Point defects theoretical modeling

Apart from its role in interacting with existing defects and impurities, hydrogen has recently been shown to induce defects as well (Johnson et al., 1987). Extended defects (described as platelets ) in the near-surface region were observed after hydrogenation and correlated with the presence of large concentrations of H. Theoretical models will be discussed in Part VIII. Part IX, finally, will contain some conclusions and point out directions for future work. As is the case for so many other topics in semiconductor physics, silicon (Si) has been the material for which the majority of... 

Compare the theoretical and experimental densities to see which point defect model best fits the data. 

Defect thermodynamics, as outlined in this chapter, is to a large extent thermodynamics of dilute solutions. In this situation, the theoretical calculation of individual defect energies and defect entropies can be helpful. Numerical methods for their calculation are available, see [A. R. Allnatt, A. B. Lidiard (1993)]. If point defects interact, idealized models are necessary in order to find the relations between defect concentrations and thermodynamic variables, in particular the component potentials. We have briefly discussed the ideal pair (cluster) approach and its phenomenological extension by a series expansion formalism, which corresponds to the virial coefficient expansion for gases. 

The quantum chemical modeling is a very useful supplement to spectroscopic experimental methods for investigation of properties of point defects, however, until recently it was used mainly for calculations of vertical excitation energies. The modeling of structural transformation in excited electronic states is still a rather complicated task, which requires state-of-the-art quantum chemical calculations. In this chapter, we first describe theoretical methods applied in ab initio and vibronic theory calculations and then demonstrate their applications in theoretical studies of various point defects in silica and germania. 

In this section, we discuss theoretical methods, which can be applied for calculations of photoabsorption and PL spectra of silica and germania nanoparticles. We start with the choice of model cluster simulating these materials and point defects in them and consider methods for geometry optimization in the ground and excited electronic states (Subsection 2.1). This is followed by the description of more advanced quantum chemical methods for accurate calculations of excitation energies (Subsection 2.2) and the section is completed by the discussion on the theoretical procedure used for predicting vibronic spectra associated with point defects (Subsection 2.3). 

In summary, a variety of ab initio and DFT methods can be applied for different types of model clusters. A comparison of the results of different methods with available experimental data should be carried out and, based on this comparison, a proper theoretical procedure should be chosen for each particular type of point defect in Si02 and Ge02. 

One of the problems where the use of the cluster approach is more appealing is in the study of surface defects. Only recently it has been recognized by the surface science community that these centers are often the most interesting ones from the point of view of the physical and chemical properties of a material. Several chemical reactions taking place at an oxide surface are directly or indirectly connected to the presence of point and extended defects. Unfortunately, defect centers are elusive species because of their low concentration even in the bulk material, and their identification by spectroscopic methods can be rather difficult. This is even more dramatic when one is interested in surface defects because the distinction from bulk defects may be extremely subtle. For all these reasons the theoretical modeling of defect centers at the surface of oxides is attracting an increasing interest. 

One possible explanation is that co-operative defects may make a large contribution to positional melting in metal crystals, as has been suggested in a theoretical model.Another explanation is that molten metals may contain clusters of atoms, particularly near their melting point. Prefreezing phenomena in metals give some support to this suggestion, but more experimental work seems desirable to test how far they occur. 

All the extrinsic defects modify the concentration of the intrinsic ones compared to the undoped ceria and therefore they modify the rate of the process. In order to get a quantitative model, the concentrations of point defects in ceria must be theoretically expressed as function of the oxygen partial pressure, the amount of foreign cation and physical constants such as equilibrium constants and diffusion coefficients[7,ll]. In the following, only two equilibrium constants will be considered ... 

Textures correspond to various arrangements of defects. When the isotropic liquid is cooled, the nematic phase may appear at the deisotropization point in the form of separate small, round objects called droplets (Fig. 12). These can show extinction crosses, spiral structures, bipolar arrangements, or some other topology depending on boundary conditions. Theoretical studies based on a simple model confirm the stability of radial or bipolar orientation (Fig. 5) [22]. Considerations based on improved theoretical models yield stable twisted... 

The properties of perovskite materials are heavily dominated by their oxygen content, as weU as by donor- and acceptor-type impurities. An essential contribution to the knowledge of the structural and electronic properties of point defects in these materials comes from theoretical approaches. The results of large-scale computer semiempirical and first-principles modeling of point defects, polarons and perovskite sohd solutions can be found in [722], focusing mostly on KNbOa and KTaOa. 

Numerous studies have attempted to elucidate the role of Mo in the passivity of stainless steel. It has been proposed from XPS studies that Mo forms a solid solution with CrOOH with the result tiiat Mo is inhibited from dissolving trans-passively [9]. Others have proposed that active sites are rapidly covered with molybdenum oxyhydroxide or molybdate salts, thereby inhibiting localized corrosion [10]. Yet another study proposed that molybdate is formed by oxidation of an Mo dissolution product [11]. The oxyanion is then precipitated preferentially at active sites, where repassivation follows. It has also been proposed that in an oxide lattice dominated by three-valent species of Cr and Fe, ferrous ions will be accompanied by point defects. These defects are conjectured to be canceled by the presence of four- and six-valent Mo species [1]. Hence, the more defect-free film will be less able to be penetrated by aggressive anions. A theoretical study proposed a solute vacancy interaction model in which Mo " is assumed to interact electrostatically with oppositely charged cation vacancies [ 12]. As a consequence, the cation vacancy flux is gradually reduced in the passive film from the solution side to the metal-film interface, thus hindering vacancy condensation at the metal-oxide interface, which the authors postulate acts as a precursor for localized film breakdown [12]. 

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