Crystal defects thermodynamic effects

It is a well-known fact that it is not feasible to manufacture crystals that are perfect in all aspects, because of the presence of crystal defects. This effect occurs because of the fact that over absolute zero, the existence of defects in crystals is thermodynamically necessary. 

After 14 years on the faculty of Imperial College, Jacobs moved from London, England, to London, Ontario, where his research program focused on the optical and electrical properties of ionic crystals, as well as on the experimental and theoretical determination of thermodynamic and kinetic properties of crystal defects.213 Over the years his research interests have expanded to include several aspects of computer simulations of condensed matter.214 He has developed algorithms215 for molecular dynamics studies of non-ionic and ionic systems, and he has carried out simulations on systems as diverse as metals, solid ionic conductors, and ceramics. The simulation of the effects of radiation damage is a special interest. His recent interests include the study of perfect and imperfect crystals by means of quantum chemical methods. The corrosion of metals is being studied by both quantum chemical and molecular dynamics techniques. 

The same defect thermodynamics and diffusion theory can be applied to ionic crystals with one important proviso, which is the need to account for the charges on the ions (and hence effective charges on the defects), and that the crystal must remain electrically neutral overall. This means that the defects will occur as multiplets to satisfy this later condition. For example, in a MX crystal they will occur as pairs the Schottky pair- a cation vacancy and an anion vacancy the cation-Prenkel pair- a cation vacancy and an interstitial cation and the anion-Frenkel pair - an anion vacancy and an interstitial anion. The concentrations of the defects in the pair are related by a solubility product equation, which for Schottky pairs in an MX equation takes the form ... 

These observations concerning ionic transport can be explained on the basis of defect chemistry and crystal stmctme of the solid materials. The ideal crystal is in fact an abstract concept that is used in crystallographic descriptions. The lattice of a real crystal always contains imperfections. A snitable classiflcation of crystalline defects can be achieved by first considering point defects and then proceeding to one- and higher-dimensional defects. Point defects are atomic defects whose effects are limited only to their immediate snrronndings. They exist in a state of complete thermodynamic equilibrinm. Examples are ionic vacancies in the regnlar crystal lattice, or interstitial atoms or ions. 

The rate (or kinetics) and form of a corrosion reaction will be affected by a variety of factors associated with the metal and the metal surface (which can range from a planar outer surface to the surface within pits or fine cracks), and the environment. Thus heterogeneities in a metal (see Section 1.3) may have a marked effect on the kinetics of a reaction without affecting the thermodynamics of the system there is no reason to believe that a perfect single crystal of pure zinc completely free from lattic defects (a hypothetical concept) would not corrode when immersed in hydrochloric acid, but it would probably corrode at a significantly slower rate than polycrystalline pure zinc, although there is no thermodynamic difference between these two forms of zinc. Furthermore, although heavy metal impurities in zinc will affect the rate of reaction they cannot alter the final position of equilibrium. 

Thermodynamic analysis can be useful also in predicting the effect of gas-phase composition on defect concentrations in the solid and, implicitly, on the electrical properties of the deposited film (I, 95, 96). This technique has been used to predict the concentration and change in electrical carriers from electrons to holes in PbS with increasing sulfur pressure over the PbS crystal (96). 

Of course, most surfeces are not exposed large single crystal faces. However the variations in gas-solid energy with changes in the lateral position t over the surface will reflect the atomic structure of the surface even if it is amorphous or if it is a defective crystal plane or planes. Many of the simulations of physical adsorption have been devoted to investigations of the effects of these variations upon the structural and thermodynamic properties of the adsorbed films [13]. Often, the reference system for the simulations is the adsorption produced by the structureless surface that means a surface for which the term in equation (13) with g=0 is the only one. In the case of an inverse 12-6 power site-site energy [14],... 

Point defects such as vacancies are thermodynamically stable entities 18) meaning, in effect, that their concentration increases with increasing temperature because their free energy of formation is negative. A crystal that is quenched from high temperatures will, at lower temperatures, contain a supersaturation of point defects. But the excess... 

Many other nonequilibrium modes of impurity incorporation occur, primarily through segregation of impurities at defect and inclusion sites. As discussed throughout this chapter, these impurities can be systematically reduced from the final product through optimization of crystallization and separation steps. In particular, the thermodynamic approach outlined in Section 3.5.1 can be effectively used commercially to select solvents and optimize processing conditions to greatly improve the purification of crystalline materials. 

The emergence of a new phase due to local structural fluctuations in a lattice of the original solid phase Ag occurs most often at the boundaries and defect sites of the crystals. Thermodynamically stable nucleus of new phase has often a critical size close to unit cell volume, which differs from the normal one. This gives rise to mechanical stresses in the transformation zone, and even the destruction of the original crystal. Such effect leads to smaller quantity of a desired product. Thermal decomposition reaction, like all topochemical reactions, proceeds more rapidly... 

Polymers are always polydisperse with a distribution in molar mass and often contain chain branches, either introduced specifically during synthesis or as a consequence of synthetic defects, and both these effects will influence the observed morphology. As we shall see later, copolymers are a special case however, the introduction of low levels of comonomers can lead to behaviour which is rather like that of random branched chains. Different molecular species crystallize in different stages indicating the thermodynamic control on the overall process, i.e. they are incorporated into the crystal structure at different temperatures and times. The intermediate and high molar mass component crystallizes early in the stacks of thick dominant crystals. Small pockets of rejected molten low molar mass material remain after crystallization... 

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