Transformation diffusion-controlled

The kinetics of diffusion-controlled phase transformations has long been a focus of research and it is vital information for industrial practice as well as being a fascinating theme in fundamental physical metallurgy. An early overview of the subject is by Aaronson et ai (1978). 

P. Franke, G. Inden. Diffusion controlled transformations in multi-particle systems. Z Metallkd 88 9 1, 1997. 

Some metals oxidise at a rate which decreases, rather than increases (Type 2 in Fig. 1.89). Cerium behaves in this fashion at temperatures between 40°C and 130°C, and Loriers has suggested that the curve derives from the competition between the two oxides Ce20j and Ce02. It was proposed that the inner layer Ce2 0j was continuous and grew under diffusion control but transformed at a constant rate to an outer layer of Ce02. That is, if we writer and z as the thickness of the inner and outer layers respectively, then... 

Electron donors (D) and electron acceptors (A) constitute reactant pairs that are traditionally considered with more specific connotations in mind - such as nucleophile/electrophile in bond formation, reductant/oxidant in electron transfer, base/acid in adduct production, and so on. In each case, the chemical transformation is preceded by a rapid (diffusion-controlled) association to form the 1 1 intermolecular complex9 (equation 2). 

Guy et al. [5] derived an equation for the diffusion-controlled release of a drug from a sphere, radius r, by applying the three-dimensional form of Fick s second law of diffusion after transformation to spherical coordinates. This equation can be rearranged as ... 

Laplace transformation, 1215 Nemst s equation and. 1217 non-steady, 1254 as rate determining step, 1261 Schlieren method, 1235 semi-infinite linear, 1216, 1234, 1255 in solution and electrodeposition, 1335 spherical. 1216. 1239 time dependence of current under, 1224 Diffusion control, 1248... 

Because of its high reactivity, direct observation of hydroxyl radicals is very difficult in natural waters. Most of the evidence for the existence of HO derives from product analysis studies and from studies of relative photolytic reactivities of a series of compounds. Because HO reacts with many organic compounds at nearly diffusion-controlled rates (Fig. 16.3), various organic substrates that do not undergo other photolytic transformations may be used as probe molecules (for more details see Hoigne, 1997 Vaugham and Blough, 1998). 

Proceeding systematically, diffusion controlled a-fi transformations of binary A-B systems should be discussed next when a and / are phases with extended ranges of homogeneity. Again, defect relaxations at the moving boundary and in the adjacent bulk phases are essential for their understanding (see, for example, [F. J. J. van Loo (1990)]). The morphological aspects of this reaction type are dealt within the next chapter. 

Diffusionless transformations have been sometimes called military , in contrast to the more civilian diffusion controlled transformations. Considering their technical relevance, the crystallographic theory of martensite transformation has been worked out in much detail, and particularly for the habit plane selection of the given 0-0 lattice structural change. The reader is referred to the corresponding metallurgical literature (D.A. Porter, K.E. Easterling (1990) D.S. Liebermann (1970) C.M. Wayman (1983)]. 

The preassociation mechanism is more efficient than the trapping mechanism because it generates an intermediate which immediately reacts by an ultrafast proton transfer (in the pre-association complex, Int) and thus avoids the diffusion-controlled step bringing the catalyst and intermediate together. This mechanism is sometimes called a spectator mechanism because, although the catalyst is present in the transition structure, it is not undergoing any transformation [10]. 

Assume that with time the growth regime of the ApBq layer with regard to component A became diffusion controlled (x> x fl), while the ApBq phase was partly transformed into the ArBs one by reaction (4.6). The A atoms released as a result of this transformation cannot, however, cross the ApBq ArBs interface in the A ApBq ArB -A]Bu- B system in the same manner as in the ApBq -ArBs-B or ApBq ArBs-AiB system. Those A atoms will immediately be combined into the ApBq compound at this interface (onto the surface of the ArBs phase from the side of ApBq) by reaction (3.12) which is opposite to reaction (4.6). It is clear that the total result of these reactions is zero. 

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