Behaviour of Fe₄O₅–Mg₂Fe₂O₅ solid solutions and their relation to coexisting Mg–Fe silicates and oxide phases

Abstract

Experiments at high pressures and temperatures were carried out (1) to investigate the crystal-chemical behaviour of Fe₄O₅–Mg₂Fe₂O₅ solid solutions and (2) to explore the phase relations involving (Mg,Fe)₂Fe₂O₅ (denoted as O₅-phase) and Mg–Fe silicates. Multi-anvil experiments were performed at 11–20 GPa and 1100–1600 °C using different starting compositions including two that were Si-bearing. In Si-free experiments the O₅-phase coexists with Fe₂O₃, hp-(Mg,Fe)Fe₂O₄, (Mg,Fe)₃Fe₄O₉ or an unquenchable phase of different stoichiometry. Si-bearing experiments yielded phase assemblages consisting of the O₅-phase together with olivine, wadsleyite or ringwoodite, majoritic garnet or Fe³⁺-bearing phase B. However, (Mg,Fe)₂Fe₂O₅ does not incorporate Si. Electron microprobe analyses revealed that phase B incorporates significant amounts of Fe²⁺ and Fe³⁺ (at least ~ 1.0 cations Fe per formula unit). Fe-L_2,3-edge energy-loss near-edge structure spectra confirm the presence of ferric iron [Fe³⁺/Fe_tot = ~ 0.41(4)] and indicate substitution according to the following charge-balanced exchange: [4]Si⁴⁺ + [6]Mg²⁺ = 2Fe³⁺. The ability to accommodate Fe²⁺ and Fe³⁺ makes this potential “water-storing” mineral interesting since such substitutions should enlarge its stability field. The thermodynamic properties of Mg₂Fe₂O₅ have been refined, yielding H°_1bar,298 = − 1981.5 kJ mol^− 1. Solid solution is complete across the Fe₄O₅–Mg₂Fe₂O₅ binary. Molar volume decreases essentially linearly with increasing Mg content, consistent with ideal mixing behaviour. The partitioning of Mg and Fe²⁺ with silicates indicates that (Mg,Fe)₂Fe₂O₅ has a strong preference for Fe²⁺. Modelling of partitioning with olivine is consistent with the O₅-phase exhibiting ideal mixing behaviour. Mg–Fe²⁺ partitioning between (Mg,Fe)₂Fe₂O₅ and ringwoodite or wadsleyite is influenced by the presence of Fe³⁺ and OH incorporation in the silicate phases.

Introduction

Over the past few years, post-spinel phases have attracted more and more attention due to the discovery of several high-pressure (hp) oxide phases with stoichiometries other than M₃O₄. Phases with M₄O₅, M₅O₆ and M₇O₉ stoichiometry have now been added to the list of potential post-spinel phases that might be present in the Earth’s deep upper mantle and transition zone (e.g., Enomoto et al. 2009; Lavina et al. 2011; Lavina and Meng 2015; Woodland et al. 2012, 2013, 2015; Guignard and Crichton 2014; Ishii et al. 2014, 2015; Myhill et al. 2016; Sinmyo et al. 2016; Uenver-Thiele et al. 2017a, b). Phases with an M₄O₅ stoichiometry (O₅-phase) were found in a number of simple chemical systems, including those containing Cr, Al, Fe³⁺ as trivalent cations, and Mg and Fe²⁺ as divalent cations (e.g., Enomoto et al. 2009; Woodland et al. 2012, 2013; Ishii et al. 2014, 2015; Uenver-Thiele et al. 2017a, b). Often the O₅-phase occurs in an M₄O₅ + M₂O₃ post-spinel assemblage, as in the case of Fe₄O₅ + Fe₂O₃, FeMgFe₂O₅ + Fe₂O₃, Fe₂Cr₂O₅ + Cr₂O₃ or Fe₂Cr₂O₅ + Cr₂O₃ becoming stable at the expense of the spinel-structured phase at conditions of the deep upper mantle (Woodland et al. 2012; Ishii et al. 2014, 2015; Uenver-Thiele et al. 2017a, b).

Solid solutions involving the Fe₄O₅ component are of particular interest because the ability to contain both Fe²⁺ and Fe³⁺ makes their stability sensitive to redox processes. The incorporation of Mg into Fe₄O₅ was first reported by Woodland et al. (2013); Boffa Ballaran et al. (2015) subsequently demonstrated that Mg can completely substitute for Fe²⁺, producing an Mg endmember, Mg₂Fe₂O₅. Both endmember compositions share the same space group Cmcm with a CaFe₃O₅-type structure (Lavina et al. 2011; Boffa Ballaran et al. 2015), suggesting that the entire Mg–Fe²⁺ solid solution series is stable at high pressures and temperatures. Myhill et al. (2016) questioned whether Fe₄O₅ could occur in a peridotitic upper mantle or transition zone environment since their preliminary calculations implied that its stability required an oxygen fugacity that exceeded the expected mantle range (e.g., Frost and McCammon 2008). However, such a conclusion was based upon incomplete knowledge of potential phase assemblages, particularly those with Mg-rich silicates. In addition, even if such a situation were generally true, this does not rule out the stability of an O₅-phase in localized environments, such as those responsible for diamond formation where olivine and pyroxene do not coexist. In fact the microtexture of magnetite in an inclusion in diamond described by Jacob et al. (2016) led Uenver-Thiele et al. (2017b) to conclude that this magnetite was originally Fe₄O₅ at the conditions of diamond formation.

The recent investigations of the phase relations for MgFe₂O₄ and Mg_0.5Fe_0.5Fe₂O₄ by Uenver-Thiele et al. (2017a, b) also place important constraints on the stability of the Mg₂Fe₂O₅ endmember and the MgFeFe₂O₅ composition. However, knowledge of the properties of (Mg,Fe)₂Fe₂O₅ solid solutions and the phases with which they can coexist under mantle-relevant conditions remains incomplete. Thus, the purpose of this study is twofold: (1) to address the crystal-chemical behaviour of the Fe₄O₅–Mg₂Fe₂O₅ join and (2) to further investigate the phase assemblages in which an O₅-phase is stable, including those involving high-pressure Mg–Fe silicates.

