1. Introduction
Various high pressure–temperature (P–T) experimental techniques have been developed in order to study mantle minerals existing in the Earth’s interior. Under increasing P–T conditions that correspond to those of the deep Earth, the crystal structures of minerals that are stable under low P–T conditions are replaced by denser structures. The pyrolitic composition of the lower mantle has been tested using high P–T experiments [1,2]. At least five oxide components are required to describe the mantle system. Even in a single bulk composition (e.g., mid-ocean ridge basalt (MORB) or pyrolite), phase changes are associated with element partitioning within the assemblage under high P–T conditions. Interactions of subducting slabs with the mantle system further complicate their phase relations [3,4]. For example, some amounts of water may be stored in nominally anhydrous lower mantle phases, but the presence of water components in subducting slabs may also stabilize hydrous phases under P–T conditions. Petrological experiments have been widely conducted in a multi-anvil apparatus up to the P–T range of the top of the lower mantle (< 30 GPa) [5], and the P–T range can be extended to the middle of the lower mantle (∼50 GPa) when sintered diamond anvils are used [2].
The ambition to explore the whole interior of the Earth has promoted extensive use of the laser-heated diamond anvil cell (DAC). Diamond is the hardest known material and is transparent to X-rays. Typically, a sample assembly less than 50 μm in diameter and about 10 μm in thickness is compressed between the tips of two diamond anvils and laser-heated from both sides of the sample [6]. Megabar pressure was first achieved 40 years ago, allowing the simulation of deep-Earth P–T conditions [7]. Through development of the DAC and laser-heating techniques, experiments have been conducted to study the structure of iron (Fe) under the inner-core P–T conditions of up to 377 GPa and 5700 K [8]. These experiments have mostly been limited to a single mineral phase or a simple system (e.g., MgO–SiO2). However, interpretations of key enigmatic features in the deep lower mantle—namely, the sharp upper boundary of the D″ layer [9], the seismic anisotropy [10], and the large low-shear-velocity provinces in the bottom third of the lower mantle [11]—require information from high P–T petrological experiments on a realistic lower mantle multicomponent system, which produces an assemblage consisting of multiple phases under high P–T conditions in a laser-heated DAC.
In a multiphase assemblage, most diffraction peaks overlap in a powder X-ray diffraction (XRD) pattern; even without overlap, powder XRD alone is inadequate for studying new structures. Single-crystal XRD is regarded as the ideal method for structural analysis, and has been widely developed for high-pressure research in a DAC [12–14]. However, single crystals of around 5 μm in size, as required for conventional single-crystal XRD experiments, are unachievable in a realistic mantle assemblage under the corresponding high P–T conditions. Instead, a polycrystalline multiphase sample is always obtained in phase equilibrium experiments corresponding to the deep mantle. In this paper, we review the applications of the multigrain XRD technique for studying multiphase systems under high P–T conditions, including in situ characterization of new phases in a multiphase assemblage, crystal structure determination of selected individual grains in a polycrystalline sample, and two-dimensional (2D) mapping through the precise determination of unit-cell parameters for individual phases at steps of a few microns.
2. Challenges in experimental petrology under high P–T conditions
Phase identification and structural analysis in a multiphase assemblage have long been recognized as a challenge in high-pressure research. Frost and Fei [15] pointed out difficulties in identifying the hydrous phases D, F and G, of dense hydrous magnesium silicates from powder XRD patterns of recovered samples when the synthesis pressure was as low as 22 GPa. However, if such a multiphase assemblage contains individual crystals with grain sizes greater than 5 μm and the structure can be preserved under ambient conditions, these grains can be picked out for single-crystal studies in the recovered sample.
