Impurity-vacancy pair

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... 

Often, however, in processes of this nature even the perturbed intrinsic emission does not appear in TL. Instead emission characteristic of an impurity is all that is seen. The interpretation generally placed on this is that the energy is transferred to the impurity. CaF2 Ce provides us with a useful example. In CaF2 the simple F-center is unstable at room temperature and does not form as a product of irradiation. However, when trivalent rare-earth impurity ions are present impurity/vacancy pairs are formed following irradiation. These are of C v symmetry with the vacancy... 

Note that we can use the same statistical mechanical approach to calculate SchottslQi" pairs, Frenkel pairs, divancies (which are associated vacancies), impurity-vacancy complexes, and line dislocation-point defect complexes. 

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

Figure 5.2 The ionic conductivity of pure NaCl as a function of temperature. Intrinsic conduction occurs in stages I and II stage III corresponds to conduction by cation vacancies present as a result of impurities. Vacancies become associated to form neutral pairs in stage IV.

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 fabrication and operation of a semiconductor detector are based on the premise that one starts with a perfect crystal containing a known amount of impurities. Even if this is true at the beginning, a semiconductor detector will suffer damage after being exposed to radiation. The principal type of radiation damage is caused by the collision of an incident particle with an atom. As a result of the collision, the atom may be displaced into an interstitial position, thus creating an interstitial-vacancy pair known as the Frenkel defect. A recoiling... 

The defect concentrations that are the result of thermal disorder are small in most oxides. The formation enthalpy of vacancy pairs in MgO is 7 eV, which gives a vacancy concentration of 10 ppm at 1000°C. In most oxides the bandgap is also large (>4eV) and at 1000°C the charge carrier concentration is lower than 10 ppm. Now, oxides can be made with an impurity concentration of at best 10-100 ppm. The concentration of impurities contributes much more to the defect concentration than the thermal disorder at these low formation equilibrium constants and the thermal (intrinsic) contribution to the defect concentration can usually be disregarded. 

Figure 1. Typical point defects in a binary ordered alloy (a) vacancy ( ) (b) split interstitial (c) bound pair of antisite defects (d) bound triple defect consisting of two vacancies and one antisite atom (e) vacancy-impurity ( ) bound pair (f) unbound wrong pair. Many other types of defects are possible, as will be discussed for example for Bll (CuTi, Section 5.3) and A15 (NbjSn, Section 9.1) compounds...

Very generally, point defects distort locally and induce electronic perturbations in the crystal these effects lead to elastic and electronic interactions between them, as well as with other defects (dislocations, grain boundaries, etc.). The complex defects so formed may introduce more distortion into the lattice than simple point defects, and therefore have greater effects on the mechanical properties. With increasing temperature, point defects become more and more randomly positioned, and complex defects (e.g. divacancies, vacancy-impurity or interstitial-impurity bound pairs) dissociate. 

Figure 9.3 Schematic representation of magnetic defects in a ferrimagnetic matrix (a) a pair of vacancies or nonmagnetic impurities similar to a Schottky defect and (b) an antisite defect.

Fig. 4.22 On the surface of a solid, there are a wide variety of atomic processes. A formation of a surface vacancy-adatom pair, or their recombination B association or dissociation of adatoms with an atomic cluster and cluster diffusion C diffusion of a surface vacancy, especially toward the lattice step D falling off a lattice step of an adatom E diffusion of a substitutional or interstitial impurity atom and its interaction with an adatom F diffusion of an adatom and its long range interactions with other adatoms G diffusion, dissociation and activation of a ledge atom H dissociation and activation of a kink atom into an adatom, a ledge atom, or an adatom on the layer above.

Following a similar line of reasoning, we find from the equilibrium condition of the pairing reaction B+V = [B, V] for the pairing of vacancies with impurities B in the A matrix... 

Various kinds of packing defects exist in the ionic crystals of NaCl type. A pair of cation and anion may be shifted from their stable positions toward the surface of the crystal, thus leaving behind a pair of vacancies. This is called the Schottky defect. The cation may leave its stable position and enter into an interstitial site. The formation of an interstitial cation and a vacancy is called the Frenkel defect. In addition to these two common kinds of defects, the presence of impurity atoms, atoms of varied valence, vacancies, and/or interstitial atoms is also possible. Some other important defects are discussed below. 

If we represent the quasi-bound state of the rapidly exchanging (on average 1/e times) vacancy and impurity atom with the position of a bond of the original lattice, then the vacancy-tracer pair walks... 

Let us say a few words on non-selective techniques which have been employed in the study of Li+ systems [93,152]. If this impurity moves off-centre in a alkali halide lattice the pair formed by the positive vacancy and the Li+ ion gives rise to an electric dipole, p. It is well known that free dipoles under an applied electric field, E, tend to place p parallel to E while thermal disorder is opposed to this effect. For this reason, if the average value of p at a given temperature is designated by... 

The first two reactions give sigmoid ur-time curves that are well expressed by the Prout-Tompkins equation. These are believed to involve a branching-chain mechanism. The third process is fitted by the contracting volume equation, possibly due to decomposition through ion-pair evaporation. The thermal stabihty of N02CJ04 is decreased [42] by the incorporation of impurities which increase the mnnber of cation vacancies, whereas the creation of anion vacancies has the opposite effect. 

Note that in LRC, the stable Frenkel pairs may be formed (e.g., under irradiation). The energy spectrum of Frenkel pair formation is somewhat spread due to the spread in energies of vacancies and interstitials formation. The width of this spectrum as well as variations in energy of vacancies and interstitials formation may amount to some eV, and the typical values of the threshold energy of Frenkel pair formation in metallic glasses as well as in crystals may amount to about 25-30 eV. To point defects of a cluster one may attribute also the interstitial and substitutional impurities that locally break the topological and compositional order. 

Silver vacancies and interstitials are formed in pairs in a pure, perfect, single crystal so that njny = 1. This ratio can be altered by doping with polyvalent impurities that require charge compensation by Frenkel defects in order to maintain charge neutrality in the host lattice. At room temperature, (CF)1/2 is approximately 1012/cm3 in AgCl and 1014/cm3 in AgBr(10) and,... 

Donors and acceptors exist in silver halides both as intrinsic and extrinsic centers. Ionized donors have been identified as interstitial silver ions and substitutional uncompensated divalent cation impurities from their IR spectra [77-79]. Ionized acceptors are probably halide ions surrounding silver ion vacancies [74,80,81] and possibly some incompletely compensated substitutional divalent anion impurities such as sulfide or selenide. Carriers trapped at donors and acceptors can undergo radiative recombination by tunneling if the spatial separation of the donor-acceptor pair is not too large [6,82], The emission energy of a donor-acceptor (D-A) pair separated by a distance r in an isotropic medium is given by... 

---