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

摘要

The supercooled liquid range (ΔT{sub}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 SiO{sub}2 systems. The Vogel-Fulcher-Tammann (VFT) equation for viscosity was used to define the equilibrium free volume. The maximum ΔT{sub}x was calculated as 56K for the SiO{sub}2 system. The calculated ΔT{sub}x was approximately six times smaller than the experimental result. The calculation results of the log Rc (Rc: critical cooling rate for glass formation)-ΔT{sub}x diagram shows a tendency similar to the experimental resu log R{sub}c decreases linearly with increasing ΔT{sub}x. An approximate solution of the differential equation was also obtained with elementary functions. It was found that the glass transition temperature (T{sub}g) and ΔT{sub}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.