Thermodynamic Effects in Ion Mixing

Equation (13.5) and the marker data presented in Fig. 13.5 can be used to estimate the average atomic displacement distance of a marker atom in a collision cascade formed in a matrix of amorphous Si. For example, from the temperature-independent data in Fig. 13.5a, a typical value of DiJlcj), for both Sn and Sb markers, is 4(10 cm ), or 0.4 nm . From Fig. 13.5b, the corresponding damage energy is 1,500 eV nm Using the atomic density of crystalline Si, 50 atoms nm for the amorphous Si value of N, the ratio of Fj lN will be 30 eV nm This indicates that should be approximately 1.6 nm for a Si displacement energy of Ad = 13 eV. 

Similar observations were also made in the different ion mixing responses of Hf/Ni and Hf/Ti bilayers (van Rossnm et al. 1984). Again, from a ballistic view, ion mixing for these two systems shonld be nearly identical. However, it was observed that the mixing rate of Hl/Ni was significantly higher than that of Hl/Ti. This difference was attribnted to differences in the heat of mixing, for the 

The heat of mixing, similar to the heat of alloy formation, gives a measure of how attractive different elements are to each other relative to their attractiveness to 

Equation (13.7) is a linear expression with with a slope defined by 

A more detailed analysis of the thermodynamic influence on ion mixing by Johnson et al. (1985) resulted in the following phenomenological expression 

Equation (13.10) is demonstrated in Fig. 13.8, which shows the experimental mixing rate d(4Dt) / d p (scaled by A-5,3//coli/-j(2) versus the ratio AHmix/AH( w. The linear relationship indicates that the amount of mixing scales with AHmiJAHcoh and that (13.10) provides a reasonable prediction of the ion beam mixing rate in metal/metal bilayer systems irradiated with heavy ions at low temperatures. 

Ballistic effects resulting from the early stages of cascade evolution are important factors in the ion mixing process, but materials properties, such as heat of mixing and cohesive energy, also influence the process. Such material properties 

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The topic of interactions between Lewis acids and bases could benefit from systematic ab initio quantum chemical calculations of gas phase (two molecule) studies, for which there is a substantial body of experimental data available for comparison. Similar computations could be carried out in the presence of a dielectric medium. In addition, assemblages of molecules, for example a test acid in the presence of many solvent molecules, could be carried out with semiempirical quantum mechanics using, for example, a commercial package. This type of neutral molecule interaction study could then be enlarged in scope to determine the effects of ion-molecule interactions by way of quantum mechanical computations in a dielectric medium in solutions of low ionic strength. This approach could bring considerable order and a more convincing picture of Lewis acid base theory than the mixed spectroscopic (molecular) parameters in interactive media and the purely macroscopic (thermodynamic and kinetic) parameters in different and varied media or perturbation theory applied to the semiempirical molecular orbital or valence bond approach [11 and references therein]. 

Ligand exchange has proved to be very successful in the separation of several enantiomers. Davankov and Rogozhin (41) used chiral copper complexes bonded to silica. The enantiomeric separation is based essentially on the formation of diastereomeric mixed complexes with different thermodynamic stabilities. It is generally accepted that chiral discrimination proceeds via the substitution of one ligand in the coordination sphere of the metal ion. Ligand exchange technique is especially effective for the enantiomeric resolution of aminoacids, aminoacids derivatives, and hydroxy acids (42). 

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