Crystal, defect, point nucleation,

By a change of temperature or pressure, it is often possible to cross the phase limits of a homogeneous crystal. It supersaturates with respect to one or several of its components, and the supersaturated components eventually precipitate. This is an additive reaction. It occurs either externally at the surfaces, or in the crystal bulk by nucleation and growth. Reactions of this kind from initially homogeneous and supersaturated solid solutions will be discussed in Chapter 12 on phase transformations. Internal reactions in the sense of the present chapter occur after crystal A has been brought into contact with reactant B, and the product AB forms isothermally in the interior of A or B. Point defect fluxes are responsible for the matter transport during internal reactions, and local equilibrium is often established throughout. 

Physically, the onset of instabihty at the point is interpreted as the formation of crystal defect there. It should be noted that local instability does not imply global instability of the configuration. If angle between the vectors k and w established in this way is larger than 60°, then the nucleated defect is expected to be a dislocation with slip plane normal k and Burgers vector approximately along w. On the other hand, if the angle between k and w and instability is less than 30°, the nucleated defect would likely be a microcrack or a void. 

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. 

The influence of plastic deformation on the reaction kinetics is twofold. 1) Plastic deformation occurs mainly through the formation and motion of dislocations. Since dislocations provide one dimensional paths (pipes) of enhanced mobility, they may alter the transport coefficients of the structure elements, with respect to both magnitude and direction. 2) They may thereby decisively affect the nucleation rate of supersaturated components and thus determine the sites of precipitation. However, there is a further influence which plastic deformations have on the kinetics of reactions. If moving dislocations intersect each other, they release point defects into the bulk crystal. The resulting increase in point defect concentration changes the atomic mobility of the components. Let us remember that supersaturated point defects may be annihilated by the climb of edge dislocations (see Section 3.4). By and large, one expects that plasticity will noticeably affect the reactivity of solids. 

This is, however, not the whole of the matter. The superstructure ordering of point defects the collection of interstitial ions along certain fines or sheets, as in Magneli s model for the precursor of his shear structures the temperature-dependent adjustment of composition of a nonstoichiometric phase at the boundary of the bivariant range the nucleation of a new phase of different stoichiometry—these depend on accumulating vacancies or interstitials in some regions of the crystal lattice at the expense of others. 

The usual and therefore most important situation where polymers crystallize is in melts eooled below the point of the fusion of a crystallite of infinite dimensions. Then, crystallization occurs by the nucleation and growth of spherulites. Another crystallization process is sometimes encountered in oriented melts and glasses. In such systems, the crystallization seems to occur at once in the whole sample and not at the interface between the growing crystallites and the amorphous matrix. Despite munerous studies, the crystallization process is not fully understood. Scattering measurements suggest a preliminary spinodal decomposition of the undercooled isotropic melt in phases with and without chain ends and chain defects before the formation of the crystallites [32]. 

There are also applications of quantum theory for instance in the onset of a failure in a material. The failure starts on the atomic scale when an interatomic bonding is stressed beyond its yield-stress threshold and breaks. The initiation and diffusion of point defects in crystal lattice turn out to be a starting point of many failures. These events occur in a stress field at certain temperatures. The phenomena of strain, fatigue crack initiation and propagation, wear, and high-temperature creep are of particular interest The processes of nucleation and diffusion of vacancies in the crystal lattice determines the material behavior at many operation conditions. 

Two final points need to be made about secondary nucleation. First, that screw-dislocation defects, described in more detail in Sect. 5.3, prodnce indesttnctible secondary nuclei for growth on top of the fold surfaces of polymer lamellae. This surface would otherwise be inactive for further growth and restrict polymer crystals to single lamellae (see Chap. 5). An example of a series of screw dislocations is shown in Fig. 3.72 on the example of poly(oxyethylene) of 6,000 molar mass grown... 

The rate and degree of crystallization may also be affected. Any interface, any surface, any defect in any system may act as a nucleation point, and the addition of more of these nucleation points wiU necessarily produce systems with finer-grained crystalline micro-structures. In nanocomposites, the material is full of nucleation sites as long as silicate dispersion is favorable, materials containing finer-grained polymer crystallites (versus the... 

Crack Nucleation. New cracks form in ceramics when an external stress forces DISLOCATIONS towards barriers such as GRAIN BOUNDARIES, impurities or other POINT DEFECTS (see CRYSTAL structure). This build-up of dislocations forms a microcrack, which grows initially by this plastic DEFORMATION PROCESS. See CRACK PROPAGATION. 

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