  Supercooled liquids give rise, by homogeneous nucleation, to solid
superclusters acting as building blocks of glass, ultrastable glass, and
glacial glass phases before being crystallized. Liquid-to-liquid phase
transitions begin to be observed above the melting temperature Tm as well as
critical undercooling depending on critical overheating (Tm-T)/Tm. Solid nuclei
exist above Tm and melt by homogeneous nucleation of liquid instead of surface
melting. The Gibbs free energy change predicted by the classical nucleation
equation is completed by an additional enthalpy which stabilize these solid
entities during undercooling. A two-liquid model, using this renewed equation,
predicts the new homogeneous nucleation temperatures inducing first-order
transitions, and the enthalpy and entropy of new liquid and glass phases. These
calculations are successfully applied to ethylbenzene, triphenyl phosphite,
d-mannitol, n-butanol, Zr41.2Ti13.8Cu12.5Ni10Be22.5, Ti34Zr11Cu47Ni8, and
Co81.5B18.5. A critical supercooling and overheating rate (Tm-T)/Tm = 0.198 of
liquid elements is predicted in agreement with experiments on Sn droplets.
