Distinction between ice phases VII, VIII, and X

Ice phases VII, VIII, and X are all based on a body-centered cubic arrangement of molecules, the differences coming from how molecular orientation breaks the symmetry. It is debatable as to whether these should even be considered distinct phases given that the standard definition of a transition between distinct phases involves a discontinuity in any derivative of the free energy. This can be hard to prove experimentally, and most previous theoretical works have been based on models which either have continuously differentiable free energies or offer no straightforward way to determine the free energy. Here we build a free-energy model based on the common definitions of the phases: ordered ice-VIII, orientationally disordered ice VII, and centered-proton ice X. All transitions in this model might or might not be associated with a discontinuity in the specific heat, depending on parameterization. By comparing with data, we find that a VII-X transition line exists, but it ends in a critical point hidden within the stability field of phase VIII. If the model is correct, there is a discontinuity between VII and X, so they are separate phases. We propose that the hidden phase boundary might be demonstrated experimentally by compression of supercooled ice VII.