Segregation model introduction

In this section, we extend the above formalism to that for an alloy surface within the CPA, which serves as the model for the pre-chemisorption substrate. The model discussed here is based on that of Ueba and Ichimura (1979a,b) and Parent et al (1980). For a comprehensive introduction to alloy surfaces see Turek et al (1996). A feature of surface-alloy models, which is different from bulk ones, is that the CP in layers near the surface is different from that in the bulk, due to the surface perturbation. Moreover, the alloy concentration in the surface layers may be quite different from that in the bulk, a feature known as surface segregation. (See Ducastelle et al 1990 and Modrak 1995 for recent reviews.) We assume that both of these surface effects are confined to the first surface layer only. 

Box G. Hunter W, Hunter J. Statistics for Experimenters, An Introduction to Design, Data Analysis, and Model Building. New York John Wiley and Sons, Inc.. 1978 556-83. Prescon J, Ramsey P, Gladysz K, et al. Bench-scale segregation tests as a predictor of blend sampling error. AAPS Annual Meeting, Indianapolis. IN, 2000,... 

Since the details of these equations are explained elsewhere, only key ideas are briefly described here. One of these is to classify the solute atom clusters into irradiation-induced clusters and irradiation-enhanced clusters. Irradiation-induced clusters correspond to solute atom clusters with or without Cu atoms, whose formation mechanism is assumed to be the segregation of solute atoms based on point defect cluster or matrix damage (heterogeneous nucleation). On the other hand, the irradiation-enhanced clusters correspond to so-called CRPs (Cu-rich precipitates) or CELs (Cu-enriched clusters), and the formation mechanism is the clustering of Cu atoms above the solubility limit enhanced by the excess vacancies introduced by irradiation. This model also assumes that the formation of solute atom clusters and matrix damage is not independent to each other, which is a very different model from the conventional two-feature models as described in the previous sections. Another key idea is the introduction of a concept of a thermal vacancy contribution in the diffusivity model. This idea is essentially identical to that shown in Rg. 11.11. This is a direct modeling of the results of atomic-level computer simulations. ... 

Models for partial micromixing Since the introduction of the parameter J, defined by Equation 3.35, to describe the degree of segregation (Danckwerts, 1953 Zwietering, 1959), there has been an explosion of models to describe the degree of segregation (i.e., of partial micromixing)... 

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