Higher pressure is generated in an apparatus at the expense of sample volume. The sample volume decreases from a few millimeters in dimension in a multi-anvil apparatus to tens of micrometers at above 60 GPa in a DAC. Furthermore, most structures obtained at ultrahigh pressures, such as MgSiO3 or (Mg,Fe)SiO3 post-perovskite (pPv), cannot be preserved under ambient conditions [16–18]. Meanwhile, the grain size in a polycrystalline sample generally decreases with increasing pressure. For example, the grain size of a hydrous phase in a mantle assemblage could be as small as about 100 nm under the high P–T conditions of the deep lower mantle [4]. The grain size of the hydrous δ-phase decreases from about 2 μm at 68 GPa to about 200 nm at 128 GPa after heating treatment at a similar temperature [4], indicating that pressure has a dominant effect on grain size. Other factors may also influence grain size; for example, lower temperature tends to decrease grain size [19]. The recovery of tiny crystals (< 1 μm) for single-crystal diffraction thus becomes practically infeasible. In conclusion, in situ characterization is needed in order to study phase changes and structural details in a multiphase system under the P–T conditions of the deep lower mantle.
High P–T conditions produce a wealth of new structures. In a high P–T experiment, a few new peaks often appear in a powder XRD pattern; however, a perfect match to a known structure is not easy to find. One type of new structure is due to atom rearrangement into a denser structure, such as the B1–B2 structural transition in NaCl. Another type involves new pressure-induced stoichiometry, such as NaCl3 and Na3Cl [20]. In situ structure determination of a high-pressure phase can be very challenging when the chemical composition is not known. In a petrological experiment, phase transitions are often associated with compositional changes under high P–T conditions. For example, in a high P–T experiment on a natural MORB composition, a four-phase assemblage of the MgSiO3-rich pPv phase, α-PbO2-type SiO2, Ca-perovskite, and CaFe2O4-type Al-phase was identified by a combination of in situ powder XRD and ex situ transmission electron microscopy (TEM) under the P–T conditions of the deep lower mantle, in which the pPv phase has a high Na2O content and a high ratio of Fe3+/total Fe [21]. Solving the complex structures of the pPv phase under realistic deep lower mantle conditions is beyond the capabilities of existing powder XRD methods. Furthermore, a minor phase will be overshadowed by the diffraction peaks of coexisting phases in a powder XRD pattern of a multiphase assemblage, making phase identification of a minor phase extremely difficult using the powder XRD technique.
In summary, conventional single-crystal or powder diffraction techniques are inadequate for studying multiphase systems under high P–T conditions. New methods are required in order to explore phase changes and their detailed structures occurring in the deep lower mantle.
3. In situ multigrain synchrotron XRD
Synchrotron radiation X-rays have been regarded as an ideal probe for in situ studies of materials under high P–T conditions in a laser-heated DAC [22–24]. Heat treatment often promotes crystal growth, and spotty powder XRD patterns of mantle phases are obtained under high P–T conditions. Fig. 1 shows a representative spotty powder XRD pattern of (Mg,Fe)SiO3 pPv [25]. Such a spotty pattern is a combined result of the small X-ray beam size (∼6 × 8 μm2 full width at half maximum) and crystal growth upon heating at about 2400 K. The recent development of high-pressure beamlines has enabled reduction of the X-ray beam to the current 2–3 μm [22], which can help to reduce the level of overlapping spots in powder XRD patterns.
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Fig. 1 A representative spotty powder XRD pattern of (Mg,Fe)SiO3 pPv. The diffraction pattern was collected at a fixed ω angle at 120 GPa after temperature quenching from 2400 K, showing the spottiness of the XRD pattern. Ne: neon. Reproduced from Ref. [25] with permission of PNAS, © 2013. |
The recent achievement of multigrain XRD in high-pressure research has made it possible to index hundreds of individual crystallite grains simultaneously through the determination of crystallographic orientations for these individual grains [25,26]. Once indexation is achieved, a multiphase assemblage can then be treated as an aggregate of thousands of individual single crystals. An accurate and efficient indexing algorithm is required to process such datasets. We have found that GrainSpotter [27], which is part of the FABLE package [28], is an efficient algorithm that can be readily applied to a rotation-scan dataset for indexing grains in an assemblage contained in a DAC [25,29,30]. In some cases, experienced crystallographers can index a few grains manually in a high-pressure rotation dataset and solve their crystal structures [6,31]. However, only by applying the multigrain XRD method to search and index tens to hundreds of grains for each individual phase simultaneously, it is possible to systematically study crystal structures of each individual phase including a minor phase.
