Quantifying the origin of metallic glass formation

Abstract

The waiting time to form a crystal in a unit volume of homogeneous undercooled liquid exhibits a pronounced minimum., X ∗ at a nose temperature' T ∗ located between the glass transition temperature T g, and the crystal melting temperature, T L. Turnbull argued that., X ∗ should increase rapidly with the dimensionless ratio t rg =T g /T L. Angell introduced a dimensionless ' fragility parameter', m, to characterize the fall of atomic mobility with temperature above T g. Both t rg and m are widely thought to play a significant role in determining., X ∗. Here we survey and assess reported data for T L, T g, t rg, m and., X ∗ for a broad range of metallic glasses with widely varying., X ∗. By analysing this database, we derive a simple empirical expression for., X ∗(t rg, m) that depends exponentially on t rg and m, and two fitting parameters. A statistical analysis shows that knowledge of t rg and m alone is therefore sufficient to predict., X ∗ within estimated experimental errors. Surprisingly, the liquid/crystal interfacial free energy does not appear in this expression for., X ∗.