Calculations of Stable and Metastable Equilibrium Diagrams of the Ag-Cu and Cd-Zn Systems
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I.
INTRODUCTION
CALCULATIONS of metastable phase equilibria can be used to guide interpretations of rapid solidification experiments. 1,: The To curve* between the liquid and a solid phase *The To curve is the locus of compositions and temperatures where the Gibbs energies of two phases are equal. In this paper, the To curve will always be that involving the liquid and the equilibrium solid phase.
determines the minimum undercooling for the partitionless formation of the solid with the same composition as the liquid. In addition to the To curve, one requires the metastable extensions of the phase boundaries, metastable miscibility gaps, and spinodals. When quantitative calculations based on assessed phase diagram and thermochemical data are lacking, smooth extrapolations of the equilibrium boundaries are often u s e d . 3'4'5 These extrapolations may be misleading, however, because quantities which can influence the extrapolation are not revealed by the equilibrium phase boundaries. An example would be a system whose phase diagram reveals the equilibrium between the two relevant phases over only a small composition and temperature range. The curvatures of the phase boundaries are not accessible from the stable diagram, and linear extrapolations are seldom correct when performed to the extent needed to interpret rapid solidification results. This problem occurs, for example, in the Al-rich portion of the A1-Fe system. Another example would be a system with substantial excess entropies. Cd-Zn is such a system: the To curve is sensitive to the model chosen for the Gibbs energies and the weight given to the thermochemical data. The goal of this study has been to make quantitative predictions of the metastable features of two systems, Ag-Cu and Cd-Zn. Experimental phase diagram and thermodynamic data were used to calculate optimized Gibbs energies of liquid and solid phases. By considering several alternative models for the Gibbs energies and alternative weights for the experimental input data, uncertainties in the metastable phase boundaries could be estimated, and the thermochemical quantities to which metastable features are most sensitive could be identified. The Ag-Cu and Cd-Zn systems were chosen because they are particularly well suited for computer calculation of thermodynamic parameters and are also experimentally interesting for rapid solidification. They are simple eutectic diagrams, for which the liquidus, solidus, and solid solubilities have been relatively accurately determined; data on the excess thermodynamic functions are also available. JOANNE L. MURRAY is with the Metallurgy Division, National Bureau of Standards, Washington, DC 20234. Manuscript submitted August 5, 1982. METALLURGICAL TRANSACTIONS A
In both cases, the two solids have the same structure, fcc for the Ag-Cu system and hcp for the Cd-Zn system. This means that the two branches of the solvus can be fitted to a single miscibility gap in the solid phase; one requires Gibbs energies for only two phases and does not rely on experimentally
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