Fig. 2 shows the setup for high-pressure multigrain XRD data collection. Similar to the “rotation method” used in conventional single-crystal crystallography, diffraction patterns in step-scans are collected on a rotation stage up to the maximum angular access allowed by the DAC design. We have achieved a good balance between an angular access of 50°–60° for X-rays and the maintenance of stable high pressures up to the core-mantle boundary (CMB) at 136 GPa. We used angular steps as small as 0.2° to improve the signal-to-noise ratio in XRD patterns. We used an exposure duration ranging from 1 to 10 s per frame in our experiments, and tested the exposure before each collection until the strongest diffraction spots were near intensity saturation. Software packages, including CrysAlis [32], XDS [33], and GSE_ADA/RSV [34], were used to calculate the intensities of the reflections in a high-pressure dataset. The structure solution and refinement steps were performed by conventional single-crystal programs, such as, the SHELX package [35].
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Fig. 2 Experimental setup for high-pressure multigrain XRD data collection in a DAC. The sample is aligned to the rotation center, and a set of 2D XRD patterns are collected at small incremental steps, e.g., 0.2°, to the angular access of a DAC, typically 50°–60°, where ω, η, and θ represent the rotation, azimuth, and Bragg angles of each reflection, respectively. |
The synthesis of high-quality individual crystallites within the assemblage is the prerequisite for applying the high-pressure multigrain XRD technique. It has been found that a quasi-hydrostatic sample environment and stable heating significantly promote crystal growth under high P–T conditions in a laser-heated DAC [29]. In mantle petrological experiments, phase chemistry is frozen after temperature quenching; most structures are temperature-quenchable but often not pressure-quenchable, so a multigrain sample is often indexed in situ at high pressure and after temperature quenching.
Spotty diffraction patterns enable multigrain indexation, but such spottiness can result in unreliable intensity measurements in an integrated powder XRD pattern, leading to unreliable estimation of phase proportions in an assemblage. Spottiness implies crystal growth in the assemblage, in contrast to the smooth rings that are displayed in an XRD pattern of a fine-grained sample. In a sample synthesis, the high-temperature conditions required for crystal growth should facilitate thermodynamic equilibrium. On the other hand, the kinetics in phase transitions in a coarse-grained starting sample can be much slower than that occurring in a fine-grained sample under similar P–T conditions, because the higher surface area in a fine-grained sample can facilitate the nucleation for a phase transformation. Spotty XRD patterns are commonly observed in high P–T experiments conducted in a laser-heated DAC, and more attention should be paid to the kinetics issues in phase transitions occurring in coarse-grained samples.
4. Applications of multigrain XRD in high-pressure experiments
Multigrain XRD enables the phase identification and structural analysis of tiny individual grains in a multiphase assemblage contained in a DAC. Here, we summarize the applications of in situ multigrain synchrotron XRD for the phase identification of unknown phases and minor phases, the determination of high-pressure crystal structures, and the refinement of unit-cell parameters by merging reflections from multiple grains for each individual phase.
4.1. Phase identification in a multiphase assemblage
The unique capability of multigrain XRD has been demonstrated for the phase identification of an unknown phase in a mixture. When Fe-bearing bridgmanite (Bdg) decomposes to a nearly Fe-free MgSiO3 Bdg and a Fe-rich phase with a hexagonal structure (H-phase), only three peaks above 2.4 Å were specific to the H-phase, with many peaks of the Bdg phase overlapping with other peaks of the H-phase [29]. By searching for the orientation matrices of individual grains, 154 grains of the H-phase were indexed from one rotation XRD dataset. A grain is indexed when tens to hundreds of reflections are shown to satisfy the stringent geometrical angles determined by its particular orientation matrix. Each reflection has three variables (ω, η, and 2θ) to constrain the orientation matrix, where ω, η, and θ represent the rotation, azimuth, and Bragg angles (Fig. 2), respectively. Furthermore, 154 individual crystallites, each with its particular orientation matrix, redundantly confirmed the same lattice.
