Vacancy-interstitial defects

Alan Allnatt s research interests at Western Ontario have been concerned with the statistical mechanics of the transport of matter through crystals. His earliest work centered on obtaining methods for calculating the equilibrium distributions and thermodynamic properties of the point defects (vacancies, interstitials, solutes) that make transport possible. He first studied dilute systems, so the methods could be largely analytical. The methods for ionic crystals,... 

Figure 12.8 Binary ionic crystal showing defects that can lead to lattice diffusion, (a) Frenkel defect vacancy-interstitial pair), (b) Schottky defect (anion-cation vacancy). (After Kingery ct a .. 1976.)...

The electrochemical growth of a continuous and homogeneous film can be well thought-out as a result of the migration of metallic cations by means of one of the above-mentioned transport processes. It is worthy to note that the dislocation of ions breeds defects (vacancies, interstitial ions, etc.). Hence, either the dislocation of defects or the migration of atoms can be used to describe the transport process [1], Mathematical details are found in the cited references and also in the reviews [2,3]. 

Point lattice defects vacancies, interstitials,and substitutional elements... 

Ionic transport in crystals usually involves migration of defects (vacancies, interstitial ions, interstitial pairs). Haven and Verkerk [46] argued that when the ionic motion involves defect mechanisms the experimental difihision coefficient, D, is different (because of correlation effects) from the calculated one, D, which obeys the Nemst-Einstein equation... 

As in any semiconductors, point defects affect the electrical and optical properties of ZnO as well. Point defects include native defects (vacancies, interstitials, and antisites), impurities, and defect complexes. The concentration of point defects depends on their formation energies. Van de WaHe et al. [86,87] calculated formation energies and electronic structure of native point defects and hydrogen in ZnO by using the first-principles, plane-wave pseudopotential technique together with the supercell approach. In this theory, the concentration of a defect in a crystal under thermodynamic equilibrium depends upon its formation energy if in the following form ... 

Define the following point defects and identify them as atomic defects or electronic defects vacancy, interstitial, substitutional impurity, misplaced atoms, electron, hole, dopant. 

Materials that contain defects and impurities can exhibit some of the most scientifically interesting and economically important phenomena known. The nature of disorder in solids is a vast subject and so our discussion will necessarily be limited. The smallest degree of disorder that can be introduced into a perfect crystal is a point defect. Three common types of point defect are vacancies, interstitials and substitutionals. Vacancies form when an atom is missing from its expected lattice site. A common example is the Schottky defect, which is typically formed when one cation and one anion are removed from fhe bulk and placed on the surface. Schottky defects are common in the alkali halides. Interstitials are due to the presence of an atom in a location that is usually unoccupied. A... 

Fig. 1.6 Poinl defects (a) vacancies (Schotlky defects) (6) interstitials (Frenkel defects) (c) ideal crystal.

The defects generated in ion—soHd interactions influence the kinetic processes that occur both inside and outside the cascade volume. At times long after the cascade lifetime (t > 10 s), the remaining vacancy—interstitial pairs can contribute to atomic diffusion processes. This process, commonly called radiation enhanced diffusion (RED), can be described by rate equations and an analytical approach (27). Within the cascade itself, under conditions of high defect densities, local energy depositions exceed 1 eV/atom and local kinetic processes can be described on the basis of ahquid-like diffusion formalism (28,29). 

The lattice may be distorted because of several reasons as vacancies, interstitials, dislocations and impurities. These lattice defects cause the so-called impurity scattering which produces the term i ei. At low temperatures, i ei is the constant electronic thermal resistance typical of metals. 

Figure 1.1 Defects in crystalline solids (a) point defects (interstitials) (b) a linear defect (edge dislocation) (c) a planar defect (antiphase boundary) (d) a volume defect (precipitate) (e) unit cell (filled) of a structure containing point defects (vacancies) and (/) unit cell (filled) of a defect-free structure containing ordered vacancies. ...

Introduction of defects (vacancies or interstitials) in a perfect lattice determines a variation in the free energy G of the lattice which may be written as ... 

