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Possible structural polymorphism in Al-bearing magnesiumsilicate post-perovskite

¹ High Pressure Science and Engineering Center, Department of Physics, University of Nevada, Las Vegas, Nevada 89154, U.S.A.
² Division of Geology and Planetary Sciences, California Institute of Technology, Pasadena, California 91125, U.S.A.
³ Department of Physics, New Mexico State University, Las Cruces, New Mexico 88003, U.S.A.
⁴ HPCAT, Advanced Photon Source, Argonne National Laboratory, Argonne, Illinois 60439, U.S.A.
⁵ Center for Condensed Matter Science and Technology, Research Academy of Science and Technology, Harbin 150080, China
⁶ Geophysical Laboratory, Carnegie Institution of Washington, Washington, D.C. 20015, U.S.A.
⁷ Physics Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, U.S.A.

Correspondence: ^* E-mail: olivert{at}physics.unlv.edu

	ABSTRACT

Top Abstract Introduction Theory Experimental methods Results and discussion Raman spectra Appendix Acknowledgments References cited

 
In the present study, we summarize indications for the existence of kinked post-perovskite structures in the MAS system. X-ray diffraction data and Raman spectra of aluminous magnesium metasilicate post-perovskite are inconsistent with the CaIrO₃ structure. Instead the observations are consistent with structures intermediate between the perovskite and the CaIrO₃ structure. Ab initio calculations show that the enthalpies of the kinked structures are slightly higher than the CaIrO₃ structure at 0 K. Finite temperature, minor element chemistry, kinetics of phase transformation, and actual stress regime are plausible reasons for the observed differences between the present and the previously reported post-perovskite phases.

Key Words: Crystal structure • post-perovskite • XRD data • quantum mechanical calculation • high-pressure studies • Raman spectroscopy

	INTRODUCTION

Top Abstract Introduction Theory Experimental methods Results and discussion Raman spectra Appendix Acknowledgments References cited

 
The major phase of the Earth’s lower mantle is magnesium metasilicate in the perovskite structure. Recently, a first-order phase transformation of this silicate-perovskite into a phase with quite different structure was proposed based on experiments at pressures and temperatures of the lowermost mantle (Murakami et al. 2004; Oganov and Ono 2004). Furthermore, first-principles calculations indicate that the CaIrO₃-type structure of MgSiO₃ is more stable than the perovskite structure at the pressures of the core-mantle boundary region at 0 K (Oganov and Ono 2004; Tsuchiya et al. 2004a). Moreover, the Clapeyron-slope of the pervoskite-to-post-perovskite phase transition has been calculated to be positive and of a magnitude that makes existence of post-perovskite in colder regions of the deepest mantle likely (Oganov and Ono 2004; Tsuchiya et al. 2004b). This discovery has the potential to change our understanding of this important region in the Earth. Marked differences in thermoelastic properties between magnesium silicate perovskite and post-perovskite may account for anomalous seismic features in the lowermost mantle. For example, the positive Clapeyron slope of the phase boundary may control size and number of plumes forming in this region of the Earth (Nakagawa and Tackley 2004; Helmberger et al. 2005; Kameyama and Yuen 2006). It is of most interest to determine the influence of minor element chemistry and the actual stress-temperature regime on the structure of post-perovskite and to examine if there are intermediates between perovskite and the reported post-perovskite phase. The observation of unexplained diffraction features in perovskite-post-perovskite assemblies synthesized from pyrope at 140 GPa (Tateno et al. 2005) may be an indication that structural intermediates occur as stable or metastable phases for mixed compositions in the magnesium-aluminum-silicate (MAS) system. Recently, Oganov et al. (2005) proposed a new type of kinked post-perovskite structures that are intermediate between perovskite and CaIrO₃-post-perovskite. Here, we present ab initio calculations, X-ray diffraction data, and Raman spectra that support the formation of such kinked post-perovskite structures in aluminous and ferrous aluminous magnesium metasilicate.

