Poirierite, a dense metastable polymorph of magnesium iron silicate in shocked meteorites

A dense magnesium iron silicate polymorph with a structure intermediate between olivine, ringwoodite, and wadsleyite was theoretically predicted about four decades ago. As this group of minerals constitute the major component of shocked meteorites, constraining their transitional forms and behaviour is of potential importance for understanding impact events on their parent bodies. Here we use high-resolution transmission electron microscopy techniques and single-crystal X-ray diffraction analyses to identify naturally occurring examples of this mineral – recently named poirierite – in shocked chondritic meteorites. We observe nanoscale lamellar poirierite topotactically intergrown within wadsleyite, and additionally within ringwoodite as recently reported. Our results confirm the intermediate structure of poirierite and suggest it might be a relay point in the shear transformations between its polymorphs. We propose that poirierite formed during rapid decompression at relatively low temperature in retrograde shock metamorphism of the meteorites. Naturally occurring poirierite is identified in three shocked meteorites where it probably formed as a metastable phase during rapid phase transitions between olivine and its high-pressure polymorphs, according to high-resolution crystallographic analyses

M ineral physicists have made long-standing efforts to elucidate the mineralogy of the deep Earth's interior. Specifically, previous phase equilibria studies have clarified a variety of high-pressure silicate and oxide polymorphs. Olivine [(Mg,Fe) 2 SiO 4 ] with Fe/(Mg+Fe) ≈ 0.11 is the most common constituent mineral in the Earth's upper mantle. It transforms into a spinelloid structure (wadsleyite) at~14 GPa and then into a spinel structure (ringwoodite) at~18 GPa in the mantle geotherm 1 . These high-pressure minerals are considered dominant in the mantle transition zone (MTZ) at depths of 410-660 km. As direct natural evidence, ringwoodite derived from the MTZ was discovered as an inclusion in a diamond 2 .
These high-pressure minerals have also attracted the attention of planetary scientists since hypervelocity impacts on asteroids, the Moon, and Mars have generated high-pressure and hightemperature conditions. Many meteorites derived from such solar system bodies yield shock-induced high-pressure minerals 3 . For olivine polymorphs, the natural occurrences of Mg 2 SiO 4 -rich ringwoodite and wadsleyite were first discovered in strongly shocked ordinary chondrites 4,5 . Recently, Fe 2 SiO 4 -rich analogues of ringwoodite and wadsleyite were also found in two ordinary chondrites and a Martian meteorite, which were named ahrensite and asimowite, respectively 6,7 .
In the shocked chondrites, the olivine in the host rocks is assumed to have partially transformed into ringwoodite or wadsleyite aggregates within or in the vicinity of the shock-induced melt vein (shock vein) via solid-state reactions 8 . An alternative hypothesis suggests that shock-induced melts with olivine-rich compositions were crystallised as ringwoodite and/or wadsleyite by fractional crystallisation 7,9 . A wide variety of Fe contents in the ringwoodite-ahrensite and wadsleyite-asimowite solid solutions would have been caused by the crystallisation of shock-induced melt and solid-state Fe diffusion depending on the crystallisation temperature, oxygen fugacity, and local composition of the melt 6,7,10-12 . The high-pressure phases of olivine formed by these two mechanisms constrain the shock metamorphic histories of the meteorites, such as the crystallisation pressure of shockinduced melt based on phase equilibiria 9,13 and shock pressure duration deduced from transfomation kinetics 14,15 .
Microstructures of ringwoodite and wadsleyite in shocked meteorites provide important insights for understanding their deformation and transformation mechanisms of (Mg,Fe) 2 SiO 4 [16][17][18] . These high-pressure phases often show nanometre-scale planar defects observable only under a transmission electron microscope (TEM). Based on the observations of the defect (stacking fault) structures combined with the topological analyses of the crystal structures of olivine, ringwoodite, and wadsleyite, shear mechanisms are posited to promote their polymorphic transformations 17,18 . The transformation model also predicted the possible occurrence of an intermediate spinelloid structure (ε phase) 17 . This hypothetical phase remained undiscovered in high-pressure syntheses products and natural samples for more than three decades. High-resolution TEM studies, however, have recently clarified that the ε phase is present in the Tenham chondrite as nanometre-scale lamellae in ringwoodite crystals with granular morphology 19 .
