Metallurgical Transactions A

, Volume 18, Issue 7, pp 1213–1228 | Cite as

Phase equilibrium in two-phase coherent solids

  • William C. Johnson
  • P. W. Voorhees
Transport Phenomena
Received:

Abstract

Phase equilibrium in a two-phase stressed coherent solid is analyzed using the thermodynamic equilibrium conditions directly. Subject to the constraints of constant temperature and external pressure, a bulk alloy composition is chosen and the corresponding volume fractions and phase compositions that satisfy the equilibrium conditions are obtained. We demonstrate unequivocally that, unlike fluids, a number of equilibrium states (combinations of volume fractions and phase composition) may exist that yield energy minima for a given temperature, pressure, and alloy composition and that these multiple metastable states may lead to a nonuniqueness in the observed physical state of the system. In addition, we show that discontinuous jumps in precipitate volume fraction both between 0 and 1 as well as jumps within the range 0 to 1 are possible with a smooth variation in alloy composition. These results are a consequence of the elastic energy, and thus the system energy, being a function of the volume fraction when two phases coexist as coherent solids. As it is difficult to display these effects on a coherent phase diagram, the concept of a phase stability diagram is introduced for both displaying and analyzing the equilibrium conditions in coherent solids. The influence of elastic inhomogeneity and the form of the free energy curves as a function of composition in the absence of stress on phase equilibrium are examined.

Keywords

Metallurgical Transaction Alloy Composition Coherency Strain Global Energy Minimum Free Energy Curve 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Copyright information

© The Metallurgical of Society of AIME 1987

Authors and Affiliations

  • William C. Johnson
    • 1
  • P. W. Voorhees
    • 2
  1. 1.Department of Metallurgical Engineering and Materials ScienceCarnegie Mellon UniversityPittsburgh
  2. 2.Metallurgy DivisionNational Bureau of StandardsGaithersburg

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