Point Defect Motions

Two reasons are responsible, for the greater complexity of chemical reactions 1) atomic particles change their chemical identity during reaction and 2) rate laws are nonlinear in most cases. Can the kinetic concepts of fluids be used for the kinetics of chemical processes in solids Instead of dealing with the kinetic gas theory, we have to deal with point, defect thermodynamics and point defect motion. Transport theory has to be introduced in an analogous way as in fluid systems, but adapted to the restrictions of the crystalline state. The same is true for (homogeneous) chemical reactions in the solid state. Processes across interfaces are of great... 

Pores are essentially negative particles, but there are some big differences (1) there is a gas/solid PB, (2) there are no solid-state reactions at the interface, and (3) kinetics of point defect motion are fastest at the surface of the pore (the PB). 

The sinh law equation has been derived from first principles. Underlying mechanisms are based upon thermally activated diffusion processes, ranging from theories of point defect motion (vacancies and interstitials) and dislocation cross slip at the low stresses, to dislocation glide... 

Point defects in solids make it possible for ions to move through the structure. Ionic conductivity represents ion transport under the influence of an external electric field. The movement of ions through a lattice can be explained by two possible mechanisms. Figure 25.3 shows their schematic representation. The first, called the vacancy mechanism, represents an ion that hops or jumps from its normal position on the lattice to a neighboring equivalent but vacant site or the movement of a vacancy in the opposite direction. The second one is an interstitial mechanism where an interstitial ion jumps or hops to an adjacent equivalent site. These simple pictures of movement in an ionic lattice, known as the hopping model, ignore more complicated cooperative motions. 

In impure metals, dislocation motion ocures in a stick-slip mode. Between impurities (or other point defects) slip occurs, that is, fast motion limited only by viscous drag. At impurities, which are usually bound internally and to the surrounding matrix by covalent bonds, dislocations get stuck. At low temperatures, they can only become freed by a quantum mechanical tunneling process driven by stress. Thus this part of the process is mechanically, not thermally, driven. The description of the tunneling rate has the form of Equation (4.3). Overall, the motion has two parts the viscous part and the tunneling part. 

The potassium ions that are produced occupy cation lattice sites, but no anions are produced so electrons occupy anion sites. In this situation, the electron behaves as a particle restricted to motion in a three-dimensional box that can absorb energy as it is promoted to an excited state. It is interesting to note that the position of the maximum in the absorption band is below 4000A (400nm, 3.1 eV) for LiCl but it is at approximately 6000 A (600 nm, 2eV) for CsCl. One way to explain this observation is by noting that for a particle in a three-dimensional box the difference between energy levels increases as the size of the box becomes smaller, which is the situation in LiCl. Schottky, Frenkel, and F-center defects are not the only types of point defects known, but they are the most common and important types. 

At r > Tr, the relaxation of a non-equilibrium surface morphology by surface diffusion can be described by Eq. 1 the thermodynamic driving force for smoothing smoothing is the surface stiffness E and the kinetics of the smoothing is determined by the concentration and mobility of the surface point defects that provide the mass transport, e.g. adatoms. At r < Tr, on the other hand, me must consider a more microscopic description of the dynamics that is based on the thermodynamics of the interactions between steps, and the kinetics of step motion [17]. 

A variety of techniques has been employed to investigate aliovalent impurity-cation vacancy pairs and other point defects in ionic solids. Dielectric relaxation, optical absorption and emission spectroscopy, and ionic thermocurrent measurements have been most valuable ESR studies of Mn " in NaCl have shown the presence of impurity-vacancy pairs of at least five different symmetries. The techniques that have provided a wealth of information on the energies of migration, formation and other defect energies in ionic solids are diffusion and electrical conductivity measurements. Electrical conductivity in ionic solids occurs by the motion of ions through vacancies or of interstitial ions. In the case of motion through vacancies, the conductivity, a, is given by... 

The motion of ions through solids results in both charge as well as mass transport. Whereas charge transport manifests itself as ionic conductivity in the presence of an applied electric field, macroscopic mass transport (diffusion) occurs in a concentration gradient. Both ionic conductivity and diffusion arise from the presence of point defects in solids (Section 5.2). For a solid showing exclusive ionic conduction, conductivity is written as... 

Up to this point we have assumed implicitly that each defect responsible for the atomic motion has an infinite lifetime. In real crystals, however, this lifetime is finite because of the dynamic nature of the point defect equilibria. This means that only m consecutive jumps are correlated (corresponding to the defect lifetime). It has been shown [R. Kutner (1985)] that under these conditions... 

Several points are to be noted. Firstly, pores and changes of sample dimension have been observed at and near interdiffusion zones [R. Busch, V. Ruth (1991)]. Pore formation is witness to a certain point defect supersaturation and indicates that sinks and sources for point defects are not sufficiently effective to maintain local defect equilibrium. Secondly, it is not necessary to assume a vacancy mechanism for atomic motion in order to invoke a Kirkendall effect. Finally, external observers would still see a marker movement (markers connected by lattice planes) in spite of bA = bB (no Kirkendall effect) if Vm depends on composition. The consequences of a variable molar volume for the determination of diffusion coefficients in binary systems have been thoroughly discussed (F. Sauer, V. Freise (1962) C. Wagner (1969) H. Schmalzried (1981)]. 

The main problem of the boundary motion, however, remains the description of relaxation processes that take place when supersaturated point defects are pumped into the boundary region A R. Outside the relaxation zone Asimple model of a relaxation box is shown in Figure 10-14c. The four exchange reactions 1) between the crystals a and /3, and 2) between their sublattices are... 

After thermalization, the defects begin to migrate, recombine, cluster, or precipitate provided the temperature is high enough to activate the motion of point defects. The various possible processes depend on defect concentration and their spatial distribution as well as on defect mobility and their interaction energies. As in non-metallic crystals, internal and external surfaces act as sinks for at least a part of the radiation induced defects in metals. 

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. 

Let us re-examine the notion of a point defect in this context. If a molecular subgroup of a molecule is imperfect, this damaged molecule constitutes a point defect in the crystal, although the defect has no immediate influence on the molecule s translational mobility. Point defects that induce (translational) motion are vacancies or interstitials. We can infer from the form of the Lenard-Jones potential that vacan-... 

From the fact that the structure of hexamethylethane is close-packed, we may infer that the point defects responsible for the translational motion of the molecules are monovacancies. The data indicate an overexponential increase in diffusivity with temperature near Tm, analogous to some observations made on inorganic crystals. Various explanations could be given for this increase such as anharmonicity of the... 

Excess Point Defects and Low-Thermal-Budget Annealing. Submicrometer VLSI (very-large-scale integration) technologies require low thermal budgets (the product of dopant diffusivity and diffusion time) to limit the diffusional motion of dopants. Two options exist to reduce the thermal... 

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