Crystal structure and thermoelastic properties of (Mg_0.91Fe_0.09)SiO₃ postperovskite up to 135 GPa and 2,700 K

Abstract

Intriguing seismic observations have been made for the bottom 400 km of Earth's mantle (the D″ region) over the past few decades, yet the origin of these seismic structures has not been well understood. Recent theoretical calculations have predicted many unusual changes in physical properties across the postperovskite transition, perovskite (Pv) → postperovskite (PPv), that may provide explanations for the seismic observations. Here, we report measurements of the crystal structure of (Mg_0.91Fe_0.09)SiO₃-PPv under quasi-hydrostatic conditions up to the pressure (P)–temperature (T) conditions expected for the core-mantle boundary (CMB). The measured crystal structure is in excellent agreement with the first-principles calculations. We found that bulk sound speed (V_Φ) decreases by 2.4 ± 1.4% across the PPv transition. Combined with the predicted shear-wave velocity (V_S) increase, our measurements indicate that lateral variations in mineralogy between Pv and PPv may result in the anticorrelation between the V_Φ and V_S anomalies at the D″ region. Also, density increases by 1.6 ± 0.4% and Grüneisen parameter decreases by 21 ± 15% across the PPv transition, which will dynamically stabilize the PPv lenses observed in recent seismic studies.

The D″ region is believed to play an important role for the dynamics of the mantle and the core. The recent discovery of the postperovskite (PPv) transition (1–3) at the P–T conditions relevant to the D″ region has provided new opportunities to understand the seismic observations and dynamic processes in the region. First-principles calculations (1, 4, 5) have predicted drastic changes in some geophysically important properties across the PPv transition (6, 7). The unusual changes have been attributed to the fundamental differences in crystal structure between perovskite (Pv), a 3D network structure with corner-sharing SiO₆ octahedra, and PPv, a 2D layered structure with both corner and edge sharing SiO₆ octahedra (1, 4, 8, 9). Therefore, measurements of the crystal structure provide a fundamental test for the predicted properties of PPv. However, synthesis of an appropriate single crystal for PPv in its stability field is extremely challenging for current techniques, making Rietveld refinement the only plausible method for studying the crystal structure. Currently only a single Rietveld refinement (10) exists for MgSiO₃-PPv at 116 GPa and 300 K (Table 1).

Table 1.

Selected Rietveld refinement results for PPv at high P–T

Parameters	(Mg0.91Fe0.09)SiO3		MgSiO3
	This study	This study	Experiment (10)	Theory (2)
Pressure, GPa	135 (2)	126 (2)	116	120
Temperature, K	2,535 (150)	300	300	0
a, Å	2.467 (2)	2.460 (1)	2.469	2.474
b, Å	8.080 (7)	8.059 (3)	8.117	8.121
c, Å	6.119 (4)	6.102 (2)	6.151	6.138
Atomic position parameters
yMg	0.247 (5, 6)	0.248 (3)	0.257	0.253
yO1	0.909 (13, 3)	0.919 (5)	0.943	0.928
yO2	0.644 (12, 3)	0.637 (5)	0.640	0.636
zO2	0.450 (10, 3)	0.432 (3)	0.442	0.441
Interatomic distances and angles
Si–O1 (×2), Å	1.70 (4, 1)	1.66 (1)	1.61	1.64
Si–O2 (×4), Å	1.73 (8, 2)	1.71 (2)	1.72	1.70
Mg–O1 (×2), Å	1.80 (8, 3)	1.85 (3)	1.95	1.88
Mg–O2 (×4), Å	1.92 (6, 2)	1.88 (2)	1.95	1.96
Mg–O2 (×2), Å	2.04 (6, 4)	2.15 (3)	2.07	2.10
∠SiO1Si, °	129 (6, 1)	134 (2)	146	138
∠SiO2Si, °	91 (5, 1)	92 (2)	92	94

For the atomic parameters at high temperature, two different estimated uncertainties are presented: the first number in the parentheses is 2σ of Rietveld refinements and the second number is the standard deviation of the four different data points measured at 2,400–2,600 K and 135 GPa. We also include a Rietveld refinement (10) and a first-principles prediction (2) for PPv. Crystal structure parameters from other first-principles studies are in agreement with Oganov and Ono (2) within 1%.

