Point defects vacancy, defined

The resulting equilibrium concentrations of these point defects (vacancies and interstitials) are the consequence of a compromise between the ordering interaction energy and the entropy contribution of disorder (point defects, in this case). To be sure, the importance of Frenkel s basic work for the further development of solid state kinetics can hardly be overstated. From here on one knew that, in a crystal, the concentration of irregular structure elements (in thermal equilibrium) is a function of state. Therefore the conductivity of an ionic crystal, for example, which is caused by mobile, point defects, is a well defined physical property. However, contributions to the conductivity due to dislocations, grain boundaries, and other non-equilibrium defects can sometimes be quite significant. 

Point Defects. Point defects are defined as atomic defects. Atomic defects such as metal ions can diffuse through the lattice without involving themselves with lattice atoms or vacancies (Figure 9), in contrast to atomic defects such as self-interstitials. The silicon self-interstitial is a silicon atom that is bonded in a tetrahedral interstitial site. Examples of point defects are shown in Figure 9. 

Besides the distortion of the coordination polyhedron, deviations of Nc from integer values can be caused by point defects (vacancy and interstitial) in a crystal structure or in the first coordination sphere of an amorphous solid. These values of Nc are defined experimentally by XRD (see Chap. 7) and by optical methods. Thus, Wemple [242] estimated by spectroscopy that in the structure of AS2S3 the N = 3.4 0.2 whereas Eq. 5.7 gives 3.7. Optical estimates of Nc of Se andTe are 2.8 and 3.0, respectively, whereas the calculated values are 2.8 and 3.1. When the composition of chalcogenide glasses (Ge-S, Ge-Se, As-Se, Ge-As-Se) is altered, there occur phase transformations with changing structural, mechanical and electric properties... 

The question raised by Anderson (1970,1971) and Anderson et al (1973) as to whether anion point defects are eliminated completely by the creation of extended CS plane defects, is a very important one. This is because anion point defects can be hardly eliminated totally because apart from statistical thermodynamics considerations they must be involved in diffusion process. Oxygen isotope exchange experiments indeed suggest that oxygen diffuses readily by vacancy mechanism. In many oxides it is difficult to compare small anion deficiency with the extent of extended defects and in doped complex oxides there is a very real discrepancy between the area of CS plane present which defines the number of oxygen sites eliminated and the oxygen deficit in the sample (Anderson 1970, Anderson et al 1973). We attempt to address these issues and elucidate the role of anion point defects in oxides in oxidation catalysis (chapter 3). 

Chemical solid state processes are dependent upon the mobility of the individual atomic structure elements. In a solid which is in thermal equilibrium, this mobility is normally attained by the exchange of atoms (ions) with vacant lattice sites (i.e., vacancies). Vacancies are point defects which exist in well defined concentrations in thermal equilibrium, as do other kinds of point defects such as interstitial atoms. We refer to them as irregular structure elements. Kinetic parameters such as rate constants and transport coefficients are thus directly related to the number and kind of irregular structure elements (point defects) or, in more general terms, to atomic disorder. A quantitative kinetic theory therefore requires a quantitative understanding of the behavior of point defects as a function of the (local) thermodynamic parameters of the system (such as T, P, and composition, i.e., the fraction of chemical components). This understanding is provided by statistical thermodynamics and has been cast in a useful form for application to solid state chemical kinetics as the so-called point defect thermodynamics. 

Let us refer to Figure 5-7 and start with a homogeneous sample of a transition-metal oxide, the state of which is defined by T,P, and the oxygen partial pressure p0. At time t = 0, one (or more) of these intensive state variables is changed instantaneously. We assume that the subsequent equilibration process is controlled by the transport of point defects (cation vacancies and compensating electron holes) and not by chemical reactions at the surface. Thus, the new equilibrium state corresponding to the changed variables is immediately established at the surface, where it remains constant in time. We therefore have to solve a fixed boundary diffusion problem. 

