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A classification of phase diagrams by means of “Elementary” Catastrophe Theory (ECT) I

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  • Vendrik, M.C.M.

Abstract

In this paper phase diagrams in field spaces are classified according to the qualitative local shapes (QLS) of their sets of first- and second-order phase transition points (PS). The QLS are defined in terms of diffeomorphisms. We proceed from a rather general Landau-type model of phase transitions and employ a variant of “elementary” catastrophe theory (ECT). This variant is developed in terms of polynomials in a more general context including also the usual “local” variant of ECT. An essential concept is GM stability of C∞ unfoldings (i.e. families) Φ of functions and a criterion for this property is derived. It is shown that, near every type of point μ0 in the field space, any GM stable Φ by appropriate diffeomorphic substitutions can be reduced to a GM standard form, i.e. an unfolding of functions, constructed from one or more simple polynomials. A finite list of GM standard forms, which is complete for less than nine fields, can be made. Further an extension of Gibbs phase rule is considered.

Suggested Citation

  • Vendrik, M.C.M., 1979. "A classification of phase diagrams by means of “Elementary” Catastrophe Theory (ECT) I," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 99(1), pages 103-144.
    • Handle: RePEc:eee:phsmap:v:99:y:1979:i:1:p:103-144
    DOI: 10.1016/0378-4371(79)90126-2
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