A note on the application of the phase rule
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Shuang-Lin Chen
Abstract
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.
References
[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) 108–248. 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) 1787.10.1016/S0021-9614(02)00170-2Search 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
© 2008, Carl Hanser Verlag, München
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- Contents
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- A model to calculate the viscosity of silicate melts
- A model to calculate the viscosity of silicate melts
- A note on the application of the phase rule
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