Introduction

Bridgmanite, with an approximate composition of MgSiO3 and the orthorhombic perovskite-type structure (space group Pbnm), is believed to be the most dominant constituent of the Earth’s lower mantle. Physical and crystal-structural properties of bridgmanite and their pressure-, temperature- and chemical-dependence provide essential information for detailed understanding of the lower mantle viewed from mineralogical aspects. The crystal structure has the two cation sites, the larger eightfold (nominally 12-fold) coordinated A-site and the smaller sixfold coordinated B-site, consisting of a network of corner-linked BO6 octahedra with the A-site atoms located at the centers of cavities in the network and being distorted largely from the ideal cubic structure with Pm\(\overline{3 }\)m symmetry owing to the tilting of BO6 octahedra (Fig. 1). In the end-member MgSiO3 bridgmanite, the A and B sites are occupied only by Mg and Si, respectively.

Figure 1
figure 1

Crystal structure of the present (Fe3+, Al)-bearing bridgmanite: (a) a view of corner-linked BO6 octahedra and (b) displacement ellipsoids projected along [001]. In (b), atoms are drawn at 80% probability level. Symmetry codes for equivalent atoms are as in Table 5. The software ATOMS (Version 5.1, Shape Software, Kingsport, TN, USA, http://www.shapesoftware.com/00_Website_Homepage/) was used for the crystal-structural representation.

Full size image

The incorporation of Fe and Al, important major elements in the mantle composition after Mg and Si, into the two cation sites can affect the physical properties such as the electric conductivity, thermal conductivity, elasticity and rheology of the lower mantle, together with the structural stability of bridgmanite itself. Because of such importance, the effect of Fe and/or Al incorporation on the physical and structural properties of bridgmanite has extensively studied1,2,3,4,5,6,7,8,9,10. The valence- and spin-states of Fe, its site-distribution, and the creation of cation- and/or oxygen-vacancies depending on these are especially relevant issues associated with the incorporation mechanism of Fe into bridgmanite, because these can strongly influence the electrical conductivity of the lower mantle1, 9, 11,12,13. The creation of oxygen vacancies14,15,16,17,18,19,20 and the incorporation manner of Fe can also be controlled by the incorporation of Al. In particular, the effect of trivalent Fe3+ incorporation is of interest in view of cation partitioning among lower-mantle minerals21. The major conclusions on the role of Fe3+ and/or Al reported by the previous studies2, 6, 7, 21,22,23,24,25,26 using Fe- and/or Al-bearing bridgmanites are as follows: (i) Fe3+ can be distributed preferentially to bridgmanite at lower-mantle pressures; (ii) the presence of Al increases Fe3+ contents in bridgmanite; (iii) oxygen vacancies (VO) may be created through the substitutions 1/2O2−  + BSi4+  ↔ 1/2VO + BFe3+ and/or 1/2O2−  + BSi4+  ↔ 1/2VO + BAl3+, where the left superscripts in the chemical formulae represent the occupied sites; (iv) Fe3+ can occupy both A and B sites. In particular, Catalli et al.6 reported from in-situ synchrotron Mössbauer spectroscopy that both Fe3+ and Al are distributed evenly between A and B sites at high pressures, which is accompanied by the high-spin (HS) to low-spin (LS) transition of Fe3+. Hummer and Fei7 also reported, from Mössbauer spectroscopy, the even site-mixing of both cations in the quenched sample synthesized at 1973–2073 K and 25 GPa. On the other hand, Vanpeteghem et al.3 reported from the single-crystal X-ray diffraction study of several (Fe, Al)-bearing bridgmanites with different Fe and Al contents that Fe3+ occupies exclusively A-site via the charge-coupled substitution AMg2+  + BSi4+  ↔ AFe3+  + BAl3+. They furthermore reported that when the Fe content exceeds the Al content, the substitution AMg2+  ↔ AFe2+ occurs for the extra Fe content. Thus, there has been the large discrepancy in incorporation mechanisms of Fe3+ and Al between studies. Acquisition of detailed total knowledge of cation distribution, iron valence, and vacancy is necessary for the reliable determination of the incorporation mechanism, but each of the previous studies has not examined them from all of single-crystal X-ray diffraction, Mössbauer spectroscopy and chemical analysis.

