Skip to main content
SpringerLink
Log in

Monotonicity theorems for two-phase solids

  • Published:
Archive for Rational Mechanics and Analysis Aims and scope Submit manuscript

Abstract

Certain alloys, such as gold-copper, have two solid phases. We establish a general mathematical framework in which we show that the fraction in one phase and the compositions within each phase are in some sense decreasing in the overall composition. The tools used include useful new lemmas on minima of functions of several variables and parameters.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. J. W. Cahn & F. Larché, A simple model for coherent equilibrium, Acta Metall. 32 (1984), 1915–1923.

    Google Scholar 

  2. R. Fosdick & J. Patiño, On the Gibbsian thermostatics of mixtures, Arch. Rational Mech. Anal. 93 (1986), 203–221.

    Google Scholar 

  3. W. C. Johnson & P. W. Voorhees, Phase equilibrium in two-phase coherent solids, Metal. Trans. A 18A (1987), 1213–1228.

    Google Scholar 

  4. J. Kestin, A Course in Thermodynamics, Blaisdell, 1966, II: 303–304.

    Google Scholar 

  5. R. V. Kohn, The relationship between linear and nonlinear variational models of coherent phase transitions, in Trans. 7th Army Conf. on Appl. Math. and Computing, ARO Report 90-1, 1990.

  6. H. Le Chatelier, Sur un énoncé des lois des équilibres chimiques, C. R. Acad. Sci. Paris 99 (1884), 786.

    Google Scholar 

  7. F. Larché, F. Morgan & J. M. Sullivan, Phase behavior in coherent equilibria, Scripta Metall. Mater. 24 (1990), 491–493.

    Google Scholar 

  8. R. T. Rockafellar, Convex Analysis, Princeton University Press, Princeton, 1970.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Williams College, Williamstown, Massachusetts

    Frank Morgan, John Sullivan & Francis Larché

  2. Geometry Center, 1300 South Second Street, Minneapolis, Minnesota

    Frank Morgan, John Sullivan & Francis Larché

  3. Université des Sciences et Techniques du Languedoc, 34095, Montpellier cedex 5, France

    Frank Morgan, John Sullivan & Francis Larché

Authors
  1. Frank Morgan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. John Sullivan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Francis Larché
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by C. Dafermos

Rights and permissions

Reprints and permissions

About this article

Cite this article

Morgan, F., Sullivan, J. & Larché, F. Monotonicity theorems for two-phase solids. Arch. Rational Mech. Anal. 124, 329–353 (1993). https://doi.org/10.1007/BF00375606

Download citation

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00375606

Keywords

Search

Navigation