Solids, dislocations

The rate of flow of electrons from such a charged particle depends on the availability of an accessible site for this transfer. Although it is known that lattice defects provide such sites and that conduction band electrons can trickle down through solid dislocation levels reduction sites for electron accumulation are usually provided by metallization of the semiconductor particle. This can be achieved through photo-platinization or by a number of vapor transfer techniques and the principles relevant to hydrogen evolution on such platinized surfaces have been delineated by Heller The existence of such sites will thus control whether single or multiple electron transfer events can actually take place under steady state illumination. 

The ease with which dislocations move, and the distortions they induce throughout the crystal, make them very important defects for mediating the mechanical response of solids. Dislocations are also important in terms of the electronic properties of solids. In semiconductors, dislocations induce states in the gap which act like traps for electrons or holes. When the dislocation line lies in a direction that produces a short circuit, its effect can be disastrous to the operation of the device. Of the many important effects of dislocations we will only discuss briefly their mobility and its relation to mechanical behavior, such as brittle or ductile response to external loading. For more involved treatments we refer the reader to the specialized books mentioned at the end of the chapter. 

Dislocations and interfaces catalyze reactions in solids, dislocation nodes and grain corners being particularly effective catalytic sites. When a particle forms on a dislocation or on a surface a portion of dislocation or surface is destroyed. The energy gain from this reduces the energy required to form the nucleus. For example, suppose a P particle forms in a on a preexisting a-y surface (a, j8, and y represent three different phases). Then the surface energy which must be supplied to form the particle is... 

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. 

W. T. Read, Jr., Dislocations in Crystals, McGraw-Hill, New York, 1953. Solid Surfaces, ACS Symposium Series No. 33, American Chemical Society, Washington, DC, 1961. 

We have considered briefly the important macroscopic description of a solid adsorbent, namely, its speciflc surface area, its possible fractal nature, and if porous, its pore size distribution. In addition, it is important to know as much as possible about the microscopic structure of the surface, and contemporary surface spectroscopic and diffraction techniques, discussed in Chapter VIII, provide a good deal of such information (see also Refs. 55 and 56 for short general reviews, and the monograph by Somoijai [57]). Scanning tunneling microscopy (STM) and atomic force microscopy (AFT) are now widely used to obtain the structure of surfaces and of adsorbed layers on a molecular scale (see Chapter VIII, Section XVIII-2B, and Ref. 58). On a less informative and more statistical basis are site energy distributions (Section XVII-14) there is also the somewhat laige-scale type of structure due to surface imperfections and dislocations (Section VII-4D and Fig. XVIII-14). 

Two point defects may aggregate to give a defect pair (such as when the two vacanc that constitute a Schottky defect come from neighbouring sites). Ousters of defects ( also form. These defect clusters may ultimately give rise to a new periodic structure oi an extended defect such as a dislocation. Increasing disorder may alternatively give j to a random, amorphous solid. As the properties of a material may be dramatically alte by the presence of defects it is obviously of great interest to be able to imderstand th relationships and ultimately predict them. However, we will restrict our discussion small concentrations of defects. 

The other major defects in solids occupy much more volume in the lattice of a crystal and are refeiTed to as line defects. There are two types of line defects, the edge and screw defects which are also known as dislocations. These play an important part, primarily, in the plastic non-Hookeian extension of metals under a tensile stress. This process causes the translation of dislocations in the direction of the plastic extension. Dislocations become mobile in solids at elevated temperamres due to the diffusive place exchange of atoms with vacancies at the core, a process described as dislocation climb. The direction of climb is such that the vacancies move along any stress gradient, such as that around an inclusion of oxide in a metal, or when a metal is placed under compression. 

Interface mismatch between two solids compensated with an edge dislocation... 

Figure 4.2 Terraces, ledges and kinks on a solid surface, together with an emerging screw dislocation, a vacant site, and an adatom...

Dislocations are known to be responsible for die short-term plastic (nonelastic) properties of substances, which represents departure from die elastic behaviour described by Hooke s law. Their concentration determines, in part, not only dris immediate transport of planes of atoms drrough die solid at moderate temperatures, but also plays a decisive role in die behaviour of metals under long-term stress. In processes which occur slowly over a long period of time such as secondaiy creep, die dislocation distribution cannot be considered geometrically fixed widrin a solid because of die applied suess. 

An example of research in the micromechanics of shock compression of solids is the study of rate-dependent plasticity and its relationship to crystal structure, crystal orientation, and the fundamental unit of plasticity, the dislocation. The majority of data on high-rate plastic flow in shock-compressed solids is in the form of ... 

Dremin, A.N. and Breusov, O.N., Processes Occurring in Solids Under the Action of Powerful Shock Waves, Russian Chem. Rev. 37 (5), 392-402 (1968). Gilman, J.J., Dislocation Dynamics and the Response of Materials to Impact, Appl. Meek Rev. 21 (8), 767-783 (1968). 

In the last chapter we examined data for the yield strengths exhibited by materials. But what would we expect From our understanding of the structure of solids and the stiffness of the bonds between the atoms, can we estimate what the yield strength should be A simple calculation (given in the next section) overestimates it grossly. This is because real crystals contain defects, dislocations, which move easily. When they move, the crystal deforms the stress needed to move them is the yield strength. Dislocations are the carriers of deformation, much as electrons are the carriers of charge. 

Ty is the quantity we want the yield strength of bulk, polycrystalline solids. It is larger than the dislocation shear strength Tj (by the factor 3) but is proportional to it. So all the statements we have made about increasing apply unchanged to... 

Nucleation in solids is very similar to nucleation in liquids. Because solids usually contain high-energy defects (like dislocations, grain boundaries and surfaces) new phases usually nucleate heterogeneously homogeneous nucleation, which occurs in defect-free regions, is rare. Figure 7.5 summarises the various ways in which nucleation can take place in a typical polycrystalline solid and Problems 7.2 and 7.3 illustrate how nucleation theory can be applied to a solid-state situation. 

Fig. 7.5. Nucleation in solids. Heterogeneous nucleotion con take place at defects like dislocations, grain boundaries, interphase interfaces and free surfaces. Homogeneous nucleation, in defect-free regions, is rare.

When other elements dissolve in a metal to form a solid solution they make the metal harder. The solute atoms differ in size, stiffness and charge from the solvent atoms. Because of this the randomly distributed solute atoms interact with dislocations and make it harder for them to move. The theory of solution hardening is rather complicated, but it predicts the following result for the yield strength... 

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