Crystal, defect, point lattice

As in crystals, defects in liquid crystals can be classified as point, line or wall defects. Dislocations are a feature of liquid crystal phases where tliere is translational order, since tliese are line defects in tliis lattice order. Unlike crystals, tliere is a type of line defect unique to liquid crystals tenned disclination [39]. A disclination is a discontinuity of orientation of tire director field. 

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. 

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... 

So important are lattice imperfections in the reactions of solids that it is considered appropriate to list here the fundamental types which have been recognized (Table 1). More complex structures are capable of resolution into various combinations of these simpler types. More extensive accounts of crystal defects are to be found elsewhere [1,26,27]. The point which is of greatest significance in the present context is that each and every one of these types of defect (Table 1) has been proposed as an important participant in the mechanism of a reaction of one or more solids. In addition, reactions may involve structures identified as combinations of these simplest types, e.g. colour centres. The mobility of lattice imperfections, which notably includes the advancing reaction interface, provides the means whereby ions or molecules, originally at sites remote from crystal imperfections and surfaces, may eventually react. 

The line widths and shapes to be expected for cubic crystals containing point defects have been derived by Cohen and Reif for both first and second order quadrupole interaction 97). In particular, for point defect concentrations greater than about 0.1 (in terms of probability /, of a lattice site being occupied by a defect) distributed in a random fashion over various possible lattice sites, the second order interaction gives rise to a lopsided central component whose shape is given by (97)... 

When crystals of mercury fulminate are heated at lower temperatures the decomposition reaction is localized mainly around lattice defects such as growth marks on the surface of crystals or points where dislocations emerge at the surface (Fig. 32(c)). 

So far, only normal diffraction (with sharp maxima at the points of reciprocal lattice) has been mentioned. Investigation of background scattering can provide extended information on various kinds of crystal defects (well beyond stacking faults and the like) as has been demonstrated e.g. on metal and feldspar structures. 

Defects which have extent of only about an atomic diameter also exist in crystals—the point defects. Vacant lattice sites may occur—vacancies. Extra atoms—interstitials—may be inserted between regular crystal atoms. Atoms of the wrong chemical species—impurities—also may be present. 

Crystals contain two major categories of defect point defects and line defects. Point defects occur where atoms are missing (vacancies) or occupy the interstices between normal sites (interstitials) foreign atoms are also point defects. Line defects, or dislocations, are spatially extensive and involve disturbance of the periodicity of the lattice. 

The specific heat of a semiconductor has contributions from lattice vibrations, free carriers and point and extended defects. For good quality semi-insulating crystals only the lattice contribution is of major significance. Defect-free crystals of group III nitrides are difficult to obtain, and thus the specific heat measurements are affected by the contributions from the free carriers and the defects. While the specific heat of AIN is affected by the contribution of oxygen impurities, the data for GaN and InN are affected by free electrons, especially at very low temperatures. 

There are two types of lattice defects that occur in all real crystals and at very high concentration in irradiated crystals. These are known as point defects and line defects. Point defects occur as the result of displacements of atoms from their normal lattice sites. The displaced atoms usually occupy sites that are not in the lattice framework they are then known as interstitials. The empty lattice site left behind by the interstitial is called a vacancy. Avacancy produced by displacement of an anion or cation, along with its interstitial ion, is called a Frenkel pair, or simply a... 

Local crystal defects called point defects, appear as either impurity atoms or gaps in the lattice. Impurity atoms can occur in the lattice either at interstitial sites (between atoms in a non-lattice site) or at substitutional sites (replacing an atom in the host lattice). Lattice gaps are called vacancies and arise when an atom is missing fi om its site in the lattice. Vacancies are sometimes called Schottky defects. A vacancy in which the missing atom has moved to an interstitial position is known as a Frenkel defect. 

A suitable classification of crystalline defects can be achieved by first considering the so-called point defects and then proceeding to higher-dimensional defects. Point defects are atomic defects whose effect is limited only to their immediate surroundings. Examples are vacancies in the regular lattice, or interstitial atoms. Dislocations are classified as linear or one-dimensional defects. Grain boundaries, phase boundaries, stacking faults, and surfaces are two-dimensional defects. Finally, inclusions or precipitates in the crystal matrix can be classified as three-dimensional defects. 

