Calculation of supercooled liquid range and estimation of glass-forming ability of metallic glasses using the Vogel-Fulcher-Tammann equation

The supercooled liquid range (DeltaT,) was calculated on the basis of the free volume theory proposed by Beukel and Sietsma. A differential equation which expresses the change in free volume from a non-equilibrium to an equilibrium state has been analyzed numerically for Ni, metallic glasses and SiO2 systems. The Vogel-Fulcher-Tammann (VFT) equation for viscosity was used to define the equilibrium free volume. The maximum AT(x) was calculated as 56K for the SiO2 system. The calculated DeltaT(x) was approximately six times smaller than the experimental result. The calculation results of the log R-c (Rc: critical cooling rate for glass formation)-DeltaT(x) diagram shows a tendency similar to the experimental result; log Rc decreases linearly with increasing DeltaT(x). An approximate solution of the differential equation was also obtained with elementary functions. It was found that the glass transition temperature (T-g) and DeltaT(x) can be obtained schematically in the free-volume-temperature diagram. All the factors expressing the glass-forming ability of the metallic glasses can be derived from the VFT parameters.