Point defects concentration

The microstmcture and imperfection content of coatings produced by atomistic deposition processes can be varied over a very wide range to produce stmctures and properties similar to or totally different from bulk processed materials. In the latter case, the deposited materials may have high intrinsic stress, high point-defect concentration, extremely fine grain size, oriented microstmcture, metastable phases, incorporated impurities, and macro-and microporosity. AH of these may affect the physical, chemical, and mechanical properties of the coating. 

Electrical Properties. Generally, deposited thin films have an electrical resistivity that is higher than that of the bulk material. This is often the result of the lower density and high surface-to-volume ratio in the film. In semiconductor films, the electron mobiHty and lifetime can be affected by the point defect concentration, which also affects electromigration. These effects are eliminated by depositing the film at low rates, high temperatures, and under very controUed conditions, such as are found in molecular beam epitaxy and vapor-phase epitaxy. 

Sinee there are six unknowns and three equations, there are three independent variables. We ean associate these with any three elementary independent modes of point defect formation which conserve the numbers of atoms. These are like basis vectors for representing arbitrary point defect concentrations. Let us define them as follows ... 

Equivalent formulae can be produced in terms of the other point defect concentrations by substituting from (8). 

Formula for the chemical potentials have been derived in terms of the formation energy of the four point defects. In the process the conceptual basis for calculating point defect energies in ordered alloys and the dependence of point defect concentrations on them has been clarified. The statistical physics of point defects in ordered alloys has been well described before [13], but the present work represents a generalisation in the sense that it is not dependent on any particular model, such as the Bragg-Williams approach with nearest neighbour bond energies. It is hoped that the results will be of use to theoreticians as well as... 

Approximate formulae for the point defect concentrations close (but not too close) to the stoichimetric composition in AB alloys have been derived. They show that the prefactors in the Arrhenius formulae are sensitive functions of the stoichiometry, besides representing the usual formation entropy term. 

The line widths and shapes to be expected for cubic crystals containing point defects have been derived by Cohen and Reif for both first and second order quadrupole interaction 97). In particular, for point defect concentrations greater than about 0.1 (in terms of probability /, of a lattice site being occupied by a defect) distributed in a random fashion over various possible lattice sites, the second order interaction gives rise to a lopsided central component whose shape is given by (97)... 

We now proceed to more realistic and complicated systems by considering crystals in which the point defects interact. If the interaction is due to forces between nearest neighbors only, then one may calculate the point defect concentrations by assuming that, in addition to single point defects, e.g. it and i2, pairs (or still higher clusters) of point defects form and that they are in internal equilibrium. These clusters are taken to be ideally diluted in the crystal matrix, in analogy to the isolated single defects. All the defect interactions are thus contained in the cluster formation reaction... 

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. 

Let us first discuss intrinsic disorder types where the number of moles of the components is almost constant and independent of the component activities. Thus, the majority point defect concentrations are also (almost) independent of the component. activities. It follows that only two types of (intrinsic) defect formation reactions are allowed... 

If majority point defect concentrations depend on the activities (chemical potentials) of the components, extrinsic disorder prevails. Since the components k are necessarily involved in the defect formation reactions, nonstoichiometry is the result. In crystals with electrically charged regular SE, compensating electronic defects are produced (or annihilated). As an example, consider the equilibrium between oxygen and appropriate SE s of the transition metal oxide CoO. Since all possible kinds of point defects exist in equilibrium, we may choose any convenient reaction between the component oxygen and the appropriate SE s of CoO (e.g., Eqn. (2.64))... 

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. 

Defect thermodynamics provide the guidelines for the solution of this practical problem. In Chapter 2, the basic ideas on how to influence point defect concentrations by doping with (heterovalent) additions were presented. Due to the electroneutrality condition and the laws of mass action, we can control the point defect... 

AGbo > [ AGa0, almost pure metal A is precipitated in the internal reduction zone. The reaction at the front is induced by a point defect flux which stems from the difference in oxygen potentials (point defect concentration) between the internal reaction front and the external surface. The reaction front and surface act as source and sink for the point defect flux. For example, when we assume that (A,B)0 contains transition-metal ions (e.g., (Ni,Mg)0), the defects are cation vacancies and compensating electron holes. The (reducing) external surface acts as a vacancy sink according to the reaction... 

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 -assert, however, that the input of mechanical energy into solids in the sense of tribochemistry always results in a change of their kinetic behavior. The change in point defect concentration, dislocation or crack density, and structure influences the transport coefficients and reactive properties (e.g., catalytic activity, nucleation rate, etc.). 

We remember that minority point defect concentrations in compounds depend on the activity of their components. This may be illustrated by the solubility of hydrogen in olivine since it depends on the oxygen potential in a way explained by the association of the dissolved protons with O" and O- as minority defects [Q. Bai, D. L. Kohlstedt (1993)]. Similarly, tracer diffusion coefficients and mobilities of Si and O are expected to depend on the activity of Si02. The value (0 lnDf/0 In aSio2)> = Si and O, should give information on the disorder type as discussed in Section 2.3. 

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