Some theoretical studies (1, 4) have predicted that bulk sound speed (V_Φ) decreases across the PPv transition whereas shear-wave velocity (V_S) increases. Shieh et al. (11) measured Pv + PPv mixtures in (Mg_0.91Fe_0.09)SiO₃ and suggested decreases in volume and bulk modulus, and therefore a decrease in V_Φ, across the PPv transition, but the Fe contents of the individual phases were not known and a limited number of diffraction lines were used for constraining volume. Mao et al. (12) have achieved denser data coverage for (Mg_0.6Fe_0.4)SiO₃-PPv at a wider pressure range. Their data indicate that the bulk modulus of PPv should be very high at CMB pressures (Table 2), suggesting a large increase in V_Φ across the PPv transition. However, no pressure medium was used in this study. The larger amount of Fe in Mao et al. (12) may cause the difference, yet a first-principles calculation showed that Fe has little effect on the bulk modulus of PPv (13).

Table 2.

Volumes (V) and bulk moduli (K) of PPv and Pv at high P

References	V, Å3	K, GPa	XFe, mol%
Experiment: Postperovskite at 125 GPa and 300 K
This work	121.3(1)	657(16)	9
Mao et al. (12)	124.7	908	40
Shieh et al. (11)	120.8	653	9?
Experiment: Perovskite at 125 GPa and 300 K
This work	123.3(5)	679(10)	9
Fiquet et al. (18)	122.0	665	0
Theory: Postperovskite at 120 GPa and 0 K
Oganov and Ono (2)	122.7	647	0
Caracas and Cohen (34)	125.2	701	100
Theory: Perovskite at 120 GPa and 0 K
Oganov and Ono (2)	124.6	648	0
Caracas and Cohen (34)	126.8	715	100

For theory, the values are obtained from the LDA results (2, 34). The values for ferromagnetic are chosen for FeSiO₃ (see also Table S4 for details).

We have measured x-ray diffraction patterns of (Mg_0.91Fe_0.09)SiO₃-PPv under quasi-hydrostatic stress conditions with a chemically inert, insulating, compressible Ar pressure medium at in situ high P–T conditions (37–126 GPa at 300 K and 135 GPa at 2,300–2,700 K) in the laser-heated diamond-anvil cell [supporting information (SI) Fig. S1]. We measured at least 25 full-diffraction rings of PPv to d-spacing ≥1.1 Å, which is a significant improvement over previous studies. Our dataset enables us to constrain the changes in density, bulk modulus, and Grüneisen parameter across the PPv transition and to measure the crystal structure of PPv through the Rietveld refinements.

Results and Discussion

To synthesize PPv, we increased pressure directly to 120–130 GPa without heating and then heated for 1.5 h at 1,500–2,700 K. During the first heating of the sample at 125 GPa, we observed the synthesis of a Pv + PPv mixture from the amorphized starting material. However, after 1 h of heating at slightly higher pressure, the sample transforms completely to PPv. The P–T conditions of the PPv transition we observed are consistent with those expected for the D″ discontinuity within experimental uncertainties. Even at the maximum P–T in our experiments, strong diffraction intensities were detected for Ar (Fig. 1), indicating that a significant amount of Ar still surrounds the sample. The sufficient amount of Ar medium reduces the thermal gradients and differential stresses in the sample.

Fig. 1.

Rietveld refinements of the x-ray diffraction patterns of (Mg_0.91Fe_0.09)SiO₃-PPv at high P–T (a–c) (crosses, observed intensities; red lines, calculated intensities; black lines, difference between observed and calculated intensities; black bars, calculated diffraction peak positions). Because of peak overlaps with the diffraction lines from the internal pressure standard (Au), the pressure medium (Ar), and the gasket (Re), some angle ranges (shown in blue lines) are excluded from the Rietveld refinements. The diffraction lines that overlap with those of PPv are labeled with “+.” (d) A Le Bail fitting result for a diffraction pattern measured at low pressure. The backgrounds of the diffraction patterns were subtracted.

After the synthesis of PPv, in situ diffraction measurements were conducted between 2,300 and 2,700 K at 135 GPa (Fig. 1a) and then the sample was temperature quenched to 126 GPa (Fig. 1b). Diffraction patterns were measured during decompression (Fig. 1 c and d). To prevent reverse transformation to Pv, we did not heat the sample during decompression. Down to 85 GPa, the diffraction peaks remained sharp, but broadened rapidly at P <80 GPa (Fig. 1d). Also the diffraction patterns of the recovered sample indicate that PPv is not quenchable to ambient conditions as reported (11).