Methods

High-pressure experiments

Five different starting compositions were employed in this study (Tables 1, 2). A starting mixture of MgO + MgFe₂O₄ in a 1:1 molar ratio as well as pre-synthesized MgFe₂O₄ and Mg_0.5Fe_0.5Fe₂O₄ were employed to investigate the crystal-chemical behaviour of solid solutions along the Fe₄O₅–Mg₂Fe₂O₅ join (Table 1). The synthesis of magnesioferrite and Mg_0.5Fe_0.5Fe₂O₄ is reported in Uenver-Thiele et al. (2017a, b), respectively. A mixture of 70 mol% MgFe₂O₄ and 30 mol% Mg₂SiO₄ was used to investigate equilibria involving Mg₂Fe₂O₅ and high-pressure Si-bearing phases (Table 2). Another starting mixture of 75 mol% MgSiO₃ and 25 mol% Fe₂O₃ (Table 2), giving a composition of Mg₃Fe₂Si₃O₁₂, was produced by combining sintered hematite with enstatite glass. The glass was produced by melting a stoichiometric mixture of MgO and SiO₂ in a Pt-crucible at 1660 °C using a high-temperature furnace for 1 h. It was quenched in ice water and re-grounded for a second cycle of melting at 1650 °C for a further 20 min. This procedure yielded a clear glass with no microscopic quench crystals.

Table 1 Conditions and run products of Si-free experiments conducted with Mg–Fe oxides

Table 2 Experimental conditions and run products for the MgO–FeO–Fe₂O₃–SiO₂ system

Experiments up to 13 GPa were performed with a 800-t Walker-type multi-anvil press at the University of Frankfurt. Pressure calibration and pressure cell design are given in Brey et al. (2008). Temperature was monitored by W₅Re₉₅–W₂₆Re₇₄ thermocouples with the electromotive force uncorrected for pressure. Capsule designs follow those described in Uenver-Thiele et al. (2017a). For experiments at pressures ≥ 14 GPa, 5000-t and 1000-t multi-anvil presses were employed at the Bayerisches Geoinstitut, Bayreuth. The experimental setup and pressure calibration are described in Keppler and Frost (2005). High-pressure assemblies with a LaCrO₃ heater were employed with the temperature monitored by W₃Re₉₇–W₂₅Re₇₅ thermocouples with the electromotive force uncorrected for pressure. Uncertainties in pressure and temperature are ± 0.5 GPa and ± 30–50 °C, respectively (Keppler and Frost 2005). Samples were packed into Pt-foil capsules, except for experiment Z1507o that employed Ag-foil as capsule material. Several experiments were conducted with small amounts of PtO₂ to avoid reduction of ferric iron. In others, PtO₂ was omitted since we intended to produce mixed-valence Fe³⁺–Fe²⁺-bearing solid solutions. The high oxygen fugacity of the experiments as imposed by the high Fe³⁺ contents of the starting materials meant that Fe-loss to the Pt capsule was negligible. The experiments were first cold pressurized, followed by heating to the desired temperature. They were terminated by turning off the power to the heater, but maintaining the pressure. Decompression was then immediately initiated. The resulting run products, as well as experimental run conditions are reported in Tables 1 and 2.

Analytical techniques

Recovered samples were characterized primarily by electron microprobe (EPMA) and powder X-ray diffraction, with selected samples also investigated by transmission electron microscopy (TEM) and micro-Raman spectrometry. Fragments of sample material were embedded in epoxy and polished for EPMA analysis. Measurements were performed at the University of Frankfurt using a five-spectrometer JEOL JXA-8900 superprobe operating in the wavelength-dispersive mode (at 15 kV, 20 nA, 1 µm spot size). Pure MgO, Fe₂O₃, Pt and CaSiO₃ were used as primary standards. Integration times for Si and Mg were 40 s on the peak and background, while for Fe and Pt an integration time of 40 s on the peak and 20 s on the background was employed. For experiment Z1507o, forsterite (Mg), fayalite (Fe) and wollastonite (Si) were employed as standards. Integration times for Mg, Fe and Si were the same as described above. A CITZAF algorithm was employed for matrix correction (Armstrong 1993).

Powder X-ray diffraction patterns were obtained on a STOE Stadi P diffractometer operating at 45 kV and 35 mA with monochromatic Mo Kα (λ = 0.70926 Å) radiation, equipped with a linear PSD or a Mythen detector at the University of Frankfurt. An internal Si standard was added to the sample material and mounted in a 0.5-mm-diameter capillary. Diffraction patterns were collected in transmission mode between 1°–100° 2θ. Several samples were analysed using a Philips X´Pert PRO diffractometer at the Bayerisches Geoinstitut. Co Kα1 (λ = 1.78897 Å) radiation, monochromated with a symmetrically cut curved Johansson Ge (111) crystal and a Philips X’celerator detector were employed. A small amount of Si powder was added to the sample as an internal standard and mounted on a silicon wafer. Data collection was performed in reflection mode at 40 kV and 40 mA and between 10° and 120° 2θ. The diffraction patterns were analysed with the General Structure Analysis System (GSAS, Larson and van Dreele 1994) software package with the EXPGUI interface of Toby (2001) for phase identification and determination of the unit-cell parameters for the (Mg,Fe)₂Fe₂O₅ solid solutions.

For selected samples, further phase identification was performed using a Renishaw micro-Raman spectrometer (RM-1000) equipped with a 633 nm HeNe laser at the University of Frankfurt. The 519 cm^− 1 peak of a Si wafer was used for calibration (Temple and Hathaway 1973). Unpolarized confocal Raman spectra were collected with a 50x microscope objective and a laser power of ~ 10 mW. The wavenumber accuracy was about ± 2 cm^− 1. The focused laser spot on the sample was approximately ~ 2 µm in diameter.