	THEORY

Top Abstract Introduction Theory Experimental methods Results and discussion Raman spectra Appendix Acknowledgments References cited

 
To assess the stability of the proposed structures we performed ab-initio calculations with the Vienna Ab-initio software package (Kresse and Hafner 1993; Kresse and Furthmüller 1996) for MgSiO₃ post-perovskite. The calculations are based on density-functional theory (Hohenberg and Kohn 1964). Electronic correlations were treated with the GGA in the parameterization of Perdew et al. (1996). We used PAW potentials (Blöchl 1994; Kresse and Joubert 1999) for Mg (valence states 3s²), Si (3s²2p⁴), and O (2s²2p⁴) with core radii of 2.000 a_B, 1.508 a_B, and 1.525 a_B for Mg, Si, and O, respectively. The calculations for MgSiO₃-perovskite and MgSiO₃-post-perovskite were performed using 6 x 6 x 4 and 6 x 4 x 6 k-point grids (Monkhorst and Pack 1976), respectively. All calculations for the intermediate structures were performed using a 1 x 2 x 2 k-point grid. An energy cut-off of 600 eV was sufficient to converge energies to within 1 meV per MgSiO₃ unit and pressures to within 0.3 GPa. All calculations were performed in symmetry preserving mode at static conditions (0 K). The initial model post-perovskite structures were generated as follows: The perovskite structure if viewed along [001] can be described as the stacking of two types of "layers" (A and B) with sequence ...BABABA... running in [010] direction (Fig. 1a). Polytypes with different layer sequences were generated by inserting layers into the perovskite structure such that a continuous SiO₆ network was maintained (Figs. 1b–1g). We adopt the nomenclature for different stacking sequences from Oganov et al. (2005): n x m represents a sequence with n, m sequential layers of type A and type B, respectively. If only A layers are added the resulting n x 1 and n x m structures all belong to space group P2₁/m (Table 1). Similarly, structures of type n x n belong to space group Pbnm. The 2 x 2 and the 3 x 1 structure have been described previously (Oganov et al. 2005). Inserting more A type layers increases the length of the edge sharing chains relative to the corner sharing Si-octahedra (Figs. 1d–1g) and the post-perovskite phase is obtained in the limit of infinite chain length. Structures of type 1 x 1 (perovskite), 2 x 2, 3 x 3, 2 x 1, 3 x 1, 4 x 1, 5 x 1, 6 x 1, 4 x 3, and (,0 – CaIrO₃-type) were relaxed to explore their relative energies and crystal chemistry and as initial structure models for the interpretation of the experimental diffraction data.

View larger version (15K): [in this window] [in a new window]   FIGURE 1. View along the [001] direction of the relaxed structures from the ab initio calculations. The two types of layers are indicated by light and dark shading of the SiO6-octahedra in each layer. Magnesium atoms are shown as black circles and unit cells are indicated by thin solid lines. (a) 1 x 1 (perovskite); (b) 2 x 1; (c) 3 x 1; (d) 4 x 1; (e) 5 x 1; (f) 2 x 2; (g) 3 x 3; (h) x 0 (CaIrO3). We also give the calculated fractional coordinates of the 2 x 1 and the 3 x 1 type structures as they are used to model the observed diffraction patterns. 2 x 1: Mg: 0.057, , 0.538; 0.269, , 0.083; 0.730, , 0.917; Si: 0, 0, 0; 0.330, 0.502, 0.555; 0.380, , 0.820; O: 0.792, 0.560, 0.140; 0.207, 0.060, 0.860; 0.306, , 0.429; 0.458, 0.555, 0.243; 0.644, , 0.313. 3 x 1: Mg: 0.042, , 0.514; 0.303, , 0.073; 0.559, , 0.989; 0.799, , 0.895; Si: 0, 0, 0; , 0, ; 0.247, 0.501, 0.583; O: 0.985, , 0.111; 0.230, , 0.455; 0.480, , 0.368; 0.7352, , 0.287; 0.845, 0.559, 0.125; 0.906, 0.443, 0.647; 0.343, 0.556, 0.283; 0.407, 0.444, 0.801.

