Crystal, defect, point plastic,

By measuring the shape of the quadrupolar echo in single crystals of RbBr and Rbl, Mehring and Kanert showed that a quadrupolar distribution function could be determined.Once this fimction was known, the authors could quantitate the dislocation density as a fimction of shear stress and presented a model to determine the density of point defects and dislocations in the lattice. It was concluded that the EFG in imdeformed RbBr single crystals was due to point defects, while plastic deformation induced dislocations. Discussion pertaining to sample doping is delayed to Section 4.3.2. 

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. 

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. 

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. ... 

Dislocations are line defects. They bound slipped areas in a crystal and their motion produces plastic deformation. They are characterized by two geometrical parameters 1) the elementary slip displacement vector b (Burgers vector) and 2) the unit vector that defines the direction of the dislocation line at some point in the crystal, s. Figures 3-1 and 3-2 show the two limiting cases of a dislocation. If b is perpendicular to s, the dislocation is named an edge dislocation. The screw dislocation has b parallel to v. Often one Finds mixed dislocations. Dislocation lines close upon themselves or they end at inner or outer surfaces of a solid. 

This chapter is concerned with the influence of mechanical stress upon the chemical processes in solids. The most important properties to consider are elasticity and plasticity. We wish, for example, to understand how reaction kinetics and transport in crystalline systems respond to homogeneous or inhomogeneous elastic and plastic deformations [A.P. Chupakhin, et al. (1987)]. An example of such a process influenced by stress is the photoisomerization of a [Co(NH3)5N02]C12 crystal set under a (uniaxial) chemical load [E.V. Boldyreva, A. A. Sidelnikov (1987)]. The kinetics of the isomerization of the N02 group is noticeably different when the crystal is not stressed. An example of the influence of an inhomogeneous stress field on transport is the redistribution of solute atoms or point defects around dislocations created by plastic deformation. 

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. 

It is worth pointing out here that if material that is subject to deformation is soluble in the liquid into which it has been immersed, one may observe the so-called Ioffe effect. This effect is, for instance, revealed when brittle crystals of sodium chloride undergo plastic deformation in a pool of water that is not saturated with salt and dissolves the surface. In this case plasticity occurs not due to a decrease in resistance to plastic flow, as in the case of adsorption plasticizing, but rather due to an increase in the strength of crystals because of the dissolution of surface layer containing structural defects. 

Whereas point defects and their chemical consequences 1-4) are familiar to workers engaged in studies of catalysts, line defects (i.e., dislocations) and their associated characteristics still tend to be regarded as rather mysterious. Indeed, the properties of dislocations appear to be sufficiently recondite for them to be conveniently invoked to explain some otherwise inexplicable results. This situation has arisen partly because, on the one hand, the role of dislocations in determining the mechanical strength and plasticity of crystals is now inexpugnable 5-7), whereas, on the other, their role in chemical reactions in general, and catalytic reactions in particular, has not, until very recently, been systematically explored. 

The word trap also expresses the fact that these point defects can frequently capture electronic excitation energy. Other well-studied X traps are those of pyrene in anthracene, with a trapping depth of AE= 59 cm b Naturally, there are also triplet X traps, e.g. in 1,2,4,5-tetrachloro-benzene, with AE = 21.3 cm . Host molecules can also act as X traps when they are perturbed not by foreign molecules but by a specific structural defect. Occasionally, in the literature a distinction is made between X and Y traps, depending on whether the lattice perturbation is caused by a structural defect in the crystal (Y trap) or by a foreign molecule (X trap). Plastic deformation of crystals can also produce discrete trapping states, for example in... 

On the other hand materials deform plastically only when subjected to shear stress. According to Frenkel analysis, strength (yield stress) of an ideal crystalline solid is proportional to its elastic shear modulus [28,29]. The strength of a real crystal is controlled by lattice defects, such as dislocations or point defects, and is significantly smaller then that of an ideal crystal. Nevertheless, the shear stress needed for dislocation motion (Peierls stress) or multiplication (Frank-Read source) and thus for plastic deformation is also proportional to the elastic shear modulus of a deformed material. Recently Teter argued that in many hardness tests one measures plastic deformation which is closely linked to deformation of a shear character [17]. He compared Vickers hardness data to the bulk and shear... 

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. 

It is noteworthy that both elastic and plastic deformations were identified in the Ca(OH)2 structures (s = 12 m /g), which may be due to the polydispersity of the specimen. Such a dependence on the degree of dispersion can be explained as follows The range of dispersion lies between single units and tens of m /g, which corresponds to a range of crystal sizes from micrometers to tenths and hundredths of a micrometer. Based on the characteristic valnes of the density of dislocations in crystals, this range corresponds to a transition from crystals with defects (similar to macroscopic real crystals) to microcrystals with properties close to those of ideal, defect-free crystals. This is the reason why the effective microhardness (yield point) can increase considerably in the range of dispersions corresponding to the transition to submicron crystals. In the latter case, the forces that... 

It is worth pointing out that the adsorption-active medium does not, by itself, create defects in the solid body it is only capable of facilitating their formation. For this reason, the ideal threadlike defect-free single crystal may be insensitive to the action of the medium. In bodies capable of plastic... 

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