Transmission electron microscopic characterizations were carried out using a 200 kV Philips CM-20FEG TEM equipped with an energy-dispersive X-ray spectrometer (NO-RAN Ge detector) and a parallel electron energy-loss spectrometer (Gatan 666 PEELS). A small chip from sample Z1586u used in the X-ray diffraction measurement was crushed under ethanol and the dispersion was placed on a Lacey carbon film on Cu-grid. For textural as well as crystallographic investigations, conventional TEM techniques such as bright field (BF) and dark field (DF) imaging, as well as selected area electron diffraction (SAED) were employed. Chemical compositions were cross-checked by energy-dispersive X-ray (EDX) analyses. The Fe-L_2,3-edge electron energy-loss near-edge structure (ELNES) of the selected sample was also examined using spectra collected in diffraction mode with a collection semi-angle of β = 2.7 mrad, an energy-dispersion of 0.1 eV per channel and 10–20 s integration time per read-out. The energy resolution is 0.8–0.9 eV, measured as the full width of the zero-loss peak at half-maximum. Quantification of the Fe-L_2,3 ELNES followed the procedure described by van Aken et al. (1998) and van Aken and Liebscher (2002), using an empirically calibrated universal curve.

Results and discussion

Phase relations of (Fe,Mg)₂Fe₂O₅ solid solutions

In order to investigate the crystal-chemical behaviour of Fe₄O₅–Mg₂Fe₂O₅ solid solutions, six additional experiments were performed in the pressure–temperature range of 12–20 GPa and 1300–1600 °C to augment the data of Woodland et al. (2013) and Uenver-Thiele et al. (2017a, b). The conditions and run products from the experiments are summarized in Table 1, along with those experiments from Uenver-Thiele et al. (2017a, b) for which unit-cell parameters and the molar volumes for the O₅-phase are presented here for the first time. Representative electron microprobe analyses of each phase synthesized in the six new experiments are listed in Table 3.

Table 3 Chemical analyses of run products of Si-free experiments obtained by EPMA

In most experiments, the O₅-phase occurs with hematite, except for two cases where an “O₅” bulk composition was used (Table 1; samples Z1584u and Z1234u). Some samples contain a coexisting unquenchable phase (UQ) that exhibits a mottled texture in backscattered electron (BSE) images (Fig. 1a–c), indicating breakdown during decompression. However, the UQ-phase is marked by straight grain boundaries of larger crystals with 120° triple junctions implying that equilibrium was attained during the experiment (see Fig. 1a-c). The bulk composition of the UQ-phase was determined from 4 µm diameter spot analyses, revealing homogenous compositions with only minor variations for each sample (Table 3). Different stoichiometries were obtained (Tables 1, 3) depending on the experimental run conditions. For example, in experiment M519 (Mg,Fe)₂Fe₂O₅ and hematite occur up to 30 µm in size and coexist together with an interstitial UQ-phase (Table 1; Fig. 1b, c). However, the mottled texture indicative of decomposition is not complete and relict domains of the original phase are apparent in BSE images (e.g., Fig. 1c). Microprobe analyses were performed in both parts of these grains; a “normal” spot size (1 µm) for the un-mottled part and a larger 4 µm spot for the mottled region (Fig. 1c). The compositions of these two regions are in perfect agreement with each other, yielding 38.97(25) wt% MgO and 52.88(44) FeO for the relict parts and 39.35(4) wt% MgO and 52.85(23) wt% FeO, for the mottled parts, respectively (Table 3). Reflections in the X-ray powder diffraction pattern also confirm the presence of a phase in addition to (Mg,Fe)₂Fe₂O₅, hematite, (Mg,Fe)O and magnesioferrite, the latter two of which are decomposition products (see Uenver-Thiele et al. 2017a). Extra reflections, corresponding to d-values of about 2.967 and 1.713 Å are observed and do not match any of the known Mg–Fe-oxide phases. It is likely that these reflections belong to the relict phase identified in the BSE images. Unfortunately, further analysis of the crystal structure of this phase is currently hampered by its apparent instability at ambient pressure and by overlapping peaks in the powder diffraction pattern. Assessing the stoichiometry of this relict phase is also ambiguous since no PtO₂ was added to the experiment and the composition of the coexisting O₅-phase of Mg_1.53(1)Fe_0.47(1)Fe₂O₅ indicates that some reduction of ferric to ferrous iron occurred during the experiment. Thus, a number of stoichiometries, each with different Fe³⁺/Fe²⁺ would be consistent with the observed bulk composition from EPMA. However, combining the robust measure of Mg/Fe_tot for this phase along with possible phase field topologies with a coexisting O₅-phase and hematite place some constraints on its stoichiometry (Fig. 2). For example, an O₉-stoichiometry with composition Mg_4.55Fe_1.45Fe₂O₉ would be essentially collinear with the O₅-phase and hematite in the system MgO–FeO–FeO_1.5, indicating that the three phases cannot be in equilibrium (Fig. 2). In addition, any phases containing more Fe²⁺ than the A ₆ B ₂ O ₉ stoichiometry should not be in equilibrium with hematite. This leaves Mg_2.85Fe_0.15Fe₂O₆, Mg_3.42Fe_0.58Fe₂O₇ or Mg_3.99Fe_1.01Fe₂O₈ as potential compositions (Fig. 2), all stoichiometries that have already been suggested to have narrow stability fields in the Fe²⁺-free MgO–FeO_1.5 binary system at pressures of 10–13 GPa and temperatures ≥ 1200 °C (Uenver-Thiele et al. 2017a). On the other hand, such an UQ-phase was not found in experiments conducted with a (Mg_0.5Fe_0.5)Fe₂O₅ bulk composition (Uenver-Thiele et al. 2017b). Thus, the phase assemblage observed in sample M519 is important in that it indicates the possibility that a variety of Fe³⁺-bearing oxide stoichiometries may be stable at high pressures and temperatures, even if Fe²⁺ apparently acts to destabilize some of these structures (like observed for wadsleyite; e.g., Fig. 3).