	EXPERIMENTAL METHODS

Top Abstract Introduction Theory Experimental methods Results and discussion Raman spectra Appendix Acknowledgments References cited

In the first set of experiments (Sample 1), we changed the pressure several times between 100 and 120 GPa and heated at each pressure point to homogenize the stress conditions in the sample. In detail the loading and heating cycles during the first experiment were as follows: Initially, the sample was pressurized to 80 GPa and heated to ~ 2000 K for 300 s to convert the orthopyroxene sample to the perovskite structure. Then the sample was pressurized to between 110 and 120 GPa and heated to 2200 (±100) K for 600 s. The pressure after heating was 105 ± 5 GPa. Because ruby was incidentally heated by the laser beam upon alignment and underwent a structural transition upon heating (Lin et al. 2004), we used the volume of NaCl to calculate the pressure (Fei et al. 2007; Sata et al. 2002) and the given uncertainties are from the combined error in volume determination and in calibration of the NaCl-scale relative to the Pt-scale (Sata et al. 2002) and to the gold scale (Fei et al. 2007). The volume was obtained upon Rietveld refinement of the NaCl structure using the experimental diffraction pattern (R_F² = 0.04). While there is no absolute calibration of pressure at 100 GPa better than ±10 GPa (Holzapfel 2003), the volume of NaCl will allow for more accurate determination of pressure once a better pressure scale is established. Thereafter, we reduced and raised pressure between 98 and 115 ± 3 GPa two further times and heated the sample each time to 2000–2200 K.

In the second experiment (Sample 2) we raised the pressure initially to 80 GPa based on ruby fluorescence (Mao et al. 1990) and heated the sample for 300 s to 1800 K. At this pressure and temperature perovskite is the stable structure, and it is known that this phase has very limited solubility of water (Bolfan-Casanova et al. 2003; Ross et al. 2003). We assume that the water of the gedrite starting material has been mostly removed during this heating. Afterward, we raised the pressure to around 100 GPa and heated the sample to 2200 ± 50 K for 380 s. Diffraction data were collected after reducing temperature to 300 K, and the pressure was found to be 93 ± 2 GPa from the platinum pressure marker (Fei et al. 2007) and 95.0 ± 1 GPa from ruby (Mao et al. 1990).

X-ray diffraction patterns were collected at the 16ID-B undulator beamline at the High Pressure Collaborative Access Team (HPCAT), section 16 of the APS-ANL synchrotron, using a monochromatic beam of 32 or 36 keV energy focused with Kirkpatrick-Baez mirrors to 10 x 14 µm² and a Mar345 image plate detector. We integrated the diffraction images and corrected for geometric distortions using the Fit2D software package (Hammersley et al. 1996).

Raman spectra were collected immediately after the diffraction experiment using the micro-Raman spectrometer of GSECARS at Sector 13 of the APS-ANL synchrotron operated with the 514.5 nm excitation line of an Ar-ion laser at 60 mW power focused to a spot of about 10 µm diameter in 180° backscattering geometry, a Spex 0.5 m monochromator with a single 1200 grooves/mm grating, 20 µm slit-width, and a liquid nitrogen cooled CCD camera detector from Oxford Instruments. We collected spectra at different locations of the silicate sample and in the pressure medium. There is no variation of the spectral features in the sample while the medium does not yield any Raman signal even at a distance of one diameter of the laser focal spot from the silicate. The recorded Raman spectra therefore belong to the silicate samples.