Here we characterize the bridgmanite single-crystal with the Fe- and Al-contents expected in a mid-ocean ridge basalt (MORB) component of subducting slabs, by a combination of these three techniques. Bridgmanite formed from the MORB composition contains larger amounts of Fe and Al (~ 0.35 per formula unit for both)27 than their amounts (~ 0.05 per formula unit for both)27 of bridgmanite expected in a pyrolytic28 lower-mantle. This difference in bridgmanite compositions can yield the difference in incorporation mechanism of Fe and Al into the crystal structure between subducting slabs and their surrounding lower-mantle. This should cause heterogeneity in physical properties and rheology of the lower mantle. Elucidating crystal chemistry of bridgmanite formed from the MORB composition is thus a key to solve controversial issues in the lower mantle such as anti-correlated seismic velocity anomalies observed in large low shear velocity provinces (LLSVPs)10. From this viewpoint, the precise crystal-chemical examination employing a single crystal is quite significant for detailed understanding of lower-mantle dynamics. In particular, the present study includes the first report on single-crystal structure of bridgmanite with the Fe- and Al-contents expected in MORB. In this paper, we discuss the incorporation mechanism of Fe and Al into bridgmanite in MORB and its structural variation with the incorporation of both cations, and provide earth-scientific implications.

Methods

Single-crystal synthesis under high pressure and chemical analyses

Single crystals of bridgmanite were synthesized at 28 GPa and 1873 K using a 5000-ton Kawai-type high-pressure apparatus installed at the Institute for Planetary Materials, Okayama University. The procedure and technique of the experiment are essentially the same as those described in our previous study29 as follows. A 10 mm regular octahedron of a sintered MgO containing 5% of Cr2O3 was employed as a pressure-transmitting medium. The starting materials were the special grade reagents of powdered MgO, SiO2, Al2O3 and Fe2O3, and mixed in a cation ratio of Mg:Fe:Si:Al = 0.65:0.35:0.65:0.35, which is very close to that27 reported for bridgmanite formed from the MORB composition. LaCrO3 surrounded by ZrO2 thermal insulator was used as a furnace material. The powder mixture was placed in a Pt capsule, which was electrically insulated from the furnace by a MgO spacer. This cell assembly was set in the anvil assembly of tungsten carbide cubes with truncated edge lengths of 3 mm, and then was compressed up to a target pressure of 28 GPa at room temperature. The temperature was then raised to a target temperature of 1873 K at a rate of 100 K/min. The temperature was controlled with a W97%Re3%-W75%Re25% thermocouple, whose junction was put at the midpoint of the outer surface of the Pt capsule. No correction was made for the pressure effect on emf. After being kept under a desired condition (28 GPa, 1873 K) for 2 h, the product was quenched by shutting off the electric power supply. The pressure was released slowly and the product was recovered at ambient condition. Numerical single-crystals of bridgmanite with a size of about 100–200 μm were found in the recovered sample. The color of the crystals is reddish-brown, suggesting the incorporation of Fe ions into the crystals. Compositions of the single crystals (Table 1) were determined by means of a JEOL JXA-8800M electron probe microanalyzer (EPMA). No contamination from the cell assembly materials into the single crystals was detected from qualitative analyses by the EPMA.

Table 1 Compositions at five analysis-points (#1–#5) from EPMA and the average of them.
Full size table

Synchrotron 57Fe-Mössbauer spectroscopy

Energy-domain synchrotron 57Fe-Mössbauer spectroscopy measurements at room temperature using a nuclear Bragg monochromator were conducted to evaluate Fe3+/ΣFe ratio of the present bridgmanite at the BL10XU beamline of SPring-8 (Ref.30). The sample was irradiated by the X-ray beam tuned at 14.4 keV from a high heat-load Si(111) double-crystal monochromator. The transmitted X-ray through the sample was monochromatized to around the nuclear resonance energy of 57Fe by a high resolution monochromator with a bandpass of about 4 meV, which consists of asymmetric Si(511) and symmetric Si(975) channel-cut crystals. The nuclear monochromator employs a single-line pure nuclear Bragg reflection 333 from an oscillating 57FeBO3 single-crystal near Néel temperature in the external magnetic field. The bandwidth of the electronically forbidden pure nuclear Bragg reflection was about 15 neV. The source Doppler shift was produced by oscillating the crystal in a sinusoidal velocity mode, which was mounted on a velocity transducer. The absorption spectrum was obtained by counting the intensity of the single-line nuclear Bragg reflection as a function of velocity. The velocity scale was calibrated with respect to a 57Fe-enriched standard metallic iron foil with 3 µm thickness under ambient conditions, and the isomer shift was also referenced to the same standard. The spectrum data were collected with a measurement time of 8.3 h. The MossA software package31 was used for the computational analysis and the spectrum was fitted using a Lorentzian model. The results are shown in Table 2.

