Coordination defect model

Hoskins and Martin (1975) have shown the polymorphic relationships of the sesquioxides in terms of their coordinated defect model. Their discussion adds new insight into possible ways of viewing these structures. 

From thermodynamic insights won in the late 1970 s new attempts to craft general structural principles by expanding the basic ideas of the c.d. model were attempted by incorporating additional coordination defects of greater complexity (Manes et al., 1980 Sorensen, 1981). 

The divacancy is a stable defect in crystalline silicon. The six dangling bonds left by the removal of two adjacent atoms reconstruct to leave two strong bonds and a pair of weakly interacting dangling bonds which comprise the gap states. The defect has four electronic levels in the gap and its neutral state has paired electrons and is diamagnetic. The divacancy model was first proposed by Spear (1974) to explain the early field effect results. A two-fold coordinated silicon atom also has Az = — 2 and so is of the same type. Adler (1978) concluded from molecular orbital arguments that this defect has the lowest formation energy of any silicon coordination defect. 

Figure 2.9. Representation of unit containing coordination defect used to model Cc 02. 201 oxides, with their orientations along [tl21p plane. Module F has no vacancies module D, has one vacancy in lower octant (there are four possible bottom vacancies whose modules have b=l,2,3 and 4) module U has one top vacancy (there are four possible IT modules with t=l,2,3 and 4) W j is one of four possible modules with two vacancies, a lop vacancy and a vacancy tn the tower octant (W with t,b=3,l 4,2 U 2,4) <.

Initially the calcium ions were placed on the faces of rings as well as at random locations in the cavity. Once many of the distinct minima had been found for specific aluminium configurations, calciums were placed in these positions to verify that no minima had been missed and optimised for all of the aluminium configurations The calcium ion positions were obtained in Cartesian co-ordinates relative to the centre of region 1, rather than fractional coordinates since ions in a defect model are not replicated periodically. In order to compare with X-ray diffraction data, approximate fractional co-ordinates for the calcium ion were found by assuming that the fractional co-ordinates of the defect centre did not change when the geometry of the defect was relaxed. Positions could then be related to the unit cell of the pure material. 

A vacancy in the anion lattice of the rare earth oxides and the relaxation of its nearest neighbours generates a cluster which can be considered as a coordinated defect (c.d.) [7]. The size of this cluster is essential for modelling studies since it determines possible connectivities and therefore the defect distribution within the different structures. The topology of these c.d.s is structure determining and the total composition of the c.d. was... 

As seen in Fig. 15, in either the mixed-alkali silicate or mixed-alkali alumino-silicate glasses, clearly distinguishable Li-O and Na-O PDF peaks and coordination shells are observed, indicating that Li and Na ions adopt distinctly separate environments in there glasses, in accordance with the defect model proposed by LaCourse[83],... 

A for all three-coordinated Si atoms, resulting in one sp defect model obtained starting the optimization with a Si...O distance of... 

A for all three-coordinated Si atoms, resulting in six sp defects optimization with NEB [52] reducing six initial Si defects to only two sp defects model obtained starting the optimization with a Si... 0 distance of 1.9 A for all three-coordinated Si atoms, resulting in one sp and one sp defects... 

The MPL spectrum exhibits two broad peaks, one at 467 nm (2.64 eV) and the other one at 422 nm (2.94 eV). These peaks appear to be related also to defects in the Si02 structure. Several such defect models have been discussed in the literature (47,48). The emission at 2.65 eV has been assigned to a new intrinsic defect in amorphous Si02 for which a two-fold coordinated Si is proposed, i.e., a Si(II) (neutral) center (48). Chemically, this is equivalent to the quasi-molecule Si02 with a 1Ai ground state, first excited singlet state, and a Bi triplet state. The... 

In spite of the absence of periodicity, glasses exhibit, among other things, a specific volume, interatomic distances, coordination number, and local elastic modulus comparable to those of crystals. Therefore it has been considered natural to consider amorphous lattices as nearly periodic with the disorder treated as a perturbation, oftentimes in the form of defects, so such a study is not futile. This is indeed a sensible approach, as even the crystals themselves are rarely perfect, and many of their useful mechanical and other properties are determined by the existence and mobility of some sort of defects as well as by interaction between those defects. Nevertheless, a number of low-temperamre phenomena in glasses have persistently evaded a microscopic model-free description along those lines. A more radical revision of the concept of an elementary excitation on top of a unique ground state is necessary [3-5]. 

The existence of active sites on surfaces has long been postulated, but confidence in the geometric models of kink and step sites has only been attained in recent years by work on high index surfaces. However, even a lattice structure that is unreconstructed will show a number of random defects, such as vacancies and isolated adatoms, purely as a result of statistical considerations. What has been revealed by the modern techniques described in chapter 2 is the extraordinary mobility of surfaces, particularly at the liquid-solid interface. If the metal atoms can be stabilised by coordination, very remarkable atom mobilities across the terraces are found, with reconstruction on Au(100), for example, taking only minutes to complete at room temperature in chloride-containing electrolytes. It is now clear that the... 

In 1983, Huskey and Schowen tested the coupled-motion hypothesis and showed it to be inadequate in its purest form to account for the results. If, however, tunneling along the reaction coordinate were included along with coupled motion, then not only was the exaltation of the secondary isotope effects explained but also several other unusual feamres of the data as well. Fig. 4 shows the model used and the results. The calculated equilibrium isotope effect for the NCMH model (the models employed are defined in Fig. 4) was 1.069 (this value fails to agree with the measured value of 1.13 because of the general simplicity of the model and particularly defects in the force field). If the coupled-motion hypothesis were correct, then sufficient coupling, as measured by the secondary/primary reaction-coordinate amplimde ratio should generate secondary isotope effects that... 

Coluccia et al. (5) proposed a model of the MgO surface that shows Mg-O ion pairs of various coordination numbers (Fig. 1). MgO has a highly defective surface structure showing steps, edges, corners, kinks, etc., which provide sites of low... 

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. 

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