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

The supercooled liquid range (ΔT_x) 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 ΔT_x was calculated as 56 K for the SiO₂ system. The calculated ΔT_x was approximately six times smaller than the experimental result. The calculation results of the log R_c (R_c: critical cooling rate for glass formation)-ΔT_x diagram shows a tendency similar to the experimental result; log R_c decreases linearly with increasing ΔT_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 ΔT_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.