According to theoretical (e.g., refs. 4-6) and experimental (7-9) studies, at high pressures corundum transforms into the Rh₂O₃(II)-type structure. This well established transition, occurring at 80-100 GPa (5-9), implies that the ruby pressure scale should not be used above ≈80 GPa in experiments that involve heating to temperatures where this phase transition will be kinetically feasible. Less clear evidence exists for a further transition. Lin et al. (9) reported that Rh₂O₃(II) structure is stable at least up to 130 GPa and 2,000 K, but above 130 GPa (at temperatures ≈1,500 K) shock-wave experiments of Weir et al. (10) indicated onset of an increase in the electrical conductivity that could be caused by a phase transition. Shock-wave Hugoniots of Al₂O₃ compiled by Hama and Suito (11) also give evidence for a possible phase transition at 130 GPa with a small increase of density. Thomson et al. (6) predicted that an orthorhombic (Pbnm) perovskite structure becomes more stable than Rh₂O₃(II), but only above 200 GPa. The discovery of postperovskite CaIrO₃-type polymorphs of Fe₂O₃ (12) and MgSiO₃ (13, 14) prompts the question of whether a similar phase exists for Al₂O₃.

In our ab initio calculations, we consider four Al₂O₃ polymorphs: corundum (space group ), Rh₂O₃(II) (Pbcn), perovskite (Pbnm), and CaIrO₃-type (Cmcm). Our calculations are based on the plane wave pseudopotential methodology and the local density approximation (LDA) as implemented in the abinit code (15), a common project of the Université Catholique de Louvain (Louvain, Belgium), Corning, and other contributors (www.abinit.org). The pseudopotentials used are of the Troullier-Martins (16) type, fully nonlocal and including partial core corrections (17); the core radii are 0.766 Å for O (1s² core) and 1.204 Å for Al (1s²2s²2p⁶ core). The plane wave kinetic energy cut-off of 45 Ha enabled convergence to within 12 meV per atom for the total energy, 0.06 meV per atom for the energy differences, and within 0.6 GPa for pressure. The Monkhorst-Pack meshes used for sampling of the Brillouin zone were 4 × 4 × 4 for Rh₂O₃(II) and perovskite structures, 6 × 6 × 6 for corundum structure, and 6 × 6 × 4 for CaIrO₃-type phase (for the latter two phases primitive 10-atom cells were used in all calculations). The dynamical matrices were calculated by using density-functional perturbation theory (18) on 2 × 2 × 2 reciprocal space grids for Rh₂O₃(II) and perovskite structures, 3 × 3 × 3 for corundum, and 3 × 3 × 2 for CaIrO₃-type phase. These, together with the computed values of the dielectric constants and Born effective charges, allowed for an accurate interpolation of the dynamical matrices throughout the Brillouin zone and the calculation of phonon densities of states and thermodynamic properties within the quasiharmonic approximation. For more methodological details, see refs. 13 and 19-21.

Let us first analyze results of calculations at 0 K. Parameters of the Vinet equation of state (22) for different phases of alumina are given in Table 1. One can notice good agreement with available experimental data at room temperature (23) and previous calculations (6). Fig. 1a shows the calculated static enthalpy differences between phases. The transition from corundum to the Rh₂O₃(II) structure is predicted to occur at 80 GPa, similar to previous calculations (5, 6) and experiment (7-9). At 131 GPa we predict a transition from the Rh₂O₃(II) structure to the CaIrO₃-type phase; perovskite structure is never stable at 0 K. It is well known that the LDA usually underestimates phase transition pressures, whereas the generalized gradient approximation tends to slightly overestimate these pressures (24). To evaluate possible errors coming from the LDA and the pseudopotentials, we performed calculations within the generalized gradient approximation (25) by using the all-electron projector-augmented wave method (26) as implemented in the vasp code (27). Projector-augmented wave potentials had [He] core (radius 1.52 a.u.) for O and [Ne] core (1.90 a.u.) for Al; we used 600-eV plane-wave cutoff and 2,400-eV cutoff for the augmentation charges. The results were similar to the LDA calculations, with pressures of 92 and 147 GPa for the corundum-Rh₂O₃(II) and Rh₂O₃(II)-CaIrO₃ transitions, respectively. Thus we estimate that our LDA predictions of phase transition pressures are likely to be shifted by ≈10-15 GPa toward lower pressures. The existence of a CaIrO₃-type phase of alumina is supported by static pseudopotential calculations (28). However, significantly higher transition pressures were reported in ref. 28, with the LDA (generalized gradient approximation) values of 105 (100) GPa and 156 (153) GPa for the corundum-Rh₂O₃(II) and Rh₂O₃(II)-CaIrO₃ transitions, respectively. This difference could be caused by the pseudopotentials used in ref. 28.

