Vacancy, accumulation

Fig. 3 -13. (a) A ion levels at the surface and in the interior of ionic compound AB, and (b) concentration profile of lattice defects in a surface space charge layer since the energy scales of occupied and vacant ion levels are opposite to each other, ion vacancies accumulate and interstitial ions deplete in the space charge layer giving excess A ions on the surface. 

In the alternative case, there is no back stress at all, implying that aU possible stresses are relaxed immediately by the lattice shift In a usual polycrystalline body with large grains, it is described by a dislocation dimb as the source and sink of vacancies, and corresponding construction of extra planes in the region of atoms accumulation, and reconstruction of planes in the region of vacancy accumulation. Vacancy is at equilibrium everywhere in the sample as assumed in Darken s analysis of interdifiusion. Then in the laboratory reference frame... 

Darken assumed that the accumulated vacancies were annilrilated within the diffusion couple, and that during tlris process, tire markers moved as described by Smigelskas and Kirkendall (1947). His analysis proceeds with the assumption tlrat the sum of tire two concenuations of the diffusing species (cq - - cq) remained constant at any given section of tire couple, and tlrat the markers, which indicated the position of tire true interface moved with a velocity v. 

The same theoretical examination as applies to the Frenkel defect may also apply to the Schottl defect in ionic compounds, in which an accumulation layer of vacancies is formed with a surface ion excess. 

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. 

A large body of experiments (e.g., [70, 73, 74]) deals with the kinetics of dimer centre accumulation in alkali halide crystals it was observed experimentally that n (F2) increases often as squared single-vacancy concentration, n2(F). In our formalism, n(F2) (iV)n(F). As it is well seen in Fig. 7.11, (N) turns out to be a linear function of 77(F) in a wide range of defect... 

The simulation shows that 1) the curve of the dependence of the number of accumulated defects on the total number of defects created reveals a tendency to saturation 2) when L = 100-400 and l = 5-20, complete separation was attained of the crystal into a region of interstitials and a region of accumulation of vacancies the location of the regions changes upon further generation of defects 3) the sum of the lengths of the wells filled with vacancies for L/l > 2 considerably exceeds the length L (when L = 2000, l = 5, Uo = nol 5 where no is the concentration of accumulated defects,... 

To determine the existence of stable steady state, a model [109] was studied of the destmction of clusters in the case vp = 700. At the initial instant of time 10 uniformly distributed clusters of 300 vacancies each, were put into the crystal , and interstitial atoms in the intervals between them (Uq 10). Then pairs of randomly distributed defects of different types were created in the crystal . The newly generated defects break up the orginally existing clusters and the concentration of defects declines to a steady-state value. The values of Uo were obtained by averaging a region of the curve of length 2.5 x 104 events of defect creation. The result unambiguously implies the existence of stable steady state in the problem of accumulation of point defects and in the problem of breakup of clusters. 

The quantity Uo characterizes the degree of aggregation only on the average. Therefore it is important in each particular case to analyze also the spatial distribution of the defects. Thus, the low-temperature accumulation of the Frenkel defects in the two- and three-dimensional cases was simulated in [36, 114] and the obtained values of Uo for d = 2 considerably exceed the same in [113]. In contrast to the latter, the authors of [36, 114] used a circle as the recombination region. In its turn, the values of u0 obtained in [115] are considerably larger than those found in [114]. We note that it was assumed in [115] that, when an interstitial atom occurs at a site where the recombination spheres of several vacancies overlap, it recombines with the closest vacancy. This demonstrates very well how any details, insignificant at first glance, can affect considerably the accumulation kinetics. 

A simulation has been carried out [105, 106, 119] of the process of accumulation of the immobile Frenkel defects restricted by tunnelling recombination of dissimilar defects, as it is observed in many solid insulators. As follows from Chapter 3, in contrast to the ionic process of instant annihilation of close pairs of the vacancy-atom type, it is characterized by a broad spectrum of recombination times. Thus, the probability for a pair of chosen defects that lie at the relative distance r to survive for r seconds is... 

The analysis conducted in this Chapter dealing with different theoretical approaches to the kinetics of accumulation of the Frenkel defects in irradiated solids (the bimolecular A + B —> 0 reaction with a permanent particle source) with account taken of many-particle effects has shown that all the theories confirm the effect of low-temperature radiation-stimulated aggregation of similar neutral defects and its substantial influence on the spatial distribution of defects and their concentration at saturation in the region of large radiation doses. The aggregation effect must be taken into account in a quantitative analysis of the experimental curves of the low-temperature kinetics of accumulation of the Frenkel defects in crystals of the most varied nature - from metals to wide-gap insulators it is universal, and does not depend on the micro-mechanism of recombination of dissimilar defects - whether by annihilation of atom-vacancy pairs (in metals) or tunnelling recombination (charge transfer) in insulators. 

Fig. 29. Sketch to illustrate the defect motion in acceptor-doped SrTiOs during high field stress. The oxygen vacancies are blocked at the electrodes and therefore accumulate at the cathode, but deplete at the anode. Electrons and holes can pass the electrodes.

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