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The Dependence on Composition of the Critical Ordering Temperature in Alloys

Published online by Cambridge University Press:  24 October 2008

C. E. Easthope
C. E. Easthope
Affiliation:
Trinity College
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Extract

The statistical treatment of order-disorder transformations, as developed by Bethe and Peierls, has been extended to alloys having superlattices of the AB and AB3 types but compositions which differ slightly from the ideal compositions required for the formation of perfect superlattices. If the composition of the alloy is specified by the concentration c of one component, which we have chosen to be the A component, then the results show that for alloys of the AB type the critical temperature should have a maximum value when c = ½, that is, for the ideal composition. This is in agreement with experiment. For alloys of the AB3 type it is found that the maximum value should occur for some value of c > ¼. This result disagrees with that obtained experimentally, but both results agree, at least qualitatively, with those obtained by the theory of Bragg and Williams.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 33 , Issue 4 , October 1937 , pp. 502 - 517
Copyright
Copyright © Cambridge Philosophical Society 1937

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References

* Bragg, and Williams, , Proc. Roy. Soc. 145 (1934), 699 and 151 (1935), 540CrossRefGoogle Scholar; Williams, , Proc. Roy. Soc. 152 (1935), 231CrossRefGoogle Scholar; Bethe, , Proc. Roy. Soc. 150 (1935), 552CrossRefGoogle Scholar; Fowler, , Statistical Mechanics, 2nd ed. (Cambridge, 1936).Google Scholar

† See Fowler, , op. cit. p. 791.Google Scholar

* Proc. Boy. Soc. 151 (1935), 562.Google Scholar

† J. Inst. Metals, 46 (1931), 547.Google Scholar

‡ Ann. d. Physik, 86 (1928), 291.Google Scholar

§ Proc. Boy. Soc. 154 (1936), 207.Google Scholar

* Results in good agreement with this formula have recently been obtained by Sykes, and Wilkinson, , J. Inst. Metals, 60 (1937), 416.Google Scholar

* For the actual expression see Peierls' paper.