Fig. 1

Back scatter electron (BSE) images of the run products from experiment Z1584u (a), exhibiting well developed crystals of (Mg,Fe)₂Fe₂O₅ together with an unquenchable phase (UQ). Here, (Mg,Fe)₂Fe₂O₅ is the most abundant phase exhibiting straight grain boundaries and triple junctions between individual grains. Hematite is present as small interstitial grains or has the same dimension as (Mg,Fe)₂Fe₂O₅. The run products produced in experiment M519, b, c indicate the assemblage of (Mg,Fe)₂Fe₂O₅ + UQ phase + hematite. The unquenchable phase also exhibits straight grain boundaries and triple junctions that are preserved from before the quench (b). However, mottled textures in the inner part of the grains point to partial decomposition during decompression of the experiment (c). The four different circles indicated in c show the position and the spot size used for microprobe analyses within mottled and relict domains of the unquenchable phase

Fig. 2

Ternary diagram for the MgO–FeO–FeO_1.5 system illustrating the possible phase relations for sample M519. Without explicitly knowing the nature of the unquenchable phase (UQ), a number of stoichiometries with different Fe³⁺/Fe²⁺, but constant Mg/Fe_tot are consistent with the microprobe analyses. However, the topologies of the coexisting phase fields place some constraint on the stoichiometry of the UQ phase (see text)

Fig. 3

Experimental data plotted along with calculated stability fields for olivine (ol), wadsleyite (wds) and ringwoodite (rgw) (after Katsura and Ito 1989) in the Mg₂SiO₄–Fe₂SiO₄ system

Mg–Fe silicates coexisting with (Mg,Fe)₂Fe₂O₅

Five experiments were performed to further explore phase relations involving the O₅-phase and Mg–Fe silicates at high pressures and temperatures (Table 2). The combination of BSE imaging and EPMA analyses reveals at least three phases coexisting in these experiments (Tables 2, 4). The most abundant phase is (Mg,Fe)₂Fe₂O₅, which does not incorporate Si in its structure, in agreement with previous observations (e.g., Woodland et al. 2013; Bindi et al. 2016). In the X-ray powder diffraction patterns, (Mg,Fe)₂Fe₂O₅ could be indexed using the crystal structure model reported by Boffa Ballaran et al. (2015). Raman spectra of the O₅-phase exhibit two characteristic peaks at ~ 315 and ~ 673 cm^− 1, along with several other overlapping peaks lying between 450 and 550 cm^− 1 (Electronic Supplementary Material S.1).

Table 4 Chemical analyses of run products of Si-bearing experiments obtained by EPMA

As anticipated, an additional phase having (Mg,Fe)₂SiO₄ stoichiometry was identified by EPMA (see Table 4) and characterized by means of X-ray diffraction and/or Raman spectroscopy. Considering that many diffraction peaks of the three (Mg,Fe)₂SiO₄ polymorphs: olivine, wadsleyite and ringwoodite overlap with those of the O₅-phase, Raman spectra often proved to be particularly useful in phase identification by comparing them with spectra from McMillan and Akaogi (1987) and Guyot et al. (1986).

The occurrence of olivine, wadsleyite or ringwoodite is consistent with the phase relations of Mg₂SiO₄–Fe₂SiO₄ solid solutions at high pressure and temperature (Katsura and Ito 1989, see Fig. 3). One exception is the presence of wadsleyite in experiment Z1531o conducted at 1350 °C and 20 GPa (Fig. 3). Considering the study of Mrosko et al. (2015), the occurrence of wadsleyite may be due to the incorporation of Fe³⁺ and OH. They reported that this combination significantly expands the wadsleyite stability field to higher pressures and higher Fe²⁺ contents at the expense of ringwoodite. In fact, Raman spectra of wadsleyite from this experiment reveal small peaks at ~ 3340 and 3580 cm^− 1, which can be attributed to OH-stretching modes (Kleppe et al. 2005). These two bands were also observed in sample Z1532u, although their intensities were significantly lower. The origin of small amounts of H₂O in Z1531o and Z1532u could lie with the fact that small amounts of PtO₂ were added to both experiments. It is known that the very fine-grained PtO₂ powder can contain adsorbed atmospheric CO₂ as indicated by the presence of traces of magnesite in such experiments (Table 2; Uenver-Thiele et al. 2017a), and it is conceivable that small amounts of H₂O could also have been adsorbed on the PtO₂ as well.

Our new experiments are richer in Mg than those previously reported by Woodland et al. (2013) and demonstrate that (Mg,Fe)₂Fe₂O₅ can coexist with silicates having mantle-relevant compositions (i.e., with X_Mg = ~ 0.9). In two experiments (Z1531o, Z1532u), traces of magnesite were detected in the X-ray powder diffraction patterns. As suggested by Uenver-Thiele et al. (2017a), its presence is likely due to CO₂ adsorbed onto the PtO₂ powder (see above). The coexistence of (Mg,Fe)₂Fe₂O₅ solid solutions with several silicate phases (olivine, wadsleyite, ringwoodite, clinopyroxene) or oxides (spinel and spinelloid V) was previously reported by Woodland et al. (2013) for rather Fe-rich bulk compositions. From the results of experiment Z1507o (Table 3), we can now add majoritic garnet to the list of phases with which O₅-phase can coexist. Microprobe analyses (Table 4) indicate a composition of 82 mol% (Mg,Fe)₄Si₄O₁₂ and 18 mol% (Mg,Fe)₃Fe₂Si₃O₁₂. In the absence of other constraints, the actual apportioning of Fe²⁺ between the two garnet components is currently not possible.

Compared to other samples that have a homogenous distribution of phases, run products from Z1587o and Z1586u are marked by distinctly different textures (Fig. 4a, b). The O₅-phase forms large crystals and is most abundant, but there are two other phases with a lower mean atomic number $\stackrel{-}{Z}$ illustrated by a lower contrast in BSE images (dark and middle grey). Olivine/wadsleyite (Z1586u) and ringwoodite (Z1587o) (dark grey in Fig. 4a, dark-middle grey in Fig. 4b) are almost entirely enclosed by another phase with a slightly different grey scale that contains distinctly less SiO₂ than the (Mg,Fe)₂SiO₄ polymorphs (Table 3). Investigation of sample Z1586u by TEM revealed nicely developed crystals (Fig. 5b) and selected area electron diffraction (SAED) patterns (Fig. 5a, c, d) could be indexed on the basis of a monoclinic cell (space group P2 ₁ /c) with lattice parameters a = 10.6249(17), b = 14.1332(28), c = 10.1015(18) Å and β = 104.08(1)°. This is consistent with phase B reported by Finger et al. (1989), which is surprising since no water was added to the experiment.

