Abstract
The vitreous transition is characterized by a freezing of atomic degrees of freedom at a temperature Tg depending on the heating and cooling rates. A kinetic origin is generally attributed to this phenomenon instead of a thermodynamic one which we develop here. Completed homogeneous nucleation laws reflecting the energy saving due to Fermi energy equalization of nascent crystals and their melt are used. They are applied to bulk metallic glasses and extended to inorganic glasses and polymers. A transition T*g among various Tg corresponds to a crystal homogeneous nucleation temperature, leading to a preliminary formation of a cluster distribution during the relaxation time preceding the long steady-state nucleation time of crystals in small samples. The thermally-activated energy barrier ΔG*2ls/kBT at T*g for homogeneous nucleation is nearly the same in all glass-forming melts and determined by similar values of viscosity and a thermally-activated diffusion barrier from melt to cluster. The glass transition T*g is a material constant and a linear function of the energy saving associated with charge transfers from nascent clusters to the melt. The vitreous transition and the melting temperatures alone are used to predict the free-volume disappearance temperature equal to the Vogel-Fulcher-Tammann temperature of fragile glass-forming melts, in agreement with many viscosity measurements. The reversible thermodynamic vitreous transition is determined by the disappearance temperature T*g of the fully-relaxed enthalpy Hr that is not time dependent; the observed specific heat jump at T*g is equal to the proportionality coefficient of Hr with (T*g − Ta) for T ≤ T*g as expected from the enthalpy excess stored by a quenched undercooled melt at the annealing temperature Ta and relaxed towards an equilibrium vitreous state. However, the heat flux measurements found in literature over the last 50 years only gave an out-of-equilibrium Tg since the enthalpy is continuous at T*g without visible heat jump.
Highlights
The vitreous state is described, up to now, as a freezing of liquid-state below a temperature Tg called vitreous or glass transition, below which the viscosity becomes time dependent with values above 1012–1013 Pa.s
The maximum undercooling ratio = (T1 − Tm)/Tm is observed as being of the order of −0.2 in liquid elements using droplet sizes of 50–10,000 micrometers instead of −2/3 [18]. This pseudo-maximum has until now been considered to be the maximum of the homogeneous nucleation rate in contradiction with a detailed study of crystallization temperature of gallium droplets as a function of their diameter
The vitreous transition is a new type of phase transition from undercooled melt to frozen state, without entropy and enthalpy change occurring at a temperature T*g, which corresponds to the maximum nucleation rate temperature of homogeneously-nucleated crystals in bulk metallic and non-metallic glass-forming melts
Summary
The vitreous state is described, up to now, as a freezing of liquid-state below a temperature Tg called vitreous or glass transition, below which the viscosity becomes time dependent with values above 1012–1013 Pa.s. The vitreous transition, observed by DSC techniques in undercooled melts, is generally time dependent and not strictly reversible, because using the same cooling and heating rates do not lead to the same transformation temperature [13]. From published values of Hr, it is shown that the reversible transition occurs at T*g, and that the transformation into the vitreous state is postponed by quenching the undercooled melt It is achieved after a time lag equal to the relaxation time by annealing at T = Ta. Some DSC techniques are able to separate the specific heat at T*g in two parts; the temperature dependent one is reversible and attached to the thermodynamic aspect of the transition, and the time dependent “irreversible” one is attached to the kinetic aspect. Summary and complementary information on the two crystal nucleation temperatures; Section
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