Crystal, defect, point types

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. 

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. 

Real crystals can contain a large variety of different types of point, line, and planar crystal defects and other entities, such as embedded particles, which interact with dislocations and can act as obstacles to glide. Solute atoms are good examples of point defects that hinder dislocation glide by acting as centers of dilation... 

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... 

Aimed at master s degree or PhD students as well as researchers and specialist engineers, this work focuses on electrochemical systems using electrolytes in solid phases (ionic crystals, ceramics, different types of glass and polymers). The fundamental concepts of electrochemistry are laid out (the thermodynamics of point defects and amorphous phases, transport mechanisms, mixed conduction, and gas electrode reactions) alongside the specific research methods used. Several applications are also described. 

The same polymer blend was studied by Stein et al. (1981), Morra and Stein (1984). Since PVDF crystallizes into several types of morphologies, different lines are shown in the Hoffman-Weeks plot (Fig. 3.24). The curve representing the melting point of PVDF as a function of the crystallization temperature for the a modification shows a break that was associated with defect exclusion from the crystal (Stein et al. 1981) and by entrapment of head-to-head defects of the PVDF chains into the crystals during rapid crystallization at large undercooling (Morra and Stein 1984). 

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. 

In the second part (applications) we discuss some recent applications of LCAO methods to calculations of various crystalline properties. We consider, as is traditional for such books the results of some recent band-structure calculations and also the ways of local properties of electronic- structure description with the use of LCAO or Wannier-type orbitals. This approach allows chemical bonds in periodic systems to be analyzed, using the well-known concepts developed for molecules (atomic charge, bond order, atomic covalency and total valency). The analysis of models used in LCAO calculations for crystals with point defects and surfaces and illustrations of their applications for actual systems demonstrate the eflSciency of LCAO approach in the solid-state theory. A brief discussion about the existing LCAO computer codes is given in Appendix C. 

These two simple experimental systems show the presence in liquid crystals of two types of defect lines and point singularities. Liquid crystals contain a large variety of lines with well-defined geometries or topologies. There are also lines that have a continuous core (for example, in the capillary tube) the axial zone corresponds to a maximum of splay and is generally considered to be a defect line, although no discontinuities apart from the singular points are present. This situation is also encountered in the third type of defect - walls. 

The presence of point defects such as vacancies or interstitial atoms or ions is well-established in atomic and ionic crystals. The situation is somewhat different in macromolecular crystals where the types of point defects are restricted by the long-chain nature of the polymer molecules. It is relatively easy to envisage the types of defects that may occur. They could include chain ends, short branches, folds or copolymer units. There is accumulated evidence that the majority of this chain disorder is excluded from the crystals and incorporated in non-crystalline regions. However, it is also clear that at least some of it must be present in the crystalline areas. 

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. 

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 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. 

On the other hand, the formation of the high pressure phase is preceded by the passage of the first plastic wave. Its shock front is a surface on which point, linear and two-dimensional defects, which become crystallization centers at super-critical pressures, are produced in abundance. Apparently, the phase transitions in shock waves are always similar in type to martensite transitions. The rapid transition of one type of lattice into another is facilitated by nondilTusion martensite rearrangements they are based on the cooperative motion of many atoms to small distances. ... 

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