Thermodynamically Improbable Phase Diagrams

Thermodynamically Improbable Phase Diagrams - S e c t i o n...

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Section I: Basic and Applied Research Thermodynamically Improbable Phase Diagrams Hiroaki Okamoto ASM International Mate~n3s Park, OH 44073 and T.B. Massalski Carnegie Mellon University Pittsburgh, PA 15213-3890 Phase diagrams showing very unlikely boundaries, while not explicitly violating thermodynamic principles or phase rules, are discussed. Phase rule violations in proposed phase diagrams often be- come apparent when phase boundaries are extrapolated into metastable regions. In addition to phase rule violations, this article considers difficulties regarding an abrupt change of slope of a phase boundary, asymmetric or unusually pointed liquidus boundaries, location of miscibility gaps, and gas/liquid equilibria. Another frequent source of phase diagram errors concerns the initial slopes of liquidus and solidus boundaries in the very dilute regions near the pure elements. Useful and consis- tent prediction can be made from the application of the van't Hoff equation for the dilute regions. 1. Introduction In the course of editing phase diagrams for the Second Edition of Binary Alloy Phase Diagrams, we discovered numerous phase diagrams that showed very unlikely phase boundaries in various respects although they did not explicitly violate phase rules. This article discusses several of the unlikely phase diagram features encountered. Explicit violations of phase rules are briefly reviewed first, followed by implicit cases of possible phase rule violations and some more subtle phase boundary features that may come under question when constructing phase diagrams is discussed in detail. I. I Typical Phase Rule Violations When a suggested phase diagram is examined, obvious violations of phase rules and other thermodynamic principles are usually checked first to confirm that the proposed phase diagram repre- sentations are generally valid. Ahypothetical phase diagram (Fig. 1) illustrates such typical violations at pointsA to T. The potential problems encountered at each point are superficially described below. Thermodynamically rigorous explanation of these problems are contained in standard textbooks and articles (e.g., [56Rhi], [66Pri], [68Gor], and [81Goo]). Most of these problems can also be demonstrated graphically with the use of appropriate free energy curves. A: A two-phase field cannot be extended to become part of a pure element side of a phase diagram at zero solute. In exampleA, the liquidus and the solidus must meet at the melting point of the pure element. B: Two liquidus curves must meet at one composition at a eutectic temperature. C: Atie line must terminate at a phase boundary. D: Two solvus boundaries (or two liquidus, or two solidus, or a solidus and a solvus) of the same phase must meet (i.e., intersect) at one composition at an invariant temperature. (There should not be two solubility values for a phase boundary at one temperature.) E: A phase boundary must extrapolate into a two-phase field after crossing an invariant point. The validity of this feature, and
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This note was uploaded on 11/16/2011 for the course EMA 3013C taught by Professor Bourne during the Spring '10 term at University of Florida.

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Thermodynamically Improbable Phase Diagrams - S e c t i o n...

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