In this study, we report further characterisations of the natural ε phase occurrences in three chondritic meteorites (Tenham, Miami and Suizhou) and discuss its formation mechanisms in shock metamorphism based on transmission electron microscopy, single-crystal X-ray diffraction, and firstprinciples calculations. ε-Mg 2 SiO 4 has been approved as a new mineral species by the Commission on New Minerals and Mineral Names, International Mineralogical Association (No. 2018-026b), and named as poirierite in honour of Jean-Paul Poirier, who greatly contributed to mineral physics, including the theoretical prediction of ε-Mg 2 SiO 4 .

Results
Transmission electron microscopy. The Tenham L6 and Miami H5 chondrites have shock veins containing host rock olivine fragments that are transformed partially or totally into its high-pressure phases (Fig. 1a). In Tenham, euhedral and subhedral ringwoodite grains with sizes of 400 ± 150 nm form polycrystalline aggregates in the shock vein (Fig. 1b). Their Fe/(Mg+Fe) ratio is 0.26 ± 0.01, which is consistent with those of ringwoodite in Tenham in previous studies [Fe/(Mg+Fe) = 0. 25-0.26], where the chemical composition is nearly the same as the host olivine 20,21 . These ringwoodite grains are randomly crystallographically oriented and exhibit pervasive planar defects on six equivalent planes on {110} (Fig. 1b). Selected-area electron diffraction (SAED) patterns from many of the ringwoodite grains showed weak extra diffraction spots corresponding to the ε-phase (poirierite) with the space group Pmma 17 (Fig. 2). Moreover, the SAED patterns of ringwoodite with the poirierite lamellae showed that both phases have a topotaxial relationship: a Poi, b Poi //<110> Rwd , and c Poi //c Rwd . Due to the extremely thin width (<10 nm) of the lamellae, the chemical composition of poirierite could not be obtained.
In Miami, euhedral and subhedral wadsleyite grains with 1200 ± 450 nm size replace olivine grains entrapped into the shock vein ( Supplementary Fig. 1a). The wadsleyite grains are randomly crystallography oriented, which is similar to that of ringwoodite in Tenham. Many of the wadsleyite grains [Fe/(Mg+Fe) = 0.24 ± 0.01] exhibit planar defects at (010) (Supplementary Fig. 1b). The parts of the wadsleyite grains with stacking faults showed weak diffraction spots corresponding to those of poirierite. The wadsleyite-poirierite intergrowth shows a topotaxy of a Poi //a Wds , b Poi //b Wds , and c Poi // c Wds ( Fig. 3 and Supplementary Fig. 2). Like Tenham, the chemical composition of poirierite in Miami could not be obtained owing to its thinness and secondary Fe-incorporation from the Fe-rich melt through the planar defects.
Single crystal X-ray diffraction. In addition to the abovedescribed chondrites, poirierite was discovered to have grown in a ringwoodite single crystal in the Suizhou L6 chondrite (Supplementary Fig. 3). The determined structure showed that it is slightly deformed from the ideal spinelloid structure, which has two basic structural modules vertically aligned up and down, and was deduced from previous topological analyses of Mg 2 SiO 4 17,22 ( Supplementary Fig. 4). Fe ions only occupy the M2 site and its refined lattice parameters are a = 5.802(11) Å, b = 2.905(9) Å, c = 8.411(16) Å, and V = 141.8(6) Å 3 .
The empirical formula for ringwoodite from Suizhou is (Mg 1.59 Fe 0.35 Na 0.03 Al 0.03 ) Σ=2 SiO 4 . The X-ray formula derived from the structural refinement for ringwoodite is (Mg 1.65 Fe 0.35 ) Σ=2 SiO 4 , whereas the formula for poirierite is (Mg 1.96 Fe 0.04 ) Σ=2 SiO 4 . The density of poirierite calculated using the formula derived from the crystal structure refinement is 3.326 g cm −3 . Fractional atomic coordinates, atomic displacement parameters, bond distances, and geometric parameters [calculated according to Robinson et al. 23 ] for poirierite are shown in Table 1. Powder X-ray diffraction data for poirierite, which were calculated based on the experimentally refined crystal structure, is shown in Supplementary Table 1.
