Anisotropy of segregation at grain boundaries and surfaces
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THERE has been continuing interest in various phenomena associated with interfacial segregation, since the thermodynamic description of adsorption phenomena by Gibbs[1] over a century ago. From a materials perspective, interest has been driven by the impact of interfacial segregation on many important materials properties. For example, in the context of polycrystalline materials, grain boundary (GB) segregation can play a role in controlling such characteristics as crystallographic texture, the GB energy distribution, GB mobility, GB embrittlement, and electromigration processes. Segregation at materials surfaces can modify catalytic properties, influence equilibrium crystal shape, affect the work function, accelerate the rate of surface diffusion, and control sintering rates as well as other kinetic phenomena. However, certain shortcomings of the Gibbsian thermodynamics of adsorption (described in more detail subsequently) prompted the later development of complementary analytical models of interfacial segregation, based on the concepts of statistical mechanics.[2–5] In the context of materials behavior, McLean[4] was the first to develop a model of that type, to deal explicitly with the phenomenon of GB segregation. Since that time, there has been a steady effort to develop improved analytical models for the prediction and interpretation of phenomena related to interfacial segregation in materials. Following the approach of McLean, the majority of these efforts have made use of the regular solution approximation, because of the simplicity it provides in the definition of the relevant model parameters, although other more sophisticated models have also been used from time to time. PAUL WYNBLATT, Professor Emeritus, is with the Department of Materials Science and Engineering, Carnegie Mellon University, Pittsburgh, PA 15213. Contact e-mail: [email protected] DOMINIQUE CHATAIN, Directeur de Recherches, is with CRMCN-CNRS, Campus de Luminy, 13288 Marseille, Cedex 9, France. Manuscript submitted March 27, 2006. METALLURGICAL AND MATERIALS TRANSACTIONS A
One factor that has played a significant role in prompting the formulation of new analytical models of GB segregation has been the development of orientation imaging microscopy (OIM).[6] This technique has made it possible to characterize vast sets of grain boundaries (GBs) with respect to the five macroscopic degrees of freedom (DoFs) of GB orientation, sometimes referred to as the GB character. Whereas computer simulation remains an important approach for predicting GB properties,[7] it cannot currently be used to predict the behavior of GBs over the vast fivedimensional space represented by the five DoFs, hence, the need for analytic techniques with the capability of calculating GB properties. Although OIM studies cannot directly reveal the presence or absence of segregation at GBs, they do provide indirect information in the form of GB orientation frequency distributions.[8,9] Furthermore, it is now well established that the GB frequency distribution in a materi
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