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Fig. 2.16 (A) Schottky and (B) Frenkel defects in a crystal
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125 2. By a shift of an ion from a stable position into an interstitial position and of another ion from an interstitial position into the hole formed 3. By a shift of an ion from a stable position into a neighbouring hole, forming a new vacancy Current is conducted by the Frenkel mechanism, e.g. in silver halides, where the charge carrier is the silver ion (transport number tAg+ = 1). Impurities in crystals favour the Frenkel mechanism. Important materials with high conductivity depending on the Frenkel mechanism include /J-alumina, a ceramic material with the composition Na 2 OllAl 2 O 3 . The structure of j3-alumina (see Fig. 2.17) consists of a compact arrangement of blocks of the y-phase of aluminium oxide of a thickness of four oxygen layers and of a spinel structure. These blocks are separated by bridging layers, containing only oxygen and sodium ions. Each bridging layer contains only one-fourth as many oxygen atoms as the compact layer in blocks. These are arranged so that the sodium ions are located in relatively small concentrations in tunnels between the oxygen ions, where they can migrate relatively freely, leading to the unusually high conductivity of j3-alumina. The conductivity mechanism depends on the Frenkel defects in the bridging layer (interstitial oxygen ions close to interstitial aluminium ions in the compact block). Other ceramic ion conductors similar to /3-alumina were introduced by Goodenough et al. in 1976; they belong to the so-called Nasicon family. Nasicon is a solid solution of the composition Na3Zr2Si2PO12, exhibiting a Na + conductivity of 0.2S/cm at 300 C. Numerous Nasicon derivatives,
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Fig. 2.17 A scheme of /3-alumina structure. The gaps between blocks of j8-phase A12O3 function as bridging layers sparsely populated by oxygen (O) and sodium ( ) ions. (According to R. A. Huggins)
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126 containing Sc, Cr, Fe, In, Yb, Ti, V . . . , etc. were also prepared and characterized as promising solid conductors for high-temperature batteries. The Nasicon structure is composed of two ZrO 6 octahedra and three (P/Si)O4 tetrahedra in a rather loose packing with opened conduction channels. Sodium cations are distributed inside these channels in two symmetrically non-equivalent positions, Na(l) and Na(2), but only some of the available positions are occupied. The migration of Na + ions through these channels is therefore rather easy and the observed ionic conductivities are higher by orders of magnitude in comparison with those of other ceramic conductors. 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 (ZrO 2 doped with Y 2 O 3 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. For Schottky defects in an ionic crystal with a cubic lattice, the diffusion coefficient is given by the relationship, e.g. for a cation, D = WPp (2.6.13)
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where a is the distance between the closest cation and anion, fi is the fraction of vacancies in the total number of cations and p is the probability of the jump of a vacancy per second, given as (2.6.14) where v is the vibrational frequency of the cations and e] is the activation energy for a jump. Crystals with Frenkel or Schottky defects are reasonably ion-conducting only at rather high temperatures. On the other hand, there exist several crystals (sometimes called 'soft framework crystals'), which show surprisingly high ionic conductivities even at the room or slightly elevated temperatures. This effect was revealed by G. Bruni in 1913; two well known examples are Agl and Cul. For instance, the ar-modification of Agl (stable above 146 C, sometimes denoted also as ^-modification') exhibits at this temperature an Ag + conductivity (t+ = 1) comparable to that of a 0 . 1 M aqueous solution. (The solid-state Ag + conductivity of ar-Agl at the melting point is actually higher than that of the melt.) This unusual behaviour can hardly be explained by the above-discussed defect mechanism. It has been anticipated that the conductivity of or-Agl and similar crystals is described
