Diffusion solid electrolytes

It is important to realize that the migration in an electric field depends on the magnitude of the concentration of the charged species, whereas the diffusion process depends only on the concentration gradient, but not on the concentration itself. Accordingly, the mobility rather than the concentration of electrons and holes has to be small in practically useful solid electrolytes. This has been confirmed for several compounds which have been investigated in this regard so far [13]. 

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. 

Figure 13. Voltage relaxation method for the determination of the diffusion coefficients (mobilities) of electrons and holes in solid electrolytes. The various possibilities for calculating the diffusion coefficients and from the behavior over short (t L2 /De ) and long (/ L2 /Dc ll ) times are indicated cc h is the concentration of the electrons and holes respectively, q is the elementary charge, k is the Boltzmann constant and T is the absolute temperature.

The kinetics of ion backspillover on the other hand will depend on two factors On the rate, I/nF, of their formation at the tpb and on their surface diffusivity, Ds, on the metal surface. As will be shown in Chapters 4 and 5 the rate of electrochemically controlled ion backspillover is normally limited by I/nF, i.e. the slow step is their transfer at the tpb. Surface diffusion is usually fast. Thus, as shown in Chapter 5, for the case of Pt electrodes where reliable surface O diffusivity data exist, obtained by Gomer and Lewis several years ago,76 Ds is at least 4.-10 11 cm2/s at 400°C and thus an O2 ion can move at least 1 pm per s on a Pt(lll) or Pt(110) surface. Therefore ion backspillover from solid electrolytes onto electrode surface is not only thermodynamically feasible, but can also be quite fast on the electrode surface. But does it really take place This we will see in the next Chapter. 

Equations 4.31 and 4.32 also suggest another important fact regarding NEMCA on noble metal surfaces The rate limiting step for the backspillover of ions from the solid electrolyte over the entire gas exposed catalyst surface is not their surface diffusion, in which case the surfacediffusivity Ds would appear in Eq. 4.32, but rather their creation at the three-phase-boundaries (tpb). Since the surface diffusion length, L, in typical NEMCA catalyst-electrode film is of the order of 2 pm and the observed NEMCA time constants x are typically of the order of 1000 s, this suggests surface diffusivity values, Ds, of at least L2/t, i.e. of at least 4 10 11 cm2/s. Such values are reasonable, in view of the surface science literature for O on Pt(l 11).1314 For example this is exactly the value computed for the surface diffusivity of O on Pt(lll) and Pt(100) at 400°C from the experimental results of Lewis and Gomer14 which they described by the equation ... 

The obvious question then arises as to whether the effective double layer exists before current or potential application. Both XPS and STM have shown that this is indeed the case due to thermal diffusion during electrode deposition at elevated temperatures. It is important to remember that most solid electrolytes, including YSZ and (3"-Al2C)3, are non-stoichiometric compounds. The non-stoichiometry, 8, is usually small (< 10 4)85 and temperature dependent, but nevertheless sufficiently large to provide enough ions to form an effective double-layer on both electrodes without any significant change in the solid electrolyte non-stoichiometry. This open-circuit effective double layer must, however, be relatively sparse in most circumstances. The effective double layer on the catalyst-electrode becomes dense only upon anodic potential application in the case of anionic conductors and cathodic potential application in the case of cationic conductors. 

Both questions have been recently addressed via a surface diffusion-reaction model developed and solved to describe the effect of electrochemical promotion on porous conductive catalyst films supported on solid electrolyte supports.23 The model accounts for the migration (backspillover) of promoting anionic, O5, species from the solid electrolyte onto the catalyst surface. The... 

A considerable decrease in platinum consumption without performance loss was attained when a certain amount (30 to 40% by mass) of the proton-conducting polymer was introduced into the catalytically active layer of the electrode. To this end a mixture of platinized carbon black and a solution of (low-equivalent-weight ionomeric ) Nafion is homogenized by ultrasonic treatment, applied to the diffusion layer, and freed of its solvent by exposure to a temperature of about 100°C. The part of the catalyst s surface area that is in contact with the electrolyte (which in the case of solid electrolytes is always quite small) increases considerably, due to the ionomer present in the active layer. 

