Lattice sites, solid electrolytes

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] ... 

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... 

The above two mechanisms may be regarded as isolated ion hops. Sometimes, especially in solid electrolytes, cooperative ion migration occurs. An example is shown in Fig. 2.1(c) for the so-called interstitialcy or knock-on mechanism. A Na" ion. A, in an interstitial site in the conduction plane of j -alumina (see later) cannot move unless it persuades one of the three surrounding Na ions, B, C or D, to move first. Ion A is shown moving in direction 1 and, at the same time, ion B hops out of its lattice site in either of the directions, 2 or 2. It is believed that interstitial Ag" ions in AgCl also migrate by an interstitialcy mechanism, rather than by a direct interstitial hop. 

The simplest model involves ion hopping between sites on a lattice (not fixed as in a solid electrolyte such as Agl) with the ions obeying a hopping type equation... 

Solid polymer and gel polymer electrolytes could be viewed as the special variation of the solution-type electrolyte. In the former, the solvents are polar macromolecules that dissolve salts, while, in the latter, only a small portion of high polymer is employed as the mechanical matrix, which is either soaked with or swollen by essentially the same liquid electrolytes. One exception exists molten salt (ionic liquid) electrolytes where no solvent is present and the dissociation of opposite ions is solely achieved by the thermal disintegration of the salt lattice (melting). Polymer electrolyte will be reviewed in section 8 ( Novel Electrolyte Systems ), although lithium ion technology based on gel polymer electrolytes has in fact entered the market and accounted for 4% of lithium ion cells manufactured in 2000. On the other hand, ionic liquid electrolytes will be omitted, due to both the limited literature concerning this topic and the fact that the application of ionic liquid electrolytes in lithium ion devices remains dubious. Since most of the ionic liquid systems are still in a supercooled state at ambient temperature, it is unlikely that the metastable liquid state could be maintained in an actual electrochemical device, wherein electrode materials would serve as effective nucleation sites for crystallization. 

Chemists and physicists must always formulate correctly the constraints which crystal structure and symmetry impose on their thermodynamic derivations. Gibbs encountered this problem when he constructed the component chemical potentials of non-hydrostatically stressed crystals. He distinguished between mobile and immobile components of a solid. The conceptual difficulties became critical when, following the classical paper of Wagner and Schottky on ordered mixed phases as discussed in chapter 1, chemical potentials of statistically relevant SE s of the crystal lattice were introduced. As with the definition of chemical potentials of ions in electrolytes, it turned out that not all the mathematical operations (9G/9n.) could be performed for SE s of kind i without violating the structural conditions of the crystal lattice. The origin of this difficulty lies in the fact that lattice sites are not the analogue of chemical species (components). 

Figure 8.1. The diffusion along IPMS by mobile ions in binary solid electrolytes, (a) Partition of the ln)ii]/-cfntrcd cubic (bcc) lattice into two primitwe cubic sub-lattices, separated by the P-surface. Average positions of the (mobile) silver cations, detected from X-ray measurements, in the solid electrolyte a-AgI are indicated by the smaller red spheres on the surface. The larger dark red spheres define the bcc lattice of the (frozen) iodine ions (only two occupied sites of the bcc array are shown), (b ) The bcc lattice can also be partitioned into two diamond sub-lattices by the D-surface. The curved net on the surface described trajectories of mobile Ag ions on the D-surface vertices of the net locate the average I" positions.

A small number of solids have an unusual structure, where only one set of ions is fixed on its lattice sites. The other ions are free to move through the lattice. These materials are intermediate between the ionic solids (where all the ions are fixed on their sites) and a liquid electrolyte (where both sets of ions move). 

The electrical conductivity of ScSZ is strongly related to the microstructure and for nanocrystalline specimens can be dominated by electronic transport in the temperature range of 600-900 C and P02 < 10 atm, while microcrystalline specimens show only ionic conductivity [7, 13], The results of the study of electrical transport in both nanocrystalline YSZ and ScSZ thin films are showing that their non-stoichiometry can be controlled by the microstructure and in addition that the electrical conductivity is also influenced by the interaction between lattice defects and type of acceptor dopants. The large increase in electronic conductivity observed for nanocrystalline ScSZ suggests that it may find use as a buffer layer on the anode site of a solid electrolyte in SOFC, which can be YSZ or microcrystalline ScSZ. Such compatibility between the electrode and... 

When elements of valence 2 or 3 are introduced into zirconia, they occupy Zr lattice sites, generating vacancies at oxygen sites. These provide zirconia with its well-known ionic conductivity, leading to its use in high temperature electrochemical cells (Subbarao and Maiti [1984], Steele [1976], Steele et al. [1981]). FSZ is mainly used for electrochemical appUcation, PSZ mainly for structural applications, while TZP is used both as a solid electrolyte and a structural ceramic. 

DICKINSON I do not understand why you use the term chemisorption. In a solid electrolyte, chemisorption must surely involve either some degree of charge transfer between the ion and the electrode or some movement of the ion from its normal lattice site. Your model does not involve either of these phenomena, but you still describe the ions as being specifically adsorbed. 

If there are more places in the lattice than mobile ions, the ions can occupy different lattice sites. Such solids are called super-ionic conductors. In this classification, in turn, it is distinguished between those solid electrolytes which exhibit that structure above the temperature of a phase transition (sometimes called as type I) and those which show that behavior over the whole temperature range (type II). As examples for the Type I, a-AgI and 8-Bi203 are mentioned, which are formed after the phase transitions ... 

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