Powder XRD patterns only contain d-spacing information, and successful indexing of several obvious peaks for a new phase can sometimes lead to an incorrect unit cell. For example, the recently discovered hexagonal hydrous phase (HH-phase) in (Fe,Al)OOH was examined using the multigrain XRD, and its lattice parameters of a = 10.5803(6) Å and c = 2.5897(3) Å were obtained at 110 GPa [36]. However, if the weak peaks of (211) and (311) in the powder XRD pattern were not selected for indexing, a small orthorhombic lattice was obtained instead, with the lattice parameters of a = 4.03(2) Å, b = 3.699(5) Å, and c = 2.78(1) Å. However, this orthorhombic lattice did not pass the three-dimensional (3D) multigrain XRD test because most of the reflections predicted from a specific orientation matrix were not found in the measured rotation dataset. It was only when the hexagonal lattice was input for searching that 104 reflections were observed at the predicted angles for one of the crystallites and 27 individual crystallites were found, each with its particular orientation matrix, confirming the correct lattice of the HH-phase [36].
The unique power of multigrain XRD has been further demonstrated by its capability to identify a minor phase in an assemblage. Most peaks of a minor phase are overshadowed by the diffraction of major phases in a powder XRD pattern. In a previous experiment, seifertite (SiO2) was found to exist as a minor phase in a lower mantle assemblage; only peak (110) was visible without overlapping with the peaks from the major phase pPv [30], as shown in Fig. 3(a). Still, over 100 grains of seifertite were confirmed by applying multigrain XRD, although most grains showed weak diffraction due to their tiny grain sizes. The proportion of a minor phase to a major phase can be roughly estimated by the relative intensities in the integrated powder diffraction peaks (Fig. 3(a)). In a multigrain XRD dataset, sometimes only a small number of grains can be indexed for a minor phase. Nevertheless, a tiny grain from a minor phase can still be identified and treated as a single crystal, which is otherwise impossible using conventional XRD techniques (Fig. 3(b)). Thus, the development of high-pressure multigrain XRD enables these previously impossible tasks and drives forward laboratory exploration of the Earth’s entire interior.
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Fig. 3 XRD data of a phase assemblage including a dominant pPv phase and a minor phase of seifertite (SiO2). (a) An integrated powder XRD pattern showing the weak proportion of SiO2 at 129 GPa and after temperature quenching; (b) the multigrain XRD pattern including two Friedel pairs of {221} from one selected grain of seifertite. S: silica. Reproduced from Ref. [30] with permission of GeoScienceWorld, © 2016. |
4.2. Crystal structure determination
The (Mg,Fe)SiO3-pPv phase has been a focus of study since its discovery in 2004 as a dominant mineral in the bottom of the lower mantle [16–18]. Compositional variations in pPv can induce changes in its density and structure; thus, even subtle structural changes have significant implications for interpretations of the seismic and dynamic features observed near the CMB. For example, the pPv phase synthesized in a MORB composition was enriched in Na2O and had a high ferric content [21]. On the other hand, the pPv phase may have become very Fe-enriched at the CMB in contact with the liquid iron core [18]. Chemical composition in individual phases can be measured by ex situ TEM on a recovered sample; however, determination of structure changes induced by chemical impurities in the pPv phase is beyond the existing capabilities of powder XRD and theoretical methods. In addition, the pPv structure cannot be preserved after recovery under ambient conditions. Thus, in situ crystal structure determination is required. A high-quality multigrain sample of (Mg,Fe)SiO3-pPv was synthesized in a quasi-hydrostatic neon (Ne) environment (Fig. 1), and in situ crystal structure determination was performed on an individual grain of pPv selected by the multigrain method [25]. The structure of this Fe-depleted pPv shows a nearly identical structure to that of the MgSiO3 predicted by theory [16]. To the best of our knowledge, this is the first single-crystal structure determination of the pPv phase; it demonstrates the feasibility of in situ crystal structure determination of submicron crystallites above megabar pressures. This technique can then be applied to investigate the structure changes induced by compositional variations in high-pressure minerals in the future.