Fig. 4

BSE images of run products of experiments: a Z1586u and b Z1587o. In both cases, olivine or ringwoodite are enclosed by Fe³⁺-bearing phase B. The sample consists of ~ 50% large crystals of (Mg,Fe)₂Fe₂O₅. In sample Z1586u, Fe³⁺-bearing phase B is much more abundant than olivine and is not only associated with olivine. In this case, the Fe content of phase B is ~ five times higher than in olivine. In sample Z1587o, phase B is as abundant as ringwoodite. However, both phases differ in their FeO content by only ~ 2 wt%, which explains the only slightly different contrast in the BSE image

Fig. 5

a Selected area electron diffraction (SAED) pattern and b high-resolution TEM lattice image along the [010] zone axis of Fe³⁺-bearing phase B from experiment Z1586u. Some stacking faults parallel to the (100) plane are visible. c SAED patterns along the [001] and d the [100] zone axes in the phase B structure, respectively

Raman spectra with peaks characteristic for phase B (McMillan et al. 1991; Liu et al. 1998) were subsequently obtained from samples Z1586u and Z1587o (Fig. 6). A number of the peaks are quite broad, which can be explained by the rather high Fe content of our samples (Table 4). Small peaks at ~ 3360 and 3412 cm^− 1 confirm the presence of OH groups in the structure.

Fig. 6

Ambient Raman spectrum of Fe³⁺-bearing phase B in sample Z1586u, with some structural OH revealed by small peaks at ~ 3360 and 3412 cm^− 1

EPMA measurements for the Fe-bearing phase B found in sample Z1586u gave a composition of Mg_11.17(4)Fe_1.04(6)Si_3.79(3)O₂₁H₂, which, from the deviation from 4 Si per formula unit, implies ~ 0.43(5) Fe³⁺ cations have entered the structure via the charge-balanced substitution: ^[4]Si⁴⁺ + ^[6]Mg²⁺ = 2Fe³⁺. Fe-L_2,3-edge energy-loss near-egde structure (ELNES) spectra based on EELS measurements were taken from this phase (sample Z1586u) to evaluate the Fe³⁺/Fe_tot ratio more quantitatively. The mixed valance state of iron was confirmed by the splitting in the white-lines, showing two separate Fe-L_2,3 maxima for ferrous and ferric iron (Fig. 7). The Fe³⁺/Fe_tot ratios determined from the spectra vary from 0.35(4) to 0.46(4) in agreement with the stoichiometric calculation from EPMA analyses. To our knowledge, this is the first report of phase B incorporating significant amounts of Fe³⁺ and it is found to coexist with (Mg,Fe)₂Fe₂O₅ as well as with either olivine or ringwoodite.

Fig. 7

Representative Fe-L_2,3-edge ELNES spectrum taken from phase B (sample Z1586u). The spectrum has been gain-normalized, background-subtracted and deconvoluted using the corresponding low-loss spectrum (not shown). The black dotted lines represent the position of the Fe-L_2,3 white-line maxima for Fe²⁺ (at ~ 707.8 eV, fixed for the energy calibration) and Fe³⁺ (~ 710 eV), respectively. The grey dashed line below the spectrum represents the double arctan background function. The Fe³⁺/ƩFe quantification was made following the method of van Aken et al. (1998)

Crystal-chemical behaviour of (Mg,Fe)₂Fe₂O₅ solid solutions

The range in composition obtained for Fe₄O₅–Mg₂Fe₂O₅ solid solutions in this study, combined with literature data indicates that a complete solid solution exists across the binary join (see Table 5). Molar volumes decrease linearly with increasing Mg content (Fig. 8a). Application of symmetric or asymmetric solution models led to no statistical improvement in the fit to the data and the uncertainties in the interaction parameters were roughly equal to the derived values. Thus, we conclude that with the present uncertainties, the molar volumes vary essentially ideally across the binary. Extrapolation to the Mg₂Fe₂O₅ endmember composition yields a molar volume of 52.99(1) cm³ (Fig. 8a), which is in agreement with the values reported from the single-crystal refinements of Boffa Ballaran et al. (2015) and Siersch et al. (2017).

Table 5 Chemical composition, unit-cell parameters and molar volume of Fe₄O₅–Mg₂Fe₂O₅ solid solutions

Fig. 8

Variations in a molar volume and lattice parameters (b–d), as a function of X_Mg in the O₅-phase. Error bars represent uncertainties obtained from refinement of the powder diffraction patterns using GSAS (Toby et al. 2001). Most errors are the same size or smaller than the symbol

The change in molar volume along the solid solution is primarily due to a near linear decrease of ~ 0.08 Å in the b-parameter with increasing Mg content (Fig. 8c), consistent with the observations of Woodland et al. (2013). Moreover, our more extensive dataset clearly indicates additional, more subtle changes in both the a- and c-parameters with composition (Fig. 8b, d), which could not be resolved by Woodland et al. (2013). Single-crystal structural refinement of the Mg₂Fe₂O₅ endmember reveals that Mg occupies all three crystallographic sites to various degrees, with a preference over Fe³⁺ for the M3 site (Boffa Ballaran et al. 2015). It is very likely that the large Fe²⁺ atom exhibits a similar site preference as Mg. Therefore the small changes in the a-parameter, which is controlled by the height of the M3 triangular prism, may be mainly due to Fe²⁺–Mg substitution at the M3 site with little or no influence from Fe³⁺. Even though the c-parameter is by far the largest in the unit-cell, it undergoes only ~ 25% of the shortening across the join compared to the b-parameter (Fig. 8b, d). These systematics can be understood by considering the following two effects of Mg–Fe²⁺ substitution on the structure of the Fe₄O₅–Mg₂Fe₂O₅ solid solutions: (1) the M2–O1–M2 angle formed by the only corner-sharing bonds in the structure can change (i.e., rotation of M2 octahedra) to accommodate some of the geometric effects of substituting a smaller Mg cation for Fe²⁺, thereby compensating for some of the necessary shortening along the c-axis; (2) significant occupancy of M1 by Mg will have a strong influence on decreasing the M1–O2 bond distance, which principally leads to shortening of the b-parameter (Boffa Ballaran et al. 2015; Woodland et al. 2013). The similarity in unit-cell parameters for (Mg,Fe)₂Fe₂O₅ solid solutions synthesized at different temperatures (see Tables 1, 2) suggests that the observed order–disorder behaviour is more a crystal-chemical phenomenon than being thermally induced or related to the quench process of the experiments.

