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Tan 1 8. BINARY ALLOY FREE ENERGY AND PHASE DIAGRAMS One of the ultimate objectives of thermodynamics is the calculation of the Gibbs free energy of the alloy phases from the characteristics of their component atoms. This would enable us to predict the phase structure of an alloy at any temperature and composition, i.e., to generate the phase diagrams. This objective is, however, immensely difficult to attain. It has only been possi- ble to make some modest predictions from general principles. The major difficulty lies with the calculation of the enthalpy H, which has to be carried out using quantum mechanics. It has been possible to do so only for a limited number of elemental crystals, since a general and yet practi- cal method of treating the complicated electronic interactions is not available when the number of atoms involved becomes large. In alloy systems, additional complications are introduced by the differences in sizes and electronic structures, etc., of the component atoms. Thus, in practice, phase diagrams are assembled from results of experimental studies of thermal properties and structures of alloys. At a given pressure value (usually taken as P=1 atm), the phase diagrams are equilibrium diagrams giving ranges of temperature and composition in which the various phases are stable. The thermal equilibrium coexistence of vapor phase materi- als of the constituent species with a stable phase is implicitly assumed and usually not shown in these diagrams. Examinations of the phase diagrams show that there are certain features common to most alloys, i.e., qualitatively, many of them posses the same characteristics. These common features can be explained by making simple assumptions on the properties of the component at- oms. An understanding of such common features provides also a framework or starting point for understanding the peculiarities associated with the alloys. Assuming that the alloy external pressure is held at 1 atm, at a given temperature the appro- priate free energy quantity needs to be considered is the Gibbs free energy G = H - TS . (8.1) In this chapter, for binary alloys composed of two elements, we first develop the Gibbs free en- ergy functions of the alloy phases, based on the pair-wise nearest atom interaction model. We then establish the relationship between these free energy functions and the phase diagrams. This is carried out by examine the behavior of the Gibbs free energy of an alloy system as a function of two independent thermodynamic variables: the temperature T and the alloy composition c. To account for the different features in phase diagrams of the various alloy systems, the behavior of
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Tan 2 the Gibbs free energy functions of these systems are also examined in terms of variations of a set of the materials' constants, the values of the alloy atom bond enthalpy h. This procedure may be viewed either as to qualitatively develop the binary alloy phase diagrams or to qualitatively jus- tify the features of the phase diagrams using the Gibbs free energy functions.
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This note was uploaded on 07/13/2011 for the course ME 218 taught by Professor Dr.tan during the Fall '11 term at Duke.

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