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)*.