The catalyst particle is usually a complex entity composed of a porous solid, serving as the support for one or more catalytically active phase(s). These may comprise clusters, thin surface mono- or multilayers, or small crystallites. The shape, size and orientation of clusters or crystallites, the extension and arrangement of different crystal faces together with macrodcfects such as steps, kinks, etc., are parameters describing the surface topography. The type of atoms and their mutual positions at the surface of the active phase or of the support, and the type, concentration and mutual positions of point defects (foreign atoms in lattice positions, interstitials, vacancies, dislocations, etc.) define the surface structure. 

The doped semiconductor materials can often be considered as well-characterized, diluted solid solutions. Here, the solutes are referred to as point defects, for instance, oxygen vacancies in TiC - phase, denoted as Vq, or boron atoms in silicon, substituting Si at Si sites, Bj etc. See also -> defects in solids, -+ Kroger-Vink notation of defects. The atoms present at interstitial positions are also point defects. Under stable (or metastable) thermodynamic equilibrium in a diluted state, - chemical potentials of point defects can be defined as follows ... 

At that date, palladium hydride was regarded as a special case. Lacher s approach was subsequently developed by the author (1946) (I) and by Rees (1954) (34) into attempts to frame a general theory of the nature and existence of solid compounds. The one model starts with the idea of the crystal of a binary compound, of perfect stoichiometric composition, but with intrinsic lattice disorder —e.g., of Frenkel type. As the stoichiometry adjusts itself to higher or lower partial pressures of one or other component, by incorporating cation vacancies or interstitial cations, the relevant feature is the interaction of point defects located on adjacent sites. These interactions contribute to the partition function of the crystal and set a maximum attainable concentration of each type of defect. Conjugate with the maximum concentration of, for example, cation vacancies, Nh 9 and fixed by the intrinsic lattice disorder, is a minimum concentration of interstitials, N. The difference, Nh — Ni, measures the nonstoichiometry at the nonmetal-rich phase limit. The metal-rich limit is similarly determined by the maximum attainable concentration of interstitials. With the maximum concentrations of defects, so defined, may be compared the intrinsic disorder in the stoichiometric crystals, and from the several energies concerned there can be specified the conditions under which the stoichiometric crystal lies outside the stability limits. 

The first question to address is the definition of a defect in an amorphous material. In a crystal any departure from the perfect crystalline lattice is a defect, which could be a point defect, such as a vacancy or interstitial, an extended defect, such as a dislocation or stacking fault, or an impurity. A different definition is required in an amorphous material because there is no perfect lattice. The inevitable disorder of the random network is an integral part of the amorphous material and it is not helpful to think of this as a collection of many defects. By analogy with the crystal one can define a defect as a departure from the ideal amorphous network which is a continuous... 

When the composition of a crystal is defined by a distinct chemical formula e.g., Si02), it is known as a stoichiometric compound. If the composition of the crystal is altered upon doping or thermal treatment, the resulting solid may deviate from the original chemical formula, forming a nonstoichiometric solid. Nonstoichiometry and the existence of point defects in a solid are often closely related. For instance, the formation of x anion vacancies per each quartz unit cell will result in the nonstoichiometric compound Si02-x ... 

Point (microscopic) defects in contrast from the macroscopic are compatible with the atomic distances between the neighboring atoms. The initial cause of appearance of the point defects in the first place is the local energy fluctuations, owing to the temperature fluctuations. Point defects can be divided into Frenkel defects and Schottky defects, and these often occur in ionic crystals. The former are due to misplacement of ions and vacancies. Charges are balanced in the whole crystal despite the presence of interstitial or extra ions and vacancies. If an atom leaves its site in the lattice (thereby creating a vacancy) and then moves to the surface of the crystal, it becomes a Schottky defect. On the other hand, an atom that vacates its position in the lattice and transfers to an interstitial position in the crystal is known as a Frenkel defect. The formation of a Frenkel defect therefore produces two defects within the lattice—a vacancy and the interstitial defect—while the formation of a Schottky defect leaves only one defect within the lattice, that is, a vacancy. Aside from the formation of Schottky and Frenkel defects, there is a third mechanism by which an intrinsic point defect may be formed, that is, the movement of a surface atom into an interstitial site. Considering the electroneutrality condition for the stoichiometric solid solution, the ratio of mole parts of the anion and cation vacancies is simply defined by the valence of atoms (ions). Therefore, for solid solution M X, the ratio of the anion vacancies is equal to mJn. 