Table 2 Comparison of hyperfine parameters from synchrotron Mössbauer spectroscopy with their reference values.
Full size table

Single-crystal X-ray diffraction intensity measurements and structure refinements

The single-crystal X-ray diffraction intensity measurements, data processing and structure refinements were conducted following essentially the same procedures and techniques as those described in our previous studies32,33,34 as follows. The single crystal with a size of 0.10 × 0.08 × 0.04 mm3 was selected and then mounted on the tip of a glass fiber for the intensity measurements. The measurements were conducted at room temperature (296 K) using a Rigaku AFC-7R four-circle diffractometer with a graphite-monochromatized MoKα radiation (λ = 0.71069 Å) at an operating condition of 60 kV and 250 mA. The unit-cell parameters were determined by the least-squares method from a set of 25 reflections within the range of 44° ≤ 2θ ≤ 46°. The intensity data of a total of 1774 reflections within 2° ≤ 2θ ≤ 100° were collected using the continuous ω–2θ scan mode and corrected for Lorentz-polarization factors and absorption effects (ψ-scan method). After that, the intensity data were averaged in Laue symmetry mmm to give 930 unique reflections. Of these, unique reflections with \(\left|{F}_{\mathrm{o}}\right|\le 3{\upsigma } \left(\left|{F}_{\mathrm{o}}\right|\right)\) were eliminated. Even if unique reflections had intensities of \(\left|{F}_{\mathrm{o}}\right|>3{\upsigma } \left(\left|{F}_{\mathrm{o}}\right|\right)\) after averaging, those averaged from data set of equivalent reflections including reflection(s) with \(\left|{F}_{\mathrm{o}}\right|\le 3{\upsigma } \left(\left|{F}_{\mathrm{o}}\right|\right)\) were also discarded since these reflections were potentially affected by multiple scattering. Moreover, unique reflections with sinθ/λ < 0.26 Å−1 were eliminated to reduce secondary extinction effects and to avoid dependence on atomic charge as far as possible in the choice of atomic scattering factors. Finally, 640 unique reflections were used in the present refinements. Internal residuals of the equivalent reflections (Rint) was 0.0131.

The structure refinements were carried out by minimizing the function Σw(Fo – Fc)2 using a full matrix least-squares program RADY35. Scattering factors of Mg2+, Al3+, Si4+, Fe3+, Fe2+ (Table 6.1.1.3 in International Tables for Crystallography36), and O2– (Tokonami37) were used. Anomalous dispersion coefficients for each scattering factor were taken from Table 4.2.6.8 in International Tables for Crystallography36. Several correction models for the secondary extinction effects were attempted during the refinements, and the isotropic correction of Type II38, 39 with a Gaussian particle size distribution model yielded the best fit. The final structure refinement converged smoothly to R = 0.0189 and wR = 0.0146. The summary of crystallographic data, data-collection and refinement parameters is given in Table 3. The refined structural parameters are given in Table 4. The selected interatomic distances are listed in Table 5. Crystallographic Information File (CIF) is deposited in the Cambridge Structural Database (CSD) (Deposition No. 2089819).

Table 3 Summary of crystallographic data, data-collection and refinement parameters.
Full size table
Table 4 Refined structural parameters.
Full size table
Table 5 Selected interatomic distances.
Full size table

Results and discussion

Chemical composition, and valence- and spin-states of Fe

Compositions at five points in a crystal measured by the EPMA and the average of them are shown in Table 1. No significant compositional fluctuation is observed among these five measurement points; this shows that the crystal is almost homogeneous in composition. The averaged composition from the EPMA analyses is calculated as the cation ratio Mg:Fe:Si:Al = 0.642(7):0.341(6):0.656(10):0.356(4) assuming O = 3. This composition shows no significant deviation from the mixing composition of the starting materials in the synthetic experiment, indicating that the crystal includes no significant cation- and/or oxygen-vacancies and is well charge-balanced by trivalent Fe3+ ions within the error. Although the preferential occupation of larger Fe3+ for A site and of smaller Al3+ for B site is inferred in terms of ionic radii40 [e.g., HS Fe3+  = 0.645 Å and Al3+  = 0.535 Å in CN (coordination number) = 6], the degree of their distribution between both sites cannot be inferred from the EPMA data alone.