First-principles calculations. Crystal structure at 0 K of Mg 2 SiO 4 poirierite was optimised within space group Pmma using the density functional theory (DFT) (Supplementary Table 2). All the atomic positions in the optimised poirierite structure are slightly displaced along the c-axis from those in the ideal ε phase 17,22 except at the M1 sites, which are fixed by the space group symmetry. These results mostly are in accordance with those obtained via single crystal X-ray diffraction (Table 1).
Crystal structures at 0 K of other Mg 2 SiO 4 polymorphs were also optimised and the relative enthalpies at pressures up to 20 GPa are shown in Fig. 4. Forsterite (Mg 2 SiO 4 -olivine), wadsleyite and ringwoodite have the smallest enthalpies at 0-13 GPa,~13-15 GPa,~15-20 GPa, respectively; however, poirierite maintains its highest enthalpy throughout the pressure range, which approaches that of wadsleyite and, more closely, that of ringwoodite, with decreasing pressure.
Phonon dispersions of the Mg 2 SiO 4 poirierite were calculated along the lines in the Brillouin zone ( Supplementary Fig. 5). All the phonon frequencies were found to be real. Raman spectra were calculated for the poirierite and other polymorphs of Mg 2 SiO 4. Comparing the calculated Raman spectra in the low-frequency region (<900 cm −1 ), poirierite shows major peaks at 480, 849, and 855 cm −1 , which are distinct from those of ringwoodite and wadsleyite (Fig. 5). In the present study, poirierite could not be identified in the chondrite samples by Raman spectroscopy, possibly due to its extremely small size. However, strong Raman peaks at~850 cm −1 will be specifically useful in identifying a mineral if it occurs in other meteorites in additional studies.

Discussion
Structural refinements through single-crystal X-ray diffraction and DFT calculations clarified that poirierite discovered in shocked chondrites has an orthorhombic unit cell with the smallest dimensions among the pre-existing spinelloid structures 22 . The structure, however, is slightly deformed from that of an ideal spinelloid structure as deduced from previous topological analyses of Mg 2 SiO 4 17, 22 . Such a structural distortion could pose difficulties to the ability of poirierite to display a thermodynamically stable phase under high pressures and temperatures. In addition, the DFT calculations results indicate that the structure does not have any phonon frequencies with complex numbers ( Supplementary Fig. 5), which suggests that the poirierite is at least dynamically stable. In summary, poirierite can form universally in natural and synthetic samples as a metastable phase.
Polymorphic phase transformations in silicates have nucleation and growth mechanism and shear mechanism 24 . In the former process, the product phase is nucleated mainly at the grain boundaries of the parental phase, and tends to have a granular morphology with random crystallographic orientations. In the latter process, the product phase forms inside the parental grains, and tends to have lamellar or lens shapes. This mechanism involves the spontaneous shearing of the oxygen sublattice associated with slight cation displacements in the parental structure and forces the host and product phases to have topotaxial relationships where their lattices coherently contact (low lattice misfits). Due to the absence of long-range atomic diffusion, the shear mechanism prefers low-temperature conditions. In addition, shear stress can promote the transformation process.
