Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-27T02:11:01.927Z Has data issue: false hasContentIssue false
  • English
  • Français

Mathematical Representation of Size and Electronic Factors

Published online by Cambridge University Press:  15 February 2011

Leo Brewer
Leo Brewer*
Affiliation:
Materials and Molecular Research Division, Lawrence Berkeley Laboratory and Department of Chemistry, University of California, Berkeley, CA 94720
Get access

Abstract

The relative sizes of the atoms and their electronic configurations are important factors in determining the thermodynamic properties of metallic phases. The regular solution model provides for an asymmetric excess Gibbs energy when there is a size difference, but the actual degree of asymmetry does not correspond to crystallographic sizes. This is due in part to the effect of electronic configurations upon the asymmetry of the Gibbs energy. The Hume–Rothery Rules indicate that the bcc, hcp, and ccp structures are associated with characteristic outer–shell electron per atom concentrations. The electronic factors require modification of the usual definition of internal pressure as used in the regular solution theory. Rather than using the energy of vaporization to the ground atomic state, the energy of vaporization to the valence state atom, which has the same electronic configuration as in the condensed state, is a more appropriate measure of the degree of cohesion and the internal pressure. The problems of providing mathematical expressions that accomodate the contributions of internal pressure, electronic factors, and size factors are discussed.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 19: Symposium E – Alloy Phase Diagrams , 1982 , 129
Copyright
Copyright © Materials Research Society 1983

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1. Hildebrand, J. H., Scott, R. L., “The Solubility of Nonelectrolytes,” 3rd ed., Reinhold Publishing Co., New York, 1950, reprinted by Dover, 1964.Google Scholar
2. Hildebrand, J. H., Scott, R. L., “Regular Solutions,” Prentice-Hall, 1962.Google Scholar
3. Hildebrand, J. H., Prausnitz, J. M., Scott, R. L., “Regular and Related Solutions,” Van Nostrand Reinhold, 1970.Google Scholar
4. Lewis, G. N., Randall, M., “Thermodynamics,” 2nd ed., revised by Pitzer, K. S. and Brewer, L., McGraw-Hill, 1961.Google Scholar
5. Brewer, L., J. Opt. Soc. Am. 61, 1101–1111 (1971).Google Scholar
6. Brewer, L., “Phase Stability in Metals and Alloys,” ed. by Rudman, R., Stringer, J., Jaffee, R. I., pp. 39–61, 241-9, 344-6, and 560-8, McGraw-Hill, 1967.Google Scholar
7. Lamoreaux, R. H., Melting Point Gram-Atomic Volumes and Enthalpies of Atomization for Liquid Elements, Lawrence Berkeley Laboratory, Rep. LBL- 5159, July 1976.Google Scholar
8. Brewer, L., Lamoreaux, R., “Molybdenum, Physiochemical Properties of its Compounds and Alloys,” At. Energy Rev., Special Issue 7, Parts I and II, IAEA, Vienna, 1980.Google Scholar
9. Brewer, L., Plutonium 1970 and Other Actinides,” TMS Metallurgy Series, Vol. 17, pp. 650–58, Ed. Miner, W. N., TMS AIME, N.Y. (1970).Google Scholar
10. Brewer, L., Science 161, 115–22 (1968).Google Scholar
11. Ellner, M., J. Less-Common Metals 75, P5–P16 (1980).CrossRefGoogle Scholar
12. Brewer, L., Acta Met. 15, 553–6 (1967).Google Scholar
13. Brewer, L., Wengert, P. R., Metall. Trans. 4, 83–104, 2674 (1973).Google Scholar
14. Brewer, L., “Calculator Programs for Thermodynamic Data and Phase Diagrams Calculations,” Lawrence Berkeley Laboratory report LBL-5485, May 1978.Google Scholar
15. Darken, L. S., Trans. Met. Soc. AIME 239, 80–96 (1967).Google Scholar
16. Brewer, L., The Role and Significance of Empirical and Semiempirical Correlations, pp. 155–74, in: Structure and Bonding in Crystals, Vol. I, Academic Press, 1981.Google Scholar
17. Brewer, L., Winn, J. S., Models for Calculation of Dissociation Energies of Homonuclear Diatomic Molecules, Faraday Discussions No. 14, 126-35 (1980).Google Scholar
18. Brewer, L., Principles of Critical Evaluation and Compilation of Phase Diagrams and Thermodynamic Data, pp. 196-206, in: Calculation of Phase Diagrams and Thermochemistry of Alloy Phases, Ed. Y. A. Chang, J. F. Smith, AINE Conf. Proceedings, 1979.Google Scholar