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 τ_X* at a ‘nose temperature’ T* located between the glass transition temperature T_g, and the crystal melting temperature, T_L. Turnbull argued that τ_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 τ_X*. Here we survey and assess reported data for T_L, T_g, t_(rg), m and τ_X* for a broad range of metallic glasses with widely varying τ_X*. By analysing this database, we derive a simple empirical expression for τ_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 τ_X* within estimated experimental errors. Surprisingly, the liquid/crystal interfacial free energy does not appear in this expression for τ_X*