First-order phase transition in cubic ice

First-order phase transition in cubic ice between the low-temperature phase VIII and the high-temperature phase VII is studied in an extended mean-field approximation. It is assumed that the arrangements of four protons around each oxygen satisfy the ice condition rigorously, i.e., there are exactly two protons at one time situated closer to the central oxygen forming an electric dipole and the remaining two protons are situated away from the central oxygen. Because of the cubic structure of the oxygen lattice and the diamond structure of the hydrogen bonding, there are six equivalent directions of the electric dipole, around each oxygen perpendicular to the cube faces, in the disorder phase, while there is only one preferred direction of the dipole in the ordered phase. This large entropy difference seems to be the main reason for the first-order phase transition in this system.