Based on the degree of continuity in the diffraction rings and preferred orientation, we selected a total of 4 high-temperature patterns and a total of 22 room-temperature patterns for Rietveld refinements (14) (Fig. S2). Selected results are shown in Table 1 with corresponding diffraction patterns in Fig. 1 a and b (entire Rietveld results are presented in Tables S1, S2, and S3). To assess the uncertainty, we also calculate the standard deviations of the fitted parameters from 4 diffraction patterns measured at 2,400–2,600 K and 135 GPa assuming that the change in atomic parameters for the 200 K temperature range would be small. The magnitude of the latter estimation is similar to the 1σ from the Rietveld refinements (Table 1).

Rietveld refinements of the diffraction patterns obtained in the diamond-anvil cell at these extreme P–T conditions inevitably suffer from various problems including texturing of the sample and a smaller number of grains in an extremely small x-ray sampling area, 5 × 5 μm². Nevertheless, the dense distribution of our data points over a wide P–T range allows us to examine the reliability of our results. Over the pressure range where structural changes are expected to be small we observe consistency among the refined parameters; for example, the Si–O bond distances and ∠SiO2Si bond angle at 110–135 GPa (Fig. 2). More importantly, within 2σ our results are in good agreement with first-principles predictions for most atomic parameters at 110–135 GPa, supporting the first-principles prediction of the crystal structure (Table 1, Fig. 2, and Fig. S3). However, yO1 of a Rietveld refinement on MgSiO₃-PPv at 116 GPa and 300 K reported by Ono et al. (10) is significantly larger than those of our result and first-principles calculations, resulting in larger differences between the Si–O1 and Si–O2 bond distances and a larger ∠SiO1Si angle.

Fig. 2.

The Si–O bond distances (Lower) and ∠SiO2Si angle (Upper) in (Mg_0.91Fe_0.09)SiO₃-PPv at 300 K (black circles) and 2,400–2,600 K (red circles). (Lower) The filled and open circles represent the Si–O1 (corner shared) and Si–O2 (edge shared) bond distances, respectively. The error bars represent 2σ uncertainties. The shaded area highlights the pressure range where structural changes are detected. The horizontal dark-gray lines represent the values from a first-principles calculation (1) at 120 GPa and 0 K. (Inset) Shown are the edge-shared SiO₆ octahedra in PPv. The blue and white spheres represent Si and O atoms, respectively. The red arrow indicates repulsion between the Si atoms in adjacent octahedra and the blue arrows show the displacement of O2 atoms observed in our study.

The volume of PPv was measured between 37 and 126 GPa at 300 K to constrain the bulk modulus (K) (Fig. 3). The volumes measured at the stable pressures of PPv (P ≥ 110 GPa) at 300 K show little data scatter. However, below 110 GPa, the volume deviates from the trend observed at higher pressures. At 110 GPa, we found a discrete increase in the peak width (Fig. S4), suggesting that PPv may undergo a previously unidentified metastable change outside of its stability field. Another distinct behavior was identified at 80 GPa where the volume rapidly increases with decompression. The latter change is consistent with the metastable behavior of Fe-rich PPv observed at P <90 GPa reported by Mao et al. (12). At the same pressure range, we also observed a steep increase in the peak widths (Fig. S4). As highlighted by a box in Fig. 1d, Le Bail fitting shows systematic misfits for the data at P <75 GPa. This may indicate that the crystal structure of the PPv phase is no longer that of the CaIrO₃ type at this pressure range, which is well below the stable pressure conditions of PPv.

Fig. 3.

Pressure–volume relations of PPv at 300 K (black solid circles) and 2,300–2,700 K (red solid circles), and Pv at 300 K (black open circles) in (Mg_0.91Fe_0.09)SiO₃. The solid and dashed curves are the fits for the data points P >110 and >80 GPa, respectively, to the Birch–Murnaghan equation. The dotted curve is the fit for the Pv data points. The shaded areas highlight the pressure ranges where changes in the compressional behavior of PPv were identified. (Inset a) Residues of equation-of-state fits when all of the data at P >110 GPa are included (filled circles) and when all of the data at P >80 GPa are included (open squares). (Inset b) The Grüneisen parameter (γ) of PPv obtained from our high-temperature data points. The horizontal shaded area in Inset b represents the range of γ of Pv in the literature (18, 24, 25).

