William C. Johnson*, P. W. Voorhees

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

86 Scopus citations


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. A number of equilibrium states (combinations of volume fractions and phase composition) may exist that yield energy minima for a given temperature, pressure, and composition. These multiple metastable states may lead to a nonuniqueness in the observed physical state of the system. Discontinuous jumps in precipitate volume fraction 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. The concept of a phase stability diagram is introduced for displaying and analyzing the equilibirum conditions in coherent solids. The influence of elastic homogeneity and the form of the free energy curves as a function of composition in the absence of stress are examined.

Original languageEnglish (US)
Pages (from-to)1213-1228
Number of pages16
JournalMetallurgical Transactions A
Volume18 A
Issue number7
StatePublished - 1987

ASJC Scopus subject areas

  • General Engineering


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