An important result of this study is the conclusion of a particle-size-dependent COads surface mobility. The value obtained for large Ft particles is significantly smaller than Deo at a solid/gas interface. However, Kobayashi and co-workers, using solid state NMR, performed measurements of the tracer diffusion coefficient Deo at the solid/electrolyte interface and for Ft-black particles (about 5nm grain... 

The speed of p- and n-type doping and that of p-n junction formation depend on the ionic conductivity of the solid electrolyte. Because of the generally nonpolar characteristics of luminescent polymers like PPV, and the polar characteristics of solid electrolytes, the two components within the electroactive layer will phase separate. Thus, the speed of the electrochemical doping and the local densities of electrochemically generated p- and n-type carriers will depend on the diffusion of the counterions from the electrolyte into the luminescent semiconducting polymer. As a result, the response time and the characteristic performance of the LEC device will highly depend on the ionic conductivity of the solid electrolyte and the morphology and microstructure of the composite. 

We shall use the familiar Gouy-Chapman model (3 ) to describe the behaviour of the diffuse double lpyer. According to this model the application of a potential iji at a planar solid/electrolyte interface will cause an accumulation of counter-ions and a depletion of co-ions in the electrolyte near the interface. The disposition of diffuse double layer implies that if the surface potential of the planar interface at a 1 1 electrolyte is t ) then its surface charge density will be given by ( 3)... 

The net result is the formation of a dense and uniform metal oxide layer in which the deposition rate is controlled by the diffusion rate of ionic species and the concentration of electronic charge carriers. This procedure is used to fabricate the solid electrolyte yttria stabilized zirconia (YSZ). 

Inorganic membranes can be categorized as shown in Table 2.1. The dense inorganic membranes consist of solid layers of metals (Pd, Ag, alloys) or (oxidic) solid electrolytes which allow diffusion of hydrogen (or oxygen). In the case of solid electrolytes transport of ions takes place. Another category of dense membranes consist of a porous support in which a liquid is... 

Similar types of electric double layer may also be formed at the phase boundary between a solid electrolyte and an aqueous electrolyte solution [7]. They are formed because one electrically-charged component of the solid electrolyte is more readily dissolved, for example the fluoride ion in solid LaFs, leading to excess charge in the solid phase, which, as a result of movement of the holes formed, diffuses into the soUd electrolyte. Another possible way a double layer may be formed is by adsorption of electrically-charged components from solution on the phase boundary, or by reactions of such components with some component of the solid electrolyte. For LaFa this could be the reaction of hydroxyl ions with the trivalent lanthanum ion. Characteristically, for the phase boundary between two immiscible electrolyte solutions, where neither solution contains an amphiphilic ion, the electric double layer consists of two diffuse electric double layers, with no compact double layer at the actual phase boundary, in contrast to the metal electrode/ electrolyte solution boundary [4,8, 35] (see fig. 2.1). Then, for the potential... 

Silver halides have the character of solid electrolytes, where the silver ion acts as the charge carrier (see [125, 204, 266] for AgCl) which moves according to the Frenkel mechanism in the crystal. This type of transport is depicted schematically in fig. 6.1. As the halide ions are located in fixed sites, no diffusion potential is formed within the membrane and (3.4.9) to (3.4.13) are valid for the membrane potential As mentioned in chapter 3, they can be used for determining either halide ions or silver. 

One of the most important aspects of point defects is that they make it possible for atoms or ions to move through the structure. If a crystal structure were perfect, it would be difficult to envisage how the movement of atoms, either diffusion through the lattice or ionic conductivity (ion transport under the influence of an external electric field) could take place. Setting up equations to describe either diffusion or conductivity in solids is a very similar process, and so we have chosen to concentrate here on conductivity, because many of the examples later in the chapter are of solid electrolytes. 

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