Lattice parameters doping effects

It has been noted that the conductivity and activation energy can be correlated with the ionic radius of the dopant ions, with a minimum in activation energy occurring for those dopants whose radius most closely matches that of Ce4+. Kilner et al. [83] suggested that it would be more appropriate to evaluate the relative ion mismatch of dopant and host by comparing the cubic lattice parameter of the relevant rare-earth oxide. Kim [84] extended this approach by a systematic analysis of the effect of dopant ionic radius upon the relevant host lattice and gave the following empirical relation between the lattice constant of doped-ceria solid solutions and the ionic radius of the dopants. 

For y=0.005, a=8.24lA y=0.01, a=8.233A y=0.015, a=8.227A. The lattice parameters show a decrease with Co and Y doping. This is perhaps due to the effects of the Co-0 bond and Y-0 bond in the octahedron when the cations are incorporated into the spinel structure. 

In crystals with a high concentration of shallow donors or acceptors, another contribution to the volume change at room temperature is the presence of free carriers in the continuum. This effect is related to the minimization of the total energy of the crystal compared to that of the undoped crystal ([24] and references therein). This purely electronic effect has been considered, together with the eventual presence of a high concentration of native defects, in the variation of the lattice parameter of Si-doped GaAs conducting substrates used in the electronic industry [3],... 

It should be noted that the demixing of doped SnO during high-temperature annealing, which is accompanied by an increase in the concentration of the second phase, is a common phenomenon for metal oxides (Nowotny 1988). Usually it is stated that this effect takes place at 800-900 °C. However, on the basis of results of the annealing influence on the lattice parameters of doped SnO... 

Figure 1.6 Effective volume of the interfadal film (normalized to the NaAOT volume) as a function of the bmimBF concentration (volume fraction) (closed circles) data from the lattice parameter of Hj phase obtained from SAXRD measurements, (closed stars) data from the selfdiffusion coefficients of AOT" and bmim measured in the Lj phase calculated from Equations 1.9 and 1.10 (see text), and (open stars) data obtained for the Lj phase doped with p-xylene (see text). The curve represents the best fit according to the Hill s cooperative binding (Eq. 1.13). Reproduced from Murgia et al. [26] with permission from American Chemical Society.

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