Interlamellar spacing in discontinuous precipitation
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I.
INTRODUCTION
~N this contribution, we examine the problem of the steadystate spacing of cooperative products of discontinuous precipitation reactions. These are among the most intriguing of solid-solid transformations; their full analysis involves consideration of interacting friction, capillary and chemical terms, all focused on a moving grain boundary. (The chemical term, in particular, is the subject of some controversy.) In this regard, discontinuous transformation products differ from the others discussed in this symposium, most of which can be modeled at least to first order on the basis of a local equilibrium hypothesis. In contrast, the nonequilibrium aspects of discontinuous precipitation are central to its description. We will begin by considering the experimental findings on discontinuous precipitation, with emphasis on the steady, cooperative growth process, and with reference to initiation and nonsteady growth modes mainly as they impinge on our primary problem of the prediction of the steady spacing. Our review of the experimental characteristics of the reaction is followed by brief consideration of existing theoretical descriptions, which in themselves place only wide limits on the range of possible spacings. The problem of the optimal spacing takes on new dimensions in the context of these theories. In a final section, we attempt the experimental test of the hypothesis that the steady state is one of optimal dissipation of free energy ~ or, equivalently, since the system is isothermal, one of maximum entropy production. 2 We will see that discontinuous precipitation reactions are peculiarly amenable to the experimental test of this hypothesis.
II.
transformation interface is therefore a grain boundary, which is generally capable of supporting a composition difference across it, and a composition gradient along it. A number of observations of quenched interface shapes, for example, Figure 2, support the general impression that the grain boundary tends to bow toward the parent phase for situations where the spacing is relatively stable. A possible exception to this statement concerns an alternate product morphology, consisting of rods of/3 in a matrix of a'; here the grain boundary will be subject to multiple curvature. A zero n e t curvature shape would appear, in section, as shown in Figure 3. 0l o
Fig. 1 - Discontinuous precipitation of/3 plates from supersaturated a ~ The a ~ ' boundary can act as a high diffusivity path.
EXPERIMENTAL CHARACTERIZATION OF DISCONTINUOUS REACTION PRODUCTS
The schematic diagram of Figure 1 serves to define an ideal lamellar discontinuous reaction, in which a supersaturated parent a ~ decomposes to yield a lamellar second phase /3, and a less-supersaturated product a'. The main I.G. SOLORZANO, formerly with the Department of Metallurgy and Materials Science, McMaster University, is now Assistant Professor, Department of Materials Science and Metallurgy, Catholic University of Rio de Janeiro, C.P. 38008-G~ivea, 22452 Rio de Janeiro, Brazil. G. R. PURDY is Prof
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