The classical nucleation equation, applied to two liquids, is completed by an additional enthalpy for solid supercluster formation governing the liquid and glass transformations. This model defines a formation rule of glacial phases, explaining the origin of the first-order transition of water from fragile-to-strong liquids at TLL = 228.5 K, only fixing Tg = 137.1 K. All thermodynamic properties and transitions, even under pressure P, are now predicted in agreement with experiments. The lowest-density liquid is, at once, the glacial phase of fragile and high-density liquids. It is formed at TLL, remains liquid during the first cooling, and gives rise to the glass Phase 3 by heating through a first-order transition without latent heat at TK2 =122.4 K. Medium-range order appears above Tg during the first heating.Phase 3 with its own Kauzmann temperature undergoes the first-order transition at TLL without latent heat and superheats up to Tn+ > Tm.
Keywords:1_ undercooled liquids and glasses; 2_ homogeneous nucleation; 3_ glacial phases; 4_ "Organized" Liquid; 5_ First-order transitions. Acronyms: HDA: High-density amorphous LDA: Low-density amorphous HDG: High-density glass LDG: Low-density glass VHDA: Very high-density amorphous LLPT: Liquid-liquid phase transition VFT: Vogel-Fulcher-Tammann