Prediction of 10-Fold Coordinated Tio2 and Sio2 Structures at Multimegabar Pressures

Prediction of 10-fold coordinated TiO2 and SiO2 structures at multimegabar pressures

Matthew J. Lylea,1, Chris J. Pickardb, and Richard J. Needsa

aTheory of Condensed Matter Group, Cavendish Laboratory, Cambridge CB3 0HE, United Kingdom; and bDepartment of Physics & Astronomy, University College London, London WC1E 6BT, United Kingdom

Edited by Ho-kwang Mao, Carnegie Institution of Washington, Washington, DC, and approved April 17, 2015 (received for review January 11, 2015)

We predict by first-principles methods a phase transition in TiO2 To investigate structures of TiO2 at pressures beyond the Fe2P- at 6.5 Mbar from the Fe2P-type polymorph to a ten-coordinated type polymorph, we generated relaxed structures using the ab initio structure with space group I4/mmm. This is the first report, to our random structure searching (AIRSS) method (26, 27), supplemented knowledge, of the pressure-induced phase transition to the I4/mmm by structures of AX type from the Inorganic Crystal Structure Da- I mmm 2 structure among all dioxide compounds. The 4/ structure was tabase (ICSD) (28). AIRSS has led to the discovery of structures found to be up to 3.3% denser across all pressures investigated. that were subsequently verified by experiment, for example, in Significant differences were found in the electronic properties of the silane (27), aluminum hydride (29), ammonia monohydrate (30), two structures, and the metallization of TiO2 was calculated to occur concomitantly with the phase transition to I4/mmm. The implica- and ammonia dihydrate (31). Crystalline structures of hydrogen obtained from AIRSS have also been important in understanding tions of our findings were extended to SiO2, and an analogous the high-pressure structures of hydrogen (32, 33). The simplest Fe2P-type to I4/mmm transition was found to occur at 10 TPa. This is consistent with the lower-pressure phase transitions of TiO2, AIRSS approach consists of repeatedly choosing a reasonable cell which are well-established models for the phase transitions in other shape and volume at random, adding the appropriate number of

AX2 compounds, including SiO2.AsinTiO2, the transition to I4/mmm atoms of each type at random positions, and relaxing the structure corresponds to the metallization of SiO2. This transformation is in until the atomic forces are negligible and the pressure is close to a the pressure range reached in the interiors of recently discovered preset target value. This procedure leads to a reasonably unbiased extrasolar planets and calls for a reformulation of the equations of scheme that allows a sparse investigation of the “structure space.” state used to model them. A more efficient AIRSS procedure can be developed by con- straining the searches, which reduces the structure space to be ab initio density functional simulation | multimegabar crystalline phase | investigated. We ensure that the atoms in the initial structures are titanium dioxide | silicon dioxide | super-Earth mantle reasonably spaced by setting bounds on the minimum interatomic distances for each of the three possible pairs of atomic species. he high-pressure behavior of TiO has attracted significant 2 The minimum initial atomic separations for the three atomic pairs interest in material and Earth sciences. Its pressure-induced T are obtained from low-enthalpy structures found in small-cell phase transitions are not only quenchable to ambient pressure but also serve as lower-pressure analogs to the structures adopted searches. We