	RESULTS AND DISCUSSION

Top Abstract Introduction Theory Experimental methods Results and discussion Raman spectra Appendix Acknowledgments References cited

 
Figure 2 shows the diffraction images of Samples 1 and 2 at 115 and 93 GPa, respectively. These images correspond to the integrated patterns shown in Figure 3a and 3b. Sample 2 exhibits a fine-spaced sequence of narrow, smooth, and continuous Debye-fringes (Fig. 2a), while Sample 1 exhibits marked texture (Fig. 2b). We discuss the data of Sample 2 first. We calculated the diffraction patterns of silicate perovskite, CaIrO₃-post-perovskite, and kinked post-perovskite structures (Table 2) and compared them to the observed patterns (Fig. 3a).

View larger version (75K): [in this window] [in a new window]   FIGURE 2. (a) Diffraction patterns from Sample 2 at 93 GPa. The diffraction is from the KBr pressure medium, from MgSiO3-perovskite, and from post-perovskite-like material. In any case, the diffraction features are Debye fringes from a powdered material with minor granularity. (b) Sample 1 at 115 GPa. This sample exhibits noticeable texture in a fine-grained sample aggregate. The intensity distribution is therefore not homogeneous along each Debye fringe but modulated. Another obvious consequence of texture is the alternating sequence of sections of enhanced and oppressed diffraction intensity along the sequence of 2 angles of observed diffraction.

View larger version (12K): [in this window] [in a new window]   FIGURE 3. Rietveldrefinements Samples 1 and 2. Black crosses = Observed signal; red line = modeled diffraction pattern; tick marks = 2-angles of observed reflections. (a) Sample 2: wavelength was 0.34531 Å. The whole pattern, including background (not shown here) was fitted. For MgSiO3-perovskite we find an RF2 of 0.09, for the 3 x 1 kinked post-perovskite RF2 is 0.24, and for KBr 0.04. The fitted cell parameters of the 3 x 1 phase are 9.608(16) x 6.043(13) x 4.248(8) Å3, β = 98.689(14)°, the cell parameters of pervoskite are 4.442(1) x 4.651(1) x 6.438(1) Å3, and the cell parameter for KBr is 2.7979(3) Å. The standard deviation is given in brackets. (b) Sample 1: wavelength was 0.3888 A. Background was subtracted in advance of Rietveld refinement because of a strong modulation from excitation halos around the intense peaks for the pressure medium. The weighted profile refinement parameter wRp was 0.09 and 2 = 31.3. The RF2 for the 2 x 1 phase was 0.25. The cell parameters are 6.804(5) x 6.289(7) x 4.161(4) Å3, β = 96.17(9)°. The cell parameter for NaCl is 2.727(1) Å and for perovskite 4.445(3) x 4.598(4) x 6.372(3) Å3.

Because of the rather large instrumental contribution and the complex background in our data R_wp is not a good measure for judging the validity of a structure model. On the other hand, the modeled silicate structures are of low symmetry and strict overlap of reflections is not significant. Therefore, R_F² is a more trustworthy measure of the proximity between the modeled structures and the observation than R_wp in the present case.

In summary, the X-ray diffraction pattern in Figure 3a shows features in ferrous aluminous MgSiO₃ at 91–95 GPa that cannot be explained by perovskite, CaIrO₃ type post-perovskite, or alumina. In contrast an intermediate 3 x 1 kinked post-perovskite structure provides a more consistent interpretation of the unexplained diffraction features especially at low 2 angles. The remaining mismatch between observed and predicted structure factors may be due to several reasons: The total fraction of the new phase is only a third of the fraction of perovskite. Thus, refinement based on whole profile fitting is more sensitive to slight mismatches in background and profiles of coexisting phases and this affects extraction of |F|² values. Furthermore, the diffraction peaks show variable width and this, again, is difficult to fit if the signal to noise ratio is not very high. Finally it is possible that the observed pattern actually belongs to a mixture of similar kinked post-perovskite structures although we can preclude presence of alumina as free phase (see above).