As mentioned previously, ringwoodite, wadsleyite and poirierite are similar because their crystal structures consist of basic structural modules ( Supplementary Fig. 4), which can be distinguished by the periodic orientational arrangements of the modules; The ringwoodite and wadsleyite structures have translational periodicity represented by ↑↓↑↓ and ↓↓↑↑, respectively 19 . The poirierite structure consists of a single orientation of the basic structural unit denoted by ↑↑↑↑ 19,22 ; therefore, inter-transformations among these structures are highly likely to occur via the shear mechanism (Fig. 6). Evidence for this mechanism in a ringwoodite-to-wadsleyite transition has been found within a topotaxial lamellar intergrowth in a shocked chondrite 25 . This was further confirmed experimentally via high-pressure experiments with Mg 2 SiO 4 26 . Similar processes were also proposed experimentally and   theoretically in the olivine-ringwoodite transformation [27][28][29][30][31] , and microstructural evidence has been found within a shocked chondrite 15 . This study revealed that poirierite has a nanoscale lamellar morphology and a topotaxial relationship with the hosts ringwoodite and wadsleyite. From these occurrences, the poirierite also appears to have formed from the host phases by the shear mechanisms in shock metamorphism 17 (Fig. 6). Ringwoodite and wadsleyite in mineral fragments in shock veins in the Tenham and Miami chondrites show polycrystalline aggregates with randomly oriented granular grains. These occurrences suggest that the olivine grains were initially transformed into stable high-pressure phases by the nucleation and growth mechanism in prograde shock metamorphism without melting (Fig. 7). According to thermal conductivity calculations, the sub-millimetre-width shock veins in the chondrites are supercooled mainly through thermal conduction on the order of 10 3°C /s before the shock pressure release 21,32 . The lowered shock-vein temperature potentially hinders the back transformations from ringwoodite/wadsleyite to olivine during the retrograde shock metamorphism.
A possible result of the ringwoodite and wadsleyite grains during decompression is their partial transformation into lamellar poirierite via shear mechanisms (Fig. 7). The closer density of poirierite (3.326 g cm −3 ) to olivine (3.254 g cm −3 ) 33 than wadsleyite (3.501 g cm −3 ) 34 , and ringwoodite (3.592 g cm −3 ) 35,36 estimated assuming the same iron content [Fe/(Mg+Fe) = 0.02], suggests that poirierite forms at a relatively lower high-pressure condition, that is within or approximate to the stability field of olivine. This is supported by the enthalpy calculations results that showed poirierite has the highest enthalpy among the Mg 2 SiO 4 polymorphs and its value approaches those of ringwoodite and wadsleyite when pressure decreases (Fig. 4).
Recently, in situ X-ray diffraction experiments under lasershock compression clarified that olivine transforms into a dense structure within nanoseconds 37 . This transformation strongly suggests that the shear mechanism is highly effective at promoting extremely rapid phase transformations, even in lowtemperature conditions. Therefore, metastable poirierite would be rapidly formed in the ringwoodite/wadsleyite aggregates by the shear mechanism during decompression (Fig. 7).
Vacancy-rich tetragonal silicate spinelloids were recently reported in the Tenham and Suizhou chondrites 38 and the Tissint Martian meteorite 39 . These tetragonal spinelloids occur as submicron-sized granular particles coexisting with (Mg,Fe)SiO 3clinopyroxene or -glass in the matrices of the shock veins in Tenham and Suizhou, and in the polymorphs of olivine, pyroxene, and chromite in the melt pockets in Tissint. In Tenham and Suizhou, the occurrences of the tetragonal spinelloid indicate that the mineral was crystallised from the shock-induced melt with an approximately bulk meteorite composition 38 . This process would prevent the formation of stable majorite-magnesiowüstite assemblages due to the highly rapid cooling mentioned above 38 . Poirierite formed in solid-state transformation mechanisms from the ringwoodite/wadsleyite aggregates entrapped in the shockinduced melts; therefore, the cooling rates of the aggregates and their surrounding melts would be comparable. However, differences in their chemistries and formation mechanisms resulted in different crystal structures.
X-ray elemental mapping and crystal structure refinement revealed that poirierite in Tenham and Suizhou is depleted in Fe compared to that in the host ringwoodite. This suggests that a nanometre-scale Mg-Fe interdiffusion occurred subsequently after the shear transformation from ringwoodite to poirierite, which is consistent with Fe being more partitioned in the spinel structure (ringwoodite) than in the spinelloid structure (wadsleyite) in high-pressure experiments 40 and shocked chondrites 9 . Poirierite with a spinelloid structures would also prefer the Mgrich composition over the spinel structure.
