Theory solute segregation

These measures of solute segregation are closely related to the spatial and temporal patterns of the flow in the melt. Most of the theories that will be discussed are appropriate for laminar convection of varying strength and spatial structure. Intense laminar convection is rarely seen in the low-Prandtl-number melts typical of semiconductor materials. Instead, nonlinear flow transitions usually lead to time-periodic and chaotic fluctuations in the velocity and temperature fields and induce melting and accelerated crystal growth on the typically short time scale (order of 1 s) of the fluctuations. 

Various crack advance theories have been proposed to relate crack propagation to oxidation rates and the stress-strain conditions at the crack tip, and these theories have been supported by a correlation between the average oxidation current density on a straining surface and the crack propagation rate for a number of systems [12,35]. There have been various hypotheses about the precise atom-atom rupture process at the crack tip—for example, the effect that the enviromnent has on the ductile fracture process (e g., the tensile ligament theory [36], the increase in the number of active sites for dissolution because of the strain concentration [37], the preferential dissolution of mobile dislocations because of the inherent chemical activity of the solute segregation in the dislocation core [38]). 

Generally speaking, the solute segregation theory is only valid for non-sensitized steel and attempts to extend it to the sensitized steels have not been successful because the tests were carried out in highly oxidizing solution in which general corrosion as well as intergranular takes place as discussed above. 

In some other theories, it has been suggested that the crack tip always remains covered with an oxide and the film is only periodically ruptured by emergence of slip steps. It has also been suggested that the crack tip remains bare because the rate of rupture of the oxide film is higher than the rate of repassivation of the film. In general, the rate of attack is determined by stress (applied or residual), electrochemical potential, total strain rate and specific ions and effect of solute segregates. 

As discussed in Section 7.2.3, radiation can induce segregation of alloy elements at defect sinks such as grain boundaries [101]. Typically, RIS is a result of inverse Kirkendall (IK) effects in which the evolution of defect concentration field drives the evolution of alloy composition field. ID rate theory modeling [44,101] is widely used to describe the coupled evolution between defect flux and composition flux. These rate theory models considered both vacancy-mediated and interstitial-mediated solute transport, as well as point defect recombination and defect loss to dislocations. At steady state, the solute segregation direction depends on the relative diffiisivity of different species-defect coupled diffusion. In austenitic Fe-Cr-Ni alloys, the vacancy-mediated solute diffusion alone is sufficient in describing the RIS trend and the interstitial-mediated solute diffusion is usually assumed to have a neutral contribution to RIS [44]. However, in Fe-Cr F/M alloys, both interstitial- and vacancy-mediated diffusion should be considered [102]. 

In the theories presented so far, a major driving force for segregation has been the fact that the surface is a region of reduced atomic coordination. In solids, there is a further driving force, namely the reduction of strain. Solute atoms that differ in size from the solvent lattice atoms create a strain in the lattice [41]. At a grain boundary, there are open sites where more space is available to the atoms. By migrating to these sites, a solute can reduce the strain energy. 

Knowing the thermal stability of clathrates permits the prediction of experimental conditions for polymerization (8). A detailed analysis of this problem requires the examination of all the involved phases, particularly the solid and liquid phases. Equations for phase equilibria were derived from within the framework of the regular solution theory they contain an interaction parameter W, (whose value is always positive or zero for ideal solutions), which measures the tendency of host and guest to segregate in the liquid phase. The melting or decomposition point is very sensitive to the value of W, especially when it exceeds 2 RT, i.e. when a miscibility gap is observed in the liquid phase. For this reason the PHTP-hydrocarbon clathrates melt congruently between 115 and 180 C, whereas the urea-hydrocarbon... 

Studies of small particles by Sinfelt [29] and his co-workers have shown that when the particles sizes become very small and dispersions tend toward unity (that is, when virtually every atom is at the surface), alloy systems exhibit phase diagrams very different from those that characterize bulk systems. For example, microclusters containing Cu and Ru, Cu and Os, or Au and Ni can be produced in any ratio of the two elements, indicating complete miscibility or solid solution behavior. In the bulk phase these elements are completely immiscible. This very different behavior of the surface phases of bimetallic systems finds important applications in the design of catalysts to carry out selective chemical reactions. Moran-Ldpez and Falicov [30] developed a theory—using pairwise interactions—of alloy surface segregation that explains this effect. Bimetallic systems remain miscible at lower temperatures in two dimensions than in three dimensions. 

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