The diffraction image of Sample 1 indicates noticeable texture of a fine-grained polycrystalline aggregate (Fig. 2b). After integration we ran an automatic indexing of the observed sample Bragg peaks using the Jade 7.5+ package. To our surprise, we found a small number of orthorhombic and monoclinic cells of mostly equal cell dimensions, volumes, and angle. This suggests that the observed peaks belong to a single phase. We examined these candidate cells with respect to CaIrO₃-type post-perovskite, our calculated post-perovskite polymorphs, and perovskite. The diffraction data from the present experiment are clearly different from perovskite and CaIrO₃-type post-perovskite (Table 1). However, all observed reflections including 12 distinct reflections below 12 °2, can be indexed by the cell of the 2 x 1 type post-perovskite structure with dimensions 6.76 x 6.32 x 4.65, β = 99.2°, which is similar to the cell of the 2 x 1 structure as obtained from the ab initio calculations for pure MgSiO₃ (Table 1).

We calculated the powder diffraction pattern of 2 x 1 kinked post-perovskite based on the atomic positions of the ab-initio calculated structure and compared it to the observed pattern. Subsequent Rietveld refinement focuses on matching the apparent texture by spherical harmonics up to second order (Fig. 3b) using the method by von Dreele (1997). Along with the profile weighted refinement parameters (see caption Fig. 3b) this procedure shows a match of calculated and observed structure factor moduli of an R_F² of 0.25. As for Sample 1, we find that the diffraction pattern of this sample is incompatible with perovskite, CaIrO₃-type post-perovskite, and alumina, while the observed pattern in this case is consistent with a 2 x 1 kinked post-perovskite. Both Samples 1 and 2 show well-resolved low angle diffraction peaks in the range of 3.5 to 6 in °2. This observation is incompatible with perovskite and CaIrO₃-type post-perovskite while it is consistent with kinked post-perovskite.

Upon subsequent extended heating cycles of Sample 1 (see experimental section) the size of crystallites increased, and the diffraction pattern changes from that of a textured powder to that of a few larger crystallites that give rise to several individual Bragg reflections at different locations of the image plate detector. The textural pattern shows that during the high P-T experiment the silicate sample had passed from a regime of formation of randomly oriented crystalline seeds into a regime of collective recrystallization and re-orientation. This state is the result of repetitive heating under conditions of small temperature gradients, due to the use of a comparatively thick envelope of pressure medium of apparently lower thermal conductivity than the sample itself (Kiefer and Duffy 2005) and due to direct heating of the silicate sample rather than using mixed-in metallic absorbers. We observe 52 reflections that belong to various crystallites. Out of this set we select seven reflections which seem to belong to one crystallite since they establish two intersecting lattice trajectories which can be mapped onto each other (Fig. 1 Appendix). Because our diffraction patterns were collected at a fixed angular position, we sample only a two-dimensional slice of the reciprocal space. It is the narrow backside aperture of the Mao-Bell cell that does not permit sampling of further angular settings. Because of the two-dimensionality of the observable portion of reciprocal space we are constrained to compare the 2 angles of these reflections to silicate-perovskite, CaIrO₃-post-perovskite, and the kinked post-perovskite structures (Table 1 Appendix). This comparison is presented in table 1 of the Appendix. It shows consistence of the observed set of 2 values with various n x 1 type kinked post-perovskites while it is inconsistent with either perovskite or CaIrO₃-type post-perovskite. This is discussed in more detail in the Appendix.

View larger version (2K): [in this window] [in a new window]   APPENDIX FIGURE 1. Correlation of observed reflections in reciprocal space. We show the array of a total of 10 reflections in two different parallel projections. The reflections establish two intersecting sequences of reciprocal lattice vectors thus spanning a two-dimensional reciprocal lattice. The observable portion of reciprocal space is essentially two-dimensional since the sample containing Mao-Bell type diamond anvil cell could not be rotated during the experiment. The two-dimensional character of the available set of reflections does not permit rigorous indexing. We, therefore, considered the 2 angles of the observed reflections only and compared them to predicted values of perovskite, CaIrO3-type post-perovskite and kinked post-perovskites as shown in Table 1.

