Metallurgical Transactions

, Volume 1, Issue 9, pp 2551–2556 | Cite as

General method of phase analysis for individual multicomponent alloys

  • Albert G. Guy
  • Walter A. Mannheimer
  • Ubirajara Quaranta Cabral
Physical Chemistry


Construction of a complete phase diagram for a 5- (or higher-) component system is so timeconsuming as to be impractical at present. The usual type of information about the phases present, their compositions, and their amounts can be obtained for a particularC-component alloy by the present method:C is the number of components and may be as large as desired. The alloy is brought to an essentially equilibrium condition at the temperature of interest, and the compositions of the phases are determined by a suitable technique; for example, by electronbeam-microprobe analyses of the quenched specimen. The generalized lever law, in determinant form, is used to determine the amounts of the phases. Repetition of this analysis at a second temperature in the same phase region permits identification of the type of variant reaction (pseudoeutectic, and so forth) that is oçcurring. For invariant reactions, a technique such as quantitative metallography is employed to determine the amounts of the phases at an early and a late stage in the reaction. The type of reaction (eutectic, quasiperitectic, and so forth) can then be determined. From experimental data on alloy E an estimate can be made of two aspects of the behavior of a neighboring composition, alloy N; 1) liquidus temperature, and 2) invariant reaction. Thermodynamic procedures should permit useful extensions of the present method.


Metallurgical Transaction Liquidus Temperature Metallurgical Transaction Volume Invariant Reaction Solidus Surface 
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  1. 1.
    Paul Gordon:Principles of Phase Diagrams in Materials Systems, McGraw-Hill Book Co., New York, 1968.Google Scholar
  2. 2.
    L. S. Palatnik and A. I. Landau:Phase Equilibria in Multicomponent Systems, Holt, Rinehart and Winston, New York, 1964.Google Scholar
  3. 3.
    Paul Alexandroff:Elementary Concepts of Topology, p. 20, Dover, New York, 1961.MATHGoogle Scholar
  4. 4.
    A. Prince:Alloy Phase Equilibria, p. 273, Elsevier, Amsterdam, 1966.Google Scholar
  5. 5.
    F. N. Rhines:Phase Diagrams in Metallurgy, p. 224, McGraw-Hill Book Co., New York, 1956.Google Scholar
  6. 6.
    Larry Kaufman:Progress of Materials Science, 1969, vol. 14, pt. 2.MathSciNetGoogle Scholar
  7. 7.
    R. Hiskes and W. A. Tiller:Mater. Sci. Eng., 1967-68, vol., 2, p. 320.Google Scholar
  8. 8.
    G. Petzow and F. Aldringer:Z. Metallk., 1968, vol. 59, pp. 145, 390, and 583.Google Scholar

Copyright information

© The Minerals, Metals & Materials Society - ASM International - The Materials Information Society 1970

Authors and Affiliations

  • Albert G. Guy
    • 1
  • Walter A. Mannheimer
    • 2
  • Ubirajara Quaranta Cabral
    • 2
  1. 1.Department of Metallurgical and Materials EngineeringUniversity of FloridaGainesville
  2. 2.Coppe (Coordination of Postgraduate Programs of Engineering)Federal University of Rio de JaneiroBrasil

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