We here show in Fig. 2a the Mössbauer spectrum of the present bridgmanite single-crystal to gain the more detailed knowledge of valence states, spin states and coordination environments of Fe. The Mössbauer spectrum seems to consist of two absorption peaks with different intensities. The coordination environments around A and B sites (the possible occupied sites of Fe) are largely distorted; this should yield quadrupole splitting, as observed by many researchers5,6,7. The doublets measured using a single crystal can be asymmetric because a certain angle is kept between the principal axis of the electric field gradient tensor in the Fe sites and the incident X-ray beam direction. The Mössbauer spectrum of the present bridgmanite single-crystal should thus be interpreted not as a superposition of singlets but as one asymmetric doublet or a superposition of several asymmetric doublets, depending on the differences in electronic states and coordination environments of Fe. The spectrum is well represented by a Lorentzian model assuming one asymmetric doublet, and the residual peak-components are undetectable from the fitting residuals (Fig. 2b). Models with additional doublets were also attempted, but were not able to significantly improve the fitting quality. The final fit, assuming one asymmetric doublet, gives an isomer shift (IS) of 0.40(3) mm/s and a quadrupole splitting (QS) of 0.86(4) mm/s. These values match well with the reference values41, 42 for HS Fe3+ on A site and are also close to those for LS Fe2+ on A site (Table 2). The latter case is however implausible in terms of the charge balance indicated by the EPMA result. Thus, Fe ions in the present sample exclusively occupy A site in trivalent high-spin state, which leads to that Al3+ ions exclusively occupy B site in consideration of the cation ratio indicated by the EPMA result.

Figure 2
figure 2

(a) Mössbauer spectrum of the present (Fe3+, Al)-bearing bridgmanite single-crystal and (b) the fitting residuals. The software IGOR Pro (Version 6.2, WaveMetrics, Inc., Lake Oswego, OR, USA, https://www.wavemetrics.com) was used for data graphing.

Full size image

To further examine the site distribution of Fe and Al and the presence of vacancies, a preliminary structure-refinement was performed by varying P(AFe3+), P(O1O2−) and P(O2O2−) as valuable occupancy parameters under the following constraints: P(AMg2+) = P(BSi4+) ≡ 0.65 (fix), P(BFe3+) = P(AAl3+) ≡ 0.35 − P(AFe3+), P(BAl3+) ≡ P(AFe3+). The resulting P(AFe3+) was 0.344(2), corresponding to P(BFe3+) = P(AAl3+) = 0.006. The resulting P(O1O2−) and P(O2O2−) were 1.001(5) and 0.999(4), respectively. Another preliminary structure-refinement was also performed by varying P(AFe3+) and P(BAl3+) as valuable occupancy parameters under the following constraints: P(AMg2+) = P(BSi4+) ≡ 0.65 (fix), P(O1O2−) = P(O2O2−) ≡ 1.0 (fix). The resulting P(AFe3+) and P(BAl3+) were 0.347(2) and 0.356(4), respectively. These show that the mixing of Fe and Al between the two cation-sites and the cation- and oxygen-vacancies are undetectable, agreeing well with the EPMA and Mössbauer results. The final refinement was thus conducted by varying P(AFe3+) as the only variable occupancy parameter in a model without any cation- or oxygen-vacancies and without any distribution of Fe into B site or Al into A site, under the following constraints: P(AMg2+) = P(BSi4+) ≡ 1 − P(AFe3+), P(BAl3+) ≡ P(AFe3+). The data provided in Tables 3, 4, 5 are from this final refinement. The final P(AFe3+) is 0.338(3) (Table 4), leading to the cation ratio Mg:Fe:Si:Al = 0.662:0.338:0.662:0.338. This is consistent excellently with the cation ratio from the EPMA.

