Vacancies in solids

A major difference between crystals and fluids refers to the necessity of distinguishing between different sites. So the autoprotolysis in water could, just from a mass balance point of view, also be considered e.g. as a formation of a OH vacancy and a IT vacancy. In solids such a disorder is called Schottky disorder (S) and has to be well discerned from the Frenkel disorder (F). In the densely packed alkali metal halides in which the cations are not as polarizable as the Ag+, the formation of interstitial defects requires an unrealistically high energy and the dominating disorder is thus the Schottky reaction... 

Fig. 14 Anodic reactions at the three-phase boundary of a SOFC V°° = oxygen vacancy in solid conducting oxide.

Since the barrier heights between the potential minima can be readily changed, diffusion process can be studied in detail by optical spectroscopy. Non-occupied minima correspond to vacancies in solid crystals and their influence on the interaction between neighbouring atoms gives information on vacancy effects in solids. 

The cell reaction can occur without molecular oxygen > Krdger-Vinks Notation of Point Defects is used) between oxide ions in NiO and the oxide ion vacancies in solid electrolytes according to... 

Wagner C (1950) Determinatimi of the concentrations of cation and anitm vacancies in solid potassiinn chloride. J Electiochem Soc 97 72-74. doi 10.1063/l.1747460... 

The oxygen vacancies in solid MgO give rise to interesting features in the optical spectra. The so called F centers are characterized by the trapped eleetrons in the eavity left by removing the anion. The removal of an O ion or a neutral O atom results in or F centers with one or two electrons trapped, respectively. It... 

Atomic scale defects, e.g. vacancies, dislocations, can be produced ikiring crystal growth. Because of their contribution to increased entropy the different forms of point defect are thermodynamically slable. The equilibrium concentration of vacancies in solids at (emperatures near the melting temperature is of the order of 10" . 

Typical surfactants have a difference in valence of one electron relative to the atom they replace. Thus, As atoms passivate Si surfaces, while S atoms can be used to passivate GaAs. H treatment of a Si surface reduces its reactivity significantly and passivates surface states. However, H is a small atom and relatively weakly bound to the surface. Furthermore, it reacts readily with other atoms that may adsorb. Hence, H passivation is delicate and of limited long-term value. Of more significance is that H can fit into many vacancies in solids, will passivate their dangling bonds, and so reduces the number of electrically-active defects. This is one reason why many chemical vapor deposition crystal growth processes include copious amounts of H as a dilutant gas. It not only contributes to control of the deposition reaction process, but it helps reduce the effects of growth defects. 

Dislocation theory as a portion of the subject of solid-state physics is somewhat beyond the scope of this book, but it is desirable to examine the subject briefly in terms of its implications in surface chemistry. Perhaps the most elementary type of defect is that of an extra or interstitial atom—Frenkel defect [110]—or a missing atom or vacancy—Schottky defect [111]. Such point defects play an important role in the treatment of diffusion and electrical conductivities in solids and the solubility of a salt in the host lattice of another or different valence type [112]. Point defects have a thermodynamic basis for their existence in terms of the energy and entropy of their formation, the situation is similar to the formation of isolated holes and erratic atoms on a surface. Dislocations, on the other hand, may be viewed as an organized concentration of point defects they are lattice defects and play an important role in the mechanism of the plastic deformation of solids. Lattice defects or dislocations are not thermodynamic in the sense of the point defects their formation is intimately connected with the mechanism of nucleation and crystal growth (see Section IX-4), and they constitute an important source of surface imperfection. 

Materials that contain defects and impurities can exhibit some of the most scientifically interesting and economically important phenomena known. The nature of disorder in solids is a vast subject and so our discussion will necessarily be limited. The smallest degree of disorder that can be introduced into a perfect crystal is a point defect. Three common types of point defect are vacancies, interstitials and substitutionals. Vacancies form when an atom is missing from its expected lattice site. A common example is the Schottky defect, which is typically formed when one cation and one anion are removed from fhe bulk and placed on the surface. Schottky defects are common in the alkali halides. Interstitials are due to the presence of an atom in a location that is usually unoccupied. A... 

Crystal structure of solids. The a-crystal form of TiCla is an excellent catalyst and has been investigated extensively. In this particular crystal form of TiCla, the titanium ions are located in an octahedral environment of chloride ions. It is believed that the stereoactive titanium ions in this crystal are located at the edges of the crystal, where chloride ion vacancies in the coordination sphere allow coordination with the monomer molecules. 

