Sites normal/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... 

As already illustrated, it is also possible to imagine a defect related to ions in interstices, that is, interstitials. Such defects were first suggested as being of importance by Frenkel and are known as Frenkel defects. In this case, an atom or ion from one sublattice moves to a normally empty site (an interstitial site) in the crystal, leaving a vacancy behind (Fig. IA5b). A Frenkel defect may involve either the... 

Figure 2. Description of the initial and boundary conditions for the hydrogen diffusion problem in the pipeline. The parameter / denotes hydrogen flux and C,(P) is normal interstitial lattice site hydrogen concentration at the inner wall-surface of the pipeline in equilibrium with the hydrogen gas pressure P as it increases to 15 MPa in 1 sec. At time zero, the material is hydrogen free,...

Another type of lattice defect for elements is interstitial atoms, in which an atom is transferred from a regular lattice point to an interstitial position, normally unoccupied by an atom. Consider a crystal which has N atoms sited on regular lattice points and N, atoms sited on interstitial lattice points (the number of interstitial lattice points is A, which is fixed by the crystal structure under consideration), by a similar calculation, the free energy increment from the ideal crystal is expressed as... 

Diffusion in interstitial solid solutions occurs by interstitially dissolved atoms jumping from one interstitial site to another. For an atom to move from one interstitial site to another, it must pass through a position where its potential energy is a maximum. The difference between the potential energy in this position and that in the normal interstitial site is the activation energy for diffusion and must be provided by thermal fluctuations. The overall diffusion rate is governed by an Arrhenius-type rate equation,... 

Point defects in a pure crystalline substance include vacancies, in which atoms are missing from lattice sites, and interstitials, in which atoms are inserted in sites different from their normal sites. In real crystals, a small fraction of the normal atom sites remain unoccupied. Such vacancies are called Schottky defects, and their concentration depends on temperature ... 

The second type of stoichiometric defect involves the movement of an ion on to an interstitial site. An interstitial site is a gap in the lattice, which is not a normal lattice site. The silver halides most commonly possess this type of defect, where the silver cation moves on to the interstitial site. The cation moves into a site in the centre of a cube of cations and anions, as shown in Figure 6.3. 

Whereas a pure molecular substance has a definite stoichiometry, this is not always true for solids. Defects in crystals can include vacancies (atoms missing from their expected sites) and interstitials (extra atoms in sites normally vacant in the unit cell). An imbalance of defects involving different elements can introduce nonstoichiometry. This is common in compounds of transition metals, where variable oxidation states are possible (see Topics D5 and H4). For example, the sodium tungsten bronzes are formulated as NaxW03, where x can have any value in the range 0-0.9. 

The kick-out mechanism is rather similar to the interstitialcy mechanism. In this case, a host self-interstitial atom diffuses around the lattice. When it reaches a substitutional impurity atom, the self-interstitial pushes the impurity atom into an adjacent interstitial site. The interstitial impurity then diffuses interstitially until it reverts back to a host lattice site by displacing a host atom. It is experimentally difficult to distinguish the kick-out mechanism from the interstitialcy mechanism. The generally accepted view is that the interstitial impurity atoms may tend to diffuse longer distances before returning to the normal lattice sites for the kick-out mechanism, whereas the impurity atoms tend to diffuse interstitially for a relatively short distance before going into the normal lattice sites for the interstitialcy mechanism. 

As a matter of fact, we can rarely come across a situation as ideal as this one in a natural environment. Other chemical elements often settle on a crystal lattice. These foreign elements can either occupy the lattice s normal sites (this is called a substitutional defect) or other sites in interstitial positiorrs. 

Delay in fracture apparently results because of the time required for hydrogen to diffuse to specific areas near a crack nucleus until the concentration reaches a damaging level. These specific areas are presumably arrays of imperfection sites produced by plastic deformation of metal just ahead of the crack. Hydrogen atoms preferably occupy such sites because they are then in a lower-energy state compared to their normal interstitial positions. The crack propagates discontinuously because plastic deformation occurs first, and then hydrogen dif-... 

To illustrate these, let us consider two isostmctural solids, NaCl and AgCl. Both these solids adopt the fee rock salt structure (Section V), with cep Cl and Na or Ag+ in the octahedral sites. In NaCl, Schottky defects are observed, with pairs of Na and Cl ions missing from their ideal lattice sites. As equal numbers of vacancies occur in the anion and cation sublattices, overall electroneutrality and stoichiometry are preserved. In AgCl a Frenkel defect is preferred with some of the silver ions displaced from their normal octahedral sites into interstitial tetrahedral sites. This leaves the anion sublattice intact, as for every cation vacancy introduced a cation interstitial is formed. The defects in AgCl and NaCl are illirstrated schematically in Figure 3.36. 

The idea of point defects in crystals goes back to Frenkel, who in 1926 proposed the existence of point defects to explain the observed values of ionic conductivity in crystalline solids. In a crystal of composition MX such as a monovalent metal halide or a divalent metal oxide or sulfide, volume ionic conductivity occurs by motion of positive or negative ions in the lattice under the influence of an electric field. If the crystal were perfect, imperfections, such as vacant lattice sites or interstitial atoms, would need to be created for ionic conductivity to occur. A great deal of energy is required to dislodge an ion from its normal lattice position and thus the current in perfect crystals would be very, very small under normal voltages. To get around this difficulty, Frenkel proposed that point defects existed in the lattice prior to the application of the electric field. This, of course, has been substantiated by subsequent work and the concept of point defects in all classes of solids, metals, ionic crystals, covalent crystals, semiconductors, etc., is an important part of the physics and chemistry of crystalline solids, not only with respect to ionic conductivity but also with respect to diffusion, radiation damage, creep, and many other properties. 

Solute atoms also interact with dislocations. Interstitial atoms are attracted to edge dislocations the interstitial sites located at the end of the extra plane can accommodate an interstitial atom more readily than a normal interstitial site in the lattice. Therefore there is a lowering of internal energy when an interstitial atom such as C in Fe... 

Figure 9.8 shows a two-dimensional representation of a crystal lattice with some common types of atomic point defects. A vacancy occurs when an atom is absent from a lattice site that is normally occupied. An interstitial occurs when an atom sits in a place in the crystal that is not a distinct lattice site, but rather in between lattice sites. Figure 9.8 shows two types of interstitials. A self-interstitial contains an atom of the same type that makes up the host crystal, while an impurity interstitial consists of a foreign atom. A substitutional impurity occurs when a foreign atom occupies a lattice site normally housed by a host atom. In compound solids, such as AB, we can have misplaced atoms, where species A sits in a B site or vice versa. 

In pure and stoichiometric compounds, intrinsic defects are formed for energetic reasons. Intrinsic ionic conduction, or creation of thermal vacancies by Frenkel, ie, vacancy plus interstitial lattice defects, or by Schottky, cation and anion vacancies, mechanisms can be expressed in terms of an equilibrium constant and, therefore, as a free energy for the formation of defects, If the ion is to jump into a normally occupied lattice site, a term for... 

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