In ABO3 perovskites with the Pbnm structure, such as CaTiO3 (Ref.43), MgSiO3 (Ref.44,45,46) and CaGeO3 (Ref.33), the great structural distortion due to the tilting of BO6 octahedra yields much longer separations between an A-site atom and four of twelve O atoms surrounding its A-site atom. As shown in Table 5, in the present bridgmanite, the four longer A⋯O separations, which are not potentially involved in chemical bonding, range between 2.9159(9) Å and 3.2292(7) Å. The remaining eight shorter separations range between 2.0057(9) Å and 2.4884(7) Å; the average of these (2.214 Å) agrees better with the expected A–O bond length (2.25 Å) from HS Fe3+ (CN = 8) than the one (2.30 Å) from HS Fe2+ (CN = 8), being concordant with the Mössbauer result. The separations between a B-site atom and six O atoms surrounding its B-site atom are close with each other, in contrast to the case of A-site atom, and range between 1.8213(7) Å and 1.8518(3) Å. The average of these (1.832 Å) agrees well with the expected B–O bond length (1.85 Å).

From the consequences of our observations and analyses described above, we conclude that in the present case, in which relatively large amounts of Fe and Al are equally contained, the following charge-coupled substitution is predominant in the incorporation of both cations into bridgmanite:

$$^{{\text{A}}} {\text{Mg}}^{{{2} + }} + \, ^{{\text{B}}} {\text{Si}}^{{{4} + }} \leftrightarrow \, ^{{\text{A}}} {\text{Fe}}^{{{3} + }} \left( {{\text{HS}}} \right) \, + \,^{{\text{B}}} {\text{Al}}^{{{3} + }}.$$
(1)

Even if there are cation- and/or oxygen-vacancies, divalent Fe2+ ions and mixing of Fe and Al between A and B sites, their amounts/degrees are negligibly small.

Structural variation with the incorporation of Fe and Al into bridgmanite

In Fig. 3, the unit-cell edge lengths (a, b, c) and volume (V) increase with increasing the ratio (Fe + Al)/(Mg + Fe + Si + Al). This is due to the increase in the mean cation size in the whole of bridgmanite crystal accompanying the incorporation of HS Fe3+ and Al3+ via the charge-coupled substitution (1) although the mean cation size on A site (<rA>) decreases by the substitution AMg2+  → AFe3+(HS).

Figure 3
figure 3

Unit-cell edge lengths (a, b, c) and volume (V) as a function of the cation ratio (Fe + Al)/(Mg + Fe + Si + Al). The literature data of the end-member MgSiO3 bridgmanite10, 45, 46, 61 and the (Fe, Al)-bearing bridgmanites3, 4, 6, 7, 10 with near contents between Fe and Al are represented together with the present data. The data graphing software used is as in Fig. 2.

Full size image

As observed in Fig. 4a, the increase in <rA> results in (i) a lengthening of the four shortest A–O bond lengths (A–O1v, A–O1, A–O2vi, A–O2v), (ii) the two almost-unchanged intermediate A–O bond lengths (A–O2vii, A–O2viii), and (iii) a shortening of the two longest A–O bond lengths (A–O2ix, A–O2x) and of the four longer potentially non-bonding A⋯O separations (A⋯O1i, A⋯O1ii, A⋯O2iii, A⋯O2iv). On the other hand, as observed in Fig. 4b, the increase in the mean cation size on B site (<rB>) expands all of B–O bond lengths following the ionic radius effect. The expansivities of B–O bond lengths with increasing <rB> are the largest in the longest B–O1 and B–O1xi bond lengths, running in the direction close to the c-axis. This can account for the observation that the expansivities of the unit-cell edge lengths with increasing the ratio (Fe + Al)/(Mg + Fe + Si + Al) are the largest in the c-axis length (Fig. 3).

Figure 4
figure 4figure 4

(a) A–O bond lengths and potentially non-bonding A⋯O separations as a function of the mean cation size on A site (<rA>), and (b) B–O bond lengths as a function of the mean cation size on B site (<rB>). The literature data from the single-crystal X-ray diffraction studies of the end-member MgSiO3 bridgmanite44,45,46 and the (Fe, Al)-bearing bridgmanites3 are represented together with the present data. The < rA > values of the samples including the Fe content larger than the Al content were calculated on the basis of the proposal of Vanpeteghem et al.3: when the Fe content exceeds the Al content, the charge-coupled substitution AMg2+  + BSi4+  ↔ AFe3+  + BAl3+ occurs for the Fe content equal to the Al content and the substitution AMg2+  ↔ AFe2+ occurs for the extra Fe content. The data graphing software used is as in Fig. 2.

