Defect formation atomistics

What is the basis of atomistic simulation calculations of point defect formation energies ... 

These rules are not foolproof but should serve as a first approximation. A more rigorous approach must be used for more quantitative assessments. One possibility is to compute defect formation energies for the compound in question using atomistic simulations or quantum mechanical theory. These formation energies can be inserted into formulas similar to those described for simple defect populations (Chapter 2) ... 

In this context, Sayle et al. have used atomistic simulation methods to investigate the interaction of ceria with impurities, particularly rhodium, palladium and platinum. The energetics of the most common valence states for the metal atoms were investigated, as well as the variation of the energy of the impurities with depth below the surface and the tendency of defects to segregate to the surfaces. Fig. 8.9. shows the substitutional defect formation energies as a function of the distance from the (111) and (110) surfaces of Ce02 for C e " ", PcP+ and Sayle etal. found that... 

A hybrid atomistic/continuum mechanics method is established in the Feng, et al. study [70] the deformation and fracture behaviors of carbon nanotubes (CNTs) in composites. The unit cell containing a CNT embedded in a matrix is divided in three regions, which are simulated by the atomic-potential method, the continuum method based on the modified Cauchy-Bom rule, and the classical continuum mechanics, respectively. The effect of CNT interaction is taken into account via the Mori-Tanaka effective field method of micromechanics. This method not only can predict the formation of Stone-Wales (5-7-7-5) defects, but also simulate the subsequent deformation and fracture process of CNTs. It is found that the critical strain of defect nucleation in a CNT is sensitive to its chiral angle but not to its diameter. The critical strain of Stone-Wales defect formation of zigzag CNTs is nearly twice that of armchair CNTs. Due to the constraint effect of matrix, the CNTs embedded in a composite are easier to fracture in comparison with those not embedded. With the increase in the Young s modulus of the matrix, the critical breaking strain of CNTs decreases. 

The nature and energetics of electronic defects are major factors which control the properties of high-temperature superconductors. Atomistic simulation techniques allow an estimation of the formation energies of these defects. Within the framework of an ionic model, valence band holes are described in localized terms as Cu3 + (hCu) or 0 (h0) and defect electrons as Cu + (eCu)- The formation energy of these defects involves a contribution from the ionization potential/electron affinity of the appropriate ion in addition to a lattice energy term (including the effects of relaxation) and a band contribution, in the case of delocalized carriers (large polarons). 

With the exception of the elegant mononucleation transients on silver deposition at defect-free silver electrodes [115, 156-159], the analysis of the macroscopic current, charge density, and/or capacitance transients does not provide direct access to structural information and molec-ular/atomistic mechanisms of 2D phase formation. Employing dynamic MC simulations of microscopic models, Rikvold and coworkers pointed out that mean-field rate equations, such as the ones based on the Avrami ansatz, are limited especially in the later stage of the overall transition [195]. For systems in which ordered phases are involved, the microscopic adlayer structure and the dynamic details of the adsorption, phase formation, and lateral diffusion processes should become important [196-198]. The combination of time-resolved dynamical MC simulations... 

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