Cubic zirconia doped with oxides such as Y2O3 or CaO is the material of choice for many high temperature applications because of its extremely high ionic conductivity at intermediate and high temperatures. A review on the properties of these specialized rare-earth stabilized zirconia materials has been prepared by Comins et al. .
The oxygen pressure dependence of the conductivity in tetragonal zirconia can be seen in Fig. 13 . This material is a mixed electronic and ionic conductor with a large ionic contribution except at very high temperatures or very low oxygen partial pressures. The electronic component of the conductivity arises from doubly-charged oxygen vacancies at lower oxygen pressures and a temperature of 1,400°C. Other contributions to conductivity are difficult to determine. The movement of oxygen vacancies can take place along two directions for the tetragonal structure: within the x-y plane along the  direction or perpendicular to this plane along the  direction. In both directions, the O-O distances are very similar (0.2640 nm within the (x, y) plane and 0.2644 nm in the direction perpendicular to that plane) . From these numbers, it would appear that there is no preferential direction for diffusion.
Fig. 13 Conductivity isotherms for tetragonal zirconia as a function of oxygen pressure  (reprinted with permission)
However, the diffusion process is controlled by the Zr-Zr distance and not by the O-O distance, since the vacancy must move between two such ions to diffuse. Along the two relevant directions, these distances are 0.3655 nm for the  direction and 0.3645 nm for the  direction. The diffusion barriers for movement of a neutral vacancy along  and  are 1.35 and 1.43 eV, respectively. This is expected from the fact that there is a smaller gap between zirconium ions along the  direction. Hence, diffusion along this direction proves to be more difficult. The diffusion barriers for movement of a doubly-charged vacancy along the two relevant directions are 0.22 and 0.61 eV, respectively. Again, movement along the  direction proves to be more difficult. This can be visualized in Fig. 14 .
Monoclinic zirconia is both an electron and ion conductor depending on the temperature and oxygen pressure (Fig. 15) [52-54]. At low pressures, it exhibits n – type behavior in which the charge carriers are double-charged oxygen vacancies, while at higher pressures it exhibits p-type behavior in which the charge carriers are singly-ionized oxygen interstitials. The transition from n-type to p-type is established by the change in sign of the conductivity curve. Assuming the -1/6 and 1/5 dependences in the two regions are good fits to the data, the total conductivity at 1,000°C can be represented by:
s 1,ooo°C = 8.5 X10-5 pOi 1/5 +1.1 x 10-9 pOi ~116 + 3.2 x 10-6. (4)
In addition, Vest et al.  determined the hole mobility at 1,000°C to be
m1 000°C = 1.4 x 10-6 cm2 • V-1 • s-1.
If the pressure is kept constant and the temperature is increased, the conductivity also increases (see Fig. 4 of Kumar et al. ). At lower temperatures (< 600°C), conductivity is predominantly ionic, and at higher temperatures (> 700°C), it is predominately electronic. Between 600 and 700°C, both ionic and electronic conductivities are seen in this material. Values of the activation energies required for each type of
Fig. 14 Simplified representation of possible diffusion mechanism for oxygen atoms in tetragonal zirconia. (a) Tetragonal cell with two octahedral empty sites, marked with black squares 1 and 2, (b) Position of oxygen 1 during its motion past the zirconium 1-3 face, (c) possible off-centered position for oxygen 1 inside octahedral site 1 (adapted from )
Fig. 15 Oxygen pressure dependence of total conductivity for monoclinic zirconia at 990°C (adapted from Kumar et al.  and Vest et al. )
conductivity are still a matter of controversy because of the complexity of the conduction processes. Earlier values include numbers such as 3.56 eV for n-type conductivity and 0.86 eV for p-type conductivity .
The conductivity of two high-pressure phases of zirconia is shown in Fig. 16 . The discontinuities in the conductivity occur approximately at 1,000°C for the sample at 16.5 GPa and 1,050°C for the sample at 18.0 GPa. At the higher temperatures, the conductivity corresponds to a so-called “cubic” high-pressure and high-temperature phase of zirconia, although its exact nature was not determined by Ohtaka et al. .
At the lower temperatures, the conductivity corresponds to the orthorhombic-II phase. From the Arrhenius plots in the figure, approximate activation energies for conduction can be obtained. For the “cubic” phase, the activation energies are 8.80 and 0.60 eV at pressures of 16.5 and 18.0 GPa, respectively, while for the orthorhombic-II phase they are 0.72 and 0.40 eV for the two pressures studied.