Using high-resolution synchrotron x-ray powder diffraction we have investigated the structural phase transitions and equations of state of titanium dioxide ͑TiO 2 ͒ under high pressure before and after heating at high temperature. The phase sequence we observe experimentally is as follows: rutile ͑RT͒ → columbite ͑CB͒ → baddeleyite ͑MI͒ → orthorhombic I ͑OI͒ → orthorhombic II ͑OII͒. The equations of state as determined from our experiments are consistent with previous measurements and computations. The only exception is the OII phase for which we find a significantly lower room-pressure bulk modulus ͑K 0 ͒ of 312 ͑Ϯ34͒ GPa and room-pressure volume ͑V 0 ͒ of 25.28 ͑Ϯ0.35͒ Å 3 as compared to previous experiments. We find that the volume decreases across the OI→ OII phase transition at room temperature by ϳ8.3%, in very good agreement with our static first-principles calculations which predict volume changes of 8.2% and 7.6% for local-density approximation and generalized gradient approximation, respectively. This volume collapse is significantly higher than previously determined but consistent with the volume decrease observed in other dioxides across this transition.

We use high-resolution synchrotron x-ray powder diffraction and density-functional theory ͑DFT͒ to investigate the phase stability, equations of state ͑EOSs͒, and mechanical hardness of zirconia ͑ZrO 2 ͒ up to ϳ54 and 160 GPa, respectively. For the equilibrium phase at ambient conditions ͑MI͒, we provide an experimental EOS that is comparable to results obtained from room-pressure Brillouin scattering experiments and bulk modulusvolume systematics but different from previous high-pressure experiments. The experimental second-order Birch-Murnaghan EOS parameters of MI-ZrO 2 are: ambient-pressure volume ͑V 0 ͒ of 35.15͑Ϯ0.03͒ Å 3 / f.u. with an ambient-pressure bulk modulus K 0 of 210͑Ϯ28͒ GPa. For the high-pressure OI phase, we find that the K 0 = 290͑Ϯ11͒ GPa, which is 19%-32% higher than previously determined, and V 0 = 33.65͑Ϯ0.07͒ Å 3 / f.u. The small volume decrease of 3.4% across the MI→ OI transition at ϳ10 GPa is associated with a 38% increase in the bulk modulus consistent with our DFT calculations that predict a ϳ36% and 39% increase in K 0 for the generalized gradient and local density approximations, respectively. In contrast to the EOS of MI and OI, we find that our experimental EOS for the high-pressure OII phase is in good agreement with previous measurements. The large volume decrease across the OI→ OII phase transition as obtained from both our experiments and calculations is ϳ10%. Our estimates, using scaling relations, indicate that this phase, while dense and quenchable, may have a comparatively low mechanical hardness of ϳ10 GPa.

Using high-resolution synchrotron powder x-ray diffraction, we have investigated the stability and equation of state ͑EOS͒ of hafnia HfO 2 phases under high pressures before and after laser heating to high temperatures. We observe three phases with increasing pressure: baddeleyite ͑monoclinic, MI͒, orthorhombic I ͑OI͒, and cotunnite ͑orthorhombic, OII͒. The OII phase is stable up to a pressure of at least 105 GPa before and after laser heating to ϳ1800 ͑Ϯ200͒ K. We provide experimental EOSs for the observed phases. The present results for MI-HfO 2 EOS are distinct from previous measurements yielding an ambient-pressure volume ͑V 0 ͒ of 34.50 ͑Ϯ0.04͒ Å 3 / f.u. and an ambient-pressure bulk modulus K 0 of 185 ͑Ϯ23͒ GPa, assuming K 0 Ј=4. In contrast, the experimental EOSs of OI and OII are in good agreement with previous studies. The measured EOSs are consistent with our density-functional theory calculations. The large volume decrease across the OI→ OII phase transition as obtained from both our experiments and calculations is ϳ9%. Despite the large increase in density and high bulk modulus of OII-HfO 2 , we find, using scaling relations, that all HfO 2 phases show similar mechanical hardness ͑H͒ of ϳ10-12 GPa, too low for HfO 2 to be considered a superhard material.

Using high-resolution, synchrotron-based powder X-ray diffraction (XRD), we have studied the high-pressure behavior of the anatase phase of nanocrystalline TiO 2 (nc-TiO 2 ) under hydrostatic conditions. We find that for anatase with a grain size larger than ∼40 nm, the room-pressure bulk modulus K 0 remains constant at ∼200 GPa to within experimental uncertainties. An ∼15% decrease in K 0 is observed for grains that are ∼20 nm in size and remains unchanged for grains down to 6 nm in diameter, indicating a rapid increase in compressibility for nc-TiO 2 anatase between 40 and 20 nm. ■ INTRODUCTIONTiO 2 anatase is an important material in many technological applications including photocatalysis, ceramics, electronic storage media, and hydrogen storage applications. 1−3 Due to its promising technological applications, 1−3 the high-pressure behavior of nc-TiO 2 anatase has attracted great interest over the past decade 4−17 with studies focusing on pressure-induced phase transitions and amorphization. 5−7,9,11,12,14−17 However, little is known about the effect of particle size on the equation of state (EOS) of TiO 2 anatase and the few available studies are inconclusive and controversial: previous experiments on ncTiO 2 anatase have found that the bulk modulus may increase or decrease with decreasing particle size. 4,8,10,13 Some of the complications likely arise from the lack of hydrostaticity in the sample under pressure, 8,10 whereas other studies do not provide the EOS of nc-TiO 2 anatase 13 or have some important issues (e.g., typographical errors or mistakes in EOS determination) in the reported EOS and/or measured value of its zero-pressure volume V 0 . 4 Thus, a consistent understanding of the behavior of nanocrystalline TiO 2 anatase as grain size is changed is presently lacking.To eliminate, or at least reduce, the controversy regarding the grain size dependence, we study the size dependence of the bulk modulus in nc-TiO 2 anatase under hydrostatic conditions at pressures up to ∼11 GPa. Therefore, this work along with a reanalysis of previous studies on nc-TiO 2 anatase 4,8,10,13 allow us to reach consistency among several studies of the size dependence of the bulk modulus of nc-TiO 2 anatase. ■ EXPERIMENTAL METHODSNanocrystalline samples of 99% TiO 2 anatase/rutile powder (Nanostructured & Amorphous Materials, Inc., 50 nm average particle size) and 99.7% TiO 2 anatase powder (Alfa Aesar, 15 nm average particle size) were used as starting materials in our diamond-anvil cell (DAC) experiments. We confirmed the grain sizes by using the full-width-half-maximum 18 of the XRD peaks to be 40(±3) and 20(±4) nm, respectively, consistent with scanning electron microscope measurements which yielded particle sizes of ∼40−60 and ∼20−30 nm, respectively. We performed two independent room temperature, highpressure DAC experiments to study the EOS of nc-TiO 2 anatase (Table 1). A mixture of methanol−ethanol−water (M-E-W) (16:3:1 by volume) was used as the pressure medium. 19 For pressures up to ∼11 GPa, M-E-W is hydrostat...