Full size image

The symmetrical constraints always request 180° for O1–B–O1xi, O2vii–B–O2xiii, and O2ix–B–O2xii angles, and the remaining twelve O–B–O angles in a BO6 octahedron vary between 87.74(3)° and 92.26(3)°. This shows that the deviation from a regular BO6 octahedron is only slightly larger in the present (Fe3+, Al)-bearing bridgmanite than in the end-member MgSiO3 bridgmanite with the twelve O–B–O angles ranging between 88.49(4)° and 91.51(4)° (Ref.44). The incorporation of Fe and Al via the charge-coupled substitution (1), thus, does not largely change the degree of distortion of BO6 octahedron and only expands the B–O bond lengths. This shows that the response of the structural distortion to the charge-coupled substitution (1) is dominated mainly by the tilting between corner-linked BO6 octahedra as will be described latter. The shortening of the two very weak A–O2 bonds and the four potentially non-bonding A⋯O separations with increasing <rA> observed in Fig. 4a can be a consequence of a flexible response of these bonds/separations to the structural distortion due to the tilting of octahedra. This brings about the decrease in the averaged A–O bond lengths (<A–O>) with increasing <rA> , in contradiction to the ionic radius effect.

We here describe the octahedral tilting using the three tilt angles \({\upphi }_{i}^{+}\), \({\upphi }_{i}^{-}\), and \({\upphi }_{i}^{0}\) (i = x, y, or z) after Yashima and Ali43. The \({\upphi }_{i}^{+}\), \({\upphi }_{i}^{-}\), and \({\upphi }_{i}^{0}\) indicate the in-phase octahedral tilt angle, the out-of-phase octahedral tilt angle, and no octahedral tilting about i-axis (i = x, y, or z), respectively. The x-, y-, and z-axes represent [100]0, [010]0, and [001]0, respectively, where the subscript “0” represents the pseudo-cubic lattice. The tilting system of Pbnm orthorhombic perovskites, represented by bridgmanite, is described by two identical out-of-phase tilting about the [100]0 and [010]0 axes (\({\upphi }_{x}^{-}={\upphi }_{y}^{-}\)) and an in-phase tilting about the [001]0 axis (\({\upphi }_{z}^{+}\)). This tilting system is expressed as \({\upphi }_{x}^{-}{\upphi }_{y}^{-}{\upphi }_{z}^{+}\) (\({\upphi }_{x}^{-}={\upphi }_{y}^{-}\)), corresponding to a–a–c+ in well-known Glazer’s notation47, 48. The tilt angles have often been defined only from the fractional coordinates of O atoms49, but those will more or less be influenced by the distortions of octahedra themselves. We here calculated the tilt angles via the symmetry-adapted mode approach50, which can completely separate the tilts and distortions of octahedra. In terms of this approach, the tilt angle \(\upphi\) is given by \(\upphi ={\mathrm{tan}}^{-1}\left(2d\mathrm{^{\prime}}\right)\), where \(d\mathrm{^{\prime}}\) is the amplitude of octahedral tilt mode. The \(d\mathrm{^{\prime}}\) values are converted from the standard supercell-normalized amplitude “As” and “normfactor” calculated using the program ISODISTORT (or the earlier ISODISPLACE)51.

The tilt angles \({\upphi }_{x}^{-}\) (= \({\upphi }_{y}^{-}\)) and \({\upphi }_{z}^{+}\) of BO6 octahedra calculated in this way increase with increasing the ratio (Fe + Al)/(Mg + Fe + Si + Al) (Fig. 5a). The \({\upphi }_{x}^{-}\) and \({\upphi }_{z}^{+}\) are almost equal in the end-member MgSiO3 bridgmanite, but the increasing rate of \({\upphi }_{x}^{-}\) with increasing the ratio (Fe + Al)/(Mg + Fe + Si + Al) is larger than that of \({\upphi }_{z}^{+}\). The A-site atom also goes away from its ideal position (0, 0, 0.25), corresponding to the A-site position in the Pm\(\overline{3 }\)m cubic structure, with increasing the ratio (Fe + Al)/(Mg + Fe + Si + Al) (Fig. 5b). The structural distortion, i.e. the deviation from the Pm\(\overline{3 }\)m cubic structure, is thus getting larger with the incorporation of Fe and Al dominated by the charge-coupled substitution (1). The expansion of the two very weak A–O2 bonds and the four potentially non-bonding A⋯O separations with decreasing <rA> (Fig. 4a), i.e. with increasing Fe3+ content on A site, is a consequence of such increase in structural distortion and a sign of the increased deviation from the Pm\(\overline{3 }\)m cubic structure, with twelve equivalent A–O bond lengths and without any octahedral tilting (\({\upphi }_{x}^{0}{\upphi }_{y}^{0}{\upphi }_{z}^{0}\)).