Table 1. Equation of state parameters for Al2O3 phases (per formula unit)

Fig. 1. Structural stability of Al2O3.(a) Static enthalpies relative to corundum. (b) Phase diagram. Hatched area with dashed boundaries corresponds to a possible stability field of Al2O3-perovskite.

Our calculated phase diagram (Fig. 1b) shows that both corundum-Rh₂O₃(II) and Rh₂O₃(II)-CaIrO₃ transitions have negative Clapeyron slopes. Taking into account these slopes and the ≈10-15 GPa underestimation of the LDA transition pressures, the agreement between the shock-wave phase transition point (≈130 GPa at 1,000-1,500 K) and our predicted Rh₂O₃(II)-CaIrO₃ transition pressure (119 GPa at 1,500 K) is excellent. We believe that Lin et al. (9) did not observe this transition because pressures a few GPa higher than those achieved in their study (up to 130 GPa at high temperature) are needed to produce this transition; also, the uncertainty of pressure calibration at such pressures and temperatures is ≈10%. We tentatively ascribe the change of the electrical conductivity of Al₂O₃ at 130 GPa (10) to this phase transition. To explore this idea further, we have performed ab initio molecular dynamics simulations at ≈150 GPa and 5,000 K, in the NVT-ensemble (29) for a 120-atom supercell. These simulations were based on the generalized gradient approximation and projector-augmented wave method and were done by using vasp, with the Γ-point for Brillouin zone sampling and 500-eV plane-wave kinetic energy cut-off. Because of a relatively short duration of these simulations (1.5 ps) we could not observe diffusion, even when oxygen vacancies were introduced. Yet, there are hints that diffusion would take place on longer time scales: we observed very vigorous and highly anisotropic motion of O atoms, especially in the presence of vacancies. The high electrical conductivity of this phase (2 S/m at 155 GPa and below 2,000 K) observed by Weir et al. (10) suggests that an isostructural postperovskite phase of MgSiO₃, the main mineral of the Earth's D″ layer (13, 14, 30, 31), could also possess high conductivity (which will rapidly increase with temperature) associated with diffusion of the O^2- ions. There are other possible explanations of the electrical conductivity of the D″ layer (32), e.g., a chemical reaction between the core and mantle producing metallic Fe-Si alloys and/or FeO (e.g., refs. 33 and 34). Note that there may be a nonnegligible electronic component in the electrical conductivity of postperovskite MgSiO₃, because this phase is expected to contain significant amounts of Fe²⁺ and Fe³⁺ in the Earth's mantle (13, 30, 31).

From Fig. 1b one can also see that perovskite phase, because of its higher entropy, may become stable at high temperatures and ≈100 GPa. However, we note that at corresponding volumes perovskite is dynamically unstable (i.e., has soft modes), and its stability field was calculated on the basis of extrapolation of thermodynamic properties from pressures above 130 GPa, where it has no soft modes. Although anharmonic effects often suppress dynamical instabilities at high temperatures and may justify such an extrapolation, the calculated stability field of perovskite phase should be treated with caution: there may, in fact, be another phase stable in that region of P-T space. The dynamical instability arises from the fact that at low pressures Al³⁺ ions are too small for the 8-fold coordinated sites in perovskite and CaIrO₃ structure. CaIrO₃-type alumina is dynamically unstable below ≈50 GPa, i.e., it cannot be quenched below 50 GPa and has to be observed in situ.

