Interstitial defects

AUan N L and W C Mackrodt 1994. Oxygen Interstitial Defects in High-T Oxides. Molecular Simnlat 12 89-100. 

The vacant sites will be distributed among the N lattice sites, and the interstitial defects on the N interstitial sites in the lattice, leaving a conesponding number of vacancies on die N lattice sites. In the case of ionic species, it is necessaty to differentiate between cationic sites and anionic sites, because in any particular substance tire defects will occur mainly on one of the sublattices that are formed by each of these species. In the case of vacant-site point defects in a metal, Schottky defects, if the number of these is n, tire random distribution of the n vacancies on the N lattice sites cair be achieved in... 

When there are ti interstitial defects distributed on N sites each requiring E l energy of formation, the equilibrium number of these at temperature T is given by... 

Lattice Vacancies and Interstitials Defects such as lattice vacancies and interstitials fall into two main categories intrinsic defects, which are present in pure crystal at thermodynamic equilibrium, and extrinsic defects, which are created when a foreign atom is inserted into the lattice. 

The effect of adsorption on concentration of the surface and volume interstitial defects in semiconductor adsorbent and resultant change in electric conductivity... 

The method can be illustrated by reference to a classical 1933 study of the defects present in wilstite, iron monoxide. Wustite adopts the sodium chloride (NaCl) structure, and the unit cell should contain 4 Fe and 4 O atoms in the unit cell, with an ideal composition FeOi.o, but in reality the composition is oxygen rich and the unit cell dimensions also vary with composition (Table 1.1). Because there is more oxygen present than iron, the real composition can be obtained by assuming either that there are extra oxygen atoms in the unit cell (interstitial defects) to give a composition FcO 1 +v, or that there are iron vacancies present, to give a formula Fci-JD. It is... 

For example, the formation of an intrinsic interstitial defect requires the simultaneous creation of a vacancy. These may not remain close together in the crystal, and it is legitimate to consider that the two defects occur in equal numbers. Thus, in silicon it is possible to write the formation equation for silicon self-interstitials, Sii as... 

Because the configurational entropy of interstitial defects has the same form as that of vacancies, a population of self-interstitial atoms is also thermodynamically stable. The creation of these defects can then also be treated as a pseudochemical equilibrium, and an equation for the relationship between the number of self-interstitials and the appropriate equilibrium constant for interstitial generation, Kv is readily... 

Figure 4.9 Clusters in the fluorite structure (a, b) transformation of a cube into a square antiprism (c, d) transformation of a cube into a cuboctahedron (e) a single square antiprism formed by tbe creation of < 110> interstitial defects (/) an M6F36 cluster in a fluorite structure matrix. Cations in the plane of tbe section are represented by smaller spheres anions above and below the plane are represented by larger spheres.

In terms of formal point defect terminology, it is possible to think of each silver or copper ion creating an instantaneous interstitial defect and a vacancy, Ag and VAg, or Cu and Vcu as it jumps between two tetrahedral sites. This is equivalent to a high and dynamic concentration of cation Frenkel defects that continuously form and are eliminated. For this to occur, the formation energy of these notional defects must be close to zero. 

In summary, non-stoichiometric compounds are found to exist over a range of composition, and throughout that range the unit cell length varies smoothly with no change of symmetry. It is possible to determine whether the non-stoichiometry is accommodated by vacancy or interstitial defects using density measurements. 

FIGURE 5.27 (a) The fluorite structure of UO2 with a unit cell marked in bold, (b) Interstitial defect cluster in U02+jf. Uranium positions... 

Interstitialcy migration depends on the geometry of the interstitial defect. However, an a priori prediction of interstitial defect geometry is not straightforward in real materials. For an f.c.c. crystal, a variety of conceivable interstitial defect candidates are illustrated in Fig. 8.5. The lowest-energy defect will be stable and predominant. For example, in the f.c.c. metal Cu, the stable configuration is the (100) split-dumbbell configuration in Fig. 8.5d [3]. 

The (100) split-dumbbell defect in Fig. 8.5d, while having the lowest energy of all interstitial defects, still has a large formation energy (Ef = 2.2 eV) because of the large amount of distortion and ion-core repulsion required for its insertion into the close-packed Cu crystal. However, once the interstitial defect is present, it persists until it migrates to an interface or dislocation or annihilates with a vacancy. The... 

Figure 8.4 Substitutional diffusion by the interstitialcy mechanism, (a) The interstitial defect corresponding to the interstitial atom (3) is separated from a particular substitutional atom B (shaded), (b) The interstitial defect moved adjacent to B when the previously interstitial atom (3) replaced the substitutional atom (2). (2) then became the interstitial atom, (c) Atom (2) has replaced B, and B has become the interstitial atom, (d) B has replaced atom (4). which has become the interstitial atom, (e) The interstitial defect has migrated away from B. As a result. B has completed one nearest-neighbor jump and the interstitial defect has moved at least four times.

Figure 8.5 Geometric configurations for a self-interstitial defect atom in an f.c.c. crystal (a) octahedral site, (b) tetrahedral site, (c) (110) crowdion, (d) (100) split, dumbbell, (e) (111) split., (f) (110) split crowdion [2].

Schottky defects are the predominant equilibrium point defects in stoichiometric zirconia ZrC>2 (see Exercise 8.15). Suppose that the soluble oxide Ta2C>5 is added to ZrCV Assume that cation vacancies form without the formation of any interstitial defects. 

To our knowledge there have been no reported measurements of equilibrium defect concentrations in soft-sphere models. Similarly, relatively few measurements have been reported of defect free energies in models for real systems. Those that exist rely on integration methods to connect the defective solid to the perfect solid. In ab initio studies the computational cost of this procedure can be high, although results have recently started to appear, most notably for vacancies and interstitial defects in silicon. For a review see Ref. 109. 

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