Quantitative understanding of the initial stage of liquid to crystalline or amorphous phase transitions

In 2005, Science magazine listed the "nature of a glassy substance"as one of the 125 most challenging scientific questions of the century. A quantitative understanding of the time-temperature transition (TTT) curve for critical nucleation of amorphous materials is crucial to answering this question. Despite extensive efforts over the past 70 years, a quantitative model for the TTT curve remains elusive due to a lack of understanding of physical properties such as the interfacial energy at the incubation time t∗ for critical nucleation. In this study, a relationship between the critical nucleation viscosity and the interfacial energy as a function of t∗ is established and a quantitative TTT model is developed. The model demonstrates excellent agreement with experimental TTT data for various amorphous materials. Most importantly, it allows the accurate and definitive determination of T0, the true minimum crystallization temperature at the lower end-point of the TTT curve, as well as the temperature below which the amorphous liquid-to-solid state transition occurs. This offers an unambiguous answer to the nature of glassy substances: Above T0, a liquid with constant amorphous structure relaxation; and below T0, a solid with stable amorphous structure.