Point charged defects

Later calculations showed that the defect binding energies were invariant to the values chosen for the point charges. As those calculated for the fully-ionic system my be directly compared to those obtained using classical simulation, geometry optimizations were carried out using the fully-ionic point-ions. 

RBa2Cu307 ceramics (R is a rare-earth metal or yttrium) EFG tensor, comparison with point charge calculation, spatial distribution of electron defects in the lattice... 

HgBa2Ca iCu 02 +2 (n = 1, 2, 3) EEG tensor at the copper, barium, and mercury sites, by Cu( Zn), Ba( Cs), and Hg ( Au) Mossbauer emission spectroscopy. Comparison with point-charge approximation and Cu NMR data showed that the holes originating from defects are localized primarily in the sublattice of the oxygen lying in the copper plane (for HgBa2Ca2Cu30g, in the plane of the Cu(2) atoms)... 

For nuclei that have perfect cubic site symmetry (e.g., those in an ideal rock salt, diamond, or ZB lattice) the EFG is zero by symmetry. However, defects, either charged or uncharged, can lead to non-zero EFG values in nominally cubic lattices. The gradient resulting from a defect having a point charge (e.g., a substitutional defect not isovalent with the host lattice) is not simply the quantity calculated from simple electrostatics, however. It is effectively amplified by factors up to 100 or more by the Sternheimer antishielding factor [25],... 

Non-stoichiometry is a very important property of actinide dioxides. Small departures from stoichiometric compositions, are due to point-defects in anion sublattice (vacancies for AnOa-x and interstitials for An02+x )- A lattice defect is a point perturbation of the periodicity of the perfect solid and, in an ionic picture, it constitutes a point charge with respect to the lattice, since it is a point of accumulation of electrons or electron holes. This point charge must be compensated, in order to preserve electroneutrality of the total lattice. Actinide ions having usually two or more oxidation states within a narrow range of stability, the neutralization of the point charges is achieved through a Redox process, i.e. oxidation or reduction of the cation. This is in fact the main reason for the existence of non-stoichiometry. In this respect, actinide compounds are similar to transition metals oxides and to some lanthanide dioxides. 

For a very low departure from the stoichiometric composition, there is in principle no reason why point lattice defects and the compensating cationic charges (constituting also a defect in the cationic lattice) should be grouped together in special regions of the lattice or occupy special lattice sites usually, they are considered randomly distributed in the lattice. 

If the defects can be considered point charges, localized on their own lattice sites, the polar electrostatic interaction between them is usually written as a long range monopolar Coulomb energy. If, on the other hand, for large concentrations of defects, local charge effects, as described in the introduction, are present, then AHjnter is much more difficult to write. 

It is worthwhile to examine the Hamiltonian in some detail because it enables one to discuss both intramolecular and intermolecular perturbations from the same point of view. To do so, we start from a zero-order Hamiltonian that contains just the spherical part of the field due to the core (which need not be Coulombic as it includes also the quantum defect [42]) and add two perturbations. U due to external effects and V due to the structure of the core. Here, U contains both the effect of external fields (electrical and, if any, magnetic [1]) and the role of other charges that may be nearby [8, 11, 12, 17]. The technical point is that both the effect of other charges and the effect of the core not being a point charge are accounted for by writing the Coulomb interaction between two charges, at points ri and r2, respectively, as... 

In the first two chapters we have seen that the Na atom, for example, differs from the H atom because the valence electron orbits about a finite sized Na+ core, not the point charge of the proton. As a result of the finite size of the Na+ core the Rydberg electron can both penetrate and polarize it. The most obvious manifestation of these two phenomena occurs in the lowest states, which are substantially depressed in energy below the hydrogenic levels by core penetration. Core penetration is a short range phenomenon which is well described by quantum defect theory, as outlined in Chapter 2. 

The cross-section for charged-defect recombination will likely be larger than that for neutral-defect recombination. In addition, dopant ions will likely provide additional recombination sites when the dopant is paired with a point defect. 

Charged point defects on regular lattice positions can also contribute to additional losses the translation invariance, which forbids the interaction of electromagnetic waves with acoustic phonons, is perturbed due to charged defects at random positions. Such single-phonon processes are much more effective than the two- or three phonon processes discussed before, because the energy of the acoustic branches goes to zero at the T point of the Brillouin zone. Until now, only a classical approach to account for these losses exists, which has been... 

In principle, the optical absorptions in this region could also be associated with point defects on the surface either with or without trapped electrons and holes. However, the properties of the charged defects have been studied extensively, and the trapped charges can be thermally annealed at temperatures far lower than the normal preparation temperatures of these samples. In addition, they are characterized by optical and EPR spectra which are not observed in these samples. Contributions from point defects with no trapped charges cannot easily be eliminated. In fact, such a surface vacancy or divacancy would represent a localized state on a low-index surface associated with 4-coordinated ions. 

The complexity of the spectra and the difficult interpretation due to the low sensitivity to surface defects, makes a theoretical support highly desirable in order to provide a firm attribution of the observed bands. The calculation of electronic excitations in solids is very challenging, and only recently accurate configuration interaction (Cl) calculations have been reported on this problem [28,29], To this end, finite clusters embedded in ECP and point charges have been used. A calibration of the accuracy of the results, possible for bulk F and F transitions where assignments are unambiguous, have shown that Cl calculations tend to overestimate the optical transitions of F centers in MgO bulk by about 15% because of limitations in the size of the basis set [28]. 

Similar defect structures may be envisioned as arising during isomerization of cw-polyacetylene to frans-polyacetylene. If two trans sequences with opposite bond alternation approach each other along a chain containing an odd number of conjugated carbon atoms, an unpaired electron (radical) wiU be left at the point where the two sequences meet. This defect, which chemists call a free radical, is similar to the solitary charged defect produced by separation of a bipolaron, except that it is neutral. 

Point (microscopic) defects in contrast from the macroscopic are compatible with the atomic distances between the neighboring atoms. The initial cause of appearance of the point defects in the first place is the local energy fluctuations, owing to the temperature fluctuations. Point defects can be divided into Frenkel defects and Schottky defects, and these often occur in ionic crystals. The former are due to misplacement of ions and vacancies. Charges are balanced in the whole crystal despite the presence of interstitial or extra ions and vacancies. If an atom leaves its site in the lattice (thereby creating a vacancy) and then moves to the surface of the crystal, it becomes a Schottky defect. On the other hand, an atom that vacates its position in the lattice and transfers to an interstitial position in the crystal is known as a Frenkel defect. The formation of a Frenkel defect therefore produces two defects within the lattice—a vacancy and the interstitial defect—while the formation of a Schottky defect leaves only one defect within the lattice, that is, a vacancy. Aside from the formation of Schottky and Frenkel defects, there is a third mechanism by which an intrinsic point defect may be formed, that is, the movement of a surface atom into an interstitial site. Considering the electroneutrality condition for the stoichiometric solid solution, the ratio of mole parts of the anion and cation vacancies is simply defined by the valence of atoms (ions). Therefore, for solid solution M X, the ratio of the anion vacancies is equal to mJn. 

---