Three-dimensional lattice model for the water/ice system

Abstract

The sites of a body-centered cubic lattice are either vacant or occupied by molecules with four hydrogen-bonded “arms”, two positive and two negative, directed tetrahedrally. Appropriately oriented nearest-neighbour molecules can form bonds by linking bonding “arms” of opposite polarity. There are also interaction energies for unbonded nearest neighbours and second-nearest neighbours. As well as disordered states, two long range ordered structures are possible, one an open bonded network on a diamond sub-lattice, like ice I(c), and the other a close-packed structure with intertwined bonded networks, like ice VII. A free energy, depending on three order variables, is derived using a zeroth-order statistical approximation modified to allow for asymmetrical bonding.

For suitable energy parameter values, there exist four phases, vapour, liquid, open ice and close-packed ice. There is a critical point, an open ice/liquid/vapour triple point and a close-packed ice/open ice/vapour triple point at a lower temperature. Between the triple points increase of pressure causes the open ice to transform into a liquid of higher density than the ice while below the lower critical point it causes it to transform to close-packed ice.