Thermodynamic properties of Mg₂Fe₂O₅

In their study of high-pressure Fe-oxides, including Fe₄O₅, Myhill et al. (2016) provided an estimate of the thermodynamic properties of the Mg₂Fe₂O₅ endmember primarily based on Mg–Fe²⁺ partitioning between (Mg,Fe)₂Fe₂O₅ and olivine solid solutions reported by Woodland et al. (2013). Experiment Z1461o, conducted at 1300 °C and 16 GPa, produced a three-phase assemblage of MgFe₂O₅ coexisting with Fe₂O₃ and MgO, indicating that it lies essentially on phase boundary defined by the equilibrium Mg₂Fe₂O₅ = 2 MgO + Fe₂O₃ (Table 1). This P–T point, along with further constraints on the position of this phase boundary as depicted in Fig. 3 of Uenver-Thiele et al. (2017a) allow us to refine the standard enthalpy (H°₂₉₈) of Mg₂Fe₂O₅ in combination with new data for the equation of state of this material from Siersch et al. (2017) and molar volume reported here. The thermodynamic properties of MgO and Fe₂O₃ were taken from the dataset of Holland and Powell (2011), as suggested by Myhill et al. (2016). The properties of Mg₂Fe₂O₅ are given in Table 6, along with their sources. The heat capacity was derived from the molar sum of the heat capacities of MgO and MgFe₂O₄, as compiled by Holland and Powell (2011). The study of Uenver-Thiele et al. (2017a) demonstrated that their data for these two phases (along with that of hematite) reproduce the experimentally determined position of the breakdown reaction MgFe₂O₄ = MgO + Fe₂O₃ reasonably well over a temperature range of ~ 400 °C. From our analysis, we obtain H°₂₉₈ = − 1981.5 kJ mol^− 1 for Mg₂Fe₂O₅. This result is ~ 5 kJ mol^− 1 less negative than that previously estimated by Myhill et al. (2016). The small amount of Mg present in the coexisting hematite [0.0618(9) Mg cations on a three-oxygen basis], as reported by Uenver-Thiele et al. (2017a) in experiment Z1461o translates to a X_Fe2O3 = 0.979. Assuming ideal mixing, this slight deviation from pure hematite contributes an uncertainty of only ~ 300 J at the conditions of the experiment.

Table 6 Thermodynamic data for Mg₂Fe₂O₅

Mg–Fe partitioning between (Mg,Fe)₂Fe₂O₅ and silicate phases

The partitioning of Mg and Fe²⁺ indicates that (Mg,Fe)₂Fe₂O₅ has a strong preference for Fe²⁺ compared to coexisting silicate phases (Fig. 9). This behaviour was also observed by Woodland et al. (2013), but we can now extend this to majoritic garnet and phase B. Defining ${K_{\text{D}}}={{X_{{{\text{F}}{{\text{e}}^{2+}}}}^{{{\text{silicate}}}} \times X_{{{\text{Mg}}}}^{{{{\text{O}}_5}}}} \mathord{\left/ {\vphantom {{X_{{{\text{F}}{{\text{e}}^{2+}}}}^{{{\text{silicate}}}} \times X_{{{\text{Mg}}}}^{{{{\text{O}}_5}}}} {X_{{{\text{Mg}}}}^{{{\text{silicate}}}} \times X_{{{\text{F}}{{\text{e}}^{2+}}}}^{{{{\text{O}}_5}}}}}} \right. \kern-0pt} {X_{{{\text{Mg}}}}^{{{\text{silicate}}}} \times X_{{{\text{F}}{{\text{e}}^{2+}}}}^{{{{\text{O}}_5}}}}}$, we obtain $K_{{\text{D}}}^{{{{{\text{grt}}} \mathord{\left/ {\vphantom {{{\text{grt}}} {{{\text{O}}_5}}}} \right. \kern-0pt} {{{\text{O}}_5}}}}}=\sim 0.09$ and $K_{{\text{D}}}^{{{{{\text{phB}}} \mathord{\left/ {\vphantom {{{\text{phB}}} {{{\text{O}}_5}}}} \right. \kern-0pt} {{{\text{O}}_5}}}}}=\sim 0.05$, respectively, where Fe²⁺ was calculated from stoichiometry (Table 7).

Fig. 9

Mg–Fe²⁺ partitioning between the (Fe,Mg)₂Fe₂O₅ and coexisting Si-bearing phases plotted as tie lines in terms of the molar Mg/(Mg + Fe²⁺) of each phase. Data from Woodland et al. (2013) are plotted as dashed tie lines for comparison

Table 7 X_Mg and X_Fe2+ as well as calculated partitioning coefficients [K_D = (X_Fe^silicate × X_Mg^O5)/(X_Mg^silicate × X_Fe^O5)] for silicate phases coexisting with the O₅-phase

For partitioning with the Mg–Fe-silicate polymorphs olivine, wadsleyite and ringwoodite, an analogous treatment can be expressed in terms of the exchange reaction:

$$\begin{gathered} {\text{F}}{{\text{e}}^{{\text{2}}+}}{\text{F}}{{\text{e}}^{{\text{3}}+}}{{\text{O}}_{{\text{2}}.{\text{5}}}}+{\text{MgS}}{{\text{i}}_{0.{\text{5}}}}{{\text{O}}_{\text{2}}}={\text{ MgF}}{{\text{e}}^{{\text{3}}+}}{{\text{O}}_{{\text{2}}.{\text{5}}}}+{\text{ FeS}}{{\text{i}}_{0.{\text{5}}}}{{\text{O}}_{\text{2}}} \hfill \\ \quad \quad {{\text{O}}_{\text{5}}}\quad \quad \quad {\text{ol}}/{\text{wads}}/{\text{rgw}}\quad \quad {{\text{O}}_{\text{5}}}\quad \quad \quad {\text{ol}}/{\text{wads}}/{\text{rgw}} \hfill \\ \end{gathered}$$

(1)

