Skip to content
Accessible Unlicensed Requires Authentication Published by De Gruyter June 11, 2013

A note on the application of the phase rule

Shuang-Lin Chen, Rainer Schmid-Fetzer, Kuo-Chih Chou, Y. Austin Chang and William A. Oates


When an equilibrium state contains degenerate phases, the number of independent phases must be considered in applying Gibbs' Phase Rule. This number can be derived from the rank of the matrix containing the coefficients of the Gibbs – Duhem equations. This provides a quantitative determination of the degrees of freedom even under such conditions of degeneracy.

* Correspondence address, Shuanglin Chen, CompuTherm, LLC, 437 S. Yellowstone Dr., Suite 217, Madison, WI 53719, USA, Tel.: +1 608 274 1414, Fax: +1 608 274 6045, E-mail:


[1] R.B.Griffiths, J.C.Wheeler: Phys. Rev. A2 (1970) 1047.Search in Google Scholar

[2] J.W.Gibbs: Trans. Conn. Acad.3 (1876) 108248. See also in J.W. Gibbs, The Scientific Papers of J. Willard Gibbs, Vol. I. Thermodynamics, Dover Publications, Inc, NY, 1961.Search in Google Scholar

[3] R.A.Alberty: J. Chem. Thermo.34 (2002) 1787.Search in Google Scholar

[4] W.R.Smith, R.W.Missen: Chemical Reaction Equilibrium Analysis: Theory and Algorithms, Krieger Publishing Co., Malabar, FL, 1991.Search in Google Scholar

[5] S.-L.Chen, J.-Y.Zhang, X.-G.Lu, K.-C.Chou, W.A.Oates, R.Schmid-Fetzer, Y.A.Chang: Acta Mater.55 (2007) 243.Search in Google Scholar

Received: 2007-10-31
Accepted: 2008-8-23
Published Online: 2013-06-11
Published in Print: 2008-11-01

© 2008, Carl Hanser Verlag, München