Vacancy pairs

Figure 3.5 STM images from a movie showing the formation, separation, and annihilation of H-vacancy clusters. The images on the left (3 nm x 2.5 nm) are repeated on the right with annotations, (a) Five vacancies near the center are labeled (A-E) and two triangular vacancy pairs (2V) are marked with dashed triangles for reference, (b) Vacancies A and B have formed a 2V cluster indicated by the triangle containing the number 2 . Vacancies C-E have formed a...

It is possible for one or more lattice defects to associate with one another, that is, to cluster together. These are indicated by enclosing the components of such a cluster in parentheses. As an example, (VMVX) would represent a defect in which a vacancy on a metal site and a vacancy on a nonmetal site are associated as a vacancy pair. 

Associated defects (vacancy pair) (VMVr) Associated defects with positive effective charge (VmVp) ... 

Conesa373 modeled the surfaces and defects on ceria, and based on computer simulations, determined the relative stabilities of surfaces (111) > (110) > (211) > (100). Although the formation of anion vacancy defects was suggested to be more difficult to form on the more stable (111) surface, he indicated that anion vacancy pairs, important for 02 uptake and release processes, were easiest to form on the ceria (111) surface. 

The quantity c is, of course, the total concentration of vacancies including those involved in nearest-neighbour vacancy pairs or in higher aggregates. 

In pure metals the properties of intrinsic vacancies have been studied recently both by equilibrium measurements and by a variety of experiments in which the defects are quenched in the metal and studied at lower temperatures. The mass action formalism has been used to describe the results in terms of free vacancies, vacancy pairs, and trivacancies. For noble metals at equilibrium higher aggregates appear to be unimportant. The mass action equations may be compared with the one above. 

For example, at 1200°K — F(2) must be greater than 0.24 eV in order that the two correction terms differ by less than 10%. However, for the small defect concentrations of interest here (e.g. c,w6x 10-5 for Fv — 1.0 eV in copper) the correction due to the vacancy-pair term is unimportant for much smaller values of — Fl2) so that differences are not practically very important. The terms of order (c°)3 are more difficult to compare and the numerical values depend on the relative magnitudes of Fw and F((123 ), as can be seen by noting that the sum of products of /-functions in Bs is equivalent to... 

Fig. 3-11. Energy for decomposing ionization of compound AB to form gaseous ions A(giD) and via electron-hole pair formation and via cation-anion vacancy pair formation r = reaction coordinate of decomposing ionization e, s semiconductor band gap . vmb) = cation-anion vacancy pair formation energy (Va- Vb-) Lab = decomposing ionization energy of compound AB.

The decomposing ionization of soUd compound AB may also take place through the formation of a cation-anion vacancy pair as follows ... 

The decomposing ionization will take place preferentially by way ofthe electron-hole pair formation, if the formation energy of the electron-hole pair, e, is smaller than the formation energy of the cation-emion vacancy pair, Hv(ab>, and vice versa. In general, compound semiconductors, in which the band gap is small (e,< Jfv(AB>), will prefer the formation of electron-hole pairs whereas, compound insulators such as sodium chloride, in which the band gap is great (e(>Hv(AB>), will prefer the formation of cation-anion vacancy pairs [Fumi-Tosi, 1964]. 

In the case in which the formation of cation-anion vacancy pairs is preferential, the ion levels of A and B ions in solid compound AB are obtained in the same way as Eqns. 3-21 and 3-22 by Eqns. 3-23 and 3-24, respectively ... 

Defect Reaction Equilibrium Constants. Recall that a Frenkel disorder is a self interstitial-vacancy pair. In terms of defect concentrations, there should be equal concentrations of vacancies and interstitials. Frenkel defects can occur with metal... 

Frenkel defects form interstitial-vacancy pairs, so that [OJ = [V ], and Equation (1.42) reduces further to... 

Turning now to the vacancy concentration in Eq. (4.72), recall from Chapter 1, and Eq. (1.48) in particular, that the concentration of vacancies is related to the free energy of formation of the vacancy, so that for a cation-anion vacancy pair, or Schottky defect, the concentration of vacancies, [V7] is given by... 

Figure 5.1 Point defects in ionic solids Schottky defect, vacancy pair, Frenkel defect and aliovalent impurity (for definitions see Section 5.2).

When divalent cation impurities (e.g. Cd, Sr ) are present in an ionic solid of the type MX consisting of monovalent ions, the negatively charged cation vacancies (created by the divalent ions) are bound to the impurity ions at low temperatures. Similarly, the oppositely charged cation and anion vacancies tend to form neutral pairs. Such neutral vacancy pairs are of importance in diffusion, but do not participate in electrical conduction. The interaction energy of vacancy pairs or impurity-vacancy pairs decreases with the increase in distance between the two oppositely charged units. 

A variety of techniques has been employed to investigate aliovalent impurity-cation vacancy pairs and other point defects in ionic solids. Dielectric relaxation, optical absorption and emission spectroscopy, and ionic thermocurrent measurements have been most valuable ESR studies of Mn " in NaCl have shown the presence of impurity-vacancy pairs of at least five different symmetries. The techniques that have provided a wealth of information on the energies of migration, formation and other defect energies in ionic solids are diffusion and electrical conductivity measurements. Electrical conductivity in ionic solids occurs by the motion of ions through vacancies or of interstitial ions. In the case of motion through vacancies, the conductivity, a, is given by... 

If we analyze the vacancy pairing V+V = V2 in crystal A, the situation is appreciably simpler since at equilibrium, = 0 throughout. It follows that pv is independent of the divacancy concentration, which means that divacancies have the same (Arrhenius) temperature dependence as monovacancies (see Eqn. (2.57)) except for a factor 2 in the exponent. 

This fraction is determined by the step-dance between a specified vacancy and the (tagged) atom during their encounter, which does not end before the atom-vacancy pair has definitely separated. Normally, a new and independently moving vacancy comes along much later and begins the next encounter with the tagged atom. 

Particle irradiation effects in halides and especially in alkali halides have been intensively studied. One reason is that salt mines can be used to store radioactive waste. Alkali halides in thermal equilibrium are Schottky-type disordered materials. Defects in NaCl which form under electron bombardment at low temperature are neutral anion vacancies (Vx) and a corresponding number of anion interstitials (Xf). Even at liquid nitrogen temperature, these primary radiation defects are still somewhat mobile. Thus, they can either recombine (Xf+Vx = Xx) or form clusters. First, clusters will form according to /i-Xf = X j. Also, Xf and Xf j may be trapped at impurities. Later, vacancies will cluster as well. If X is trapped by a vacancy pair [VA Vx] (which is, in other words, an empty site of a lattice molecule, i.e., the smallest possible pore ) we have the smallest possible halogen molecule bubble . Further clustering of these defects may lead to dislocation loops. In contrast, aggregates of only anion vacancies are equivalent to small metal colloid particles. 

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. 

One of the causes of point defects is a temperature increase which results in an increased thermal movement of the atoms which can subsequently lead to the atoms escaping from their place in the lattice. Other causes are the effects of radiation and inbuilt, foreign atoms. In an atomic lattice a vacancy can occur due to the movement of an atom, an absence of an atom or molecule from a point which it would normally occupy in a crystal. In addition to this vacancy an atomic will form elsewhere. This combination of an atomic pair and a vacancy is called the Frenkel defect. In ionic crystals an anion and a cation have to leave the lattice simultaneously due to the charge balance. As a result a vacancy pair remains and this is called the Schottky defect. Both defects can be seen in figure 4.8. 

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