	RAMAN SPECTRA

Top Abstract Introduction Theory Experimental methods Results and discussion Raman spectra Appendix Acknowledgments References cited

View larger version (12K): [in this window] [in a new window]   FIGURE 4. Raman spectra of the two samples at the pressures of 95 and 115 GPa. The Raman spectra were collected right after the diffraction experiment without changing pressure or additional heating. Both spectra are dominated by Raman peaks above 700 cm–1 where perovskite does not have measurable Raman scattering intensity (Serghiou et al. 1998; Karki et al. 2002). These strong features are not single broad peaks but are composed of several overlapping peaks which appear as shoulders in the spectra, in particular in the spectrum of Sample 1 (lower spectrum). The lower frequency part of the spectrum is complex and involves more Raman peaks than expected for the CaIrO3-type structure (see text). Sample 1 (lower spectrum) exhibits marked texture (Fig. 2b) and the observed Raman peak intensities are not expected to represent an average. The upper spectrum (Sample 2) is from a powdered sample.

Figure 4, lower part, shows the Raman spectrum of Sample 1 (textured) at 115 ± 5 GPa. The spectrum also shows a strong broad, structured peak between 700 and 1000 cm^–1 while there are sharp and intense peaks between 250 and 500 cm^–1. For this textured sample intensities are likely controlled by crystallite orientation (see Figs. 2b and 3b caption), while the spectrum of Sample 2 gives an average over a powder.

Sample 1 shows at least 22 Raman peaks (Table 3) none of which adheres to perovskite, whereas the CaIrO₃-structure exhibits only 12 Raman active modes according to the Bilbao Crystallographic Server (Kroumova et al. 2003). The broad peaks between 700 and 1000 cm^–1 are again consistent with the concept of Raman-active modes involving silicate-octahedral breathing motions. The more complex structure of the Raman signal in this range (Table 3) showing at least seven peaks rather than three (Caracas and Cohen 2006) indicates a symmetry reduction that may be consistent with kinked post-perovskite structures.

The larger than expected number of Raman peaks suggests a lower symmetry and larger unit cell than that of the CaIrO₃-type phase, not inconsistent with the 2 x 1 and the 3 x 1 structure, which have 42 and 54 Raman active modes, respectively (Kroumova et al. 2003).

The spectra from Samples 1 and 2 are similar but not identical. However, their composition and, according to our analysis of the X-ray diffraction data, their structures are different also while sharing a common construction principle (Figs. 1b and 1c). Both spectra share the occurrence of Raman peaks above 800 cm^–1, which are not expected for perovskite (Serghiou et al. 1998; Karki et al. 2000; Caracas and Cohen 2006), but may be a signature of post-perovskite structures. The larger half width of these high-energy Raman peaks in comparison to the lower energy peaks in the same spectra may be due to disorder and to Al substitution on the Si sites, but this remains speculative as long as we are lacking definitive structure solutions for the observed phases.

In summary, our ab-initio calculations have reproduced the n x m type kinked post-perovskite structures found in metadynamics calculations by Oganov et al. (2005), and we extended our calculations to further polymorphs of this type. We have shown that kinked post-perovskites correspond to local minima in the energy hypersurface at 0 K. Above 100 GPa, the calculated enthalpy of the kinked structures is lower than that of perovskite but remains higher than that of CaIrO₃-type post-perovskite. Thus kinked type structures are not stable at 0 K, but they may be stabilized at high temperature due to thermal contributions to the Gibbs free energy that are neglected in our calculations. The energetic preference for the CaIrO₃-type at 0 K holds for pure MgSiO₃ as well as for charge-coupled aluminum substitutions in MgSiO₃. Both X-ray diffraction data and Raman spectra on aluminous magnesium metasilicate show features that are not expected for perovskite or CaIrO₃-type post-perovskite. Our Raman spectra show similarities with the predicted spectrum for CaIrO₃-type post-perovskite. However, the large number of Raman peaks suggests lower symmetry and larger unit cell size than that of CaIrO₃-type post-perovskite. These observations from Raman and X-ray diffraction data and the comparison to the diffraction patterns derived from our ab-initio calculations suggest that the structures in our experiments are more consistent with kinked structures of the type n x 1 than with perovskite or CaIrO₃-type post-perovskite.

