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 tau(star)(X) at a 'nose temperature' T-star located between the glass transition temperature T-g, and the crystal melting temperature, T-L. Turnbull argued that tau X-star 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 Tg. Both t(rg) and m are widely thought to play a significant role in determining tau(star)(X). Here we survey and assess reported data for T-L, T-g, t(rg), m and tau X star for a broad range of metallic glasses with widely varying tau(X)star. By analysing this database, we derive a simple empirical expression for tau(star)(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 tau(star)(X) within estimated experimental errors. Surprisingly, the liquid/crystal interfacial free energy does not appear in this expression for tau(star)(X).