The discovery of poirierite further elucidates the new sheartransformation paths in the polymorphic phase transition in olivine (Fig. 6c). The poirierite structure has a similar cation arrangement in each interstice of the close-packed oxygen layers as that within the olivine structure, although olivine and poirierite are composed of hexagonal-and cubic-close-packed oxygen ions, respectively. This structural similarity increases the possibility of a shear mechanism from olivine to poirierite via oxygen layer sliding along the [010] Olivine direction on (100) Olivine 17 . If this assumption is correct, the olivine-wadsleyite transformation could be enhanced via the poirierite structure by the shear mechanism at low temperature and/or high-stress conditions, such as in shocked meteorites and the Earth's oceanic slabs subducting into the deep mantle 19 . To test this hypothesis, experimental and theoretical studies and investigations on the presence of poirierite in the olivine in shocked meteorites are currently being performed.
This study confirms the natural occurrences of poirierite and highlights two new pathways for shear transformations associated with nanoscale Fe-Mg interdiffusion among the olivine polymorphs. Further studies of the formation conditions (temperature, pressure, and differential stress) of poirierite will lead to more detailed insights into the shock metamorphism of planetary materials and potentially also into the dynamics of the deep earth. Unusually, a smaller density of poirierite than wadsleyite and ringwoodite is also a key parameter for its formation process. Tenham: A polished thin section (catalogue number: NSM-MF15737) has been deposited at the Department of Geology and Paleontology, National Museum of Nature and Science, Japan. Tenham is classified as an L6 ordinary chondrite and mainly consists of olivine, low-Ca pyroxene, high-Ca pyroxene, plagioclase, kamacite and troilite. It is highly shocked and comprised of shock veins <1 mm thick. This meteorite contains various types of high-pressure silicate minerals within and in the vicinity of the shock veins: ringwoodite, wadsleyite, majorite, majorite-pyrope garnet, tetragonal majorite, akimotoite, bridgmanite and lingunite 4,32,[41][42][43][44] .
Miami: This meteorite is classified as an H5 ordinary chondrite (database of the Meteoritical Bulletin: https://www.lpi.usra.edu/meteor/metbull.php) and consists mainly of olivine, low-Ca pyroxene, high-Ca pyroxene, plagioclase, kamacite and troilite. A polished thin section includes thin shock veins <200 µm thick. The shock veins in Miami contain abundant high-pressure minerals including wadsleyite and tuite.
Electron microscopies. The polished thin sections of the Tenham, Miami and Suizhou chondrites were initially examined with scanning electron microscopes (Hitachi SU1510 at the Kochi Institute for Core Sample Research (KOCHI), Japan Agency for Marine-Earth Science and Technology; JEOL JSM-7100F at the National Institute of Polar Research (NIPR); Zeiss Evo MA15 at the MEMA laboratory of the Università degli Studi di Firenze) to observe the shock veins and fragments of host rocks therein. Portions of ringwoodite and wadsleyite from Tenham and Miami were processed into ultrathin foils~150 nm thick using a Ga ion beam after the deposition of carbon protection layers in a focused ion beam (FIB) apparatus (Hitachi SMI-4050 at KOCHI). The ultrathin foils were mounted on Cu grids using a micromanipulator equipped with the FIB and studied using a TEM (JEOL JEM-ARM200F at KOCHI) operated at an accelerating voltage of 200 kV. Phase identification of the olivine polymorphs was performed using SAED and the chemical compositions of the samples were obtained using energy-dispersive X-ray spectrometry (EDS) with a 100 mm 2 silicon drift detector. The Fe/Mg ratios of ringwoodite and wadsleyite were determined using experimental thickness-corrected k-factors obtained from the San Carlos olivine standard. The intensities of the characteristic X-rays of each element were measured using a fixed acquisition time of 30 s, beam spot size of 100 nm, and beam current of 200 pA. Crystal structure diagnosis was performed via single-crystal electron diffraction considering the d-spacings and the interangles of the reciprocal lattice vectors of the respective unit cells. The reflection conditions based on the symmetry of each crystal were evaluated by considering their dynamical effect on electron diffraction. The details are described in a previous paper 19 .  Madon and Poirier (1983) 17 ], respectively. Polyhedra in yellow are (Mg,Fe)O 6 octahedra and those in blue are SiO 4 tetrahedra. Arrows show the directions on shear planes (dotted lines). c Shear mechanisms and their representative crystallographic relationships. Two-direction arrows represent the shear transformation mechanisms between the phases. The arrows denote shear mechanisms previously observed in shocked chondrites 15,25 and high-pressure experiments [26][27][28][29][30] (blue), Tomioka and Okuchi (2017) 19 and this study (green), and the theoretical model 17 (red), respectively.
