Solid solution point defects

From a thermodynamic point of view a solid containing point defects constitutes a solid solution where the point defects are dissolved in the solid. In analogy with liquid solutions, the solid may be considered to be the solvent and the point defects the solute. Similarly, the defect equilibria may be treated in terms of the thermodynamics of chemical reactions and solutions. 

Usually, a solid is generated starting from a solution that can be either fluid (mi rture of gas or liquid solution) or solid (real solid with point defects and thus re rded as a solution of structure elements). The thermodynamics of such heterogenous systems is not basically different from what we have already considered, but the concept of supersaturation is usually used. 

An effect which is frequently encountered in oxide catalysts is that of promoters on the activity. An example of this is the small addition of lidrium oxide, Li20 which promotes, or increases, the catalytic activity of dre alkaline earth oxide BaO. Although little is known about the exact role of lithium on the surface structure of BaO, it would seem plausible that this effect is due to the introduction of more oxygen vacancies on the surface. This effect is well known in the chemistry of solid oxides. For example, the addition of lithium oxide to nickel oxide, in which a solid solution is formed, causes an increase in the concentration of dre major point defect which is the Ni + ion. Since the valency of dre cation in dre alkaline earth oxides can only take the value two the incorporation of lithium oxide in solid solution can only lead to oxygen vacaircy formation. Schematic equations for the two processes are... 

In this chapter shock modification of powders (their specific area, x-ray diffraction lines, and point defects) measurements via analytical electron microscopy, magnetization and Mossbauer spectroscopy shock activation of catalysis, solution, solid-state chemical reactions, sintering, and structural transformations enhanced solid-state reactivity. 

Now, suppose that we have a solid solution of two (2) elemental solids. Would the point defects be the same, or not An easy way to visualize such point defects is shown in the following diagram, given as 3.1.3. on the next page. It is well to note here that homogeneous lattices usually involve metals or solid solutions of metals (alloys) in contrast to heterogeneous lattices which involve compounds such as ZnS. 

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. 

The preceding paragraphs illustrate that analogies between point defects in a crystal and solute molecules in a solution have been used previously but in a fairly elementary way. However, the implications of the existence of such analogies in the formulation of the statistical mechanics of interacting defects has not been considered in detail apart from an early paper by Mayer,69 who was interested primarily in the relation of defect interactions, to the solid-liquid phase transition in crystals with short-range forces. The... 

Another defect problem to which the ion-pair theory of electrolyte solutions has been applied is that of interactions to acceptor and donor impurities in solid solution in germanium and silicon. Reiss73>74 pointed out certain difficulties in the Fuoss formulation. His kinetic approach to the problem gave results numerically very similar to that of the Fuoss theory. A novel aspect of this method was that the negative ions were treated as randomly distributed but immobile while the positive ions could move freely. 

The second type of impurity, substitution of a lattice atom with an impurity atom, allows us to enter the world of alloys and intermetallics. Let us diverge slightly for a moment to discuss how control of substitutional impurities can lead to some useful materials, and then we will conclude our description of point defects. An alloy, by definition, is a metallic solid or liquid formed from an intimate combination of two or more elements. By intimate combination, we mean either a liquid or solid solution. In the instance where the solid is crystalline, some of the impurity atoms, usually defined as the minority constituent, occupy sites in the lattice that would normally be occupied by the majority constituent. Alloys need not be crystalline, however. If a liquid alloy is quenched rapidly enough, an amorphous metal can result. The solid material is still an alloy, since the elements are in intimate combination, but there is no crystalline order and hence no substitutional impurities. To aid in our description of substitutional impurities, we will limit the current description to crystalline alloys, but keep in mind that amorphous alloys exist as well. 

As indicated in my report, we now know the rates of lateral diffusion of phospholipids in lipid bilayers in the fluid state, and in a few cases the rates of lateral diffusion of proteins in fluid lipids are also known. At the present time nothing is known about the rates of lateral diffusion of phospholipids in the crystalline, solid phases of the substances. As mentioned in my report, there are reasons to suspect that the rates of lateral diffusion of phospholipids in the solid solution crystalline phases of binary mixtures of phospholipids may be appreciable on the experimental time scale. Professor Ubbelohde may well be correct in pointing out the possibility of diffusion caused by defects. However, such defects, if present, apparently do not lead to significant loss of the membrane permeability barrier, except at domain boundaries. 

We wish here to obtain the thermodynamic equations defining the liquidus surface of a solid solution, (At BB)2, ). It is assumed that the A and atoms occupy the sites of one sublattice of the structure and the C atoms the sites of a second sublattice. For the specific systems considered here Sb and play the role of C in the general formula above. It is also assumed that the composition variable is confined to values near unity so that the site fractions of atomic point defects is always small compared to unity. This apparently is the case for the solid solutions in the two systems considered. Then it can be shown theoretically (Brebrick, 1979), as well as experimentally for (Hgj CdJ2-yTe)l(s) (Schwartz et al, 1981 Tung et al., 1981b), that the sum of the chemical potentials of A and C and that of and C in the solid are independent of the composition variable y ... 

