Point defects interstitial

No material is completely pure, and some foreign atoms will invariably be present. If these are undesirable or accidental, they are termed impurities, but if they have been added deliberately, to change the properties of the material on purpose, they are called dopant atoms. Impurities can form point defects when present in low concentrations, the simplest of which are analogs of vacancies and interstitials. For example, an impurity atom A in a crystal of a metal M can occupy atom sites normally occupied by the parent atoms, to form substitutional point defects, written AM, or can occupy interstitial sites, to form interstitial point defects, written Aj (Fig. 1.4). The doping of aluminum into silicon creates substitutional point defects as the aluminum atoms occupy sites normally filled by silicon atoms. In compounds, the impurities can affect one or all sublattices. For instance, natural sodium chloride often contains... 

An exactly similar situation can be envisaged if the crystal contains a high population of interstitial point defects. Should these aggregate onto a single plane, a dislocation loop will once again form (Fig. 3.14c). 

The preceding analysis provides a powerful method for determining the diffusivities of species that produce an anelastic relaxation, such as the split-dumbbell interstitial point defects. A torsional pendulum can be used to find the frequency, u>p, corresponding to the Debye peak. The relaxation time is then calculated using the relation r = 1/ojp, and the diffusivity is obtained from the known relationships among the relaxation time, the jump frequency, and the diffusivity. For the split-dumbbell interstitials, the relaxation time is related to the jump frequency by Eq. 8.63, and the expression for the diffusivity (i.e., D = ra2/12), is derived in Exercise 8.6. Therefore, D = a2/18r. This method has been used to determine the diffusivities of a wide variety of interstitial species, particularly at low temperatures, where the jump frequency is low but still measurable through use of a torsion pendulum. A particularly important example is the determination of the diffusivity of C in b.c.c. Fe, which is taken up in Exercise 8.22. 

Solution. Using a torsion pendulum, find the anelastic relaxation time, r, by measuring the frequency of the Debye peak, cup, and applying the relation cupr = 1. Having r, the relationship between r and the C atom jump frequency F is found by using the procedure to find this relationship for the split-dumbbell interstitial point defects in Exercise 8.5. Assume the stress cycle shown in Fig. 8.16 and consider the anelastic relaxation that occurs just after the stress is removed. A C atom in a type 1 site can jump into two possible nearest-neighbor type 2 sites or two possible type 3 sites. Therefore,... 

If the vacancies are subsaturated, the dislocation tends to produce vacancies and therefore acts as a vacancy source. In that case, Eq. 11.5 will still hold, but fiy will be negative and the climb force and climb direction will be reversed. Equation 11.5 also holds for interstitial point defects, but the sign of will be reversed. 

The existence of free interstitial point defects forming the complements to the vacancy centers is generally not observed following irradiation at room temperature. At these temperatures the interstitials cluster together to form interstitial aggregates and dislocation loops. However, lattice disorder can slow down or prevent the aggregation process due to interstitial trapping. 

Figure 8.3a displays a simplified block model of a metal oxide surface showing one-dimensional defects in the form of steps. These steps in turn give rise to point defects in the form of kink sites. Terraces can also possess a variety of different surface sites such as adatoms, vacancies, and substitutional and interstitial point defects. Figure 8.3b shows that the... 

The addition of substitutional and interstitial point defects can also introduce additional energy levels. Using MgO as our example let us consider the incorporation of AI2O3. There are two defect reactions we can envision ... 

Dislocation theory as a portion of the subject of solid-state physics is somewhat beyond the scope of this book, but it is desirable to examine the subject briefly in terms of its implications in surface chemistry. Perhaps the most elementary type of defect is that of an extra or interstitial atom—Frenkel defect [110]—or a missing atom or vacancy—Schottky defect [111]. Such point defects play an important role in the treatment of diffusion and electrical conductivities in solids and the solubility of a salt in the host lattice of another or different valence type [112]. Point defects have a thermodynamic basis for their existence in terms of the energy and entropy of their formation, the situation is similar to the formation of isolated holes and erratic atoms on a surface. Dislocations, on the other hand, may be viewed as an organized concentration of point defects they are lattice defects and play an important role in the mechanism of the plastic deformation of solids. Lattice defects or dislocations are not thermodynamic in the sense of the point defects their formation is intimately connected with the mechanism of nucleation and crystal growth (see Section IX-4), and they constitute an important source of surface imperfection. 

