axis bonds. The mechanism by which KOH induces the proton-ordering
transition in ice Ih is unclear. Furthermore, the ferroelectric structure of ice XI
is unexpected. There has been continued debate and research as to whether the
H-bond arrangements in the high-temperature phase of ice are actually random or
partially ordered [16, 17], whether a phase transition to a fully H-bond ordered
structure exists [15, 18-20], and if so, its identity. Hydrogen-bond order-disorder
transitions in other parts of the ice phase diagram have been long known [21], and
new examples continue to emerge [22-24].
Like the phases of ice, water clusters can be grouped into families among
which the oxygen atoms occupy nearly the same position, and that differ in the
direction of the H-bonds between those oxygens. Unlike ice structures, where the
energy difference per water between different H-bond structures is on the order of
0 . 1 kcal mol 1 , the energy difference between H-bond isomers in water clusters
can amount to several kilocalories per mole per water. As a result, the H-bond
disordered ice phases tend toward nearly complete disorder while only the low-
est energy isomer or isomers of water clusters are typically observed in cluster
beam experiments. The properties of the cubic water clusters (Fig. 3) illustrate this
Figure 3. The 14 symmetry-distinct H-bond arrangements possible when the oxygen atoms of
eight waters form a cubic structure. The point group symmetry is indicated when it is higher than C 1 .
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