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Paraequilibrium and other Restricted Equilibria

Published online by Cambridge University Press:  15 February 2011

Mats Hillert
Mats Hillert*
Affiliation:
Div. of Physical Metallurgy, Royal Inst. of Technology, S-10044 Stockholm, Sweden
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Abstract

After a review of the historic development of the concept of paraequilibrium in the field of alloyed steels, the basic principles of restricted thermodynamic equilibrium at a migrating interface during phase transformations are outlined. As a demonstration they are first applied to classical nucleation. In addition to the case of paraequilibrium they are then applied to adiabatic and to isochoric conditions. It is argued that a full equilibrium model, with a spike of the intensive property in front of the migrating interface may be more realistic. It is shown that the full equilibrium conditions require about twice as much undercooling or underpressure as the restricted equilibrium conditions because of the consumption of driving force in the spike.The concept of restricted equilibrium only applies to heterogeneous phase transformations. For homogeneous reactions, the same experimental conditions will give full equilibrium.

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Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 19: Symposium E – Alloy Phase Diagrams , 1982, 295
Copyright
Copyright © Materials Research Society 1983

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References

REFERENCES

1. Hultgren, A., “Metallographic Study on Tungsten Steels”, John Wiley and Sons, New York 1920.Google Scholar
2. Hultgren, A., “Metallografi” K.T.H. Stockholm 1944.Google Scholar
3. Bowman, F.E., Trans. ASM 38 (1946) 61.Google Scholar
4. Hultgren, A.. Trans. ASM 39 (1947) 915.Google Scholar
5. Picklesimer, M.L., McElroy, D.L., Kegley, T.M. Jr., Stansbury, E.E. and Frye, J.H. Jr., Trans. TMS-AIME 218 (1960) 473.Google Scholar
6. Purdy, G.R., Weichert, D.H. and Kirkaldy, J.S., Trans. TMS-AIME 230 (1964) 1025.Google Scholar
7. Aaronson, H.I. and Domian, H.A., Trans. TMS-AIME 236 (1966) 781.Google Scholar
8. Gilmore, J.B., Purdy, G.P. and Kirkaldy, J.S., Met. Trans. 3 (1972) 3123.Google Scholar
9. Razik, N.A., Lorimer, G.W. and Ridley, N., Acta Met. 22 (1974) 1249.Google Scholar
10. Al-Salman, S., Lorimer, G.W and Ridley, N., Acta Met. 27 (1979) 1341.Google Scholar
11. Sharma, R.C., Purdy, G.R. and Kirkaldy, J.S., Met. Trans. 10A (1979) 1129.CrossRefGoogle Scholar
12. Hillert, M., “Paraequilibrium”, Internal Report, Swedish Inst. for Metal Research 1953.Google Scholar
13. Hillert, M., Jernkontorets Ann. 136 (1952) 25.Google Scholar
14. Rudberg, E., Jernkontorets Ann. 136 (1952) 91.Google Scholar
15. Kirkaldy, J.S., Can.J.Phys. 36 (1958) 907.Google Scholar
16. Hillert, M., in “Phase Transformations” ASM 1970, p. 181.Google Scholar
17. Hillert, M., in “The Mechanism of Phase Transformations in Crystalline Solids”, Monograph and report series No. 33. Inst. Metals 1969, p. 231.Google Scholar
18. Hillert, M., “Thermodynamics of the Massive Transformation”, Met. Trans. (in press).Google Scholar
19. Hillert, M., “An Analysis of the Effect of Alloying Elements on the Pearlite Reaction”, Pittsburgh Conference of Solid–Solid Phase Transformations 1981. Ed. Aaronson, H.I..Google Scholar
20. Cahn, J.W., Acta Met. 10 (1962) 179.Google Scholar
21. Hillert, M., Met. Trans. 3 (1972) 2729.CrossRefGoogle Scholar
22. de Donder, Th., Bull.Ac.Roy.Belg. (CI.Sc) (5) 7 (1922) 197, 205.Google Scholar
23. Hirth, J.P., Pound, G.M. and Pierre, G.R. St., Met. Trans. 1 (1970) 939.Google Scholar
24. Hillert, M., Acta Met. 6 (1958) 122.CrossRefGoogle Scholar