Solid electrolytes mobility

The electrical conductivity also increases with increasing metal oxide content, due to the high mobility of the metal ions. For example several glass compositions have been used as solid electrolytes in galvanic cells in which other metal ions apart from the alkaline and alkaline earth ions have been incorporated. The electrochemical cell... 

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]. 

This relationship makes it possible to calculate the maximum ionic conductivity of solid electrolytes. Assuming that the mobile ions are moving with thermal velocity v without resting and oscillating at any lattice site, this results in a jump frequency... 

Making use of Eq. (25), the maximum conductivity of a solid electrolyte with monovalent mobile species is given by... 

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.

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 first half of this chapter concentrates on the mechanisms of ion conduction. A basic model of ion transport is presented which contains the essential features necessary to describe conduction in the different classes of solid electrolyte. The model is based on the isolated hopping of the mobile ions in addition, brief mention is made of the influence of ion interactions between both the mobile ions and the immobile ions of the solid lattice (ion hopping) and between different mobile ions. The latter leads to either ion ordering or the formation of a more dynamic structure, the ion atmosphere. It is likely that in solid electrolytes, such ion interactions and cooperative ion movements are important and must be taken into account if a quantitative description of ionic conductivity is to be attempted. In this chapter, the emphasis is on presenting the basic elements of ion transport and comparing ionic conductivity in different classes of solid electrolyte which possess different gross structural features. Refinements of the basic model presented here are then described in Chapter 3. 

The parameter c Eqn (2.1), is capable of variation by many orders of magnitude in ionic solids. In good solid electrolytes such as Na "-alumina and RbAg4l5, all of the Na /Ag ions are potentially mobile and hence c is optimised. At the other extreme, in pure, stoichiometric salts such as NaCl, ionic conduction depends on the presence of crystal defects, whether... 

In most solid electrolyte systems, it is not possible to vary the composition sufficiently so as to have the complete spectrum of mobile ion concentrations, from n,. = 0 to n,. = 1. Instead, the properties are usually limited to one or other of the wings in the type of behaviour... 

The occurrence of such ion trapping is clearly undesirable since it inevitably leads to a decrease in conductivity. In practice, in materials that contain potential traps such as charged aliovalent impurities/dopants, the conductivity values of a particular sample may actually decrease with time as the mobile ions gradually become trapped. Such ageing effects greatly limit the usefulness of a solid electrolyte in any device that needs to have a long working-life. 

Solid electrolyte behaviour has been reported in a wide range of materials and is now known for a considerable number of mobile ions. Some key examples for each ion are listed in Table 2.1. 

Solid electrolyte Mobile ion Conductivity/S cm temperature/°C Activation energy/e-y Reference... 

Much of the recent research in solid state chemistry is related to the ionic conductivity properties of solids, and new electrochemical cells and devices are being developed that contain solid, instead of liquid, electrolytes. Solid-state batteries are potentially useful because they can perform over a wide temperature range, they have a long shelf life, it is possible to make them very small, and they are spill-proof We use batteries all the time—to start cars, in toys, watches, cardiac pacemakers, and so on. Increasingly we need lightweight, small but powerful batteries for a variety of uses such as computer memory chips, laptop computers, and mobile phones. Once a primary battery has discharged, the reaction cannot be reversed and it has to be thrown away, so there is also interest in solid electrolytes in the production of secondary or storage batteries, which are reversible because once the chemical reaction has taken place the reactant concentrations can be... 

Sprik et al, 1993 Signorini et al, 1990), a typical example being the orientational disorder associated with NH in NH Br. Detailed simulations have been reported on (NaCN),, t(KCN),t and other mixed alkali halides and alkali cyanides. Other systems studied include potassium and calcium nitrate crystals and their mixtures. The transition from the crystalline to the superionic conductor phase in solid electrolytes has also been successfully investigated. Molecular dynamics studies of Agl were carried out by Parrinello, Rahman Vashishta (1983). LijSO has been investigated by molecular dynamics by Impey et al. (1985). Here, the Li ions become mobile at high temperatures. The ions exhibit orientational disorder and the orientational... 

Electrokinetic phenomena depend on the relative motion of the phases constituting the double layer. In the treatment of electro-osmotic mobility, the electrolyte was considered to move within a stationary capillary—a moving cylinder of liquids within a static cylinder of solid. But the arguments only need relative motion the arguments would be equally valid if one considered a moving cylindrical solid within a stationary liquid. 

Hence the partial pressure of oxygen and the temperature determine whether the solid will exhibit n-type, p-type or ionic conduction. Although the concentration of defects is important it is also necessary to consider the mobilities of the individual defects higher ionic mobilities will result in a larger domain for electrolytic conduction. Figure l4 shows the dominant mode of conduction in some mixed oxide materials, exhibiting solid electrolyte behaviour, as a function of temperature and oxygen partial pressure. 

In both cases, ctj i depends on PO2- Figure 1.43 shows that eqn (1.167) is dominant in the pressure range I O2 > 10 atm and eqn (1.168) is dominant in the pressure range 02 < 10 atm. In the former case, CT , depends on temperature because ion mobility is temperature dependent. The relation between the ionic and electronic conductivity for solid electrolytes is shown schematically in Fig. 1.44. Since ionic conductivity originates from diffusion of ions in the solid phase, (Tio is closely related to the coefficient of self diffusion of ions ( X,o ) shown by the following equation... 

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