Little is known about estimating the point defect energy of covalent crystals or molecular crystals. In the zeroth approximation one can proceed, as for ionic crystals, via the lattice energy Uj which can be estimated from the enthalpy of sublimation and the zero point energy. 

Defects in crystalline solids occur for structural reasons, because the atoms (or ions) are not arranged ideally in the crystal when all the lattice sites are occupied, and for chemical reasons, because inorganic compounds may deviate from the fixed composition determined by the valence of the atoms. There are different types of structural defects in a crystalline solid which are normally classified into three groups (1) point defects, (2) line defects, and (3) planar defects. Point defects are associated with one lattice point and its immediate vicinity. They include missing atoms or vacancies, interstitial atoms occupying the interstices between atoms, and substitutional atoms sitting on sites that would normally be occupied by another type of atom. These point defects are illustrated in Fig. 7.2 for an elemental solid (e.g., a pure metal). The point defects that are formed in pure crystals (i.e., vacancies and interstitials) are sometimes referred to as intrinsic or native defects. 

As discussed in Sec. 3.1.3 the presence of defects and impurities can promote loss in piezoelectric crystals. Defects are divided into two main groups, point and extended defects. The point defects include the aluminum-related centers as well as oxygen-vacancy centers. Aluminum ions can easily substitute for silicon in quartz however, charge compensation is required. Aluminum has a - -3 charge whereas the silicon valence is +4. An additional positive charge is required that can be supplied by H-I-, Li- -, Na- -, or holes at interstitial sites in the crystal lattice. Iron-related defects are also possible since iron is also a trivalent (-1-3) ion. 

Eshelby, J. D. (1954). Distortion of a Crystal by Point Imperfections. Journal of Applied Physics, Vol. 25, No. 2, (February 1954), pp. 255-261. ISSN 0021-8979 Eshelby, J. D. (1956), The continuum theory of lattice defects. Solid State Physics Advances in Research and Applications. Frederick Seitz and David Turnbull, (Ed.), Vol. 3, (1956), pp. 79-144, Elsevier, ISBN 978-0-12-374292-6, Amsterdam, the Netherlands Friedel, J. (1954). Electronic structure of primary solid solutions in metals. Advances in Physics, Vol. 3, No. 12, (October 1954), pp. 446-507, ISSN 0001-8732 Fan, G. J. Choo, H. Liaw, P. K. (2007). A new criterion for the glass-forming ability of liquids. Journal of Non-Crystalline Solids, Vol. 353, No.l, (January 2007), pp. 102-107, ISSN 0022-3093... 

To date, the phonon confinement effects have not been explicitly detected for CVD diamond films and results remained unsatisfactory in the case of DND. To improve the agreement between the predictions of the model and experimental Raman spectra of DND, effects such as crystal size distribution, lattice defects, and the energy dispersion of the phonon modes were taken into consideration and incorporated into the PCM. This work has shown that phonon wave vectors from small vibration domains lead to a broad shoulder peak at 1250 cm", that is often observed in the Raman spectrum of DND. Although the agreement between experimentally obtained and calculated Raman spectra has been significantly improved, some limitations remain, as was pointed ont in Ref. 98. The limitations imposed by the small ND size on the applicability of the PCM arise from the assumption that nanocrystals of 3-20 nm in size, showing extensive surface reconstruction and lattice defects, are assumed to have the phonon density of states of bulk diamond. 

It is well known [73] that plastic deformation in crystals can occur when the applied shear stress can cause one plane of atoms to slip over another plane because there is an imperfect match between these adjacent planes at a particular point in the crystal lattice. These points of imperfection are called dislocations [74] and were identified by electron diffraction techniques to relate to specific crystal defects. Dislocations are observed in polyethylene single crystals by Peterman and Gleiter [75] and give credence to the idea that yield in crystalline polymers can be understood in similar terms to those used by metallurgists for crystalline solids. 

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