We have also been able to confirm the stability of CaIrO₃-type phase of Al₂O₃ predicted above by using high-pressure experiments with the laser-heated diamond-anvil cell. A symmetric-type diamond cell with 50° conical apertures was used (35). To avoid problems caused by metastability, we decided to conduct experiments at pressures much higher than 130 GPa. Powdered Al₂O₃ was loaded into 50-μm holes drilled in rhenium gaskets. No pressure-transmitting medium was used in this study. Gold powder was mixed with the sample to provide an internal pressure calibrant and an absorber of laser heating. The efficiency of laser absorbance for gold was sufficiently high to heat the sample. The samples were heated with a TEM₀₁-mode Nd:YLF laser using double-sided laser heating techniques that minimized temperature gradients (both axial and radial) of the heated area. The size of the heating spot was ≈20-30 μm. The sample temperature was measured from both sides by using the spectroradiometric method. The heated samples were probed by angle-dispersive x-ray diffraction using the synchrotron beam line BL10XU at SPring-8 in Hyogo, Japan. The incident x-ray beam was monochromatized to a wavelength of 0.4145 Å. The x-ray beam size was collimated to 15 μm diameter. Alignment of the x-ray and laser spots can be achieved within 5 μm. Angle-dispersive x-ray diffraction patterns were obtained on an imaging plate. The distances between the sample and the detectors were measured by using CeO₂ as a standard. The observed intensities on the imaging plate were integrated as a function of 2θ to give conventional, 1D diffraction profiles. Experimental details have been described elsewhere (36). Pressure was determined from the measured unit cell volume of gold (37). It is known that several equations of state of gold have been reported, and there is a significant discrepancy among them. The uncertainty of pressure associated with the equation of state for gold was ≈10%. Initially, the sample was compressed to ≈170 GPa at room temperature, where the stability field of CaIrO₃-type phase was expected from calculations. However, no diffraction peaks of CaIrO₃-type phase of Al₂O₃ could be identified. After the desired pressure was achieved, the sample was heated to ≈2,500 K to overcome potential kinetic effects on possible phase transition. During the heating, new diffraction peaks appeared at 200 GPa and 2,500 K. After quenching to 163 GPa and 300 K, these diffraction peaks remained stable. The decrease of sample pressure was likely caused by effects of the thermal expansion and the stress relaxation during laser heating. All of the diffraction peaks were reasonably well indexed by the CaIrO₃-type structure (Fig. 2). Other peaks belonged to the gold internal pressure calibrant and the rhenium gasket. These experimental results agreed with the predicted phase diagram of Al₂O₃ (Fig. 1).

Fig. 2. Experimental powder diffraction pattern at 163 GPa and 300 K. Cmcm, CaIrO3-type Al2O3 phase; Au, gold used as an internal pressure calibrant; Re, rhenium of the gasket; *, broad peaks from the sample before transition. Observed unit cell dimensions of (more ...)

To clarify the effect of Al incorporation on the postperovskite phase transition in MgSiO₃, we have considered the coupled Al-Al substitution in perovskite and postperovskite phases of MgSiO₃ according to reactions

Fig. 3. Al-Al coupled substitution enthalpy difference between perovskite and postperovskite. Positive values indicate greater solubility of Al2O3 in perovskite.

Earlier, we found that phase (13) based on the observation of an analogous phase in Fe₂O₃ (12). We believe that studies of analogous materials (such as Al₂O₃, Fe₂O₃, NaMgF₃, and CaTiO₃) will continue to provide important insight into the properties of the Earth's lowermost mantle and set interesting physical questions. In particular, the nature of high-pressure stability of the CaIrO₃-type phases with their layered structure originally came as a surprise (12-14) and still remains enigmatic. It is unclear why some analogous materials adopt this structure at high pressure (e.g., Fe₂O₃, MgSiO₃, Al₂O₃), whereas others do not [e.g., CaSiO₃ (38)].

We thank T. Koyama, N. Sata, and Y. Ohishi for fruitful discussion and experimental help. Calculations were performed at the Eidgenössische Technische Hochschule Zurich and the Swiss National Supercomputing Centre (Manno). The synchrotron radiation experiments were performed at the high-pressure research beamline BL10XU, SPring-8 (Proposal 2003A0013-LD2-np).