Ice XI
Ice XI is the hydrogen-ordered form of Ih, the ordinary form of ice. Different phases of ice, from ice II to ice XVI, have been created in the laboratory at different temperatures and pressures. The total internal energy of ice XI is about one sixth lower than ice Ih, so in principle it should naturally form when ice Ih is cooled to below 72 K. The low temperature required to achieve this transition is correlated with the relatively low energy difference between the two structures. Water molecules in ice Ih are surrounded by four semi-randomly directed hydrogen bonds. Such arrangements should change to the more ordered arrangement of hydrogen bonds found in ice XI at low temperatures, so long as localized proton hopping is sufficiently enabled; a process that becomes easier with increasing pressure. Correspondingly, ice XI is believed to have a triple point with hexagonal ice and gaseous water at (~72 K, ~0 Pa).
Ice XI has an orthorhombic structure with space group Cmc21 containing eight molecules per unit cell. Its lattice parameters are a=4.465(3) Å, b=7.859(4) Å, and c=7.292(2) Å at 5 K. There are actually 16 crystallographically inequivalent hydrogen-ordered configurations of ice with an orthorhombic structure of eight atoms per unit cell, but electronic structure calculations show Cmc21 to be the most stable. Another possible configuration, with space group Pna21 is also of interest, as it is an antiferroelectric crystal, which Davidson and Morokuma incorrectly suggested as the most stable structure in 1984.
In practice, ice XI is most easily prepared from a dilute (10 mM) KOH solution kept just below 72 K for about a week (for D2O a temperature just below 76 K will suffice). The hydroxide ions create defects in the hexagonal ice, allowing protons to jump more freely between the oxygen atoms (and so this structure of ice XI breaks the 'ice rules'). More specifically, each hydroxide ion creates a Bjerrum L defect and an ionized vertex. Both the defect and the ion can move throughout the lattice and 'assist' with proton reordering. The positive K+ ion may also play a role because it is found that KOH works better than other alkali hydroxides. The exact details of these ordering mechanisms are still poorly understood and under question because experimentally the mobility of the hydroxide and K+ ions appear to be very low around 72 K. The current belief is that KOH acts only to assist with the hydrogen reordering and is not required for the lower-energy stability of ice XI. However, calculations by Toshiaki Iitaka in 2010 call this into question. Iitaka argues that the KOH ions compensate for the large net electric dipole moment of the crystal lattice along the c-axis. The aforementioned electronic structure calculations are done assuming an infinite lattice and ignore the effects of macroscopic electric fields created by surface charges. Because such fields are present in any finite size crystal, in non-doped ice XI, domains of alternating dipole moment should form as in conventional ferroelectrics. It has also been suggested that the ice Ih => ice XI transition is enabled by the tunneling of protons.
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