The standard state Gibbs free energy of this equilibrium can be expressed as:

$$\Delta G{^\circ _{({\text{P}},{\text{T}})}}=-{\text{RT}}\ln {K_{\text{D}}}-{\text{RT}}\ln K_{\gamma},$$

(2)

where K_D is defined as above and Kγ accounts for non-ideal behaviour. Assuming the observed ideal volume of mixing for (Mg,Fe)₂Fe₂O₅ solid solutions is representative of general ideal mixing behaviour for this phase, Eq. (2) becomes:

$$\Delta G{^\circ _{({\text{P}},{\text{T}})}}={\text{ }}-{\text{RTln}}{K_{\text{D}}}+W_{{{\text{Fe}} - {\text{Mg}}}}^{{{\text{silicate}}}}~({\text{2X}}_{{{\text{F}}{{\text{e}}^{2+}}}}^{{{\text{silicate}}}}~-{\text{ 1}})$$

(3)

when taking into account the known non-ideal behaviour of olivine, wadsleyite or ringwoodite, here modelled as symmetric solid solutions. Values for K_D at the P and T of our experiments can be computed by combining standard thermodynamic data for the Fe and Mg-endmembers of silicate phases from Holland and Powell (2011) with data from Myhill et al. (2016, 2017) for Fe₄O₅ and our results for Mg₂Fe₂O₅ (Table 6). The interaction parameters, $W_{{{\text{Fe}} - {\text{Mg}}}}^{{{\text{silicate}}}}$, for olivine (2000 kJ), wadsleyite (7500 kJ) and ringwoodite (4160 kJ) on a single-site basis were taken from Frost (2003). The results of these calculations are presented in Table 7, along with the K_D values obtained from our five new Si-bearing experiments and several samples from Woodland et al. (2013). There is reasonable agreement for partitioning with olivine, supporting our assumption that (Mg,Fe)₂Fe₂O₅ solid solutions behave ideally. On the other hand, there are discrepancies in K_D values for Mg–Fe²⁺ partitioning with wadsleyite and ringwoodite, implying that these silicate phases, particularly wadsleyite, should have even higher Mg contents than those measured in the experimental run products (Table 7). For ringwoodite, the differences in K_D are fairly small, on the order of ~ 0.04–0.05 and a likely explanation is that the presence of Fe³⁺ influences Mg–Fe²⁺ partitioning. This effect is not expected for olivine due to the lack of significant Fe³⁺ incorporation into this phase (e.g., Koch et al. 2004). Similar small differences are also observed for wadsleyite-bearing experiments of Woodland et al. (2013). However, samples Z1531o and Z1532u from this study both exhibit much larger differences in calculated and observed K_D (Table 7). These differences are even much larger than can be accounted for by considering the effect of strongly non-ideal interactions between the Mg₂SiO₄ and ${\text{(Fe}}_{{5/3}}^{{3+}}{\square _{1/3}})$Fe³⁺O₄ components in wadsleyite ($W_{{{\text{Fe}}^{3+} - {\text{Mg}}}}^{{{\text{wadsleyite}}}}$ = 20 kJ) as described by Frost and McCammon (2009) for oxidizing conditions (Re–ReO₂ buffer). However, the work of Mrosko et al. (2015) suggests that our results may be due to the combination of Fe³⁺ and OH incorporation in wadsleyite. Thus, we attribute the differences in calculated and observed K_D to the presence of Fe³⁺ and OH in wadsleyite. However, it is clear from the K_D values presented in Table 7 that the O₅-phase will always have the highest Fe content in mantle-relevant assemblages.

Redox stability of (Mg,Fe)₂Fe₂O₅ solid solutions

A number of experiments reported in Table 1 contain a (Mg,Fe)₂Fe₂O₅ solid solution coexisting with hematite, which allows us to estimate the oxygen fugacity (ƒO₂) of equilibration via the equilibrium:

$${\text{F}}{{\text{e}}^{{\text{2}}+}}_{{\text{2}}}{\text{F}}{{\text{e}}^{{\text{3}}+}}_{{\text{2}}}{{\text{O}}_{\text{5}}}+{\text{ }}0.{\text{5 }}{{\text{O}}_{\text{2}}}={\text{ 2 F}}{{\text{e}}_{\text{2}}}{{\text{O}}_{\text{3}}},$$

(4)

where

$$\Delta G{^\circ _{({\text{P}},{\text{T}})}}=-{\text{RTln}}K=-{\text{2RTln}}~a_{{{\text{F}}{{\text{e}}_2}{{\text{O}}_3}}}^{{{\text{hem}}}}+{\text{RTln}}~a_{{{\text{F}}{{\text{e}}_4}{{\text{O}}_5}}}^{{{{\text{O}}_5}}}+{\text{ }}0.{\text{5RTln}}f{{\text{O}}_{\text{2}}}$$

(5)

From the very limited deviation in hematite composition from the pure Fe₂O₃ as described above, we can reasonably assign unit activity of Fe₂O₃ for this phase. This, along with the assumption of ideal mixing on sites in (Mg,Fe)₂Fe₂O₅ (i.e., a = X²) and rearranging yields the following simplification to Eq. 5:

$$\Delta G{^\circ _{({\text{P}},{\text{T}})}}-{\text{2RTln}}(X_{{{\text{F}}{{\text{e}}^{2+}}}}^{{{{\text{O}}_5}}})=0.{\text{5RTln}}f{{\text{O}}_{\text{2}}}$$

(6)

The ƒO₂ can then be computed by combining compositional data from this study and from Uenver-Thiele et al. (2017b) with standard state thermodynamic data for hematite, Fe₄O₅ and O₂ from Holland and Powell (2011), Myhill et al. (2016) and Stagno and Frost (2010), respectively. The systematics of equilibrium (4) relative to the Re–ReO₂ and the metastable fayalite–magnetite quartz (FMQ) oxygen buffers are illustrated in Fig. 10 as a function of pressure at 1300 and 1500 °C. Also plotted are the results of the few samples that were equilibrated at these two temperatures. As expected, the experiments employing PtO₂ to minimize the formation of Fe²⁺ record the highest ƒO₂, lying about 5 log units above FMQ. Somewhat lower ƒO₂ values are computed for the two experiments where no PtO₂ was added and partial reduction of Fe³⁺ occurred (M519, M566; Fig. 10; Table 2). Unsurprisingly the lowest ƒO₂ values are calculated for the experiments with the Mg_0.5Fe_0.5Fe₂O₄ starting composition, where Fe³⁺/∑Fe = 0.8. However, our experiments with coexisting (Mg,Fe)₂Fe₂O₅ and hematite were clearly performed under strongly oxidizing conditions, as was intended for investigating the behaviour of Fe³⁺ under deep mantle conditions. Although such conditions are much more oxidizing than generally expected for the deep upper mantle and transition zone (e.g., Frost and McCammon 2009), this does not exclude their appearance due to local excursions to high oxygen fugacities through interactions with subducted material or migrating carbonatite melts. These regions, where redox gradients occur, may also be important for the crystallization of diamond (Stachel et al. 1998).

