The tetragonal zirconia structure (Fig. 3 , Table 2), with space group P42/nmc (primitive) [8, 9] and a cation coordination number of 8, is derived from the cubic fluorite structure by the movement of oxygen anions along one of the cubic axes, which results in a tetragonal distortion along that axis, as shown in Fig. 3 for a distortion along the c-axis. The two zirconium ions in the primitive structure are located at (0, 0, 0) and (*/г, /г, */2), and the four oxygen ions are located at (0, */2, z), (У2, 0, – z), (0, /, / + z), and (/, 0, / – z), where z = 0.185. This results in a body-centered tetragonal (bct) structure, which is sometimes described as a pseudofluorite structure.
The transition from cubic to tetragonal is displacive in which four Zr4+ cations in the 4a cubic positions split into two groups to occupy the 2b positions in the tetragonal structure, and the O2- anions in the 8c cubic positions also split into two groups to occupy the 4d positions in the tetragonal structure. The directions of a and b axes in the tetragonal primitive lattice are 45° from those in the cubic cell. The c axis in both structures remains the same. Following the literature convention of reporting the parameter dz = 0.25 – z, where z represents the third coordinate of the oxygen position 4d (0, /, z), the calculated da ratio and internal parameter dz of the tetragonal phase as a function of volume are shown in Fig. 4 .
Extra zirconium ions from the pseudofluorite cell
Zirconium ions from the body-centered tetragonal cell
Fig. 3 Tetragonal zirconia unit cell in both the body-centered tetragonal and pseudofluorite descriptions (adapted from Aldebert and Traverse )
Fig. 4 Calculated c/a ratio and internal structural parameter, dz, of the tetragonal phase as a function of volume  (reprinted with permission)