The use of thermodynamic models in the prediction of the glass-forming range of binary alloys
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I. INTRODUCTION The most common method for producing metallic amorphous alloys is through the rapid quenching of melts. This requires that the nucleation and growth of crystals be suppressed during fast cooling to a temperature below the glass transition temperature Tg. Early experiments showed that glass formation was easiest near a eutectic composition, where the liquidus temperature T, has a minimum. This was interpreted in terms of a lower thermodynamic driving force for nucleation at elevated reduced glass transition temperatures, Trg = Tg/T,.1 However, some alloy systems, especially those formed by an early and a late transition metal, exhibit glass formation over composition ranges extending well beyond the eutectic composition on either side. It has been observed that under conditions of very rapid cooling (dT/dt—1010 K / s ) , the main competition to glass formation arises from composition-invariant single phase crystallization.2 Attempts have been made to correlate the glass-forming range (GFR) 3 in rapidly quenched alloys with the thermodynamic limit for partitionless crystallization of the equilibrium phases in the system.4'5 This limit is described by To curves, which are the temperature-composition locus of the equality between the free energies of the liquid and crystal phases. In essence this criterion states that if T0 B. T. Mathias Visiting Scholar at the Center for Materials Science. Permanent address: Division of Applied Sciences, Harvard University, Cambridge, Massachusetts 02138. a)
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J. Mater. Res. 2 (4), Jul/Aug 1987
http://journals.cambridge.org
vored thermodynamically for T> To, then, as the liquid temperature is lowered, the alloy will be trapped in the glassy state. However, Lin and Spaepen67 found that thin molten layers of Fe-B and Ni-Mo formed by laser pulses solidify into the glassy state at compositions well outside the GFR predicted by the To criterion. Two difficulties are encountered in applying the To criterion quantitatively. First, in order to calculate the To curves, an accurate description of the free energies of the phases as a function of composition and temperature is needed. This description is usually obtained from numerical fits to thermodynamic and phase equilibrium data.8 This approach is model dependent and, as will be shown in this paper, can lead to significant differences upon extrapolations to metastable regimes. The second difficulty is more fundamental in nature and has to do with the neglect in the r o -curves approach of kinetic constraints for partitionless crystallization. These constraints, when properly accounted for, predict a GFR larger than that deduced from the To curves. This second problem will be discussed in a forthcoming publication. II. DERIVATION OF THE To CURVES The modeling of phase equilibria requires knowledge of the free energy of each phase as a function of temperature and composition. As mentioned in Sec. I, our interest is in the equilibrium between the terminal solid solutions and the liquid phase. In particular, we want to desc
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