Figure 5
figure 5

(a) Tilt angles \({\upphi }_{x}^{-}\) (= \({\upphi }_{y}^{-}\)) and \({\upphi }_{z}^{+}\) of BO6 octahedra calculated from the symmetry-adapted mode approach50 and (b) the positional parameters x and y of A-site atoms, located at the coordinates (x, y, 0.25), as a function of the ratio (Fe + Al)/(Mg + Fe + Si + Al). The data calculated from the positional parameters reported in the end-member MgSiO3 bridgmanite44,45,46 and the (Fe, Al)-bearing bridgmanites3 are plotted together with the present data. The data graphing software used is as in Fig. 2.

Full size image

Implications for the Earth’s lower mantle

Bridgmanite is now believed to undergo the phase transition to post-perovskite phase with CaIrO3 structure, associated with the D′′ seismic discontinuity, at 125 GPa and 2500 K (Ref.52, 53). However, some high-pressure studies54,55,56 suggested that another perovskite phase with a different symmetry can intervene between the Pbnm perovskite phase and the post-perovskite phase. To examine the possibility of such phase transitions in ABO3 perovskites at high pressures and high temperatures, it is effective to discuss the relative compressibility of AO12 and BO6 polyhedra57, 58. The compressibility ratio (βB/ βA) of the two polyhedra is given by βB/βA = MA/MB (Ref.57), where the subscripts “A” and “B” represent the AO12 and BO6 polyhedra, respectively. In Pbnm orthorhombic perovskites with largely distorted AO12 (practically AO8) polyhedra, such as bridgmanite, the parameters MA and MB are defined as follows:

$${M}_{\mathrm{A}}=\left(8{R}_{\mathrm{A}8}/B\right) {\mathrm {exp}} \left[\left({R}_{0}-{R}_{\mathrm{A}8}\right)/B\right]+\left(4{R}_{\mathrm{A}4}/B\right) {\mathrm {exp}} \left[\left({R}_{0}-{R}_{\mathrm{A}4}\right)/B\right]$$
(2)
$${M}_{\mathrm{B}}=\left({6R}_{\mathrm{B}}/B\right)\mathrm{exp}\left[\left({R}_{0}-{R}_{\mathrm{B}}\right)/B\right]$$
(3)

where RA8, RA4 and RB are the average distances of eight shorter A–O bonds, of four longer A⋯O separations and of six B–O bonds, respectively; R0 and B the bond valence parameters. According to Angel et al.58, in perovskites exhibiting zone-boundary type phase transitions, when the BO6 octahedra are more rigid than the AO12 polyhedra (i.e., MA/MB < 1), the phase transition temperature Tc rises with increasing pressure as a consequence of the increase in the octahedral tilting; thus, the phase boundary has a positive Clapeyron slope (dP/dTc > 0). Conversely, when the BO6 octahedra are less rigid than the AO12 polyhedra (i.e., MA/MB > 1), Tc reduces with increasing pressure as a consequence of the decrease in the tilting; thus, the phase boundary has a negative Clapeyron slope (dP/dTc < 0).

The MA/MB ratios at ambient condition, from Eqs. (2) and (3), are calculated to be 0.67 for the end-member MgSiO3 bridgmanite44,45,46, 0.72 for the present (Fe3+, Al)-bearing bridgmanite, and 0.63 for CaTiO3 perovskite43 as a good analog of bridgmanite, using the R0 and B values determined by Brown and Altermatt59 and the average interatomic distances reported for each compound. It follows therefore that if these A2+B4+O3-type Pbnm perovskites undergo phase transitions to perovskite phases with different symmetries at high pressures and high temperatures, their phase boundaries have positive Clapeyron slopes.

