Experimental and theoretical identification of a new high-pressure phase of silica

Abstract

Following the discovery of stishovite (the highest-pressure polymorph of silica known from natural samples), many attempts have been made to investigate the possible existence of denser phases of silica at higher pressures. Based on the crystal structures observed in chemical analogues of silica1,2,3, high-pressure experiments on silica4,5,6,7,8,9,10,11 and theoretical studies12,13,14,15,16, several possible post-stishovite phases have been suggested. But the likely stable phase of silica at pressures and temperatures representative of Earth's lower mantle remains uncertain. Here we report the results of an X-ray diffraction study of silica that has been heated to temperatures above 2,000 K and maintained at pressures between 68 and 85 GPa. We observe the occurrence of a new high-pressure phase which we identify with the aid of first-principles total-energy calculations. The structure of this phase (space group Pnc2) is intermediate between the α-PbO2 and ZrO2 structures, and is denser than other known silica phases.

Main

Experiments at extreme conditions are usually associated with significant difficulties; these include limited size of sample (and bad access to it) in a diamond-anvil cell, non-quenchable phase transitions, and pressure and temperature gradients. The available experimental data on SiO2 at mantle pressures are either from unheated samples6,9,10,11 or from heated samples quenched at high pressures8, and then there are only few lines observed in the X-ray diffraction spectra. The present experimental study is designed to minimize the difficulties encountered in earlier studies. We used two different starting materials (silica gel and quartz), laser-heated these materials at various pressures and followed the transformations both with increasing and decreasing pressure. We used the Mao–Bell type of diamond-anvil cell following the sample preparation method described elsewhere17. We conducted three separate sets of experiments.

In the first set of experiments, a 10-µm-thick iron foil was surrounded by dried silica gel. In the two other sets of experiments, we used quartz and platinum in the same manner. In the first set of experiments, an area of 60 µm diameter was heated to 2,000(±50) K at 80 GPa with a Nd : YAG laser for several dozen minutes. In the experiments with quartz and platinum, samples were heated over an area of 80 µm diameter for at least 30–40 min at different pressures (40–68 GPa). The temperature was measured using the spectroradiometric method17. The quenched samples, still under pressure, were studied at the Brookhaven National Laboratory synchrotron X-ray facility or the X-ray facilities in Uppsala University. The pressures were determined using the equation of state18,19. There is a close agreement (±2 GPa) between the pressures obtained from different pressure scales. The pressure was rather homogenous within the studied areas (maximum difference; 5 GPa at a pressure of 80 GPa). An estimated thermal pressure value of 7% (ref. 17) has been added to the reported pressures.

After heating at a pressure of 85(±5) GPa in the experiment with iron and silica gel and at 68(±5) GPa in the experiments with quartz and platinum, the silica closest to the metal was found to have recrystallized to a dense form of SiO2 over large areas (Figs 1, 2 and Table 1). X-ray diffraction shows a mixture of three phases: metal (ε-Fe or Pt), a CaCl2-like phase and the new silica phase. The metal reflections are quite strong in all patterns and can be easily identified (Figs 1, 2). Some reflections can be explained by the presence of CaCl2-like structure in the sample (Table 1). This happens because the heating produced by the Nd YAG laser is very localized; only the part of SiO2 which is in contact with the metal foil (acting as a hot-plate) has the same temperature as the foil. Away from the heated area both in the axial and radial directions, the temperature decreases rapidly. Therefore, while stishovite (or the CaCl2-like phase) in the immediate surroundings of the metal would be converted to a new phase, the temperature away from the metal foil will be lower; in these latter areas stishovite (or the CaCl2-like phase) will remain stable.

Figure 1: a, X-ray diffraction pattern of the sample containing silica gel and iron as starting materials after laser heating during decompression.
figure1

