Stoichiometric Defect Reactions

A stoichiometric defect reaction by definition is the one where the chemistry of the crystal does not change as a result of the reaction. The three most 

Schottky defects When these defects are formed, electric-charge-equivalent numbers of vacancies are formed on each sublattice. 

The Frenkel defect reaction for a trivalent cation is given in Equation 10.3. 

The same reaction on the oxygen sublattice is given in Equation 10.4. 

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In a non-stoichiometric crystcd, the lattice may have either excess charge or excess cations and/or anions situated in the lattice. Consider the semiconductor, Ge. It is a homogeneous solid and is expected to contain excess charge. The defect reactions associated with the formation of p-type and n-type lattices are ... 

Due to participation in oxidation-reduction reactions the reducing or inflammable gases affect the stoichiometricity of oxide and, consequently the concentration of stoichiometric defects which usually control the dope electric conductivity of adsorbent [26, 67, 85, 86, 90]... 

Analyses of the defect chemistry and thermodynamics of non-stoichiometric phases that are predominately ionic in nature (i.e. halides and oxides) are most often made using quasi-chemical reactions. The concentrations of the point defects are considered to be low, and defect-defect interactions as such are most often disregarded, although defect clusters often are incorporated. The resulting mass action equations give the relationship between the concentrations of point defects and partial pressure or chemical activity of the species involved in the defect reactions. 

CQ is the concentration of available sites for the crystallization of barium sulfate. This is equal to the sum of the initial concentration of already precipitated sulfate in the medium (Cg0) and of the potentially precipitable sulfate, equal to the concentration of that of the two reactants (Ba + or S0 2-) n stoichiometric defect. It was checked that the addition of EDTA did not change the rate of reaction. 

At a specified point in the tank, 100 cm of hydrochloric acid 1.2N(Cg0 = 0.83 moles. m- after complete mixing in the tank in the absence of reaction) were injected by means of a cylinder obturated at its lower end by an elastic membrane which becomes inflated and bursts out when submitted to the pressure of the liquid pushed by a piston. The acid was thus injected without any preferential direction. This locally released acid B triggers reactions f2j and 3]. If the local micromixing state is perfect, the acid is totally and instantaneously neutralized, as it is in stoichiometric defect with respect to A. The first reaction being very fast as compared to the second one, the precipitate S does not appear. Conversely, if mixing of the acid is not instantaneously... 

Stoichiometric reaction is one in which no mass is transferred across the crystal boundaries. The three most common stoichiometric defects are Schottky defects, Frenkel defects, and antistructure disorder or misplaced atoms. 

In compound crystals, balanced-defect reactions must conserve mass, charge neutrality, and the ratio of the regular lattice sites. In pure compounds, the point defects that form can be classified as either stoichiometric or nonstoichiometric. By definition, stoichiometric defects do not result in a change in chemistry of the crystal. Examples are Schottky (simultaneous formation of vacancies on the cation and anion sublattices) and Frenkel (vacancy-interstitial pair). 

In both cases the first reaction (Equations 4.33a and 4.34a) is instantaneous (e.g., a neutrahzation) while the second reaction has characteristic reaction time comparable to the characteristic mixing time. The reactant A2 is added in an overall stoichiometric defect to the stream of Aj in consecutive reactions or to the stream of solution containing A and A in parallel reactions. If the aggregates of A2 are rapidly mixed forming homogenous solution with a rate much faster than the rate of the second reaction t. ), species A2 will be almost totally consumed by... 

In view of the many types of point defects that may be formed in inorganic compounds and that each type of defect may have varying effective charge, numerous defect reactions may in principle be formulated. In the following, a few simple cases will be treated as examples. First, we will consider defect stmcture situations in stoichiometric compounds (Schottky, Frenkel and intrinsic electronic disorders) and then defect structure situations in nonstoichiometric oxides will be illustrated. Finally, examples of defect reactions involving foreign elements will be considered. 

Hydride ions have been suggested to dissolve in oxides accompanied by protons by disproportionation of hydrogen gas. Write defect reactions for this in the case that the hydride dissolves a) interstitially, and b) substitutionally. (Assume in both cases that the oxide is perfectly stoichiometric and has no defects as a starting point). 

Nickel oxide, NiO, which adopts the sodium chloride structure (Fig. 1.14), can readily be made slightly oxygen rich, and, because the solid then contains more oxygen than nickel, the crystal must also contain a population of point defects. This situation can formally be considered as a reaction of oxygen gas with stoichiometric NiO, and the simplest assumption is to suppose that the extra oxygen extends the crystal by adding extra oxygen sites. Atoms are added as neutral atoms, and... 

Results of the ideal solution approach were found to be identical with those arrived at on the basis of a simple quasichemical method. Each defect and the various species occupying normal lattice positions may be considered as a separate species to which is assigned a chemical potential , p, and at equilibrium these are related through a set of stoichiometric equations corresponding to the chemical reactions which form the defects. For example, for Frenkel disorder the equation will be... 

From the above results it is clear that the amount of Te deposited in the first atomic layer on the Au surface is critical but not structure controlling. Control over the coverage of Te in subsequent cycles should not be as critical, as it should be naturally controlled by the previously deposited Cd atomic layer. The first Te layer, however, involves the reaction of Te with the Au substrate to form a Au-Te surface compound, not CdTe. The coverages of the Te atomic layer structures formed on Au have nothing to do with the formation of stoichiometric CdTe. A homogeneous atomic layer of Te on Au at the correct coverage [1/2 ME on Au(lOO)] (Fig. 41B), with no pits or islands, should produce the lowest defect density in the... 

Vanadium is present as V " in stoichiometric VPP however, the latter can host V " or V species as defects, without undergoing substantial structural changes (5,6). Therefore, the role of the different V species in the catalytic behavior of VPP in n-butane oxidation has been the object of debate for many years (7-9). Moreover, the catalyst may contain crystalline and amorphous vanadium phosphates other than (VO)2P207 (10) for instance, outer surface layers of V phosphates may develop in the reaction environment, and play active roles in the catalytic cycle. This is particularly true in the case of the fresh catalyst, while the equilibrated system (that one which has been kept under reaction conditions for 100 hours at least) contains only minor amounts of compounds with V species other than V. ... 

Non-stoichiometric compounds are found for the higher oxides of tungsten, molybdenum, and titanium—WOs-, MoOs-, and Ti02- f, respectively. The reaction of these systems to the presence of point defects is entirely different from what has been discussed previously. In fact, the point defects are eliminated by a process known as crystallographic shear (CS). 

Oxidation of zinc to zinc oxide is another example whose kinetics have been interpreted in terms of the Wagner model (Wagner Grunewald, 1938). At 670 K, the reaction has been found to be independent of oxygen pressure between 0.02 and 1 atm. ZnO is a n-type semiconductor, having a stoichiometric excess of zinc accommodated as interstitials the defect equilibrium could be represented as... 

For elemental solids and stoichiometric compound crystals, the primary influence of irradiation on their kinetic behavior is due to the increase in Acv(s Ac,). We would expect the enhancement in the component diffusion to be in proportion to the increase in the (average) defect concentrations, thus influencing all homogeneous, inhomogeneous, and heterogeneous solid state reactions. 

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