A DAC has a limited angular access; in a multigrain sample, several grains with different orientations can be scaled and merged to increase the coverage of a structure for the structure determination [30]. Clearly, reflection conditions combined from multiple grains can provide a more definite determination of the space group of a high-pressure phase. The intensities of the reflections from each selected grain were calculated using the XDS software, and compatibility between the data sets was checked by merging them using the XSCALE software in the XDS package [33]. For example, a total of 613 reflections were combined from the merged datasets of six grains to provide a redundancy of 6.6 and data completeness of 92% in the d-spacing range down to 0.72 Å, which allowed high-quality structure refinement for seifertite at 129 GPa [30]. Note that CrysAlis and other softwares may also be used for integration and scaling purpose. In situ crystal structure determination enabled by high-pressure multigrain synchrotron XRD opens up a new area of megabar crystallography by providing crystallographic solutions that are otherwise extremely difficult to achieve using conventional XRD techniques [25,30].
4.3. Determination of unit-cell parameters in a multiphase assemblage
The determination of unit-cell parameters for individual phases in an assemblage is a common task in mineralogical and petrological studies. To ensure a high-quality sample and reliable pressure determination, a pressure medium and/or thermal insulator, a pressure calibrator, and sometimes a laser absorber are loaded together with the sample into a DAC chamber of only tens of micrometers in diameter. During high P–T treatment or after temperature quenching, most peaks from these materials overlap in a powder XRD pattern. Only a few peaks can be selected for the unit-cell determination of the sample or the pressure scale, which leads to large uncertainties. Fortunately, multigrain XRD makes it possible to constrain the unit-cell parameters from many reflections belonging to an individual grain. The 3D orientation and geometrical relationships in the multigrain dataset allow the separation of reflections with close d-spacing. Using seifertite as an example, the uncertainties in the unit-cell parameters were gradually reduced by increasing the number of reflections merged from multiple grains in the refinement [30]. For this reason, uncertainties of the unit-cell parameters from the multigrain dataset are mainly defined by the resolution of the monochromator within 0.1%.
Conversely, precise unit-cell parameters can be used to evaluate subtle compositional effects on the mineral phases. Iron enters the crystal structures of all dominant lower mantle phases—silicate Bdg, pPv, and ferropericlase [37,38]. Multigrain XRD was applied to calculate the unit-cell parameters of the coexisting pPv and H-phase in (Mg,Fe)SiO3 at 119 GPa [39]. Because the uncertainties of the unit-cell parameters were reduced by increasing the number of reflections in the refinement (> 150 reflections), the refined unit-cell parameters were able to resolve small differences of the Fe content across the center area (20–30 μm) of a laser-heated area, while the sample pressure remained unchanged in the Ne quasi-hydrostatic environment. The unit-cell volumes of the pPv phase decreased by only 0.16% over a 10 μm distance from the heating center to a colder region, while the unit-cell volume of the H-phase decreased by 0.54% over the same distance, indicating that both phases were more Fe-enriched in the slightly hotter center [39]. In contrast to the Soret effect that drives heavy elements, such as Fe, from hot to cold regions, we conclude that the observed Fe distribution was caused by a temperature effect on the element partitioning. Thus, high-pressure multigrain XRD can be applied to calculate the unit-cell parameters of each individual phase precisely that allows 2D mapping of element partitioning or phase distributions.
