Solids with cation vacancies

Once again, the electrons are from the material s valence band, therefore causing an electron hole conduction. As for the surface potentials, the remarks made about the first case apply for all other cases. 

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Figure 4.9. Insertion mechanism of an oxygen atom in the lattice of a MOl +x-type oxide 4.4.4. Solids with cation vacancies (see Figure 4.10)...

Ionic binary solids with cation vacancies of B... 

Ionic binary solids with cation vacancies of B are characterized by the following conditions on concentrations [Vg] 0 and [V ] = [Bj = [A ] = 0 Then, the simplified expression of the distance from stoicWometiy for B is... 

In stage I, a CO3 ion and an F center are produced, and in stage II the F center is destroyed by the adsorption of an oxygen atom. These F centers, however, decay with time, probably due to combination with cationic vacancies from the interior of the solid. 

Transition from Linear to Parabolic Kinetics When thermodynamic equilibrium is nearly estabhshed at the surface and also at the oxide/metal interface, oxidation is virtually controlled by diffusion in the solid oxide. For oxides such as FeO, NiO, CoO, CU2O, and so on with cation vacancies Vm as the prevailing defects, the growth occurs by outward flux of cations and inward flux of vacancies, both fluxes are equal and given by... 

Another possibility is the location of ion in interstitial position, for example interstitial solid solution of Na in C3A. Still another possibihty is the cationic vacancies formation. It is the substitntion of calcium ions by chrominm(III) in octahedral positions in C3S with cationic vacancy formation (extraction sohd solntion). 

Niekel oxide NiO is metal deficient with cation vacancies predominating. If it is doped with Li, which goes into solid solution on the regular Ni lattice sites, develop equations for the defect equilibria and constract the Brouwer diagram. 

In conclusion, if an element of an alloy which constitutes an ideal solid solution is oxidized selectively by a gas, the diffusion in alloy of the oxidized element is compensated by a diffusion of vacancies in opposite direction. The paraboUc law of oxidation can have two different origins a pure mode of diffusion in oxide and a diffusion-mixed mode in both oxide and alloy. If the oxide is a p-type semiconductor with cationic vacancies, the two modes can be distinguished by both influences of gas pressure and initial alloy compositioa... 

These studies show that the thiospinel structure is quite flexible with opportunity for cation vacancies at the 8 a site. Our investigation on such cation-deficient thiospinels is significant in that it shows that additional vacancies are possible in the 8 a site. Most of the cation-deficient compounds known earlier (predominantly copper compounds) were obtained by extraction of Cu by using various oxidizing reagents. These studies show that such cation-deficient quaternary thiospinels can also be obtained by direct solid-state reactions. 

Extrinsic Defects Extrinsic defects occur when an impurity atom or ion is incorporated into the lattice either by substitution onto the normal lattice site or by insertion into interstitial positions. Where the impurity is aliovalent with the host sublattice, a compensating charge must be found within the lattice to pre-serve elec-troneutality. For example, inclusion of Ca in the NaCl crystal lattice results in the creation of an equal number of cation vacancies. These defects therefore alter the composition of the solid. In many systems the concentration of the dopant ion can vary enormously and can be used to tailor specific properties. These systems are termed solid solutions and are discussed in more detail in Section 25.1.2. 

Atoms in the free surface of solids (with no neighbors) have a higher free energy than those in the interior and surface energy can be estimated from the number of surface bonds (Cottrell 1971). We have discussed non-stoichiometric ceramic oxides like titania, FeO and UO2 earlier where matter is transported by the vacancy mechanism. Segregation of impurities at surfaces or interfaces is also important, with equilibrium and non-equilibrium conditions deciding the type of defect complexes that can occur. Simple oxides like MgO can have simple anion or cation vacancies when surface and Mg + are removed from the surface,... 

For a 1 1 solid MX, a Schottky defect consists of a pair of vacant sites, a cation vacancy, and an anion vacancy. This is presented in Figure 5.1 (a) for an alkali halide type structure the number of cation vacancies and anion vacancies have to be equal to preserve electrical neutrality. A Schottky defect for an MX2 type structure will consist of the vacancy caused by the ion together with two X anion vacancies, thereby balancing the electrical charges. Schottky defects are more common in 1 1 stoichiometry and examples of crystals that contain them include rock salt (NaCl), wurtzite (ZnS), and CsCl. 

The NaCl structure is also found in compounds like TiO, VO and NbO, possessing a high percentage of cation and anion vacancies. Ternary oxides of the type MggMn 08 crystallize in this structure with of the cation sites vacant. Solid solutions such as Li,j )Mg Cl (0 x 1) crystallize in the rocksalt structure stoichiometric MgCl may indeed be considered as having a defect rocksalt structure with 50% of ordered cation vacancies. 

When divalent cation impurities (e.g. Cd, Sr ) are present in an ionic solid of the type MX consisting of monovalent ions, the negatively charged cation vacancies (created by the divalent ions) are bound to the impurity ions at low temperatures. Similarly, the oppositely charged cation and anion vacancies tend to form neutral pairs. Such neutral vacancy pairs are of importance in diffusion, but do not participate in electrical conduction. The interaction energy of vacancy pairs or impurity-vacancy pairs decreases with the increase in distance between the two oppositely charged units. 

Equation (1.204) shows an equilibrium between the solid and gas phases for metal M, assuming that the molecular species of metal gas is M(g). Towards the right-hand side, the reaction gives an excess metal atom (neutral), Mm, with a vacancy at an anion site, Vx. Equation (1.205) shows an equilibrium between the solid and gas phases for anion X, assuming that the molecular species of anion gas is X2(g). Towards the right-hand side, the reaction gives an excess anion (neutral), Xx, with a vacancy at a cation site, Vm- In place of these two reactions, we can choose the following reactions ... 

In the next step, we discuss the demixing of semiconducting oxide solid solutions (A, B)0 as illustrated in Figure 8-2. Instead of formulating the constant cation vacancy flux as in the steady state condition of Eqn. (8.1), let us express this condition explicitly and note that the frame connected to the oxide sample surface moves with the same velocity as the components so that the composition does not change with time... 

In the KI/C12 reaction, an interesting effect of high defect concentration in preventing growth of nuclei of a new solid phase was disclosed [103]. Solid samples differed widely in their initial ionic conductivity and hence in their initial concentration of cation vacancies. The ones with high vacancy concentration reacted very slowly with chlorine and the colour of iodine was seen uniformly as a pale coloration of the whole solid, which had reacted to the extent of only a few percent after several days. Samples with a low vacancy concentration reacted more rapidly and a sharp boundary developed between an outer, iodine-blackened completely reacted region and a pale-coloured inner region. In the un-reactive samples, electronic (presumably positive hole) conductivity appeared transiently for a few hours and then decayed. In the reactive... 

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. 

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