enforce various levels of symmetry during structural relaxations because low-energy structures are likely to possess in many other important AX2 systems (1, 2). In particular, the symmetry (34). Symmetry constraints prevent some structural re- densities of high-pressure silicas (SiO2) significantly affect vis- cosity and convection within the Earth’s mantle and extrasolar laxations, but searching with symmetry constraints is very useful planets. The central pressures of such planets can reach 30 TPa, because it often leads to the identification of low-enthalpy struc- which is extreme enough to compress electronic shells and in- tures. In our searching, we have used numbers of formula units per volve core electrons in bonding. The phase stability and properties cell of 1, 2, 3, 4, 6, 8, 12, and 16. of systems at extreme pressures is mostly the realm of theory (3– 11), although recent advances in diamond anvil cell techniques Significance have seen the achievement of pressures as high as 640 GPa (12), and high-energy lasers now permit X-ray diffraction measurements The highest-pressure phase of TiO ,SiO, and several other im- – 2 2 at pressures approaching 1 TPa (13 15). A recent ramped com- portant dioxides was hitherto believed to be nine-coordinated pression experiment on diamond reached about 5 TPa, although Fe2P-type. We searched for low-enthalpy phases of TiO2 using diffraction measurements were not attempted (16). density functional theory methods, finding that the most stable TiO also has a rich phase diagram at elevated pressures. High- 2 form of TiO2 at pressures above 650 GPa is a ten-coordinated pressure studies have shown that the rutile and anatase forms structure with space group I4/mmm.TiO2 is the well-established transform to a columbite (α-PbO ) phase (17), then to a baddeleyite 2 high-pressure model for many AX2 compounds, and our study structure at around 20 GPa (18, 19), and then to an orthorhombic shows that SiO2 should also form in the I4/mmm structure above (OI) phase (1), followed by a cotunnite structure (1, 19−21). Re- 10 TPa. The high-pressure I4/mmm polymorph of SiO is likely to Pca 2 cently, a new phase of TiO2 of 21 symmetry was predicted in be a major constituent of giant rocky planets at multiterapascal density functional theory (DFT) calculations, which is very close pressures, and our results call for a reformulation of the equa- to thermodynamic stability at around 50 GPa (22, 23), although it tions of state used to model them. has not so far been observed in experiments. The highest-pressure phase of TiO2 identified in experiments so far is the Fe2P-type Author contributions: C.J.P. and R.J.N. designed research; M.J.L. and C.J.P. performed ðP62mÞ structure (2). This phase was predicted in DFT calculations research; M.J.L., C.J.P., and R.J.N. analyzed data; and M.J.L. and R.J.N. wrote the paper. for SiO2 at very high pressures (8), but TiO2 exhibits similar phase The authors declare no conflict of interest. transitions at lower pressures, and diamond anvil cell experiments This article is a PNAS Direct Submission. were able to identify Fe2P-type TiO2 at 210 GPa (2). Experimental Freely available online through the PNAS open access option. and theoretical evidence has been reported for a stable Fe2P-type 1To whom correspondence should be addressed. Email: [email protected]. high-pressure phase of ZrO2 (24), and theoretical evidence has been This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10. reported for a stable high-pressure form of Fe2P-type GeO2 (25). 1073/pnas.1500604112/-/DCSupplemental.