The metastable behavior at P <110 GPa can also be identified in the measured crystallographic parameters. Our Rietveld refinements show that the ∠SiO2Si bond angle increases discontinuously and the Si–O2 bond distance becomes smaller than the Si–O1 bond distance at 110 GPa. Both of these indicate that O2 is displaced toward a line connecting adjacent Si⁴⁺ ions as shown in Fig. 2 Inset. We note that O2 is shared by two adjacent octahedra through their edges, whereas O1 is shared by corners. Although the edge sharing improves packing efficiency, it is less effective in shielding the repulsion between two adjacent Si⁴⁺ ions with strong positive charges compared with corner sharing. The inward displacement of O2 may enhance the shielding and help to reduce the repulsion between adjacent Si⁴⁺ ions. However, this may not be necessary in the stability field perhaps because of the balance with external stress. This also suggests that the properties of PPv measured at conditions outside its stability field (P ≤ 110 GPa) can be contaminated by metastability.

Because of the metastable behavior of PPv at low pressure, it is not appropriate to set the reference state at ambient conditions for the equation of state. We use the second-order Birch–Murnaghan equation (15) by setting the reference state at 125 GPa and 300 K, which are the stable conditions for PPv. When all of the data points at P >80 GPa are included in the fit, we obtain a very high bulk modulus at 125 GPa, K_125GPa = 833 ± 16 GPa, which is comparable to Mao et al. (12) (Table 2). However, we found systematic residues after the fit as shown in Fig. 3a, indicating that the compressional behavior also changes at 110 GPa, consistent with our Rietveld results. Therefore, we conduct a separate fit only for the data at P >110 GPa. The fit residues show that the data points at P <110 GPa deviate systematically from the trend observed at P >110 GPa. For this fit, we obtained K_125GPa = 657 ± 16 GPa, which is consistent with previous measurements on Pv + PPv mixtures (11) and the first-principles predictions (1, 4, 16) (Table 2). We also conducted volume measurements on perovskite (Pv) synthesized from the same starting material by using the same pressure scale (Fig. 3). This allows us to obtain robust constraints on density and bulk modulus changes across the PPv transition without being seriously affected by the inconsistencies among different pressure scales (17). Our fitted bulk modulus (K₀) of Pv to the third-order Birch–Murnaghan equation is in agreement with previous reports (18) within the estimated uncertainty (Table 2).

By combining our measurements on Pv and PPv, we find that density increases by 1.6 ± 0.4% and bulk modulus decreases by 3.3 ± 2.7%, resulting in a 2.4 ± 1.4% decrease in bulk sound speed (V_Φ) across the PPv transition. This agrees with the previous first-principles predictions (1, 4). Combined with a shear-wave velocity (V_S) increase proposed by Brillouin spectroscopy (19) and first-principles (1, 4) studies, our result indicates that lateral variations in mineralogy between Pv and PPv can result in the anticorrelation between the V_Φ and V_S anomalies at the lowermost mantle, consistent with previous first-principles predictions (6, 7): V_S would be higher but V_Φ would be lower at a PPv-rich region than those at a Pv-rich region. Seismic studies have documented the anticorrelation at the mid- to lowermost-mantle (20–22). Therefore, lateral variations in the mineralogy may provide a viable explanation for some of the anomalies existing below the PPv transition depth in the mantle (2), which is perhaps 2,500–2,700 km. However, according to Mao et al. (23) the transition depth may be significantly elevated (by 300–400 km per 10% Fe) with an Fe enrichment.

A total of 11 volume data points of PPv were measured at the P–T conditions directly relevant to the D″ layer. All of the data points exhibit nearly constant volume at different temperatures (V = 121.85 ± 0.08 ų), which allows us to constrain thermal pressure, (dP/dT)_V = αK_T (α is the thermal expansion parameter and K_T is the isothermal bulk modulus). Because temperature is sufficiently higher than the expected Debye temperature of PPv, a Grüneisen parameter (γ) can be obtained for each data point from: γ = αK_TV/C_V = (dP/dT)_V V/3R (C_V is the specific heat and R is the gas constant, Fig. 3b).

The measured γ of PPv at 135 GPa and 2,300–2,700 K is 0.79 ± 0.12, which is smaller than that of Pv (0.94–1.07) at the same P–T conditions (18, 24, 25), suggesting a 21 ± 15% decrease in γ across the PPv transition (Fig. 3b). Care must be taken with this comparison, because the estimations for PPv and Pv are based on different pressure scales, the consistency of which is unknown. Furthermore, calculation of the γ of Pv at 135 GPa from the existing data requires a long extrapolation. Nevertheless, recent Raman measurements on Pv and PPv in MgGeO₃ found a large decrease in the rate of pressure-induced phonon shift, which is consistent with a 25 ± 6% reduction in γ across the PPv transition (8). The lower γ indicates that the density jump across the PPv transition at mantle temperature can be higher than 1.6% which is observed at 300 K. Therefore, the higher density of PPv would dynamically stabilize the PPv lenses documented in recent seismic studies (26, 27) and influence the flow at the base of the mantle (28).

