Isothermal para-equilibrium phase diagrams for ternary systems
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METALLURGICAL TRANSACTIONS A
Isothermal Para-Equilibrium Phase Diagrams for Ternary Systems W.A. OATES and TED B. FLANAGAN In ternary systems A-B-X, where A and B are metals and X is an interstitial component whose chemical potential can be controlled via the gas phase, a valuable supplement to the usual composition triangle method of presenting the results for isothermal phase equilibria is to plot A/zx [or log(p)] against mole ratio, ~: = n~/(nA + nB), where ni is the moles of substance i.~ Their topography is identical with that of binary temperature-composition phase diagrams, so that their interpretation is straightforward. They can be derived from the appropriate experimental thermodynamic data supplemented with model calculations and/or direct phase boundary determinations. Normally, these isothermal phase diagrams refer to complete equilibrium (CE). However, there are many instances in metallurgy when, at the temperature of interest, the component X is mobile whereas components A and B are effectively immobile. This situation arises particularly in the case of alloy-hydrogen systems where, at the technologically significant temperatures in the vicinity of ambient, H atoms can be extremely mobile while the atoms of a substitutional alloy solvent are effectively 'frozen.' Hultgren 2 introduced the name para-equilibrium (PE) to describe the pseudo-binary situation where a mobile component has the same chemical potential in two contacting phases but the immobile components have not. The work of Hillert3 and Gilmour et al. 4 is noteworthy in developing this concept to understand certain aspects of transformations in Fe-X-C alloys. However, in discussing these particular transformations it is only necessary to consider the equilibrium in the Fe-rich corner of an isothermal section of a normal xc-xx phase diagram. In this communication we use the same concept of PE but consider the implications for all the possible equilibria in a ternary system. In particular, we consider the representation of PE on A/~x-~ diagrams where A/Xx = /Zx -- p.x~ = RT In Px and/xxe is the reference state for X, e.g., 1 atm. For complete equilibrium between two condensed phases in a ternary system, the tangent planes to the free energy surfaces of the two phases gives the location of the phase boundaries. In terms of chemical potentials, the phase boundaries are determined by the three conditions: =
=
[1]
/XA = /X;,
[2]
~B = /X~
[31
where the superscripts g and ' refer to gas and compound phases, respectively. The terms without a superscript refer to the metal-rich phase. When X = H, the compound phase W.A. OATES is Associate Professor, Department of Metallurgy, University of Newcastle, Newcastle, New South Wales, Australia. TED B. FLANAGAN is Professor, Department of Chemistry, University of Vermont, Burlington, VT 05405. Manuscript submitted March 6, 1984.
VOLUME 16A, JANUARY 1985-- 139
corresponds to the hydride phase and the metal-rich phase to the interstitial solution of hydrogen in the metal alloy. For PE the location o
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