Crystal, defect, point

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... 

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. 

Issues associated with order occupy a large area of study for crystalline matter [1, 7, 8]. For nearly perfect crystals, one can have systems with defects such as point defects and extended defects such as dislocations and grain... 

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. 

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... 

The physical properties of tellurium are generally anistropic. This is so for compressibility, thermal expansion, reflectivity, infrared absorption, and electronic transport. Owing to its weak lateral atomic bonds, crystal imperfections readily occur in single crystals as dislocations and point defects. 

The effect of different types of comonomers on varies. VDC—MA copolymers mote closely obey Flory s melting-point depression theory than do copolymers with VC or AN. Studies have shown that, for the copolymers of VDC with MA, Flory s theory needs modification to include both lamella thickness and surface free energy (69). The VDC—VC and VDC—AN copolymers typically have severe composition drift, therefore most of the comonomer units do not belong to crystallizing chains. Hence, they neither enter the crystal as defects nor cause lamellar thickness to decrease, so the depression of the melting temperature is less than expected. 

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. 

Crystal structure, crystal defects and chemical reactions. Most chemical reactions of interest to materials scientists involve at least one reactant in the solid state examples inelude surfaee oxidation, internal oxidation, the photographie process, electrochemieal reaetions in the solid state. All of these are critieally dependent on crystal defects, point defects in particular, and the thermodynamics of these point defeets, especially in ionic compounds, are far more complex than they are in single-component metals. I have spaee only for a superficial overview. 

Fig. 5.20. The shock-induced polarization of a range of ionic crystals is shown at a compression of about 30%. This maximum value is well correlated with cation radius, dielectric constant, and a factor thought to represent dielectric strength. A mechanically induced point defect generation and migration model is preferred for the effect (after Davison and Graham [79D01]).

T. Sinno, R. A. Brown, W. Van Ammon, E. Dornberger. Point defect dynamics and the oxidation-induced stacking-fault ring in Czochralski-grown silicon crystals. J Electrochem Soc 145 302, 1998. 

The presence of small concentrations of point defects changes the density of a crystal, and four values of the density can be calculated, depending on... 

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... 

Point defects are always present in every material in thermodynamic equilibrium. Considering the formation of n vacancies, the increase in configuration entropy is determined by the number of different possible ways of taking n atoms out of the crystal comprising N atoms in total. This number, c1, is given by... 

Jacobs et al. [59,925,926] (Fig. 17). While this scheme conveniently summarizes many features of the observed behaviour, a number of variations or modifications of the mechanisms indicated have been proposed. Maycock and Pai Vemeker [924,933] emphasize the possible role of point defects and suggest, on the evidence of conductivity measurements, that the initial step may be the transfer of either a proton or an electron. Boldyrev et al. [46] suggest that proton conduction permits rapid migration of HC104 within the reactant and this undergoes preferential decomposition in distorted regions. More recently, the ease of proton transfer and the mobilities of other species in or on AP crystals have been investigated by a.c. [360] and d.c. [934] conductivity measurements. Owen et al. [934] could detect no surface proton conductivity and concluded that electron transfer was the initial step in decomposition. At the present time, these inconsistencies remain unresolved. 

It should be clear that the presence of line defects in a crystal lattice leads to a disruption of the continuity of the lattice just as the presence of point defects affects the packing of a given lattice. The line defect. 

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