The other major defects in solids occupy much more volume in the lattice of a crystal and are refeiTed to as line defects. There are two types of line defects, the edge and screw defects which are also known as dislocations. These play an important part, primarily, in the plastic non-Hookeian extension of metals under a tensile stress. This process causes the translation of dislocations in the direction of the plastic extension. Dislocations become mobile in solids at elevated temperamres due to the diffusive place exchange of atoms with vacancies at the core, a process described as dislocation climb. The direction of climb is such that the vacancies move along any stress gradient, such as that around an inclusion of oxide in a metal, or when a metal is placed under compression. 

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... 

An account of the mechanism for creep in solids placed under a compressive hydrostatic suess which involves atom-vacancy diffusion only is considered in Nabano and Hemirg s (1950) volume diffusion model. The counter-movement of atoms and vacancies tends to relieve the effects of applied pressure, causing extension normal to the applied sU ess, and sluinkage in the direction of the applied sU ess, as might be anticipated from Le Chatelier s principle. The opposite movement occurs in the case of a tensile sU ess. The analysis yields the relationship... 

There is a qualitative distinction between these two types of mass transfer. In the case of vapour phase transport, matter is subtracted from the exposed faces of the particles via dre gas phase at a rate determined by the vapour pressure of the solid, and deposited in the necks. In solid state sintering atoms are removed from the surface and the interior of the particles via the various diffusion vacancy-exchange mechanisms, and the centre-to-cenU e distance of two particles undergoing sintering decreases with time. 

It was shown earlier that the NabaiTO-Hemirg model of creep in solids involved the migration of vacancies out of the stressed solid accompanied by counter-migration of atoms to reduce dre length of the solid in the direction of the applied stress. This property could clearly contribute to densification under an external pressure, given sufficient time of application of the stress... 

Fig. 10.4. Ball bearings can be used to simulate how atoms are packed together in solids. Our photograph shows a ball-bearing model set up to show what the grain boundaries look like in a polycrystalline material. The model also shows up another type of defect - the vacancy - which is caused by a missing atom.

If one is interested in the configuration of a singular surface or a vicinal surface close to the singular orientation, the surface is better characterized by the local height hj. The description assumes that there should be no vacancy in the crystal, no floating-solid atoms in the ambient phase, nor... 

Whether you recdize it or not, we have already developed our own symbolism for defects and defect reactions based on the Plane Net. It might be well to compeu e our system to those of other authors, who have also considered the same problem in the past. It was Rees (1930) who wrote the first monograph on defects in solids. Rees used a box to represent the cation vacancy, as did Libowitz (1974). This has certain advantages since we can write equation 3.3.5. as shown in the following ... 

According to our nomenclature, as used in the table, Vm is a vacancy at an M cation site, etc. The first five pairs of defects given above have been observed experimentally in solids, whereas the last four have not. This answers the question posed above, namely that defects in solids occur in pairs. 

While this maybe true for the reaction in 4.7.2., l.e. - Mi2+ <. Xj, what of the case for BaSiOs where diffusion was limited to one direction It is not reasonable to assume that the solid would build up a cheirge as the Mj2+ ions are diffusing (and the Si04= ions are not) and we must search for compensating species elsewhere. It turns out that charge compensation occurs by diffusion of chained vacancies in the lattice. 

The point defects are decisive for conduction in solid ionic crystals. Ionic migration occurs in the form of relay-type jumps of the ions into the nearest vacancies (along the held). The relation between conductivity o and the vacancy concentration is unambiguous, so that this concentration can also be determined from conductivity data. 

Point defects in solids make it possible for ions to move through the structure. Ionic conductivity represents ion transport under the influence of an external electric field. The movement of ions through a lattice can be explained by two possible mechanisms. Figure 25.3 shows their schematic representation. The first, called the vacancy mechanism, represents an ion that hops or jumps from its normal position on the lattice to a neighboring equivalent but vacant site or the movement of a vacancy in the opposite direction. The second one is an interstitial mechanism where an interstitial ion jumps or hops to an adjacent equivalent site. These simple pictures of movement in an ionic lattice, known as the hopping model, ignore more complicated cooperative motions. 

The chemistry of iron(IV) in solid-state materials and minerals is restricted to that of oxides, since other systems such as iron(IV)-halides are not stable [186]. Iron(lV) oxides are easy to handle because they are usually stable in air, but they often have a substoichiometric composition, with oxygen vacancies contributing to varying degrees. Moreover, the samples may contain different amounts of iron(lll) in addition to the intended iron(IV) oxide, a complication which may obscure the Mossbauer data [185]. Even iron(V) was found in iron(IV) oxides due to temperature-dependent charge disproportionation [188, 189]. 

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