  The momentum distribution of the protons in ice Ih, ice VI, high density
amorphous ice and water in carbon nanotubes at low temperatures has been
measured using deep inelastic neutron scattering. We find that the momentum
distribution for the water in the nanotubes is qualitatively unlike that in any
other phase of water or ice. The kinetic energy of the protons is 35mev less
than that in ice Ih at the same temperature, and the high momentum tail of the
distribution, characteristic of the molecular covalent bond and the stretch
mode of the proton in the hydrogen bonds, is not present. We observe a phase
transition between 230K and 268K in the nanotube data. The high momentum tail
is present in the higher temperature measurement, which resembles that of ice
Ih at the same temperature. Molecular dynamics simulations show the phase
transition to be associated with the reordering of the hydrogen bonds of the
2-D ice layer, coating the interior of the nanotube at low temperatures, into a
3-D structure at 268K. We conclude that the protons in the hydrogen bonds in
the 2-D ice layer are coherently delocalized, and that the 2-D ice layer is a
qualitatively new phase of ice.
