Point defect: also equilibrium

Figure 11.15b also shows an interesting way of extrapolating the equilibrium hole fraction h T,P = 0) to lower temperatures. When considering the vacancies of the S-S lattice as Schottky point defects, their equilibrium concentration heq may be expressed by the Schottky equation. 

In this section, the phenomenon of point defects, such as vacancies and interstitial, in crystals is briefly introduced. The oxide entropy change (A5) increases when more points defects, also known a imperfections, generate within a crystal. Metal oxides at equilibrium may contain nearly equal numbers of cations and anion vacancies. Thus, the number of point defects (n) producing a minimum free energy change, AG = AHf — TAS, can be modeled by the Arrhenius law [21-23]... 

The doped semiconductor materials can often be considered as well-characterized, diluted solid solutions. Here, the solutes are referred to as point defects, for instance, oxygen vacancies in TiC - phase, denoted as Vq, or boron atoms in silicon, substituting Si at Si sites, Bj etc. See also -> defects in solids, -+ Kroger-Vink notation of defects. The atoms present at interstitial positions are also point defects. Under stable (or metastable) thermodynamic equilibrium in a diluted state, - chemical potentials of point defects can be defined as follows ... 

Balanced populations of point defects do not alter the anion to cation ratio, or overall stoichiometry of the crystal. In addition, the numbers of such defects must be such as to maintain charge neutrahty. Calculations similar to those for monatomic solids show that the free energy of crystals containing such balanced populations of point defects is lower than that for a defect-free crystal, and these defects are also intrinsic defects, occurring in pure crystals under equilibrium conditions at all temperatures above OK. Two important examples of such balanced point defect populations have been described. 

Virtually all minerals contain defects. In addition to point defects (e.g., vacancies that exist in a thermodynamically determined equilibrium number, impurities etc ), macroscopic minerals contain line defects (dislocations), and planar defects such as stacking foults, antiphase boundaries and twins. Intergrown layers of different structure or composition, and polytypic disorder also may be present. 

Point defects are important in conferring mobility on crystal components. They also increase the entropy of a crystal and there is always a small equilibrium concentration present that can be calculated by thermodynamic methods [24]. 

Line defects in a crystalline material are known as dislocations. Dislocations are formed due to nonequilibrium conditions such as ion implantation and thermal processing. Under equilibrium conditions, there is no requirement for the presence of dislocations or any other defect (except native point defects) in the crystal. An edge dislocation may be viewed also as having an extra half-plane inserted into the crystal (see Fig. 9.9). 

In addition to a vacancy-driven process, diffusion under irradiation may also be enhanced by the formation and diffusion of other point defects, such as selfinterstitials, divacancies, and other defect aggregates, which are not present under equilibrium conditions. A general statement for the atomic diffusion coefficient can be written in terms of the various point defects as... 

Kink, step, and terrace atoms have large equilibrium con central Ions on any real surface. On a rough surface, 10-20% of the atoms are often in tjtcp sites, with about 5% in kink sites. Steps and kinks are also called line rff/t t fj. to distinguish them from atomic vacancies, or adatoms, which arc called poittt dejects. These point defects arc also present in most surfaces and are important participants of atom transport along die surface, although their equilibrium concent rat ions are much less than 1 % of a monolayer even at the melting point. Thus the available data indicate... 

Surfaces are heterogeneous on the atomic scale. Atoms appear in flat terraces, at steps, and at kinks. There are also surface point defects, vacancies, and adatoms. These various surface sites achieve their equilibrium surface concentrations through an atom-transport process along the surface that we call surface diffusion. Adsorbed atoms and molecules reach their equilibrium distribution on the surface in the same way. This view of surface diffusion as a site-to-site hopping process leads to the random-walk picture, in which the mean-square displacement of the adsorbed particle along the. r-component of the coordinate is given by... 

The direct method includes direct observation by electron microscope and field emission technique structural analysis using X-ray, neutron and electron diffractometry, or channelling technique and also resonance techniques such as ESR, NMR, and Mossbauer absorption. The techniques used in the indirect method include the measurement of a property sensitive to the nonstoichiometric composition, such as lattice constant, density, equilibrium partial pressure, and electric conductivity. The defect structure is estimated from the correspondence between the defect model assumed and the measured change of the property. With the indirect method, it is rather difficult to estimate defect structures more complex than the simple point defect. 

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