Our study shows that the dominant mantle silicate undergoes significant changes in crystal structure across the PPv transition, which may lead to unexpected changes in some physical properties, such as decreases in bulk sound speed and Grüneisen parameter found in this study. From the observed strong lateral heterogeneities, seismic studies (29) have inferred large variations in temperature and composition at the lowermost mantle. Yet the large Clapeyron slope of the PPv transition and the proximity of the transition to the CMB (2, 5, 8) will make the mineralogy at the lowermost mantle very sensitive to both temperature and composition. Our study shows that some of the lateral heterogeneities can be explained by changes in mineralogy at the D″ region. Therefore, the strong heterogeneity at the D″ region may be a consequence of complex interactions among temperature, composition, and mineralogy.

Experimental Methods

A powder form of natural enstatite with 9 mol% Fe was mixed with 8 wt% gold powder, which serves as an internal standard for pressure measurements and a laser coupler for heating. The powder was compressed to foils with thicknesses <5 μm. Rhenium gaskets were indented to thicknesses <25 μm and a hole was drilled at the center of the indentation for the sample chamber. Diamond anvils with 200-μm flat and 100-μm beveled culets were used for measurements for Pv and PPv, respectively. We used symmetric-type diamond-anvil cells (DACs). Argon was cryogenically loaded in the DACs together with the sample foil as a pressure-transmitting and insulation medium (Fig. S1). To prevent direct contact between diamond anvils and the sample foil, two to four particles (2–3 μm in diameter) of the starting material were placed between the sample and diamond anvils as spacers.

Angle-dispersive diffraction measurements on PPv were conducted at the 13IDD beamline of the Advanced Photon Source (APS) using the MarCCD detector. We measured diffraction patterns of Pv at the 13IDD beamline of APS and the 12.2.2 beamline of the Advanced Light Source (ALS) by using the Mar345 imaging plate. We used a monochromatic beam with an energy of 30 keV. The size of the x-ray beam was 5 × 5 μm² and 10 × 10 μm² at GeoSoilEnviro Consortium for Advanced Radiation Sources (GSECARS) and 12.2.2, respectively. This is smaller than the size of the laser-heated spot that is ≈20 μm in diameter. The sample-to-detector distance and the tilt of the detector were calibrated by using the diffraction patterns of CeO₂ or LaB₆.

For the synthesis of high-pressure phases and annealing of deviatoric stresses, we used laser-heating systems at Massachusetts Institute of Technology, GSECARS, and 12.2.2. We used Nd:YLF laser beams with a TEM₀₁ mode. For in situ double-sided laser heating at GSECARS, we colinearly aligned the sample, incident x-ray beam, and laser beams, to measure x-ray diffraction from the center of the heated spot, which has a smaller thermal gradient. Temperature of the samples was estimated by fitting the measured thermal radiation spectra to the Planck equation. The wavelength dependence of the emissivity of the sample is unknown and assumed to be constant. The uncertainty in temperature measurements is ≈ ±150 K at the studied pressure range (30). Pressure is calculated from the volume of gold, which is constrained by three to four diffraction lines, and the equation of state is according to Tsuchiya (31).

To measure the equation of state of Pv, separate samples were prepared for low-pressure measurements by using the same starting material and the same pressure scale (gold). Ar and NaCl are used as pressure media for data at below and above 54 GPa, respectively. The Pv phase was synthesized at 50 GPa and 2,000 K for 30 min. Before each diffraction measurement, we annealed the samples to reduce differential stresses by using laser heating.

One-dimensional diffraction patterns were obtained by integrating diffraction rings using the Fit2D software (32). The absorption from the cBN backing plate and the diamond anvils was corrected. Based on the degree of continuity of the diffraction rings and preferred orientation, we selected a total of 4 among 11 high-temperature diffraction patterns and a total of 22 among 38 room-temperature diffraction patterns for Rietveld refinements (14).

In the Rietveld analysis, we refined all of the atomic position parameters as well as unit-cell parameters, preferred orientation function, peak profile shape function, scale factors, and thermal parameters. During the refinement, the temperature factors of the atoms are constrained to be the same, to prevent “overfitting” of the data (33).