Stability of Rutile-type TiO_2 under High Pressure
【摘要】：正The various structures of TiO2, ZrO2 and HfO2 have been exhibited under high pressure experimentally. The stable phase at the ambient condition of TiO2 is the rutile type and it transforms to the -PbO2 type and baddeleyite structures by applying pressure.fl] This sequence is in contrast with that of ZrO2 and HfO2: Their stable structure is the baddeleyite structure at the ambient condition. In this paper, the theoretical study on the rutile-to- -PbO2-type phase transition of TiO2 is reported, in which the first-principles electronic structure calculation was performed. This study provides the explanation on the stability of the normal phase of TiO2, and the difference in the stable form of these oxides from a point of view of the electronic structures, in addition to the conventional view by using the ionic radii.
The total energy calculation of TiO2 was performed as a function of volume based on the density-functional theory: The exchange-correlation energy was estimated within the generalized-gradient approximation. The Kohn-Sham equations were solved self-consistently with the pseudopotential method and the one-body wave-functions were expanded with the plane-wave basis sets which are constructed with the cutoff energy of 90 Ry. The estimated error of the calculation is 5 mRy/f .u.
Table 1 is the calculated structural properties of the rutile and -PbO2 structures of TiO2. The result for
-PbO2 is in excellent agreement with the experiment as well as that for the rutile type. The calculation has also shown that the observed linear compressibilities along the a, b, and c axes can be explained with high accuracy. By the comparison between the calculated free energies of the both
structures, the transition pressure was obtained as 7.3 GPa. The experiment 1] has shown the transition pressure is 3.6 GPa, indicating that the calculation explains the relative stability of the rutile-type structure at lower pressures.
The calculated electronic structures for these structures have shown that the rutile-type tends to have the filled O-2p states at lower position in energy and to have the empty Ti-3d states at higher position. This fact indicates that the covalency in the Ti-O bond stabilizes the rutile-type structure. In the case of Zr and Hf, the atomic d-level is located at higher position energetically and such covalency cannot be expected. Therefore, it can be considered that, due to the relatively weak covalency of the bond, the rutile-type structure does not appear at zero-pressure for ZrO2 and HfO2.