The tilt angles of the end-member MgSiO3 bridgmanite at ambient condition are calculated to be \({\upphi }_{x}^{-}\) = 11.7° and \({\upphi }_{z}^{+}\) = 11.6° from the reported structural parameters45. These values are much larger than those of CaTiO3 perovskite (\({\upphi }_{x}^{-}\) = 8.3°, \({\upphi }_{z}^{+}\) = 8.8°), which were reported to undergo the phase transitions of Pbnm → I4/mcm at 1512 K and of I4/mcm → Pm\(\overline{3 }\)m at 1635 K under ambient pressure43. As mentioned above, when MA/MB < 1, the larger tilting yields the higher Tc, and the rise in pressure further promotes the rise in Tc because of a positive Clapeyron slope. If the same sequence of the high-temperature phase transitions to higher symmetric LP (low pressure)–HT (high temperature) phases as CaTiO3 perovskite also appears in the end-member MgSiO3 bridgmanite at high pressures, thus, Tc should become much higher than those observed in CaTiO3 perovskite at ambient pressure. The incorporation of Fe and Al into bridgmanite would further raise Tc because it increases the tilt angles \({\upphi }_{x}^{-}\) and \({\upphi }_{z}^{+}\) as shown in Fig. 5a.

In the end-member MgSiO3 bridgmanite, Wang et al.54 observed the discontinuous changes in the unit-cell parameters and volume at ~ 600 K and 7.3 GPa, suggesting the phase transition to another perovskite phase. This P–T condition corresponds to a much lower temperature despite a higher pressure than the phase-transition points observed in CaTiO3 perovskite. Even if there exists such phase transition in the end-member MgSiO3 bridgmanite, therefore, it would be the phase transition not to a higher symmetric LP-HT phase, such as in CaTiO3 perovskite, but to a lower symmetric HP (high pressure)–LT (low temperature) phase.

At extreme conditions corresponding to deeper parts of the lower mantle, a few in-situ energy-dispersive X-ray diffraction studies using a laser-heated diamond anvil cell have suggested the phase transition of Pbnm bridgmanite to another perovskite phase. For example, Meade et al.55 reported the phase transition from Pbnm (orthorhombic) to Pm\(\overline{3 }\)m (cubic) at 64 GPa and 1850 K for (Mg, Fe)SiO3 bridgmanite. Shim et al.56 reported the phase transition of the end-member MgSiO3 bridgmanite from Pbnm to one of the three possible symmetries [P21/m (monoclinic), Pmmn (orthorhombic), or P42/nmc (tetragonal)] above 83 GPa and 1700 K. These suggested space groups after the phase transitions or the presence itself of the phase transitions were not entirely definitive because of low resolution and unreliable peak intensities in the powder X-ray diffraction patterns measured at these extreme conditions. These suggested phase-transition points are however at higher temperatures and higher pressures than those of CaTiO3 perovskite, being consistent with the prediction that the larger octahedral tilting and higher pressure raise Tc. The possibility that bridgmanite changes into another perovskite phase with a different symmetry from Pbnm before the phase transition to the post-perovskite phase cannot thus be ruled out, whether it is the higher symmetric LP-HT phase or the lower symmetric HP-LT phase. Although bridgmanite including high Al and/or Fe contents, such as the present sample (Mg0.662Fe0.338Si0.662Al0.338O3) with their contents very close to those27 reported for bridgmanite formed from the MORB composition, is predicted to have further higher Tc, the phase transition of such bridgmanite to another perovskite phase might be found in slabs that fell/subducted into the lowermost parts of the lower mantle.

The compressibility ratio βB/βA of bridgmanite can provide important knowledge of its elastic velocity as well. Comparison of the end-member MgSiO3 bridgmanite45 and the present (Fe3+, Al)-bearing bridgmanite shows that the incorporation of Fe3+ and Al through the charge-coupled substitution (1) makes MA unchanged, decreases MB, increases the density ρ, and consequently increases βB/βA (= MA/MB), where MA = 12.87, MB = 19.23 and ρ = 4.103 g/cm3 for the former; MA = 12.92, MB = 17.85 and ρ = 4.357 g/cm3 for the latter. We can consider that the increase in βB/βA, depending only on MB, corresponds to the decrease in the bulk modulus K. The bulk sound velocity \({V}_{\mathrm{B}}=\sqrt{K/\uprho }\) is thus expected to decrease with increasing Fe3+ and Al contents, which is consistent with the theoretical calculation60 for (Fe3+, Al)-bearing bridgmanite. This approach from crystallography can thus be a helpful method to gain important insights into the seismic properties within the lower mantle. For this purpose, systematic crystal-chemical studies of bridgmanites with a variety of valence- and spin-states of Fe and compositions are necessary.