Configurational Entropies of Mixing in Solid Alloys
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Basic and Applied Research: Section I
Configurational Entropies of Mixing in Solid Alloys W. A. Oates
(Submitted October 25, 2006) Entropy becomes an increasingly important contributor to the Gibbs energy at high temperatures with both non-configurational and configurational contributions to be considered. Some examples of where configurational entropies alone are important in determining the domain of phase stability of a solution phase are given. In phenomenological calculations, the modeling of configurational entropy should allow for short range order and be readily applicable to multicomponent systems. The use of Fowler-Yang-Li transforms is important in this regard by providing the opportunity for changing the functional variables in cluster calculations of the Gibbs energy from cluster probabilities or correlation functions to the considerably fewer point probabilities, just as in the Bragg-Williams approximation.
Keywords
alloys, chemical potentials, entropy, thermodynamics
1. Introduction Metallurgy students of my generation were strongly influenced by the monographs of Prof. Hume-Rothery.[1-5] His name will always be particularly remembered for his work on first isolating the principal factors responsible for the stability of alloy phases. In the first editions of these monographs, there is no mention of any role for entropy, S, in determining phase stability, although Gibbs energies, G, are mentioned in the later, co-authored, editions.[6-8] The awareness of the important contribution of S has become much more widely recognized since then and, in this Lecture, I will concentrate on some aspects of its role in determining high temperature phase stability. Although the contributions made by solid state physicists over the last two decades in the ‘ab initioÕ calculation of alloy phase stabilities has been outstanding, it seems clear that some degree of empiricism will continue to be important for some years to come in the evaluation and description of high temperature phase stabilities. The required accuracies in calculated Gibbs energies of just a few joules per mole of alloy at temperatures in the region of 1,000 K are still some way off the accuracy attainable by This article was presented at the Multi-Component Alloy Thermodynamics Symposium sponsored by The Alloy Phase Committee of the joint EMPMD/SMD of The Minerals, Metals, and Materials Society (TMS), held in San Antonio, Texas, March 12-16, 2006, to honor the 2006 William Hume-Rothery Award recipient, Professor W. Alan Oates of the University of Salford, UK. The symposium was organized by Y. Austin Chang of the University of Wisconsin, Madison, WI. Patrice Turchi of the Lawrence Livermore National Laboratory, Livermore, CA, and Rainer Schmid-Fetzer of the Technische Universitat Clausthal, Clauthal-Zellerfeld, Germany. W. A. Oates, Institute for Materials Research, University of Salford, Salford M5 4WT, UK; Contact e-mail: [email protected]
‘first principlesÕ calculations. There is the added problem of attempting to focus the interest of physicists
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