Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-27T02:31:09.540Z Has data issue: false hasContentIssue false
  • English
  • Français

A Pair-Wise Interaction Model for Multi-Sublattice Phases

Published online by Cambridge University Press:  15 February 2011

J.N. Pratt  and
I.P. Jones
J.N. Pratt
Affiliation:
Department of Metallurgy and Materials, University of Birmingham, England.
I.P. Jones
Affiliation:
Department of Metallurgy and Materials, University of Birmingham, England.
Get access

Abstract

The use of simple nearest neighbour pair-wise interaction models for the description of the thermodynamic properties of ordered alloys is reviewed and extended to the treatment of phases containing several sublattices. Employing individual sublattice occupation parameters to define atomic distributions, enthalpies corresponding to these are described by the summation of pair-wise interaction energies over all the resulting first co-ordination shell neighbours. Invariant like and unlike bond energies are assumed, their respective values being estimated using heats of vaporisation of the elements and a heat of formation of the phase at a single composition. Combination of the enthalpies with corresponding configurational entropies yields an expression for the free energy of the phase which may be minimised with respect to variation of the sublattice occupation parameters. This leads to the prediction of the stable atomic distributions and the variation of these and the thermodynamic properties with composition. The application of the model to sigma phases and other multi-sublattice structures is discussed

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 19: Symposium E – Alloy Phase Diagrams , 1982 , 135
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. Wagner, C. and Schottky, W., Zeit. physik. Chem. B11, 163 (1930).Google Scholar
2. Wagner, C., Thermodynamics of Alloys (Addison-Wesley Press, Cambridge, Mass., 1952) pp. 54–66.Google Scholar
3. Oelander, A., Zeit. physik. Chem. A165, 65 (1933).Google Scholar
4. Orr, R.L., Lawrence Radiation Lab. Report, UCRL-16320 (1965).Google Scholar
5. Libowitz, G.G. and Lightstone, J.B., J. Phys. Chem. Solids 28, 1145 (1967).Google Scholar
6. Libowitz, G.G., J. Solid State Chem. 1, 50 (1969).Google Scholar
7. Libowitz, G.G., Met. Trans. 2, 85 (1971).Google Scholar
8. Lightstone, J.B. and Libowitz, G.G., J. Phys. Chem. Solids 30, 1025 (1969).Google Scholar
9. Chang, Y.A., Treatise on Materials Science 4 (Academic Press, New York, 1974) pp. 173–259.Google Scholar
l0. Chang, Y.A. and Newmann, J.P., to be published, Progress in Solid State Chemistry, 1982.Google Scholar
11. Chang, Y.A., Gyuk, I. and Franks, J., Acta Met. 19, 939 (1971).Google Scholar
12. Liang, W.W., Chang, Y.A. and Lau, S., Acta Met. 21, 629 (1973).CrossRefGoogle Scholar
13. Gyuk, I., Liang, W.W. and Chang, Y.A., J. Less-common Met. 38, 249 (1974).Google Scholar
14. Ipser, H., Neumann, J.P. and Chang, Y.A., Monatsh. fur Chemie 107, 1471 (1976).Google Scholar
15. Neumann, J.P., Chang, Y.A. and Lee, C.M., Acta Met. 24, 593 (1976).Google Scholar
16. Steiner, A. and Komarek, K.L., Trans. Met. Soc. AIME 230, 786 (1964).Google Scholar
17. Ettenberg, M., Komarek, K.L. and Miller, E., Trans. Met. Soc. AIME 242, 1801 (1968).Google Scholar
18. Ettenberg, M., Komarek, K.L. and Miller, E., Met. Trans. 2, 1173 (1971).Google Scholar
19. Edelin, G., Acta Met. 27, 455 (1979).Google Scholar
20. Bakker, H. and van Ommen, A.H., Acta Met. 26, 1047 (1978).Google Scholar
21. Schapink, F.W., Scripta Met. 3, 113 (1969).Google Scholar
22. Neumann, J.P., Chang, Y.A. and Ipser, H., Scripta Met. 10, 917 (1976).Google Scholar
23. Nevitt, M.V., in Electronic Structure and Alloy Chemistry of the Transition Elements, Beck, P.A. ed. (Interscience, New York 1963) pp. 105–123.Google Scholar
24. Hall, E.O. and Algie, S.G., Int. Met. Rev. 11, 61 (1966).Google Scholar
25. Kasper, J.S., in Theory of Alloy Phases (ASM, Cleveland 1964) p. 264.Google Scholar
26. Waterstrat, R.M. and Kasper, J.S., Trans. Met. Soc. AIME 209, 872 (1957).Google Scholar
27. Kasper, J.S. and Waterstrat, R.M., Acta Crystall. 9, 289 (1956).Google Scholar
28. Gautier, F., Ducastelle, F. and Giner, J., Phil. Mag. 31, 1373 (1975).Google Scholar
29. Shao, J. and Machlin, E.S., Calphad 2, 213 (1978).Google Scholar
30. Hayes, F.H. and Kubitz, R., Proc. Calphad VIII (Stockholm, 1979) p. 229.Google Scholar
31. van der Rest, J. and Giner, J., Phil. Mag. 33, 785 (1976).CrossRefGoogle Scholar
32. Spencer, P.J. and Putland, F.H., J. Iron and Steel Inst. 211, 293 (1973).Google Scholar
33. Höster, T., Private Comm. (Rhein-Westf. Tech. Hoch.,Aachen, 1980).Google Scholar
34. Katayama, I., Aoki, M. and Kozuka, Z., Nippon Kinz. Gakk., 39, 1210 (1975).Google Scholar
35. Müller, F. and Kubaschewski, O., High Temp.-High Press. 1, 543 (1969).Google Scholar
36. Bernard, C., Ansara, I. and Rand, M.H., Proc. Calphad VIII (Stockholm, 1979) p. 216.Google Scholar
37. Bergman, B.G. and Shoemaker, D.P., Acta Crystall. 7, 857 (1954).Google Scholar
38. Dickens, G.J., Douglas, A.M.B. and Taylor, W.H., Acta Crystall. 9, 297 (1956).Google Scholar
39. Algie, S.H. and Hall, E.O., Acta Crystall. 20, 142 (1966).Google Scholar
40. Forsyth, J.B. and d'Alte da Viega, L.M., Acta Crystall. 16, 509 (1963).CrossRefGoogle Scholar
41. Miedema, A.R., J. Less-common Met. 46, 67 (1976).Google Scholar
42. Pearson, W.B., Brandon, J.K. and Brizard, R.Y., Zeit. fur Krist. 143, 387 (1976).Google Scholar