Transport in ionic solids

If the molar volume of the solid solution does not depend on composition, this relation then yields 

Equation (4.78) is named a Darken-type equation because it was first derived by Darken for a special situation [L. S. Darken (1948)]. 

Chemical diffusion has been treated phenomenologically in this section. Later, we shall discuss how chemical diffusion coefficients are related to the atomic mobilities of crystal components. However, by introducing the crystal lattice, we already abandon the strict thermodynamic basis of a formal treatment. This can be seen as follows. In the interdiffusion zone of a binary (A, B) crystal having a single sublattice, chemical diffusion proceeds via vacancies, V. The local site conservation condition requires that /a+/b+7v = 0- From the definition of the fluxes in the lattice (L), we have 

The flux jA, relative to an external marker which we may fix outside the diffusion zone, is then 

From Eqn. (4.81), we see that if one adopts the lattice as the reference frame (which also is Pick s frame for constant molar volume), then 

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The kinetic expressions applicable to diffusion-controlled reactions have been discussed in Chap. 3, Sect. 3.3. Mass transport in ionic solids has been reviewed by Steele and Dudley [1182],... 

Steele, B.C.H. and G.J. Dudley, 1975, Mass transport in ionic solids, in Roberts, L.E.J., ed., MTP International Review of Science, Inorganic Chemistry Series Two, Vol. 10, Solid State Chemistry (Butterworths, London) p. 181. 

In some ionic crystals (primarily in halides of the alkali metals), there are vacancies in both the cationic and anionic positions (called Schottky defects—see Fig. 2.16). During transport, the ions (mostly of one sort) are shifted from a stable position to a neighbouring hole. The Schottky mechanism characterizes transport in important solid electrolytes such as Nernst mass (Zr02 doped with Y203 or with CaO). Thus, in the presence of 10 mol.% CaO, 5 per cent of the oxygen atoms in the lattice are replaced by vacancies. The presence of impurities also leads to the formation of Schottky defects. Most substances contain Frenkel and Schottky defects simultaneously, both influencing ion transport. 

In ionic solids, there are normally local electric fields which act on the ions during transport. These fields are induced externally and/or internally, that is, as a result... 

In the following sections closer attention is given to the two principal mechanisms whereby charge is transported in a solid, i.e. electronic and ionic conduction. 

The liquid state of ionic compounds seems also to be rather simply analyzed. The change from crystal to liquid is much less dramatic in ionic solids than in covalent solids, since the ionic crystal is already close-packed. The liquid is presumably a somewhat random, but locally neutral, conglomeration of ions. Most of the studies of ionic compounds made in this part of the book have not depended greatly on details of structure and so remain appropriate in the liquid. It should be noted, however, that for studies of transport and diffusion, one should... 

According to the previous discussion, a PEVD process relies on mass and charge transport in two solid state ionic materials of a PEVD system, i.e., the solid electrolyte (E) and the product (D). Since mass and charge transport occur in solid state ionic materials, the conductivity mechanism imposes some restrictions, and fundamental considerations in a PEVD system can be obtained through the local equilibrium approach. In the following, mass and charge transport in both phases will be discussed. 

Electrochemical studies of HTSC began immediately after their discovery [2]. At present, there are more than 400 publications on this problem, not counting the numerous studies of ionic transport in HTSC solid electrolytes, which are only selectively presented in this review. Hence, the electrochemistry of HTSC can be considered as a new direction in electrochemical science and technology. 

It should be noted that the conductivity in ionic solids involves ion transport mechanism between coordinating sites (site-to-site hopping) and local structural relaxation. In general, the conductivity measured by ac measurements, can be expressed as a function of the conductivity from dc measurements, and the frequency (Bruce et al., 1983a,b Skinner and Munnings, 2002 Girdauskaite et al., 2006 Khrokunov et al., 2006 Berenov et al., 2007) ... 

Atkinson, A. Surface and Interface Mass Transport in Ionic Materials. Solid State Ionics 28/30 (1988)... 

L. Heyne [1983] Interfacial Effects in Mass Transport in Ionic Sohds, in Mass Transport in Solids, ed. F. Beniere and C. R. A. Catlow, Plenum Press, New York, pp. 425-456. 

The combination of chemical and electrical potentials and potential gradients forms the basis for the treatment of all mass transport processes involving charged species (ions) in ionic solids, and is the theme of this chapter. The theory is termed Wagner-type after Carl Wagner, who was the first to derive it, originally to describe oxidation of metals. 

A deeper insight into electrochemical reaction mechanisms is possible by electrochemical studies employing solid electrolyte instead of liquid electrolyte With a solid electrolyte having preponderantly only one mobile ionic species electrode polarization can be studied under thermodynamically well-defined conditions without superimposed side effects by solvents and without the complications created by the presence of hydrated films or hydrolytic layers. Such measurements can be used, for instance, for the study of electrodeposition, formation of monolayers or of dendrites due to nucleation, for the study of polarization phenomena in ionic solids, solid-state reaction kinetics, transport phenomena, thermodynamics or constitutional diagrams, and for the development of practical devices. 

Ionic transport in solids originates from the atomic disorder in real crystals compared with ideal crystal lattices. The most important defects of this kind are ... 

Ionic transport in solid electrolytes and electrodes may also be treated by the statistical process of successive jumps between the various accessible sites of the lattice. For random motion in a three-dimensional isotropic crystal, the diffusivity is related to the jump distance r and the jump frequency v by [3] ... 

Improvement of the ionic current by fast transport in the electrodes. High electronic mobility and low electronic concentration favor fast chemical diffusion in electrodes by building up high internal electric fields [14]. This effect enhances the diffusion of ions toward and away from the solid electrolyte and allows the establishment of high current densities for the battery. 

There are three broad categories of materials that have been utilized in this endeavor. In the first, even in fully stoichiometric compounds, the ionic conductivity is high enough to be useful in devices because the cation or anion substructure is mobile and behaves rather like a liquid phase trapped in the solid matrix. A second group have structural features such as open channels that allow easy ion transport. In the third group the ionic conductivity is low and must be increased by the addition of defects, typically impurities. These defects are responsible for the enhancement of ionic transport. 

Fig. 3. Oxygen transport in solids. 02 is dissociated and ionized at the reduction interface to give O2 ions, which are transferred across the solid to the oxidation interface, at which they lose the electrons to return back to 02 molecules that are released to the stream, (a) In the solid electrolyte cell based on a classical solid electrolyte, the ionic oxygen transport requires electrodes and external circuitry to transfer the electrons from the oxidation interface to the reduction interface (b) in the mixed conducting oxide membrane, the ionic oxygen transport does not require electrodes and external circuitry to transfer the electrons to the reduction interface from the oxidation interface, because the mixed conductor oxide provides high conductivities for both oxygen ions and electrons.

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