Modelling defect structures

Bond valences can be used in conjunction with other techniques, particularly powder diffraction where, for example, light atoms are difficult to refine in the presence of heavy atoms. Adding the chemical constraints of the bond valence model can stabilize the refinement, particularly in the case of superstructures that have high pseudo-symmetry (Thompson et al. 1999). 

Many inorganic compounds are not stoichiometric, but have atoms missing or additional atoms occupying interstitial sites or substituting for other atoms. 

Such defects can give rise to unusual physical and chemical properties as discussed more fully in the following chapters. Here it is worth pointing out that bond valences can be used to explore the local environments around defects which are difficult to observe using the standard techniques of X-ray and neutron diffraction. 

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Various defect models have been proposed to explain the defect structure of the doped LaMn03 oxides particularly in the oxygen-excess region. At high oxygen... 

However, a detailed model for the defect structure is probably considerably more complex than that predicted by the ideal, dilute solution model. For higher-defect concentration (e.g., more than 1%) the defect structure would involve association of defects with formation of defect complexes and clusters and formation of shear structures or microdomains with ordered defect. The thermodynamics, defect structure, and charge transfer in doped LaCo03 have been reviewed recently [84],... 

In Chap. C, the thermodynamic and structural outlook of the bond, which had been the matter of discussion in Part A of this chapter, is further developed, and the model formalism, which takes advantage of the well known Friedel s model for d-transition metals but is inspired by the results of refined band calculations, is presented for metals and compounds. Also, a hint is given of the problems which are related to the nonstoichiometry of actinide oxides, such as clustering of defects. Actinide oxides present an almost purely ionic picture nevertheless, covalency is present in considerable extent, and is important for the defect structure. 

Hiickel calculations have been employed extensively in other approaches such as the angular overlap model and the method of moments developed by Burdett and coworkers. Stabilities of crystal structures, pressure- and temperature-induced transitions, dynamical pathways in reactions and other phenomena have been analysed using angular overlap models. Thus, the electronic control of rutile structures and the stability of the defect structure of NbO have been examined (Burdett, 1985 Burdett Mitchell, 1993). In the case of NbO, the structure is stable at involving the formation... 

The defect structure of Fei O with the NaCl-type structure had been estimated to be a random distribution of iron vacancies. In 1960, Roth confirmed, by powder X-ray diffraction, that the defect structure of wiistite quenched from high temperatures consists of iron vacancies (Vp ) and interstitial iron (Fcj) (there are about half as many FCj as Vpe). This was a remarkable discovery in the sense that it showed that different types of crystal defects with comparable concentrations are able to exist simultaneously in a substance, Roth also proposed a structure model, named a Roth cluster, shown in Fig. 1.84. Later this model (defect complex = vacancy -F interstitial) was verified by X-ray diffraction on a single crystal and also by in-situ neutron diffraction experiments. Moreover, it has been shown that the defect complex arranges regularly and results in a kind of super-structure, the model structure of which (called a Koch-Cohen model) is shown in Fig. 1.85 together with the basic structures (a) and (b). 

In contrast to that model, we generated statistical homogeneous defect structures with a broken coordination number of next neighbors. The exclusion volume of the segments should be accounted for. To our knowledge, there is no mathematical method that allows one to describe the radial distance distribution of such structures analytically. It must be calculated on a computer by generating the structure steadily. 

Starting from the mixture model, the structural behavior of water in the presence of dissolved simple ions is discussed from the point of view of defect formation and lattice distortions at interfaces. The observed behavior of the ions and the water lattice is applied to a number of unsolved biological problems in an attempt to elucidate the specific interface phenomena that are characteristic of such systems. 

Ab initio methods provide elegant solutions to the problem of simulating proton diffusion and conduction with the vehicular and Grotthuss mechanism. Modeling of water and representative Nation clusters has been readily performed. Notable findings include the formation of a defect structure in the ordered liquid water cluster. The activation energy for the defect formation is similar to that for conduction of proton in Nafion membrane. Classical MD methods can only account for physical diffusion of proton but can create very realistic model... 

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. 

To model defects in solids, a small cluster is usually used, which is cut of a solid structure, and cleaved chemical bonds are saturated using H atoms or OH groups [24], As follows from the available experimental data, the F atom is suitable for the saturation of a free valence of the Si atom formed due to the cleavage of the Si-O bond. 

X-ray studies have established that /9-R105 boron has a very porous (only 36% of space is filled in the idealized model) and defective structure with the presence of interstitial atoms and partial occupancies. The B57 fragment can dispose of excess electrons by removal of some vertices to form nido or arachno structures, and individual Bi2a units can gain electrons by incorporating capping vertices that are accommodated in interstitial holes (see Fig. 13.4.11(b)). 

Yu. V. Trushin and U. G. Samsanidze, Evolution of the Defective Structure of Crystals (Computer-Aided Modeling), Akad. Nauk SSSR, Fiz.-Tekh. Inst., Leningrad, 1984. 

The EH calculations agree with the CNDO results if a planar nondefect geometry is used. When the model containing defects serves as the lattice, electron-capture processes are favored at the expense of Ag+ capture at the Ag center, as shown in Table XIII. This leads to the alternative pathway shown in Fig. 24, and would explain a dependence of photochemistry on surface-defect structure. 

Amorphous metals can be prepared in a wide variety of stable and metastable compositions with all catalyti-cally relevant elements. This synthetic flexibility and the isotropic nature of the amorphous state with no defined surface orientations and no defect structure (as no long-range ordering exists) provoked the search for their application in catalysis [21]. The drastic effect of an average statistical mixture of a second metal component to a catalytically active base metal was illustrated in a model experiment of CO chemisorption on polycrystalline Ni which was alloyed by Zr as a crystalline phase and in the amorphous state. As CO... 

A serious limitation of (but not an objection to) the hydridic model is its inability to rationalize the nonstoichiometry of metallic hydrides. The difficulty arises in part because of the use of the Madelung constant (or an approximate equivalent) and a Born-Lande or exponential repulsion term. It is not yet clear how these may be calculated for a defect structure where ions are randomly missing from their sites. It is reasonable that mutual repulsion of outer electrons will be less in such a structure, but no quantitative interpretation has been made. 

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