The sample was heated at 2,000(±100) K. The initial diffraction pattern at 85(±5) GPa contains lines of a new phase with Pnc2 structure (marked as S), CaCl2-like silica phase (C) and ε-iron (Fe). At 74(±5) GPa the reflections of the Pnc2 structure almost completely disappear owing to conversion to the CaCl2-like silica phase with lattice parameters a = 4.041(±3) Å, b = 3.846(±4) Å, c = 2.588(±2) Å. At lower pressure, 42(±5) GPa, the CaCl2-like silica phase transforms to stishovite (a = 4.029(±4) Å, c = 2.595(±6) Å). The pressures were determined on the bases of the iron equation of state17,18. b, X-ray diffraction pattern of the sample, containing silica gel and iron as starting materials, after laser heating during decompression. The bottom curve is from the sample heated to 2,450(±150) K during 40 min at 68(±5) GPa. The diffraction pattern shows lines of the new phase Pnc2 (marked as S), CaCl2-like silica phase (C) and platinum (Pt). The upper curve corresponds to the case when the pressure was decreased to 55(±5) GPa and platinum heated again to about 1,500(±200) K for nearly 40 min by scanning with the laser. Then only the CaCl2-like (a = 4.071(±4) Å, b = 3.876(±4) Å, c = 2.607(±3) Å) reflections remain. These experiments establish the reversibility of the transformation.

Figure 2: Examples of diffraction patterns collected during the transformation of quartz at high pressure after heating, using a CCD (charge-coupled device) area detector and monochromatic Mo Kα1,2 radiation (rotation anode generator, 18 kW).
figure2

The irradiated area corresponds to 50 µm and the exposure time is 6 hours. a, Quartz at 45(±5) GPa before heating. The letter Q denotes quartz (or quartz II11) reflections. Owing to preferred orientation, the (200) reflection of Pt is more intense than the (111) reflection. b, Same sample after heating at 2,350(±150) K using a Nd : YAG laser. The quartz reflections have disappeared and the (101) reflection of stishovite (St) has appeared. Note that we cannot distinguish between the stishovite and CaCl2 structures within the angle range shown here. c, Same sample after pressurizing at 68(±5) GPa and heating at 2,450(±150) K. New reflections at 3.02 Å and 2.48 Å appear. These reflections can be indexed as (011) and (111) of the Pnc2 structure (S). Letter D denotes a single spot from the diamond anvil.

Table 1 Table 1 Assignments of reflections and comparison between observed and calculated d values

A number of diffraction lines (for example, lines with d values of 2.9905, 2.4615 and 1.4181 Å at 85(±5) GPa in the experiment with silica gel or lines at 3.0130, 2.4719, 2.0685, 1.8296 and 1.4220 Å at 68(±5) GPa in the experiment with quartz) belong neither to the metal nor to the CaCl2-like phase (or stishovite) and must be considered as being due to the new phase (Table 1). These lines cannot belong to any iron phase, because they are absent in the diffraction patterns of those parts of the sample that consist mainly of ε-Fe, and they appear only in the presence of silica. Moreover, they appear also in experiments with platinum. We cannot explain these reflections as being due to either pressure gradients or some reaction between metal and SiO2. After collecting the data at high pressure, we released the pressure gradually and noted the disappearance of the peaks of the new silica phase (Fig. 1).

Different investigators have suggested a number of possible post-stishovite phases of SiO2. Such phases have been obtained from theoretical simulations or observed experimentally in related systems; these are CaCl2, α-PbO2 and modified α-PbO2 (space group I2/a), ZrO2, intermediate between α-PbO2 and ZrO2 (space group Pnc2), α-PbCl2, fluorite and modified fluorite (space group Pa3) structures1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16. We have considered the diffraction patterns of these phases and tried to index our experimental diffraction pattern accordingly. It was found that all reflections in our diffraction pattern can be easily explained by the presence of a mixture of metal, a CaCl2-like phase and a structure with Pnc2 symmetry. At high pressure α-PbO2 and Pnc2 structures are similar15,16 and it is difficult to distinguish these two structures on the basis of our experimental data. But on the basis of theoretical considerations (see below) the Pnc2 structure is preferable.