The concepts required for a quantitative treatment of the reactivity of solids were now clear, except for one important issue. According to the foregoing, point defect energies should be on the same order as lattice energies. Since the distribution of point defects in the crystal conforms to Boltzmann statistics, one was able to estimate their concentrations. It was found that the calculated defect concentrations were orders of magnitude too small and therefore could not explain the experimentally observed effects which depended on defect concentrations (e.g., conductivity, excess volume, optical absorption). Jost [W. Jost (1933)] provided the correct solution to this problem. Analogous to the fact that NaCl can be dissolved in H20... 

Defect thermodynamics is more complicated when applied to binary (or multi-component) compound crystals. For binary systems, there is one more independent thermodynamic variable to control. In the case of extended binary solid solutions, one would normally choose a composition variable for this purpose. For compounds with very narrow ranges of homogeneity (i.e., point defect concentrations), however, the composition is obviously not a convenient variable. The more natural choice is the chemical potential of one of the two components of the compound crystal. In practice one will often use the vapor pressure ( activity) of this component. 

We have discussed point defects in elements (A) and in nearly stoichiometric compounds having narrow ranges of homogeneity. Let us extend this discussion to the point defect thermodynamics of alloys and nonmetallic solid solutions. This topic is of particular interest in view of the kinetics of transport processes in those solid solutions which predominate in metallurgy and ceramics. Diffusion processes are governed by the concentrations and mobilities of point defects and, although in inhomogeneous crystals the components may not be in equilibrium, point defects are normally very close to local equilibrium. 

In the case of nonideal solid solutions, the vacancies (or other point defects) by necessity interact differently with components A and B in their immediate surroundings. Therefore, the alloy composition near a vacancy differs from the bulk composition Nb. This is analogous to the problem of energies and concentrations of gas atoms dissolved in alloys under a given gas vapor pressure [H. Schmalzried, A. Navrotsky (1975)]. Let us briefly indicate the approach to its solution and transfer it to the formulations in defect thermodynamics. 

Theoretical point defect calculations for solid solutions are difficult because the defect surroundings are not isotropic. This is particularly true for metals considering... 

In other cases, however, and in particular when sublattices are occupied by rather immobile components, the point defect concentrations may not be in local equilibrium during transport and reaction. For example, in ternary oxide solutions, component transport (at high temperatures) occurs almost exclusively in the cation sublattices. It is mediated by the predominant point defects, which are cation vacancies. The nearly perfect oxygen sublattice, by contrast, serves as a rigid matrix. These oxides can thus be regarded as models for closed or partially closed systems. These characteristic features make an AO-BO (or rather A, O-B, a 0) interdiffusion experiment a critical test for possible deviations from local point defect equilibrium. We therefore develop the concept and quantitative analysis using this inhomogeneous model solid solution. 

However, a shift of the AO crystal does not always occur in gradients. If, for example, in the oxygen potential gradient, cations are immobile and anions are the mobile species (e.g., in U02), the cation sublattice is a closed subsystem and thus cannot be shifted. Therefore, if oxygen is transported via anionic (plus electronic) defects across the AO slab, the whole crystal is stationary. Likewise, if the solid solution (A,B)0 is exposed to an oxygen potential gradient and transport is by way of anionic point defects, there is again no crystal shift. 

By a change of temperature or pressure, it is often possible to cross the phase limits of a homogeneous crystal. It supersaturates with respect to one or several of its components, and the supersaturated components eventually precipitate. This is an additive reaction. It occurs either externally at the surfaces, or in the crystal bulk by nucleation and growth. Reactions of this kind from initially homogeneous and supersaturated solid solutions will be discussed in Chapter 12 on phase transformations. Internal reactions in the sense of the present chapter occur after crystal A has been brought into contact with reactant B, and the product AB forms isothermally in the interior of A or B. Point defect fluxes are responsible for the matter transport during internal reactions, and local equilibrium is often established throughout. 

These assumptions, however, oversimplify the problem. The parent (A,B)0 phase between the surface and the reaction front coexists with the precipitated (A, B)304 particles. These particles are thus located within the oxygen potential gradient. They vary in composition as a function of ( ) since they coexist with (A,B)0 (AT0<1 see Fig. 9-3). In the Af region, the point defect thermodynamics therefore become very complex [F. Schneider, H. Schmalzried (1990)]. Furthermore, Dv is not constant since it is the chemical diffusion coefficient and as such it contains the thermodynamic factor /v = (0/iV/01ncv). In most cases, one cannot quantify these considerations because the point defect thermodynamics are not available. A parabolic rate law for the internal oxidation processes of oxide solid solutions is expected, however, if the boundary conditions at the surface (reaction front ( F) become time-independent. This expectation is often verified by experimental observations [K. Ostyn, et al. (1984) H. Schmalzried, M. Backhaus-Ricoult (1993)]. 

Let us now compare the internal oxidation of nonmetallic (oxide) solid solutions with the internal oxidation of metal alloys. The role of the (neutral) point defect... 

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. 

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