Quantifying the origin of metallic glass formation

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