Divalent dopants

For comparison to the divalent dopant ions, the conductivity of a monovalent ion (Na ) is given in Table 1. The value of 100 Q l cm observed after n-doping using the sodium-ammonia solution is comparable to values obtained for sodium doped film using other methods such as sodium naphthalide/tetrahydrofuran solutions (20,21). It is clear that divalent dopant ions decrease the maximum conductivities observed when compared to monovalent ions. It is therefore likely that some localization of charge is occurring in the divalent doped polyacetylenes. 

The highest conductivity observed so far for Mg 2 doped polyacetylene is 0.6 cm The small Mg 2 ions thus appear to limit the maximum conductivity for these divalent dopant ions. This electrolysis method could likely be extended to Be 2 nd Al ions and such experiments are currently in progress. 

By modeling A-cation transport in Ca- and Sr-substituted manganites Lai, j A,j Mn03, in which the divalent dopant cations are compensated by electron holes (Mn" sites), it was found that the migration energies decreased in the order La > Sr > Ca (although the ionic radius of La lies between that of Sr and Ca ). This unexpected trend could be explained by assuming that the electrostatic and ion polarizibility factors, as well as steric hindrance at the saddle point, are important. 

The dependence of zirconia conductivity at 1000°C on the dopant concentration is shown in Fig. 1 (Arachi et al. 1999). Similar conductivity data at 800°C has also been reported by Badwal et al. (1997). The maximum conductivity occurs at a vacancy concentration of around 3.5-4% (about 8 mol% M2O3) for trivalent dopants and 6-7% (13% MO) vacancy concentration for divalent dopants. Although, the ionic conductivity of 3 mol% Y203-Zr02 having tetragonal phase (commonly known as 3YSZ) is lower by a... 

FIGURE 1.14 Ionic conductivity of doped ceria at 1073 K against the radius of dopant cation, rc shown in the horizontal axis is for the critical radius of divalent or trivalent cation, respectively. (Data from Inaba, H. and Tagawa, H., Solid State Ionics, 83, 1, 1996.)... 

LaMn03 is an intrinsic p-type conductor. Electronic conductivity is enhanced by substitution of the La3+ site with divalent ions such as strontium or calcium. Of the alkaline-earth dopants, Sr substitution is preferred for SOLC applications because the resultant perovskite forms stable compounds with high conductivity in the oxidizing atmosphere found at the cathode [41], Extensive data show that La, xSi. MnO where x = 0.1 - 0.2, provides high conductivity while maintaining mechanical and chemical stability with YSZ [41, 42],... 

Lanthanum chromite is a p-type conductor so divalent ions, which act as electron acceptors on the trivalent (La3+ or Cr3+) sites, are used to increase the conductivity. As discussed above, the most common dopants are calcium and strontium on the lanthanum site. Although there is considerable scatter in the conductivities reported by different researchers due to differences in microstrucure and morpohology, the increase in conductivity with calcium doping is typically higher than that with strontium doping [4], The increase in conductivity at 700°C in air with calcium additions is shown in Figure 4.1 [1, 2, 28-44], One of the advantages of the perovskite structure is that it... 

The solute and solvent atoms should have similar valences in order for maximum solubility. For instance, if a divalent atom were to replace a hexavalent solvent atom, the solvent lattice would be incapable of stabilizing the dopant atom, since too few bonding interactions would be possible between solute and solvent atoms. 

Impurity atoms ( 3.7). The presence of substitutional atoms can lead to modified chemical centers on the surface. The replacement of Mg ions by Ni ions, as in MgO-NiO solid solutions, introduces transition metal atoms in a MgO matrix and can alter the local properties of the material. Even more effective is the replacement of a divalent Mg cation by a monovalent dopant like Li. In order to compensate the charge, some O anions at the surface become O, a paramagnetic species. 

In the /i"-alumina structure, the phase is stabilized at high temperatures by small amounts of monovalent (e.g., Li20) or divalent (e.g., MgO, ZnO, NiO) oxidesIn these stabilized structures, the cation dopant substitutes directly for trivalent aluminum ions in the spinel block (i.e., LiXi, MgAi) and is electrically compensated by additional sodium ions (Nai) in the conduction plane. 

The crystalline form of interest in Zr-based ceramic compounds is the cubic fluorite structure based on the mineral CaF2. In this structure, consisting of interpenetrating face-centered-cubic and simple cublic arrays of cations (Zr ) and anions (O ), respectively, oxygen ion conductivity is enhanced by replacing zirconium (Zr ) ions on the cation lattice with soluble dopant cations having a valence less than 4, typically divalent (Mg, Ca ) and trivalent (Y, Yb , Sc ) cations. These dopants, which are in solid solution, are incorporated into the zirconia structure by the following types of defect reaction ... 

Empirical calculations carried out for cations show that vacancy compensation is clearly the preferred route, at least for large dopant cations (radius >0.8A). Formation of interstitials is also ruled out by measurements of true density and comparison with calculated values . For the smaller cations (i.e. Al ), some compensation via dopant interstitial may occur. The reactions described in Eq. 2.18 and 2.21 (for a divalent cation) therefore summarise the main route to defect formation in solid solutions of the type Ce. jMj02,o.5x and Ce, xMx02.x respectively. 

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