6898–6901 | PNAS | June 2, 2015 | vol. 112 | no. 22 www.pnas.org/cgi/doi/10.1073/pnas.1500604112 Downloaded by guest on October 1, 2021 Fig. 2. Crystal structures of (A)Fe2P-type and (B) I4/mmm TiO2 at 645 GPa. The hexagonal unit cell of the Fe2P-type structure (space group P62m)and tetragonal unit cell of I4/mmm TiO2 are depicted. The lattice parameters for the Fe2P-type structure are (a, b, c, α, β, γ) = (4.4157, 4.4157, 2.3998, 90°, 90°, 120°). The atomic coordinates are Ti1 (1a) (1, 1, 0), Ti2 (2d) (1/3, 2/3, 1/2), O1 (3g) (0.26168, 1, 1/2), and O2 (3f) (0.59427, 0, 0). The lattice parameters and atomic coordinates for the I4/mmm structure are (a, b, c, α, β, γ) = (2.2060, 2.2060, 5.3699, 90°, 90°, 90°), Ti (2b) (1/2, −1/2, 0), and O (4e) (1, −1, 0.16336).

of the I4=mmm structure contains a single Ti atom that is 10-fold coordinated, which is the highest coordination number found in any dioxide to date. The Ti−O bond distances are 1.65−1.80 Å and 1.75−1.80 Å in Fe2P-type and I4=mmm structures, re- Fig. 1. Relative static lattice enthalpies of TiO structures, plotted with respectively, at 645 GPa. This indicates that the higher densities 2 I =mmm spect to the Fe2P-type structure. (A) The pressure regime between 0 GPa and achieved in 4 arise from the higher coordination and 40 GPa, and (B) the high-pressure postcotunnite regime. Inset focuses on the denser polyhedral packings. Volume compression curves show Fe2P-type to I4/mmm transition, which is predicted to occur at 636 GPa and that the I4=mmm unit cell volume is smaller than the Fe2P-type 647 GPa, using the LDA+U and PBEsol functionals, respectively. volume across all pressures studied, and that I4=mmm is 3.3% more dense at the transition pressure. The greater density of I =mmm Results and Discussion 4 leads directly to greater stability than Fe2Ptypeat EARTH, ATMOSPHERIC, sufficiently high pressures. AND PLANETARY SCIENCES ðΔHÞ Static enthalpy differences calculated relative to the high- Charge densities of the Fe2P-type and I4=mmm structures of pressure Fe2P-type structure are plotted in Fig. 1 as a function of TiO2 are illustrated in Fig. 3. In the F2P-type structure, the pressure. Fig. 1A illustrates the structural phase transitions up to charge densities are observed to be mostly spherical and cen- the cotunnite-type structure. At ambient pressure, the enthalpy of tered on the atoms. This is consistent with a Bader analysis of the α rutile is calculated to be slightly higher than that of the -PbO2- electron density, which assigns net charges on the Ti and O type polymorph, which is consistent with other theoretical in- atoms of +1.91 and −0.96e, respectively. This corresponds to an vestigations (2). The calculated static enthalpies of the known high- ionicity of ∼48%. In I4=mmm, the charge densities are seen to be pressure polymorphs baddeleyite, OI, and cotunnite are shown. deformed between neighboring atoms and take the form of O lone Fig. 1B portrays the postcotunnite regime of the phase diagram. The cotunnite−Fe2P-type transition is calculated to occur at 143 GPa, in good agreement with previous investigations (2). The high-density Fe2P-type structure has previously been thought to be the final high-pressure phase in several dioxides (2, 8). How- ever, we found an even higher density structure with space group I4=mmm that becomes more stable than Fe2P-type above 636 GPa or 647 GPa, using the LDA+U and PBEsol density functionals, respectively. We found the TiO2 I4=mmm structure using AIRSS, although this structure has also been predicted as a high- pressure phase of TiS2 (35). The crystal structures of the Fe2P-type and I4=mmm polymorphs are compared in Fig. 2. The Fe2P-type hexagonal unit Fig. 3. Charge densities of the two high-pressure polymorphs of TiO at 645 P m 2 cell (space group 62 ) contains three ninefold coordinated Ti GPa. (A) The (001) plane of the Fe2P-type structure. (B) The (010) plane of polyhedra. Conversely, the lower (tetragonal) symmetry unit cell the I4/mmm structure.

Lyle et al. PNAS | June 2, 2015 | vol. 112 | no. 22 | 6899 Downloaded by guest on October 1, 2021 optimizing quartz and cristobalite at ambient pressure. Static enthalpies are plotted in Fig. 6, revealing a high-pressure analog to the phase diagram found for TiO2. The Fe2P-type to I4=mmm transition was found to occur at 9.8 or 10.0 TPa using the PBEsol or LDA functional, respectively. This pressure corresponds to the core of an extrasolar planet with a mass 40 times that of Earth (40 M ⊕ ). The Si−O bond lengths at 10 TPa are 1.14−1.27 Å and 1.29 Å in the Fe2P-type and I4=mmm structures, respectively. I4=mmm silica is denser than Fe2P-type across all pressures tested and is 1.4% denser at the transition pressure. This indicates a need to reformulate the equations of state used to model the deep mantles of terrestrial exoplanets and the cores of gas giants. Silica is found to maintain much wider band gaps than iso- structural TiO2, even at terapascal pressures. The compression- induced band gap narrowing is seen to metallize the I4=mmm structure by 1.4 TPa, while no metallization was observed in the Fe2P-type polymorph at the pressures tested. Hence, as well as altering the coordination environment and density, the I4=mmm transition also brings about the metallization of silica.

Fig. 4. Calculated band gaps of Fe2P-type and I4/mmm TiO2 structures as a function of pressure. A vertical red line represents the static PBEsol transition pressure, which is also the metallization pressure.