The solid-state clusters are distinguished from liquid ones by the rigidity of their structure. As a defining criterion for rigidity we shall choose the stability of point defects, i.e., vacancies and interstitial atoms, in the body of the cluster. 

Point-defect ordering (e.g., vacancy-dopant pairs) leads to interesting complications. Preparation conditions themselves (e.g., oxygen partial pressure and temperature in oxides) thermodynamically define and control this defect content and structure. It is important to realize that point defects are thermodynamically allowed and defined they are not anomalous in the least. Therefore, undoped, high-purity compounds may exhibit sizable nonstoichiometry due to intrinsic point defects. Doping (intentional addition of an impurity) allows one to precisely control the point-defect content and nonstoichiometry and, thereby, the properties. Transport properties are influenced by the point defects. Electrical conduction (hole or electron transport) and solid state diffusion of atoms generally vary with the quantity and type of point defects. 

Jogs are formed by climb. They are favorable sites for the absorption and emission of point defects. In thermal equilibrium, the atoms at jog sites are in dynamic equilibrium and arrive and leave the jog at equal rates. If there is an increase in vacancies, for example, in the vicinity of a dislocation line above the thermal equilibrium value, the probability of atomic exchange at a jog with a vacancy increases, climb occurs and the extra plane (defining the dislocation line) shrinks. Therefore, excess vacancies promote the process of climb. Similarly, an excess of interstitial atoms adds atoms to the existing jog, which causes it to grow. In summary, when atoms are removed from an extra plane, the crystal collapses... 

Finally, there are zero-dimensional or point defects that could also be considered part of the microstructure of the material. These include vacancies or foreign atoms substituting at atomic positions in a crystal lattice as well as interstitial atoms residing in between the normal atomic sites. They are not discussed further in this chapter, partly due to limited space and partly because they are not amenable to observation by the same sorts of microscopic techniques typically used to define the other aspects of the material microstructure. More information can readily be found in the many existing treatises on point defects and crystal chemistry in the literature. ... 

It is important to note that there is no question of uniquely partitioning the Frenkel pair creation energy between the vacancy and the interstitial in the bulk they can only b created simultaneously. It is only when a surface is present that they may be created in unequal numbers. We now consider the necessary modifications to our scheme when the crystal is semi-infinite and bounded by a particular crystallographic plane. We suppose for the sake of simplicity that only one particular type of surface site is important in point defect creation and tentatively focus on the kink sites, (figure (8)). Let there be Ng such surface sites per unit area with energy W+ relative to the normal bulk lattice site, figure (IG). We may then define for this particular... 

If a point defect (ion or ion vacancy) is introduced into the solid, its potential energy will be changed from the one defining the previous ideal solid and the defect located at infinity. This new potential energy will depend on the position of the defect in the solid. The point defect has a position of equihbrium in the system that will keep the new potential energy at a minimum... 

Section 5.2 we conceive, in this description, the point defects as species, that we add to the perfect crystal that is, they must be true relative elements. The more vivid representation [167] in the form of structure elements (V vacancy, i interstitial position, see Section 1.2), which now takes account of the actual structure of the real crystal in Eq. (5.78), but only includes the centres actually affected and defines the charge relative to the perfect lattice, reads ... 

Define the following point defects and identify them as atomic defects or electronic defects vacancy, interstitial, substitutional impurity, misplaced atoms, electron, hole, dopant. 

Defects in these crystal structures are essential to determining the properties of the materials. The crystalline defects relevant to semiconductors will be discussed in detail in Chapter 7. Amorphous materials have no regular order so there are no well-defined defects in the material. Nonetheless, we will see in Chapter 8 that the continuum of distortions in the structures of amorphous semiconductors play a key role in determining their properties. Here we will list only the types of atomic-scale (point) defects in crystalline materials and leave more complex structures and detailed discussion to Chapters 7 and 8. Point defects in crystals include vacancies, interstitials, and antisites. Vacancies are missing atoms in the crystal structure. They are essential to the diffusion of atoms among lattice sites in many materials. Interstitials are atoms lying in spaces between atoms in the crystal structure. More open lattices such as the diamond structure accommodate interstitial atoms relatively... 

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