Our calculations show that at 0 K and for pure and aluminous MgSiO₃, kinked structures become more stable than perovskite at Mbar pressures but remain less stable than CaIrO₃-type post-perovskite, consistent with previous predictions from metadynamics simulations (Oganov et al. 2005). In the absence of detailed knowledge of the activation barriers between the local minima that belong to different n x m structures, it is not possible to assess the thermal stability of the kinked structures from theory alone. Thus, it is not clear if kinked structures are stable or metastable for sufficiently long time to be relevant for the evolution of the Earth’s lowermost mantle or if they are remnants of an incomplete phase transition. However, independent of the possibility of a natural occurrence of kinked post-perovskite structures in the deep mantle our results support the previous conjecture that the perovskite post-perovskite structural transition proceeds via intermediate kinked structures rather than by homogeneously straining the perovskite structure.

	APPENDIX

Top Abstract Introduction Theory Experimental methods Results and discussion Raman spectra Appendix Acknowledgments References cited

 
In this appendix we present diffraction data collected at 115 GPa in the third heating-loading cycle of the first experiment. Upon heating the sample recrystallized to a coarse-grained aggregate of just a few crystallites and the initial powder diffraction fringes evolved into arrays of single-crystal reflections that belong to these various crystallites. We singled out a set of reflections that appear to establish two intersecting stacks of lattice planes (Fig. 1). The 2 values of these reflections are compared to calculated values of CaIrO₃-type post-perovskite and various kinked post-perovskites. Some n x 1 type kinked phases match the observed 2x values but CaIrO₃-type post-perovskite does not (Table 1). Even an extreme distortion of the CaIrO₃-type cell to a density of 5.9 g/cm³ (second set of 2 values) does not improve the match to a satisfactory degree (Table 1).

	ACKNOWLEDGMENTS

Top Abstract Introduction Theory Experimental methods Results and discussion Raman spectra Appendix Acknowledgments References cited

 
We thank T. Tsuchiya, R. Wentzcovitch, and A. Oganov for fruitful discussions. We thank C. Prewitt and an anonymous reviewer for providing helpful comments improving the manuscript. We gratefully acknowledge P.D. Asimow for providing the opx starting material. We thank V. Prakapenka for allowing us to use the GSECARS Raman spectrometer at APS. GSECARS is supported by the NSF-Earth Sciences, DOE-Geosciences, and the State of Illinois. This work was supported through NSF grant 0552010 and the NNSA Cooperative Agreement DE-FC88-01NV14049. Use of the HPCAT facility was supported by DOE-BES, DOE-NNSA, NSF, DOD-TACOM, and the W.M. Keck Foundation. A.P.S. is supported by DOE-BES under contract no. W-31-109-Eng-38.

	Footnotes

 
Open Access: Thanks to the authors’ generous funding this article is available to all online (http://ammin.geoscienceworld.org) and the MSA web site, which also has information about the MSA Open Access policy at http://www.minsocam.org/MSA/ammin/e-pub_policy.htm (scroll down).

MANUSCRIPT HANDLED BY PRZEMYSLAW DERA

MANUSCRIPT RECEIVED June 30, 2006; MANUSCRIPT ACCEPTED November 12, 2007

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Top Abstract Introduction Theory Experimental methods Results and discussion Raman spectra Appendix Acknowledgments References cited

 

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