pairs, which is in agreement with an electron localization function (ELF) analysis. The Bader charges are +1.67 and −0.84e on the Ti and O atoms, respectively, equating to a lower ionicity of ∼42%. This is interesting since structures with lower ionicities are less sensitive to the Coulomb interactions with neighboring atoms. This means that the stabilizing effect of 10-fold coordination is less pronounced in I4=mmm TiO2 thanitwouldbeintheFe2P-type. This is also consistent with the longer bond distances in I4=mmm. Hence, we expect the favorable energetics of the I4=mmm structure to arise from the efficient packing of O lone pairs when the material is highly compressed. Calculated band gaps of these phases are shown in Fig. 4 as a function of pressure. The band gaps are observed to correlate negatively with pressure. Tsuchiya and coworkers (2) previously found the Fe2P-type structure to have the smallest band gap of any known TiO2 polymorph; they calculated a band gap of 0.66 eV at 160 GPa, which compares well with our value of 0.50 eV. Above 160 GPa, we find the band gap is further reduced until the I4=mmm transition at 647 GPa, where TiO2 becomes a metal (we calculate the I4=mmm structure to be metallic at all pressures). Fig. 5 depicts the band structures and densities of states of these phases. Both structures have dominant O 2p and Ti 3d components in the valence and conduction bands, respectively. The band gap narrowing in the Fe2P-type polymorph is seen to arise from a single Ti 3d state in the conduction band, which ap- pears to be preferentially stabilized by pressure near the Γ-point. Low-pressure structures of silica (e.g., quartz, zeolites) adopt tetrahedral Si coordination, but, at pressures between 10 GPa and 250 GPa, sixfold coordination is preferred, e.g., the stisho- vite (a rutile-type silica), CaCl2, α-PbO2, and pyrite structures. The cotunnite transition (ninefold coordination) becomes stable at about 700 GPa, and, at about the same pressure, Fe2P-type silica becomes most stable. Recent theoretical investigations have shown that MgSiO3 and CaSiO3, which are major constit- uents of the Earth’s mantle, separate into SiO2 and B2 (CsCl structure) oxides at extrasolar planet core conditions (5, 8). This highlights the importance of SiO2 as a mantle mineral at very high pressures. We performed calculations with the PBEsol functional for I =mmm Fig. 5. Electronic band structures of (A)Fe2P-type and (B) I4/mmm TiO2 at silica in the Fe2P-type and 4 structures described above 645 GPa. The calculated Fermi energies (EF) are indicated by horizontal black up to pressures of 17 TPa. PBEsol has been shown to outperform lines. Electronic densities of states, and their projections onto atomic orbitals, other functionals in silica (36), and we found the same when are also shown.

6900 | www.pnas.org/cgi/doi/10.1073/pnas.1500604112 Lyle et al. Downloaded by guest on October 1, 2021 several density functionals and found that the LDA+U functional (39) with U = 5 eV predicts the correct energy ordering of rutile < brookite < anatase at low pressures, but it fails to predict the experimentally verified transition to the cotunnite structure at high pressures. See ref. 40 for

further discussion of values of U for TiO2. The PBEsol functional (41) cor- rectly predicts the stability of cotunnite and other known high-pressure phases. The PBEsol functional is also essentially exact in the limit of a uniform electron gas, and it provides an excellent description of the response of the electron gas to an applied potential. These properties, which are also shared by the LDA and PBE functionals (42), are particularly useful at high pressures, where the charge density becomes more uniform. Spin polari- zation is accounted for within LDA+U, although no magnetically ordered phases were found in our low-enthalpy structures. Brillouin zone sampling − grids of spacing 2π ×0.07 Å 1 and an energy cutoff of 340 eV were used for the searching. For the final results reported in this paper, we used a smaller − k-point spacing of 2π ×0.03 Å 1 and energy cutoffs of 700 eV and 850 eV

for TiO2 and SiO2, respectively. We relaxed about 6,000 structures obtained from AIRSS and a further 2,500 from the ICSD. Vibrational contributions Fig. 6. Relative static lattice enthalpies of high-pressure silica structures, to the TiO2 enthalpies were considered within the quasi-harmonic approximation using PBEsol and resulted in no adjustments to the static transi- plotted with respect to the Fe2P-type structure. Inset focuses on the Fe2P-type to I4/mmm transition, which is predicted to occur at 9.8 TPa or 10.0 TPa using tion pressure. the PBEsol or LDA functional, respectively. This pressure corresponds to the core of an extrasolar planet with a mass 40 times that of Earth (40 M ⊕ ). ACKNOWLEDGMENTS. We gratefully acknowledge financial support from the Engineering and Physical Sciences Research Council of the United Kingdom and Peterhouse, Cambridge. Computational resources were pro- Methods vided by the High Performance Computing Service at the University of Cambridge and the Archer facility of the United Kingdom’snationalhigh- The first-principles DFT calculations were performed using the CASTEP plane performance computing service, for which access was obtained via the wave basis set code (37) and ultrasoft pseudopotentials (38). We tested United Kingdom Car-Parrinello consortium.

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