N is here the number of lattice defects (vacancies or interstitials) which are responsible for non-stoichiometry. AHfon is the variation of lattice enthalpy when one noninteracting lattice defect is introduced in the perfect lattice. Since two types of point-defects are always present (lattice defect and altervalent cations (electronic disorder)), the AHform takes into account not only the enthalpy change due to the process of introduction of the lattice defect in the lattice, but also that occurring in the Redox reaction creating the electronic disorder. 

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

Equation (1.44) states that the structural energy increases associated with the creation of defects are offset by entropy increases. The entropy is the number of ways the defects (both interstitials and vacancies) can be arranged within the perfect lattice, and it can be approximated using statistical thermodynamics as... 

Figure 5.44 depicts the central section of a possible defect cluster for FeO. (a) Determine the vacancy interstitial ratio for this cluster, (b) Assuming that this section is surrounded by Fe ions and oxide ions in octahedral sites as in the Koch-Cohen cluster, determine the formula of a sample made totally of such clusters, (c) Determine the numbers of Fe and Fe ions in octahedral sites. 

The lattice defects are classified as (i) point defects, such as vacancies, interstitial atoms, substitutional impurity atoms, and interstitial impurity atoms, (ii) line defects, such as edge, screw, and mixed dislocations, and (iii) planar defects, such as stacking faults, twin planes, and grain boundaries. 

The properties of the wide band-gap semiconductor SiC have been extensively studied by HFEPR because knowledge of the defect states is needed for its application in high power and radiation resistant devices. (The main method of doping SiC is by ion implantation that inevitably also introduces defects into the lattice.) The primary defects that can be produced are vacancies, interstitials and anti-sites. In contrast to silicon the primary defects in SiC seem to be stable at and even far above room temperature. 

The resulting equilibrium concentrations of these point defects (vacancies and interstitials) are the consequence of a compromise between the ordering interaction energy and the entropy contribution of disorder (point defects, in this case). To be sure, the importance of Frenkel s basic work for the further development of solid state kinetics can hardly be overstated. From here on one knew that, in a crystal, the concentration of irregular structure elements (in thermal equilibrium) is a function of state. Therefore the conductivity of an ionic crystal, for example, which is caused by mobile, point defects, is a well defined physical property. However, contributions to the conductivity due to dislocations, grain boundaries, and other non-equilibrium defects can sometimes be quite significant. 

Irradiation of all kinds of solids (metals, semiconductors, insulators) is known to produce pairs of the point Frenkel defects - vacancies, v, and interstitial atoms, i, which are most often spatially well-correlated [1-9]. In many ionic crystals these Frenkel defects form the so-called F and H centres (anion vacancy with trapped electron and interstitial halide atom X° forming the chemical bonding in a form of quasimolecule X2 with some of the nearest regular anions, X-) - Fig. 3.1. In metals the analog of the latter is called the dumbbell interstitial. 

It should be remembered that even for isotropic defects their elastic interaction is anisotropic, due to crystalline anisotropy, equation (3.1.4). A pair of the simplest Frenkel defects - vacancy and an interstitial atom - attract each other in the direction (100), but their interaction becomes repulsive, e.g., along (111) and (101) axes. 

Up to now we have been discussing in this Chapter many-particle effects in bimolecular reactions between non-interacting particles. However, it is well known that point defects in solids interact with each other even if they are not charged with respect to the crystalline lattice, as it was discussed in Section 3.1. It should be reminded here that this elastic interaction arises due to overlap of displacement fields of the two close defects and falls off with a distance r between them as U(r) = — Ar 6 for two symmetric (isotropic) defects in an isotropic crystal or as U(r) = -Afaqjr-3, if the crystal is weakly anisotropic [50, 51] ([0 4] is an angular dependent cubic harmonic with l = 4). In the latter case, due to the presence of the cubic harmonic 0 4 an interaction is attractive in some directions but turns out to be repulsive in other directions. Finally, if one or both defects are anisotropic, the angular dependence of U(f) cannot be presented in an analytic form [52]. The role of the elastic interaction within pairs of the complementary radiation the Frenkel defects in metals (vacancy-interstitial atom) was studied in [53-55] it was shown to have considerable impact on the kinetics of their recombination, A + B -> 0. 

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