Plastic deformation point defects

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. 

This is the kinetic equation for a simple A/AX interface model and illustrates the general approach. The critical quantity which will be discussed later in more detail is the disorder relaxation time, rR. Generally, the A/AX interface behaves under steady state conditions similar to electrodes which are studied in electrochemistry. However, in contrast to fluid electrolytes, the reaction steps in solids comprise inhomogeneous distributions of point defects, which build up stresses at the boundary on a small scale. Plastic deformation or even cracking may result, which in turn will influence drastically the further course of any interface reaction. 

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. 

Recrystallization occurs when a crystalline material is plastically deformed at a relatively low temperature and then heated [1]. The as-deformed material possesses excess bulk free energy resulting from a high density of dislocations and point-defect debris produced by the plastic... 

P. Omling, E. R. Weber, L. Montelius, H. Alexander and J. Michel, Electrical properties of dislocations and point defects in plastically deformed silicon , Phys. Rev. B, 32, 6571 (1985). 

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 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. 

It is necessary to emphasize that the effect of uphill diffusion should be distinguished from the directional diffusion of point defects that can also take place under conditions of a homogeneous stressed state (diffusive creep). Nevertheless, the indicated mechanisms of plastic deformation have a lot in common, because they both are diffusive mechanisms of plastic deformation of crystalline solids. 

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... 

Covalent bonds are directional in character and must be broken as defects move. We will see that dislocations in Si do not move easily at room temperature so the material does not easily deform plastically and is brittle at this temperature. This simple fact has many consequences for the electronics industry. Where would silicon technology be if dislocations moved readily under an applied stress The same consideration applies to point defects except that interstitials in Si do not need to break bonds ... 

Hardness is a measure of a material s ability to resist elastic and plastic deformation. The hardness of non-ideal material is determined by the intrinsic stiffness of the material, as well as by the nature of its defects, be they point defects, dislocations, or macroscopic defects such as microcracks etc. For ideal systems, the hardness of a material will scale with its bulk modulus. 

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... 

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