We have also studied the stishovite (or CaCl2-type)–Pnc2 structural transition by means of accurate first-principles, total-energy calculations. This is necessary because our interpretation of the diffraction patterns is based on the results from lattice dynamics simulations using semi-empirical inter-atomic potentials14,15. Only ab initio calculations can confirm results of such semi-empirical methods. Figure 3ashows the results of our present first-principles theoretical total-energy calculations; Fig. 3shows the difference in total energies between different structures as a function of volume and where the Pnc2 structure is used as a reference energy level. One can see from Fig. 3that ideal α-PbO2 is clearly not stable in any region over the whole studied volume range. In the lattice dynamics calculations at pressures >70 GPa, the density of the Pnc2 structure becomes greater than that of stishovite; at 100 GPa and 300 K the difference amounts to 0.9% and increases with pressure up to 1.8% at 150 GPa. The Pnc2 structure becomes more stable than the CaCl2-like structure at pressures above 93 GPa and 300 K which agrees well with the FPLMTO (full potential linear muffin-tin orbital; see Fig. 3 legend) result where the transition pressure at 0 K is 80 GPa (as discussed below). We find the following sequence of phase transitions; stishovite → CaCl2Pnc2 structure → Pa3. The first transition takes place at 45 GPa, the second at 80 GPa and the third at 220 GPa. The transition at 45 GPa is in agreement with the calculation by Kingma et al.10. We have found that the Pa3 structure is stable at pressures above 220 GPa whereas Cohen20 found the Pa3 structure to be stable already at 157 GPa because he did not consider the new crystal phase. The transition pressure to the Pnc2 structure, derived from the present zero-temperature calculations (80 GPa), is somewhat lower than that obtained from the room-temperature lattice dynamics14 (93 GPa) and molecular dynamics15 (120 GPa) simulations but higher than the experimental result. A possible reason for this small discrepancy between the predictions of theory might be (1) the difference in theoretical methods and/or (2) the influence of the vibrational energy which is not considered in the first-principles calculations. We thus conclude, based on first-principles calculations, that a Pnc2 structure must be viewed as a strong candidate for explaining the experimentally observed X-ray results of this study. In Table 2we present theoretically optimized structural parameters for the Pnc2 structure at two different volumes.

Figure 3: a, Calculated total energies (relative to E = −876.000 Ry) of the stishovite, CaCl2, Pnc2 and Pa3 crystal structures for SiO2 as a function of volume.
figure3

From the standard ‘common tangent’ construction we derive the following volume collapses at the structural transitions; ΔV/V = 1.5% for CaCl2Pnc2 and ΔV/V = 3.5% for Pnc2 → Pa3. The theoretical technique used here is a so-called full potential linear muffin-tin orbital method (FPLMTO)21. The only approximation which enters this theory is the use of the local density approximation to the exchange-correlation potential (Hedin-Lundqvist parametrization22). The truncation of the expansion of wavefunctions, charge density and potential is also an approximation but the numerical error introduced by this truncation can always be reduced to a desired small value. Thus a high level of numerical accuracy has been maintained throughout the calculations. The basis functions, electron densities, and potentials were expanded in combinations of spherical harmonic functions (with a cut-off Imax = 8) inside non-overlapping spheres surrounding the atomic sites (muffin-tin spheres) and in a Fourier series in the interstitial region. The muffin-tin sphere occupies 40% of the unit cell. The basis functions within the muffin-tin spheres are linear combinations of radial wavefunctions and their energy derivatives, computed at energies appropriate to their site and principal, as well as orbital, atomic quantum numbers, whereas outside the muffin-tin spheres the basis functions are combinations of Neuman or Hankel functions23,24. b, Energy difference between the stishovite, CaCl2, Pnc2, Pa3, α-PbO2 and I2/a crystal structures for SiO2 as a function of volume. The Pnc2 structure is used as the zero energy reference level.

Table 2 Table 2 Theoretically optimized structural parameters of the Pcn2 phase of silica

Because the only experimental data we have available so far is for quenched samples at high pressures, we do not know how the density of SiO2 would increase (owing to its phase transition) along the geothermal gradient in the mantle. However, the demonstrated reversibility of the phase transition shows clearly that the Pnc2 phase is the densest phase; on release of pressure the Pnc2 structure reverses to stishovite (or CaCl2-type silica). The only constraints we have on the chemical composition of the lower mantle are from the seismic density data. To reproduce this density profile mineralogically, any combination of silicates and oxides may be chosen. It is therefore important that we know the structure and physical properties of any phase which could be a candidate for the mantle. Through this study, we have established that silica with the Pnc2 structure is such a phase.

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Acknowledgements

We thank J. Hu and G. Shen for their help in conducting the X-ray experiments, and N. Dubrovinsky for discussions. This work has been supported by the Swedish Natural Science Research Council (NFR), the Royal Swedish Academy of Sciences, and the Swedish Materials Consortium No. 9 financed by NUTEK, NFR and the Wallenberg Foundation.

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Correspondence to S. K. Saxena.

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Dubrovinsky, L., Saxena, S., Lazor, P. et al. Experimental and theoretical identification of a new high-pressure phase of silica. Nature 388, 362–365 (1997). https://doi.org/10.1038/41066

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