Pretransition phenomena in first-order order-disorder transitions
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Most o f the transitions of interest in metallurgy are first order, and there is a long history in our field of considerable interest in what initiates such transformations. In this paper we shall be concerned with precursor p h e n o m e n a associated with one such transition, the order-disorder transformation in alloys like CuaAu. According to the symmetry rules set forth by Landau and Lifschitz, 1 this reaction c a n n o t be higherorder. Also, it has been shown 2 that there is very little change in strain energy associated with the transformation, so that this transition is not first order due to the strain as is the case for some first-order transformations like CuAu I and CuPt. 3 (This will be discussed further below.) Cook and co-workers have recently provided some new thoughts in this area (see Ref. 3 for a recent review), which we will briefly summarize here. Consider a Landau expansion of the Helmholtz free energy (F) in powers of order parameters r/, (i = 1,2,3...) 1 F = F o + A,flJfl)~ + Buk*l,~lfllk + Cvk?l,~lfllk~lt + . . .
[laJ Here ,/, may be thought of as the amplitude of a displacement, a n d / o r the degree of chemical order; it is assumed that this order is uniform throughout the material. If for simplicity we assume that there is only one order parameter independent of direction: F = AY/2 d- B~/3 + CT/4 -t- . . .
[lb]
The constant A will be taken as a ( T - To) where T O will be defined shortly. Two free energy curves are shown in Fig. 1 both of which give rise to first-order transitions. In Fig. l(a), B = 0, C < 0; and a term E ~ has been added for stability (E > 0). In Fig. l(b), B < O, C > O. For the m o m e n t consider only the portions of both figures with positive 7.
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HAYDN CHEN is Assistant Professor, Department of Metallurgy and Mining Engineering, University of Illinois, Urbana, IL 61801. J. B. COHEN is Englehart Professor, Department of Materials Science and Engineering, Northwestern University, Evanston, IL 60201. This paper is based on a presentation made at a symposiumon "Pretransformation Phenomena, Fluctuations and Related Effects" held at the annual meeting of The Metallurgical Society of AIME, New Orleans, Louisiana, February 18-22, 1979, under the sponsorship of the Structures Activity, Materials Science Division, ASM. METALLURGICAL TRANSACTIONS A
At high temperatures, the curves are nearly parabolic and similar in shape to that for a higher order transition (with an equilibrium state at complete disorder, r/ = 0). Fluctuations are possible due to the small additional energy from thermal excitations needed for s m a l l excursions in the order parameters. As the transition is approached, a secondary m i n i m u m develops. This occurs because of terms higher than the quadratic in Eqs. [l]. (Several such minima are possible, especially for a system with multiple order parameters.) Thermal excitation m a y then produce long-lived metastable regions with a high degree of order, called "heterophase fluctuations" by Frankel 4 who first proposed them. At the critical tempe
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