  Using variable temperature scanning tunneling microscopy and dI/dz barrier
height spectroscopy, the structure of water on h-BN/Rh(111) nanomesh has been
investigated. Below its desorption temperature, two distinct phases of water
self-assemble within the 3.2 nm unit cell of the nanomesh. In the 2 nm holes,
an ordered phase of nano-ice crystals with about 40 molecules is found. The ice
crystals arrange in a bilayer honeycomb lattice, where the hydrogen atoms of
the lower layer point to the substrate. The phase on the 1 nm wires, is a low
density gas phase, which is characterized by contrast modulations and streaky
noise in the STM images. Tunneling barrier measurements infer the proton
positions in the nano-ice clusters.
