Abstract
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*.
Highlights
The waiting time to form a crystal in a unit volume of homogeneous undercooled liquid exhibits a pronounced minimum tX* at a ‘nose temperature’ T* located between the glass transition temperature Tg, and the crystal melting temperature, TL
The glass forming ability (GFA) of a liquid is defined by the temperature-dependent waiting time, tX(T), for a detectable fraction of crystal(s) to nucleate and grow in a unit volume of liquid undercooled to a temperature ToTL, where TL is the melting temperature or the liquidus temperature of an alloy[5,6,7,8]
References and details of methods used to evaluate published data are provided in the Supplementary Information together with a discussion of experimental errors in the data
Summary
The waiting time to form a crystal in a unit volume of homogeneous undercooled liquid exhibits a pronounced minimum tX* at a ‘nose temperature’ T* located between the glass transition temperature Tg, and the crystal melting temperature, TL. For a uniform shape with characteristic sample dimension d (for instance, a rod diameter or plate thickness), a Fourier time scale or thermal relaxation time can be defined as tQBd2/Dt, where Dt is the liquid thermal diffusivity and is roughly constant among the various metallic glass alloy compositions (typically 2–4 mm[2] s À 1). This time scale characterizes cooling at the center of symmetry. The temperature dependence of the sum W(T) þ DG(T) is dominated by the rapid drop of W(T) for
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