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Recently Siegrist et al. proposed a structure for a high-T, superconductor * * * We would like to thank colleagues who made preprints, referenced here, available to us before publication.

We define the concentration range where a dilute alloy of transition impurities in a noble matrix is a spin glass, by the possibility of representing its properties through universal functions of the T/c and H/c variables. The susceptibility of a spin glass contains one reversible part χr which shows a sharp peak at a temperature TM ~ c. This sharp peak is due to the presence of a remanent magnetization which appears when T < TM. The remanent magnetization of a spin glass is represented by an universal curve in the reduced diagram σr = f (T/c). Its properties are like those of the remanent magnetization of monodomains. We interpret it by supposing that at T << TM a spin glass (in which the magnetic moments randomly distributed are frozen at T = 0 in random directions) is spontaneously divided in regions, each one containing in average n impurities and having a resulting moment Mg described by a Gaussian distribution ([MATH]2 = ηµ20, where µ0 is the individual magnetic moment)

An undercooled liquid is unstable. The driving force of the glass transition at T g is a change of the undercooled-liquid Gibbs free energy. The classical Gibbs free energy change for a crystal formation is completed including an enthalpy saving. The crystal growth critical nucleus is used as a probe to observe the Laplace pressure change p accompanying the enthalpy changeV m ×p at T g where V m is the molar volume. A stable glass-liquid transition model predicts the specific heat jump of fragile liquids at T ≤ T g , the Kauzmann temperature T K where the liquid entropy excess with regard to crystal goes to zero, the equilibrium enthalpy between T K and T g , the maximum nucleation rate at T K of superclusters containing magic atom numbers, and the equilibrium latent heats at T g and T K . Strongto-fragile and strong-to-strong liquid transitions at T g are also described and all their thermodynamic parameters are determined from their specific heat jumps. The existence of fragile liquids quenched in the amorphous state, which do not undergo liquid-liquid transition during heating preceding their crystallization, is predicted. Long ageing times leading to the formation at T K of a stable glass composed of superclusters containing up to 147 atoms, touching and interpenetrating, are evaluated from nucleation rates. A fragile liquid-liquid transition occurs at T g without stable-glass formation while a strong glass is stable after transition.

Graphical abstract:Abstract: 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 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 T/Tm = 0.198 of liquid elements is predicted in agreement with experiments on Sn droplets.