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127 by a qualitatively different transport model, the so-called disordered sub-lattice motion. Every ionic crystal can formally be regarded as a mutually interconnected composite of two distinct structures: cationic sublattice and anionic sublattice, which may or may not have identical symmetry. Silver iodide exhibits two structures thermodynamically stable below 146 C: sphalerite (below 137 C) and wurtzite (137-146 C), with a plane-centred I" sublattice. This changes into a body-centred one at 146 C, and it persists up to the melting point of Agl (555 C). On the other hand, the Ag+ sub-lattice is much less stable; it collapses at the phase transition temperature (146 C) into a highly disordered, liquid-like system, in which the Ag + ions are easily mobile over all the 42 theoretically available interstitial sites in the I~ sub-lattice. This system shows an Ag + conductivity of 1.31 S/cm at 146 C (the regular wurtzite modification of Agl has an ionic conductivity of about 10~3 S/cm at this temperature). Attempts have been made to lower the temperature of appearance of the sub-lattice motions. It was found that substitution in the I~ sub-lattice of Agl, e.g. by WO|~, stabilizes this structure up to rather low temperatures: crystals of (AgI)1_A.(Ag2WO4)A. show, for x = 0.18, an Ag + conductivity of 0.065 S/cm at 20 C. Addition of cationic species, for instance in Ag2HgI4, Ag4RbI6, and Ag7[N(CH3)4]I8 has a similar effect. Lanthanum fluoride (and fluorides of some other lanthanides) has an unusual type of defect (see Section 6.3.2), namely Schottky defects of the molecular hole type (whole LaF3 molecules are missing at certain sites). Charge carriers (F~) are formed as the result of interaction of LaF3 with this hole, leading to dissociation with formation of LaF2+ and F~. Only the alkali metal ions are mobile in oxygen-containing glasses such as the silicates or borates of the alkali metals. The relatively large free space in the glass permits a jump from one oxygen atom to another with simultaneous charge transfer between the oxygens forming bridges between the silicon or boron atoms. Similarly, as in the transport of ions in electrolyte solutions, random ion motion predominates over ordered motion in the direction of the field during the passage of electric current through solid substances. 2.6.3 Transport in melts The mobility of ions in melts (ionic liquids) has not been clearly elucidated. A very strong, constant electric field results in the ionic motion being affected primarily by short-range forces between ions. It would seem that the ionic motion is affected most strongly either by fluctuations in the liquid density (on a molecular level) as a result of the thermal motion of ions or directly by the formation of cavities in the liquid. Both of these possibilities would allow ion transport in a melt.
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128 2.6.4 Ion transport in polymers Ion conducting polymers (polymer electrolytes) attract increasing attention not only from the academic point of view, but also for their prospective applications in batteries, sensors, electrolysers and other practical devices. Although the ion conducting polymers can formally be regarded as 'solid electrolytes', the mechanism of ion transport is different from that in the above-discussed inorganic crystals with lattice defects, and it resembles the ion transport in liquid media. This follows from the fact that ions are transported in a polymeric host material, which is essentially not as rigid as the defect crystal of the classical inorganic solid electrolyte, i.e. the host motions or rearrangements virtually contribute to the ion transport as well. The ion conducting polymers therefore present a special class of electrolytes with features intermediate between those of solid (defect crystals) and liquid (solutions, melts) electrolytes. The ion conducting polymers contain, besides the organic polymeric backbone, ions in more or less strong interactions with the polymer, and in some cases also solvent molecules. Ion solvating polymers. Polymers that are conducting even in the dry state, i.e. without attached solvent molecules, are termed ion solvating {or ion-coordinating) polymers. These contain electronegative heteroatoms (prevailingly oxygen, sometimes also nitrogen, sulphur, or phosphorus), which interact with cations by donor-acceptor bonds similar to those in solvated ions in solutions. The complexes of ions with polymers are simply formed by dissolving inorganic salts in suitable polymeric hosts. The most important solvating polymeric hosts are two polyethers: poly(ethylene oxide) (PEO) and poly(propylene oxide) (PPO):
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CH CH2 O CH3 PEO PPO Lithium perchlorate is dissolved in PEO owing to the coordination of Li+ cation by oxygen atoms in the polymeric chain. The complex thus formed has the helical structure (Fig. 2.18), and exhibits ionic conductivities of up tol(T 4 S/cmat60 o C. The mechanism of ion transport in such systems is not fully elucidated, but it is presumably dependent on the degree of crystallinity of the polymeric complex (which further depends on the temperature and the salt type). The ionic conductivity was initially attributed to cation hopping between fixed coordination sites in the depicted helical tunnel, i.e. in the crystalline part of the polymer. A more detailed analysis revealed, however, that the cation hopping
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