5. Combination of in situ XRD and ex situ TEM techniques: An example
In high P–T petrological experiments, ex situ chemical analysis on recovered samples is required to connect compositional changes associated with structural transformations determined by in situ XRD. The focus ion beam (FIB) has been widely used to cut and lift out a thin cross-section in a laser-heated sample in a DAC [40]. The thin section can then be analyzed in a TEM. Ex situ TEM analysis combining electron diffraction and energy dispersive spectrometer (EDS) chemical analysis can be used to verify the phases under ambient conditions. The consistency between in situ multigrain XRD and ex situ TEM analysis should be carefully checked. To ensure consistency, we always prepared a TEM specimen from the heating center where in situ XRD data were measured under high P–T. Meanwhile, 2D XRD scans were performed to record the phase distribution under high P–T as well as after recovery to ambient conditions. Note that most high-pressure structures are unquenchable to ambient conditions, and the recovered sample can sometimes be contaminated in the sample preparation for a TEM thin section.
Here, we provide an example to demonstrate the identification of hydrous phases in a multiphase assemblage through the combination of in situ synchrotron XRD and ex situ TEM. The identification of hydrous phases in realistic lower mantle compositions is essential in order to understand the deep-water storage. We used a hydrous gel as our starting material with a composition of 30 mol% Al2O3–10 mol% Fe2O3–60 mol% MgSiO3 containing about 7 wt% H2O. As shown in Fig. 4, the XRD pattern contains a dominant pPv phase and a hydrous δ-phase, with only one weak peak indicating the presence of the cubic pyrite-type phase (py-phase). After multigrain indexing, we unambiguously confirmed the py-phase by sorting out 42 grains with 13–18 reflections consistent with the Pa-3 space group. Fig. 4(b) shows a composition-mapping image of a thin cross-section from the recovered sample prepared by FIB, showing several grains belonging to a very Fe-rich phase. EDS analysis verified only the elements Fe and oxygen (O) in the grains, while hydrogen (H) is undetectable if present. The grains range from 50 to 200 nm in size. From the 2D element mapping, the volume proportion of the py-phase is estimated to be less than 3 vol% in the assemblage. The chemical composition of these Fe-rich grains and their volume proportion in the assemblage are consistent with the in situ XRD observation of the py-phase under the high P–T conditions.
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In this experiment, we used a higher Al2O3 content than realistic compositions in order to enhance the diffraction peaks of the δ-phase in the XRD patterns. In general, volatile-bearing phases exist as minor phases in a mantle assemblage. Regardless, this example demonstrated that high-pressure multigrain XRD is capable of identifying individual tiny grains of a minor hydrous phase with less than 3 vol% in an assemblage through a combination of in situ phase identification and ex situ chemical analysis.
6. Conclusions
This paper provides an overview of the high-pressure multigrain XRD technique, along with examples of its successful applications in studying multiphase systems under the P–T conditions of Earth’s deep lower mantle. The crystal size in a multiphase assemblage can be as small as about 100 nm when the sample is synthesized under megabar pressures, making it infeasible to recover individual grains; thus, in situ characterization is needed. Meanwhile, peak overlapping renders the powder XRD method inadequate for investigating unknown phases and minor phases.
In situ multigrain XRD relies on an intense synchrotron X-ray beam, DAC rotation, and a fast indexing algorithm to identify tens to hundreds of crystallites belonging to each individual phase in a multiphase assemblage; in this way, it enables robust phase identification and structure determination in a multiphase assemblage. Examples were presented to illustrate the unique capabilities of the high-pressure multigrain XRD technique, including detecting the breakdown of iron-bearing Bdg into an iron-rich H-phase and Fe-free Bdg, identifying the HH-phase (Fe,Al)OOH, determining the crystal structures of (Mg,Fe)SiO3-pPv and seifertite (SiO2) under megabar pressures, measuring the unit-cell parameters of seifertite to a precision level of 0.1%, and examining subtle variations of Fe content in the coexisting pPv and H-phase over a temperature gradient. In some cases, the in situ high-pressure multigrain XRD technique can be combined with ex situ TEM analysis in order to connect structural transformation with compositional changes, which was demonstrated by the discovery of the py-phase FeOOH coexisting with the pPv phase in a model composition of subducted slabs under high P–T conditions. Through these effective illustrations, we have explained key challenges in studying multiphase systems and showed the important role of high-pressure multigrain XRD in exploring the Earth’s deep interior.