Conduction planes

Figure 7. Ionic conductivities for various monovalent (a) and multivalent (b) ions in f) and / " -alumina single crystals in the direction of the conduction plane [4, 19J.

The ionic conductivity for various ions in the piP"-alumina structure along the conduction planes shows a maximum for an optimum size of the ions. It should be neither too small nor too big to fit the available pathways in the lattice [8]. 

The spinel blocks in (3-alumina are related by mirror planes that mn through the conduction planes that is, the orientation of one block relative to another is derived by a rotation of 180°. A second form of this compound, called (3"-alumina, has similar spinel blocks. However, these are related to each other by a rotation of 120°, so that three spinel block layers are found in the unit cell, not two. The ideal composition of this phase is identical to that of (3-alumina, but the unit cell is now rhombohedral. Referred to a hexagonal unit cell, the lattice parameters are a = 0.614 nm, c = 3.385 nm. The thickness of the spinel blocks and the conduction planes is similar in both structures.3... 

The disposition of the atoms in the conduction plane itself is identical to that in (3-alumina (Fig. 6.10b). However, the local environment of the conduction planes is different in the two phases because the oxygen ions on both sides of the conduction plane are superimposed in (3-alumina and staggered in (3"-alumina (Fig. 6.KM). This means that Beevers-Ross and anti-Beevers-Ross sites are not present. Instead the sodium sites, which have a tetrahedral geometry, are called Beevers-Ross-type (BR-type). The mid-oxygen (mO) sites, located midway between the BR-type sites, also have a different geometry in the two phases. 

In both of these materials the distribution of the ions in the conduction planes changes with temperature. At high temperatures the large cations tend to occupy all suitable sites in a random manner. Thus in (3-alumina the BR, aBR, and mO sites, and in (3"-alumina the BR-type and mO sites, are occupied statistically. 

Figure 6.10 Structure of (3-alumina (a) idealized structure projected down [110] drawn as Al3+ centered polyhedra (h) conduction plane, containing one Na+ and one bridging O2-ion per unit cell, this forming the in-conduction-plane vertex of the tetrahedra in (a).

The open nature of the conduction planes allows the Na+ ions to be easily replaced in all these phases. In general, the (3-alumina phase is less flexible to replacement the 3"-alumina more so, and the sodium can be replaced by almost any monovalent, divalent, or trivalent ion. The idealized formulas of these exchanged solids are A+A1h017, Ao A1iiOi7, or Aoj AlnOi . 

O O Below Conduction Plane O O Above Conduction Plane... 

Figure 6.10 (Continued) (c) conduction plane and the two adjacent oxygen planes. The...

Both the oxides (3- and (3"-alumina show extremely high Na+ ion conductivity. As the structure suggests, the conductivity is anisotropic, and rapid sodium ion transport is limited to the two-dimensional conduction plane. There is almost unimpeded motion in the Na+ layers, especially in (3"-alumina, which lacks interstitial oxygen ion defects in the conduction plane, and the conductivity is of the same order of magnitude as in a strong solution of a sodium salt in water. The conductivity is a... 

The high conductivity of (3-alumina is attributed to the correlated diffusion of pairs of ions in the conduction plane. The sodium excess is accommodated by the displacement of pairs of ions onto mO sites, and these can be considered to be associated defects consisting of pairs of Na+ ions on mO sites plus a V N l on a BR site (Fig. 6.12a and 6.12b). A series of atom jumps will then allow the defect to reorient and diffuse through the crystal (Fig. 6.12c and 6.12d). Calculations suggest that this diffusion mechanism has a low activation energy, which would lead to high Na+ ion conductivity. A similar, but not identical, mechanism can be described for (3"-alumina. 

Figure 6.12 Correlated diffusion in (3-alumina (a) the Na+ positions in the conduction plane of ideal NaAlnOi7 (b) the creation of associated defects by location of pairs of Na+ ions on mO sites (c) the ionic jumps involved in diffusion of an associated defect and (d) the final position of the defect.

The phase Na2Sx is sodium polysulfide, a material with a sulfur content of between 3 and 5. The anode reaction takes place at the liquid sodium - (3"-alununa interface. Here sodium atoms lose an electron and the Na+ ions formed enter the conduction planes in the electrolyte. The cathode reaction, which occurs at the interface between the (3"-alumina and the liquid sulfur forms sodium polysulfides. Despite the desirable properties of the cell, technical and economic considerations have acted so as to curtail large-scale commercial production. 

It is also easily shown that the corresponding equations for a charged conducting sphere near a grounded conducting plane are given by... 

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 beta-alumina structures show a strong resemblance to the spinel structure. They are layered structures in which densely packed blocks with spinel-like structure alternate with open conduction planes containing the mobile Na ions. The and /S" structures differ in the detailed stacking arrangement of the spinel blocks and conduction planes. Fig. 2.9. 

In both P- and j9"-alumina, the conduction planes contain a nonintegral number of Na ions and there are considerably more sites available than Na ions to fill them. The structures are often described in terms of the supposedly ideal 1 11 stoichiometry with the formula NaAliiOi7. In such a case, of the three out of four oxide ions that are missing from the conduction planes, only one half of their vacant sites would contain a Na ion, as indicated schematically in Fig. 2.10. In practice, excess Na" ions are almost always present (e.g. ion A in Fig. 2.1(c)) but rarely in suflBcient quantities to fill all the available vacancies this then gives rise to the high carrier concentrations in these phases. 

The excess of Na ions (above the NaAlnOi7 stoichiometry) requires some means of charge balance and the mechanism is found to be different in the P and P" structures. In P", some AP ions in the spinel blocks are replaced by Li /Mg " the consequent reduction in positive charge compensates that of the excess Na" ions in the conduction planes. In P,... 

The different oxide stacking sequences in j8 and j8". Fig. 2.9, and in particular, the presence of mirror symmetry in the conduction plane of j8 but not P", lead to differences in detail in the nature of the sites for Na" ions in the conduction plane. Such differences together with the different charge compensation mechanisms cause the electrical properties of p and P" to differ somewhat, and in particular lead to rather different conduction mechanisms. 

The Na+ ions in the conducting plane have been substituted for by many other (mostly monovalent) cations, and Al3+ in the spinel block has also been substituted for by other di- and trivalent cations. This exchange results in a very complex crystal... 

As long as the /1-alumina sensor remains homogeneous as far as Na+ is concerned (which is achieved by the high fraction of Na20), we see from Eqn. (15.6) that the electron potential varies inversely with the oxygen activity. We have already mentioned that /1-alumina is able to incorporate a number of different cations into the conducting plane. This non-specificity hampers the use of / -alumina as a universal sensor material under ordinary conditions. If more than one mobile component is... 

Single crystals of /S-A1203 are essentially two dimensional conductors. The conducting plane has hexagonal symmetry (honeycomb lattice). This characteristic feature made -alumina a useful model substance for testing atomistic transport theory, for example with the aid of computer simulations. Low dimensionality and high symmetry reduce the computing time of the simulations considerably (e.g., for the calculation of correlation factors of solid solutions). 

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