Single-crystal X-ray diffraction. Multiphase structure refinement was performed using single-crystal X-ray diffraction data collected on a poirierite fragment intergrown with ringwoodite from the Suizhou chondrite. A small crystal ( The number of extracted and independent reflections was sufficient for identifying the Fd 3m space group of ringwoodite and refining its structure-carried out with the program SHELXL-97 49 using the atomic coordinates given previously 50 -and to begin the structure solution of the poirierite. In detail, the observed conditions (hk0: h = 2n; h00; h = 2n) for the reflections belonging to the poirierite structure, together with the statistical tests on the distribution of |E| values that strongly indicated the presence of an inversion centre (|E 2 -1 | = 0.965), pointed to the space group Pmma (Supplementary Table 1). The structure solution was then initiated in this space group. The positions of most of the atoms (all the cation positions and most of the O atoms) were determined through direct methods 49 . A least-squares refinement on F 2 using these positions and isotropic temperature factors produced an R factor of 0.085. Three-dimensional difference Fourier synthesis yielded the position of the remaining oxygen atoms. The program SHELXL-97 49 was used for the refinement of the poirierite structure. Site-scattering values for the two phases were refined using scattering curves for neutral species 51  First-principles calculations. The first-principles calculations based on the density functional theory (DFT) on poirierite and the known Mg 2 SiO 4 polymorphs were performed using the Quantum Espresso code 52 . The crystal structure of poirierite at 0 K was optimised using the Perdew-Burke-Ernzerhof (PBE) exchange-correlation density functional and norm-conserving pesudopotentials 53 with an energy cutoff of 120.0 Ry with 12 × 20 × 8 k-point grids where space group is Pmma. The parameters (lattice parameters and atomic positions) of the poirierite structure model, which were proposed in a previous topological study 17,22 , were used as initial parameters for the DFT calculations.
Phonon dispersions of poirierite were calculated using the PBE exchangecorrelation density functional. Norm-conserving pesudopotentials with an energy cutoff of 120.0 Ry with 12 × 20 × 8 k-point grids. Raman spectrum calculations of poirierite, wadsleyite and ringwoodite were performed with the local density approximation for exchange-correlation due to the ability of the Quantum Espresso code in the calculations. Norm-conserving pesudopotentials with an energy cutoff of 120.0 Ry with 12 × 20 × 8, 12 × 12 × 12, and 20 × 20 × 20 k-point grids were adopted for poirierite, wadsleyite and ringwoodite, respectively. The structural parameters of poirierite were fixed at those DFT-optimised in the present study, while those of wadsleyite and ringwoodite were fixed at those determined by previous single-crystal X-ray diffraction studies 35,54 . Data availability SEM and TEM micrographs and DFT calculation results in this paper are available at https://zenodo.org/deposit/4284231. The X-ray crystallographic coordinates for structures reported in this article have been deposited at the Cambridge Crystallographic Data Centre (CCDC), under deposition number CCDC 2049451. These data can be obtained free of charge from The Cambridge Crystallographic Data Centre via www.ccdc. cam.ac.uk/data_request/cif. Received: 7 May 2020; Accepted: 16 December 2020; Fig. 7 Schematic of the formation process of poirierite in the shockinduced melt veins of the Tenham and Miami chondrites. The phase boundaries between Fe-bearing olivine (Ol), wadsleyite (Wds) and ringwoodite (Rwd) are simplified by considering only univariant reactions. In the samples investigated in this study, olivine grains entrapped in the host rock were initially transformed into randomly oriented polycrystalline wadsleyite and ringwoodite in solid-state transformations and then rapidly cooled (>10 3°C /sec) at an equilibrium shock pressure (~25 GPa) 21,32 . The polycrystalline wadsleyite and ringwoodite partly transformed into the lamellar poirierite on (010) Wds and {110} Rwd by shear mechanisms during decompression at relatively lower temperatures where long-range atomic diffusion is hindered.