A point defect refers to a localized defect (such as a monovacancy) or impurity (such as interstitial O). This includes any relaxation and/or distortion of the crystal around it. Many point defects are now ratlier well understood, especially in Si, tlranks to a combination of experiments providing infonnation of microscopic nature... 

Point defects and complexes exliibit metastability when more than one configuration can be realized in a given charge state. For example, neutral interstitial hydrogen is metastable in many semiconductors one configuration has H at a relaxed bond-centred site, bound to the crystal, and the other has H atomic-like at the tetrahedral interstitial site. 

In addition to the configuration, electronic stmcture and thennal stability of point defects, it is essential to know how they diffuse. A variety of mechanisms have been identified. The simplest one involves the diffusion of an impurity tlirough the interstitial sites. For example, copper in Si diffuses by hopping from one tetrahedral interstitial site to the next via a saddle point at the hexagonal interstitial site. 

However, most impurities and defects are Jalm-Teller unstable at high-symmetry sites or/and react covalently with the host crystal much more strongly than interstitial copper. The latter is obviously the case for substitutional impurities, but also for interstitials such as O (which sits at a relaxed, puckered bond-centred site in Si), H (which bridges a host atom-host atom bond in many semiconductors) or the self-interstitial (which often fonns more exotic stmctures such as the split-(l lO) configuration). Such point defects migrate by breaking and re-fonning bonds with their host, and phonons play an important role in such processes. 

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. 9. Schematic of a two-dimensional cross section of an AgBr emulsion grain showing the surface and formation of various point defects A, processes forming negative kink sites and interstitial silver ions B, positive kink site and C, process forming a silver ion vacancy at a lattice position and positive kink...

A crystalline solid is never perfect in that all of tire lattice sites are occupied in a regular manner, except, possibly, at the absolute zero of temperature in a perfect crystal. Point defects occur at temperatures above zero, of which the principal two forms are a vacant lattice site, and an interstitial atom which... 

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... 

One feature of oxides is drat, like all substances, they contain point defects which are most usually found on the cation lattice as interstitial ions, vacancies or ions with a higher charge than dre bulk of the cations, refened to as positive holes because their effect of oxygen partial pressure on dre electrical conductivity is dre opposite of that on free electron conductivity. The interstitial ions are usually considered to have a lower valency than the normal lattice ions, e.g. Zn+ interstitial ions in the zinc oxide ZnO structure. 

The third term in Eq. 7, K, is the contribution to the basal plane thermal resistance due to defect scattering. Neutron irradiation causes various types of defects to be produced depending on the irradiation temperature. These defects are very effective in scattering phonons, even at flux levels which would be considered modest for most nuclear applications, and quickly dominate the other terms in Eq. 7. Several types of in-adiation-induced defects have been identified in graphite. For irradiation temperatures lower than 650°C, simple point defects in the form of vacancies or interstitials, along with small interstitial clusters, are the predominant defects. Moreover, at an irradiation temperatui-e near 150°C [17] the defect which dominates the thermal resistance is the lattice vacancy. 

At the beginning of the century, nobody knew that a small proportion of atoms in a crystal are routinely missing, even less that this was not a mailer of accident but of thermodynamic equilibrium. The recognition in the 1920s that such vacancies had to exist in equilibrium was due to a school of statistical thermodynamicians such as the Russian Frenkel and the Germans Jost, Wagner and Schollky. That, moreover, as we know now, is only one kind of point defect an atom removed for whatever reason from its lattice site can be inserted into a small gap in the crystal structure, and then it becomes an interstitial . Moreover, in insulating crystals a point defect is apt to be associated with a local excess or deficiency of electrons. 

Investigations based on equation (a) are indirect. Direct structural studies using diffraction techniques (X-ray or neutron), or electron microscopy, while they cannot detect the low concentrations of defects present in NiO or CoO are indispensible to the study of grossly non-stoichiometric oxides like FeO, TiOj, WOj etc., and particularly electron microscopes with a point-to-point resolution of about 0.2 nm are widely used. The first direct observation of a point defect (actually a complex of two interstitial metal atoms, and two oxygen atoms in Nb,2029) was made" using electron microscopy. 

The smallest imperfections in metal crystals are point defects, in particular vacant lattice sites (vacancies) and interstitial atoms. As illustrated in Fig. 20.21a, a vacancy occurs where an atom is missing from the crystal structure... 

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