Defect formation thermodynamics

Analysis of mechanisms of the defect formation, thermodynamics, interaction, association and - diffusion in solid materials, validated by deep experimental studies centered on numerous particular cases, including - solid electrolytes such as -> stabilized zirconia (see also - defects in solids, -> vacancies, -> electrolytic domain, -> electronic defects, -> doping). 

Point defect populations profoundly affect both the physical and chemical properties of materials. In order to describe these consequences a simple and self-consistent set of symbols is required. The most widely employed system is the Kroger-Vink notation. Using this formalism, it is possible to incorporate defect formation into chemical equations and hence use the powerful methods of chemical thermodynamics to treat defect equilibria. 

Defects are often deliberately introduced into a solid in order to modify physical or chemical properties. However, defects do not occur in the balance of reactants expressed in traditional chemical equations, and so these important components are lost to the chemical accounting system that the equations represent. Fortunately, traditional chemical equations can be easily modified so as to include defect formation. The incorporation of defects into normal chemical equations allows a strict account of these important entities to be kept and at the same time facilitates the application of chemical thermodynamics to the system. In this sense it is possible to build up a defect chemistry in which the defects play a role analogous to that of the chemical atoms themselves. The Kroger-Vink notation allows this to be done provided the normal mles that apply to balanced chemical equations are preserved. 

However, a detailed model for the defect structure is probably considerably more complex than that predicted by the ideal, dilute solution model. For higher-defect concentration (e.g., more than 1%) the defect structure would involve association of defects with formation of defect complexes and clusters and formation of shear structures or microdomains with ordered defect. The thermodynamics, defect structure, and charge transfer in doped LaCo03 have been reviewed recently [84],... 

Lipid membranes are quite deformable, allowing water and head groups into their interiors when perturbed. A "water defect" is shown in Figure 1C, where water and lipid head groups enter the hydrophobic interior of only one of the bilayer leaflets. Figure ID shows a "water pore," where both leaflets are perturbed. At the molecular level, pore and defect formation are directly related to specific lipid-lipid interactions. It is important to understand the free energy required for pore formation in membranes and the effect of lipid composition on the process. In Section 3 of this chapter, we review recent MD studies of the thermodynamics of pore formation. 

The key role of electron microscopy is illustrated by Merritt and Hyde (1973) in studies of rutile. In the studies, the coexistence of (121) and (132) CS planes revealed only by TEM, is shown to lead to more correct thermodynamical interpretations. However, thermodynamic treatments in the literature tend to be incomplete as they have not included the reaction mechanism or the nature of the CS defect formation. 

Walter Haus Schottky (1886-1976) received his doctorate in physics under Max Planck from the Humboldt University in Berlin in 1912. Although his thesis was on the special theory of relativity, Schottky spent his life s work in the area of semiconductor physics. He alternated between industrial and academic positions in Germany for several years. He was with Siemens AG until 1919 and the University of Wurzburg from 1920 to 1923. From 1923 to 1927, Schottky was professor of theoretical physics at the University of Rostock. He rejoined Siemens in 1927, where he finished out his career. Schottky s inventions include the ribbon microphone, the superheterodyne radio receiver, and the tetrode vacuum tube. In 1929, he published Thermodynamik, a book on the thermodynamics of solids. Schottky and Wagner studied the statistical thermodynamics of point defect formation. The cation/anion vacancy pair in ionic solids is named the Schottky defect. In 1938, he produced a barrier layer theory to explain the rectifying behavior of metal-semiconductor contacts. Metal-semiconductor diodes are now called Schottky barrier diodes. 

Defects in SAMs The density of defects in SAMs may ultimately determine the usefulness of the materials in micro- and nanofabrication [77]. Although SAMs are representative self-assembling systems and tend to reject defects, formation of defects in these systems is inevitable because the true thermodynamic equilibrium is never achieved in the preparation of a SAM. A variety of factors have been found to influence the formation and distribution of defects in a SAM, including the molecular structure of the surface, the length of the alkyl chain, and the conditions used to prepare the SAM [78]. A range of techniques have been employed to... 

Thermodynamics of Point Defect Formation in Elemental Crystals... 

Equation (6.7) was derived with the implicit assumption that only one type of vacancy forms. The thermodynamics of Schottky defect formation is slightly more complicated, however, because disorder can now occur on... 

The reason why we first investigated the Statistical Mechanics approach to defect formation is that it gives us a good basis for understanding the application of chemical thermodynamics to the defect solid state. 

Note that this involves a precipitation mechanism where aggregates form. Grain boundaries form junctions between grains within the particle, due to vacancy and line-defect formation. This situation arises because of the 2nd Law of Thermodynamics (Entropy). Thus, if crystallites are formed by precipitation from solution, the product will be a powder consisting of many small particles. Their actual size will depend upon the methods used to form them. Note that each crystallite can be a single-crystal but, of necessity, will be limited in size. 

Many industrial crystallization processes, by necessity, push crystal growth rates into a regime where defect formation becomes unavoidable and the routes for impurity incorporation are numerous. Since dislocations, inclusions, and other crystal lattice imperfections enhance the uptake of impurities during crystallization, achieving high purity crystals requires elimination of impurity incorporation and carry-over by both thermodynamic and non-thermodynamic mechanisms. Very generally, the impurity content in crystals can be considered as the sum of all of these contributions... 

The basic tools for the modeling of the solid and liquid states belong to three main categories. We can mention first the Molecular Mechanics which rely on site-site or covalent potentials and which are used to study in particular defect formations, to calculate accoustic and optical phonon modes by lattice dynamics and to estimate mechanical and thermodynamical properties. The easy implementation of the Molecular Mechanics scheme supports its intensive use in the past and its success in commercial softwares. 

The Thermodynamics of Defect Formation in Self-Assembled Systems... 

The thermodynamics of microphase separation in BCPs has been reviewed several times following the original work of Bates (Bates, 1991). The theory will not be detailed in depth here except to show how it relates to intermolecular forces through the solubility parameter and how the thermodynamics of defect formation in these systems can be properly understood. Most of the understanding of microphase separation of BCPs is centred on a term known as the interaction parameter y. Assuming a simple di-block copolymer made up of sub-units A and B, the x value resulting from the interactions between block A and block B can be written as ... 

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