Point Defects and Impurities

For the deformation of NiAl in a soft orientation our calculations give by far the lowest Peierls barriers for the (100) 011 glide system. This glide system is also found in many experimental observations and generally accepted as the primary slip system in NiAl [18], Compared to previous atomistic modelling [6], we obtain Peierls stresses which are markedly lower. The calculated Peierls stresses (see table 1) are in the range of 40-150 MPa which is clearly at the lower end of the experimental low temperature deformation data [18]. This may either be attributed to an insufficiency of the interaction model used here or one may speculate that the low temperature deformation of NiAl is not limited by the Peierls stresses but by the interaction of the dislocations with other obstacles (possibly point defects and impurities). 

In an ideal situation dislocation lines would penetrate the whole crystal. In reality they mostly extend from one grain boundary to another one or they are pinned by impurities. If the lines form a closed circle inside the crystal, they are called loops. Summarizing, one may say that dislocations can arise from vacancy clusters as well as from interstitial clusters due to their pressure on the lattice. Very often they are the final products of an annealing procedure. Dislocations already existing interact with point defects and impurities acting as traps or sinks. 

Deviation from the ideal crystal, lattice vibrations, point defects and impurities are examples of what modifies the electron s trajectory. The interaction with such an imperfection is local, intense and of very short duration. We speak of collision and we call T the mean time between two collisions. In the absence of an appUed electric or magnetic field, to any electron of velocity v corresponds an electron of velocity -V and overall, the charge flow generated by all the electrons of an energy band is nil. In the presence of an applied electric field E pp, any electron is accelerated, according to Newton s laws ... 

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 main scattering processes limiting the thermal conductivity are phonon-phonon (which is absent in the harmonic approximation), phonon defect, electron-phonon, electron impurity or point defects and more rare electron-electron. For both heat carriers, the thermal resistivity contributions due to the various scattering processes are additive. For... 

Apart from its role in interacting with existing defects and impurities, hydrogen has recently been shown to induce defects as well (Johnson et al., 1987). Extended defects (described as platelets ) in the near-surface region were observed after hydrogenation and correlated with the presence of large concentrations of H. Theoretical models will be discussed in Part VIII. Part IX, finally, will contain some conclusions and point out directions for future work. As is the case for so many other topics in semiconductor physics, silicon (Si) has been the material for which the majority of... 

It is important that the copper is in the monovalent state and incorporated into the silver hahde crystals as an impurity. Because the Cu+ has the same valence as the Ag+, some Cu+ will replace Ag+ in the AgX crystal, to form a dilute solid solution Cu Agi- X (Fig. 2.6d). The defects in this material are substitutional CuAg point defects and cation Frenkel defects. These crystallites are precipitated in the complete absence of light, after which a finished glass blank will look clear because the silver hahde grains are so small that they do not scatter light. 

In a perfect crystal, all atoms would be on their correct lattice positions in the structure. This situation can only exist at the absolute zero of temperature, 0 K. Above 0 K, defects occur in the structure. These defects may be extended defects such as dislocations. The strength of a material depends very much on the presence (or absence) of extended defects, such as dislocations and grain boundaries, but the discussion of this type of phenomenon lies very much in the realm of materials science and will not be discussed in this book. Defects can also occur at isolated atomic positions these are known as point defects, and can be due to the presence of a foreign atom at a particular site or to a vacancy where normally one would expect an atom. Point defects can have significant effects on the chemical and physical properties of the solid. The beautiful colours of many gemstones are due to impurity atoms in the crystal structure. Ionic solids are able to conduct electricity by a mechanism which is due to the movement of fo/ 5 through vacant ion sites within the lattice. (This is in contrast to the electronic conductivity that we explored in the previous chapter, which depends on the movement of electrons.)... 

The interaction energy between a solute particle (impurity atom, point defect) and an edge dislocation (screw dislocations do not interact, to first order) is... 

Fig. 4.7. Model clusters used for simulating silanone and dioxasilyrane point defects and Al impurity atom ([A104]° defect) in Si02 (a) silanone, X2Si = O, in the ground electronic state (b) X2Si = O in excited electronic states (c) dioxasilyrane, X2Si(02), in the ground electronic state (d) X2Si(02) in excited electronic states and (e) Al(OSiX3)4.

In addition to mechanical properties, other physical properties of polycrystaUine materials, such as electrical and thermal conduction, are also affected by microstmcture. Although polycrystals are mechanicaUy superior to single crystals, they have inferior transport properties. Point defects (vacancies, impurities) and extended defects (grain boundaries) scatter electrons and phonons, shortening their mean free paths. Owing to... 

Defects can be further classified into point defects and extended defects. Unassociated point defects are associated with a single atomic site and are thus zero-dimensional. These include vacancies, interstitials, and impurities, which can be intrinsic or extrinsic in nature. Extended defects are multi-dimensional in space and include dislocations and stacking faults. These tend to be metastable, resulting from materials processing. The mechanical properties of solids are intimately related to the presence and dynamics of extended defects. A discussion of extended defects is deferred until Chapter 10. For now, only point defects are covered. Their importance in influencing the physical and chemical properties of materials cannot be overemphasized. 

It may seem surprising to apply thermal equilibrium concepts to amorphous silicon, because the amorphous phase of a solid is not the equilibrium phase. However, a subset of bonding states may be in equilibrium even if the structure as a whole is not in its lowest energy state. The attainment of equilibrium is prevented by bonding constraints on the atomic structure. The collective motion of many atoms is required to achieve long range crystalline order and the topological constraints are formidable. On the other hand the transformation of point defects requires the cooperation of only a few atoms. Therefore any partial thermal equilibrium may be expected at point defects or impurities. 

Impurities are invariably present in solids, and in low concentrations, they may form point defects. The impurity atom can occupy atom sites normally occupied by the... 

Pure and high-quality crystals can be grown. Concentrations of impurities, point defects, and dislocations are generally low see Defects in Solids). 

---