Cation vacancy diffusion

The same analysis can be applied to more complex situations. Suppose that cation vacancy diffusion is the predominant migration mechanism, in a sodium chloride structure crystal, of formula MX, which contains Schottky defects as the major type of intrinsic defects. The relevant defect concentration [ii] is [Eq. (2.11)]... 

To summarize the case of cation vacancy diffusion, the coupled growth equations for the oxide layers can be written in the form... 

Allen and Weber demonstrated that increasing temperature will enhance the likelihood of cationic vacancies diffusing through the lattice. This is typically observed by a deviation in the Ti versus T plot from the behaviour noted earlier. This change in behaviour is accompanied by a decrease in the halogen NMR signal linewidth (Figures 9 and 10). This characteristic temperature... 

To illustrate this, suppose that cation vacancy diffusion is the predominant migration mechanism... 

Figure 11.10 shows the formation of p-type metal deficit oxides nonstoichiometric oxides with metal deficits. The defects are cation vacancies and oxygen interstitials. They are compensated through the formation ofpositive electronic defects (electronic holes). Electron charges are transferred to the metal-oxide interface by the movement of electron holes in the opposite direction. Metal cations diffuse at the oxide-air-gas interface, while the cation vacancies diffuse in opposite direction. The oxide film is formed at the oxide-metal interface. 

In the case of lattice diffusion, the effective diffusion coefficient can vary considerably with the addition of a dopant because the dopant addition can drastically change the concentration of defects, as explained in Chapter 12. Consider, as an example, an MO oxide with vacancies as major defects. If the activation energy of cation vacancy diffusion, lower than that of anion... 

The cation vacancies diffuse and are consumed (as well as the electron holes) at the internal interface, which will be the X interface, where there is an excess of metal, which we will express as follows ... 

Pieraggi B and Rapp R A (1988), Stress generation and vacancy annihilation during scale growth limited by cation-vacancy diffusion , Acta Metall, 36(5), 1281-1289. 

The electrons required to reduce 02 to o - come from individual cations which are thereby oxidized to a higher oxidation state. Alternatively, if suitable interstitial sites are not available, the excess ions can build on to normal lattice sites thereby creating cation vacancies which diffuse into the crystal, e.g. ... 

We denote by x the distance from the metal surface, and by n x) and rip x) the concentrations of cation vancancies and positive holes in the oxide. Let and Vp be their mobilities, and and Dp their diffusion coefficients. Let F x) be the electrostatic field in the oxide. J, the flux of cation vacancies (number crossing unit area per second), will be expressed by... 

Our picture of the transport process in these thick oxide layers is that there is a uniform concentration gradient of defects (cation vacancies and positive holes) across the layer. But it is important to notice that the oxidation flux is exactly twice that to be expected if diffusion alone were responsible for the transport of cation vacancies. The reason for this is, of course, that the more mobile positive holes set up an electric field which assists the transport of the slower-moving cation vacancies. 

Note that the cheurged vacancy diffuses as one of the reacting species to form the defect compound. This situation is quite common in the solid state chemistry of compounds conteiining multivalent cations. The trivalent Ni3+ also gives rise to a new compound, N1A104. Yet the same... 

These diffuse through the lithium iodide via cation vacancies that form as part of the intrinsic Schottky defects in the crystals, to reach the iodine in the cathode (Fig. 2.3b). The electrons lost by the lithium metal on ionizing traverse the external circuit and arrive at the interface between the cathode and the electrolyte. Here they react with the iodine and the incoming Li+ ions to form more lithium iodide. 

When Schottky defects are present in a crystal, vacancies occur on both the cation and anion sublattices, allowing both cation and anion vacancy diffusion to occur (Fig. 5.12a). In the case of Frenkel defects interstitial, interstitialcy, and vacancy diffusion can take place in the same crystal with respect to the atoms forming the Frenkel defect population (Fig. 5.12b). 

Figure 5.13 Diffusion of a cation-anion divacancy within the (100) plane of a sodium chloride structure crystal (a-c) shows diffusion by way of individual cation and anion vacancy diffusion.

Diffusion in the extrinsic region can readily be modified by doping, although knowledge of the mechanism by which the diffusion takes place is important if this is to be immediately successful. For example, sodium chloride structure materials that conduct by a vacancy mechanism can have the cation conductivity enhanced by doping with divalent cations, as these generate compensating cation vacancies. The inclusion of cadmium chloride into sodium chloride can be written ... 

The high-pressure region is associated with the electroneutrality equation [h ] = 2[V ]. Holes predominate, so that the material is a p-type semiconductor in this regime. In addition, the conductivity will increase as the g power of the partial pressure of the gaseous X2 component increases. The number of metal vacancies (and nonmetal excess) will increase as the partial pressure of the gaseous X2 component increases and the phase will be distinctly nonstoichiometric. There is a high concentration of cation vacancies that would be expected to enhance cation diffusion. 

Let us now consider the crystal MO. If the diffusion takes place by migration of cationic vacancies, the number of atoms that undergo the process depends on the vacancy concentration [Vm] and the thermal state of single atoms M (the jump takes place only whenever atom M in the neighborhood of the vacancy has sufficient energy to perform it). The diffusion coefficient associated with the vacancy migration process is given by... 

Magnetite transforms to maghemite (and thence to hematite) in water or alkali under hydrothermal conditions. Conversion to maghemite also involves outward migration of cations via cation vacancies (Swaddle Oltmann, 1980). The hydrothermal transformation is slower than that in air at the same temperature (180 °C) and it has been suggested that this is because the cation vacancies which assist cation diffusion are reduced or eliminated by the large excess of water. 

Assume that ionic diffusion in Fei.xO occurs via cation vacancies. A defect reaction that conserves charge and atoms can be written as... 

Diffusion of K+ ions in KCl occurs by interchange of the potassium ions with cation vacancies (see Figure 4.40d). It makes sense, then, that the diffusivity of potassium ions in KCl, Dk,ci is both a function of the potassium ion mobility, A. and the cation vacancy concentration, [V[ ... 

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. 

A variety of techniques has been employed to investigate aliovalent impurity-cation vacancy pairs and other point defects in ionic solids. Dielectric relaxation, optical absorption and emission spectroscopy, and ionic thermocurrent measurements have been most valuable ESR studies of Mn " in NaCl have shown the presence of impurity-vacancy pairs of at least five different symmetries. The techniques that have provided a wealth of information on the energies of migration, formation and other defect energies in ionic solids are diffusion and electrical conductivity measurements. Electrical conductivity in ionic solids occurs by the motion of ions through vacancies or of interstitial ions. In the case of motion through vacancies, the conductivity, a, is given by... 

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