Fig. 10

logƒO₂ of the equilibrium between Fe^2 + ₂Fe^3 + ₂O₅ and hematite plotted against pressure at 1300 and 1500 °C along with values calculated for several samples run at the same temperatures. The arrows indicate the shift in logƒO₂ related to Mg incorporation in Fe₄O₅. Also shown for reference are the positions of the metastable FMQ and Re–ReO₂ redox buffer equilibria (Ballhaus et al. 1991; Myhill et al. 2016, 2017)

Concluding remarks

Combining the results on the crystal-chemical behaviour of Fe₄O₅–Mg₂Fe₂O₅ solid solutions of this study with those of Uenver-Thiele et al. (2017a, b) and Woodland et al. (2013), it is apparent that complete solid solution exists across the binary join. A steady decrease in molar volume with increasing Mg content indicates ideal mixing behaviour. The variation in molar volume arises primarily from shortening along the b-axis with increasing Mg content. Although our results are in good agreement with the observations of Woodland et al. (2013), our wider compositional range also reveals more subtle changes in the a- and c-parameters with composition.

The stability of the O₅-phase depends on the phase assemblage and bulk composition. For example, the study of Si-free bulk compositions (Uenver-Thiele et al. 2017a, b) demonstrates that the minimum pressure for (Mg,Fe)₂Fe₂O₅ coexisting with hematite is ~ 10–11 GPa at ~ 1500–1600 °C. However, the maximum stability of the O₅-phase in these Si-free systems depends on the redox conditions, and thus, on the Fe²⁺/Mg ratio of (Mg,Fe)₂Fe₂O₅ (compare results of Uenver-Thiele et al. 2017a with b). The endmember assemblage Mg₂Fe₂O₅ + Fe₂O₃ remains stable up to 20 GPa, whereas the maximum stability of Mg_0.5Fe_0.5Fe₂O₅ + Fe₂O₃ lies at ~ 14–16 GPa at ~ 1000–1300 °C and decreases to higher temperatures. This contrasts with the results of the Si-bearing experiments where hematite is absent. Here, (Mg,Fe)₂Fe₂O₅ can be stabilized down to depths corresponding to the lower transition zone (~ 20 GPa) under more reducing conditions, consistent with the results of Myhill et al. (2016) who found Fe₄O₅ to be stable to at least 22 GPa.

In Si-bearing bulk compositions, (Mg,Fe)₂Fe₂O₅ can occur, even though it does not incorporate Si into its structure, consistent with previous studies (e.g., Woodland et al. 2013; Bindi et al. 2016). The new experiments reported here demonstrate that the list of known Si-phases with which (Mg,Fe)₂Fe₂O₅ can coexist (olivine, wadsleyite, ringwoodite, spinelloid V or clinopyroxene; Woodland et al. 2013) can now be extended to include majoritic garnet and Fe³⁺-bearing phase B. Chemical analyses of the garnet (Z1507o) indicate a composition of 82 mol% (Mg,Fe)₄Si₄O₁₂ and 18 mol% (Mg,Fe)₃Fe₂Si₃O₁₂. Since phase B with the chemical formula Mg₁₂Si₄O₁₉(OH)₂ is known to become stable under hydrous conditions, its presence in our “dry” experiments was surprising, particularly since no PtO₂ was added to these experiments that could have been a source of adsorbed H₂O. Raman spectra obtained from phase B confirmed the presence of some structural water as OH; however, further quantification of the exact amount of OH by infrared spectroscopy or secondary ion mass spectrometry (SIMS) is required. A possible explanation for the stabilization of phase B might be the incorporation of Fe³⁺, which is reported here for the first time. EPMA and EDX measurements in the TEM gave consistent results with a composition of Mg_11.17(4)Fe_1.04(6)Si_3.79(3)O₂₁H₂. Additional Fe-L ELNES analysis yielded a ${\text{F}}{{\text{e}}^{{\text{3}}+}}/\sum {{\text{Fe}}=\sim 0.{\text{41}}\left( {\text{4}} \right)}$, confirming that Fe³⁺ entered the structure via the charge-balanced substitution: ^[4]Si⁴⁺ + ^[6]Mg²⁺ = 2Fe³⁺. Based on the fact that phase B can not only store water, but also can accommodate Fe³⁺ and Fe²⁺ makes this hydrous magnesium silicate even more interesting as a possible mantle phase. From only two experiments, we have little constraint on the P–T stability of Fe³⁺-bearing phase B, except that it appears to be stable between at least 14 and 20 GPa at fairly low temperature (Table 3). An analogous substitution involving Cr³⁺ was recently reported for anhydrous phase B (Bindi et al. 2016; Sirotkina et al. 2017). Assuming the crystal chemistry of phase B and anhydrous phase B is similar with respect to substitution of trivalent cations, the incorporation of Cr³⁺ and Fe³⁺ together has the potential for expanding the stability field of phase B, particularly in terms of redox conditions. The same situation also holds for (Mg,Fe)₂Fe₂O₅ in that the substitution of other trivalent cations (i.e., Cr and Al) will act to stabilize this phase to lower oxygen fugacities and also to a potentially wider range of pressures and temperatures, making it even more relevant for the mineralogy of the deep upper mantle and transition zone. The incorporation of such cations will also expand the range of bulk compositions in which the O₅-phase can be stable. Investigation of such solid solutions is currently underway.