Pressure–volume–temperature equation of stateof ε–FeOOH to 11 GPa and 700 K

Akio SUZUKI

Department of Earth Science, Graduate School of Science, Tohoku University, Sendai 980–8578, Japan

A new synchrotron X–ray diffraction study of ε–FeOOH has been carried out to determine the pressure–volume–temperature (P–V–T ) equation of state (EOS). The P–V–T data fitted a third–order Birch–Murnaghan EOSyielded: isothermal bulk modulus KT0 of 135(3) GPa; its pressure derivative K′ of 6.1(9); (∂KT/∂T )P of−0.05(2) GPa K−1; a0 of 2.6(7) × 10−5 K−1 and a1 of 1.0(3) × 10−7 K−2, where the volumetric thermal expansioncoefficient is described as α0,T = a0 + a1 × (T − 300).

Keywords: Iron oxide hydroxide, High pressure, Thermal equation of state, Synchrotron radiation, Hydrousphase

INTRODUCTION

Oxide hydroxide with the InOOH structure is now con-sidered crucial to the water reservoir in the Earth’s deepinterior. Suzuki et al. (2000) synthesized a high–pressurepolymorph of diaspore (α–AlOOH) and named it δ–AlOOH. Sano et al. (2008) investigated the stability ofδ–AlOOH using a laser–heating diamond anvil cell. Theyshowed that δ–AlOOH is stable close to the core–mantleboundary. Recently, Nishi et al. (2014) synthesized a hy-drous magnesium silicate and named phase H. Becauseof the structural similarity, phase H was expected to formsolid solutions with δ–AlOOH (Nishi et al., 2014). Ohiraet al. (2014) investigated the stability of the solid solutionof δ–AlOOH and phase H. They showed that the solidsolution coexisted with MgSiO3–perovskite and post–per-ovskite. Therefore, the solid solution can be a carrier ofwater into the base of the lower mantle. Terasaki et al.(2012) studied the reaction between δ–AlOOH and anFe–Ni alloy and implied that δ–AlOOH transports hydro-gen to the Earth’s core. Because of the importance of thehydrogen carrier to the Earth’s deep interior, a number ofstudies on the stabilities and properties of isostructuralphases have been also carried out recently (e.g., Gleasonet al., 2013; Suzuki, 2013).

Iron oxide hydroxide, ε–Fe3+OOH, is a high–pres-

sure polymorph of goethite, and is isostructural with δ–AlOOH (Suzuki, 2010). It is also expected that ε–FeOOHforms a solid solution with δ–AlOOH and phase H be-cause of the structural similarity. Therefore, the study ofthe properties of δ–AlOOH, phase H, ε–FeOOH and theirsolid solution under high pressure and high temperatureconditions is very important. An X–ray diffraction (XRD)study under high pressure and high temperature condi-tions was carried out by Gleason et al. (2008). However,the pressure–volume–temperature (P–V–T ) equation ofstate (EOS) was not determined. The room temperaturecompression curve was reported by Suzuki (2010) andGleason et al. (2013). Gleason et al. (2013) found a dis-continuous change in the compression curve around 53GPa and reported the spin transition of Fe in ε–Fe3+OOH.Suzuki (2010) determined the bulk modulus and its pres-sure derivative of KT0 of 126(3) GPa and 10(1), respec-tively. However, the thermoelastic properties have notbeen reported. In this study, we carried out new synchro-tron XRD measurements to determine the thermal EOSof ε–FeOOH.

EXPERIMENTAL METHODS

Synchrotron XRD experiments were performed at thebeamlines AR–NE7A and AR–NE5C of the Photon Fac-tory at KEK (High Energy Accelerator Research Organi-zation) in Tsukuba, Japan. A large volume press, MAX–III, was used at AR–NE7A in the pressure range of 7.69–

doi:10.2465/jmps.160719cA. Suzuki, akio.suzuki.c5@tohoku.ac.jp Corresponding author

Journal of Mineralogical and Petrological Sciences, Volume 111, page 420–424, 2016

LETTER

11.07 GPa (Runs 1 and 2). A Kawai–type apparatus wasdriven by a hydraulic press. The 22–mm WC cubes witha truncated edge length of 5.0 mm were used. The exper-imental techniques have been previously reported (Suzu-ki, 2013). A cubic type multianvil apparatus installed atthe AR–NE5C beamline, MAX80, was used in Run 3 ofthe experiment in the pressure range of 0.68–3.27 GPa.Pressure was generated using a so–called 6–6 type assem-bly (Nishiyama et al., 2008). The pressure medium was acube made of pyrophyllite heated at 1073 K for 2.5 h.A cube with an edge length of 9 mm was compressed bysix WC anvils with a 6.0–mm truncated edge length. Acylindrical graphite heater was used to generate high tem-perature. The EOS of NaCl was used as the pressure scale(Brown, 1999). White X–ray beam from the bendingmagnet light source was collimated by WC slits. XRDdata were collected using a Ge–solid state detector, andthe energy dispersive method was adopted.

A mixture of powders of natural goethite from USAand NaCl was weighed in 2:1, then homogenized in anagate mortar. Electron microprobe and XRD studies con-firmed that the sample was pure α–FeOOH. This mixturewas pelletized and loaded in a graphite furnace of thecell (Runs 1 and 2). The transformation from goethiteto ε–FeOOH was observed in heating under high pressureat 600 K and 8.3 GPa. These conditions are very close tothe phase boundary between α– and ε–FeOOH (Gleasonet al., 2008). Because the transformation occurred at 600K, the XRD study on the stable condition of α–FeOOHwas limited to 400 K. XRD data were obtained with de-creasing temperature and pressure.

In the stability field of goethite, the ε–FeOOH sam-ple could not be annealed under high pressure because ittransformed to goethite by heating. Therefore, ε–FeOOHwas synthesized at 8.5 GPa and 700 K at Tohoku Uni-versity and used as a starting material in Run 3. PowderXRD study (Bruker D8 Advance) confirmed the forma-tion of ε–FeOOH. The unit cell parameters were deter-mined to be a = 4.9544(2) Å, b = 4.4594(3) Å, c =2.9999(1) Å and V = 66.278(6) Å3. To minimize the de-viatoric stress, a powder of ε–FeOOH and NaCl wasloaded in a Teflon® container with Daphne 7373.

RESULTS AND DISCUSSION

The unit–cell parameters under high pressure and hightemperature conditions are summarized in Table 1 andthe unit cell volumes are displayed in Figure 1. TheXRD study was carried out in the pressure range of0–11 GPa and the temperature range of 300–700 K.The high–temperature Birch–Murnaghan (HTBM) for-malism was adopted to describe the thermoelastic param-

Table 1. Unit–cell parameters of ε–FeOOH

Figure 1. Isothermal compression curves at 300, 400, 500, 600,and 700 K (solid lines).

P–V–T equation of state of ε–FeOOH to 11 GPa and 700 K 421

eters. The P–V–T data have been fitted to the third–orderBirch–Murnaghan EOS using the ‘EosFit7c’ program(Angel et al., 2014):

(1),

where P is the pressure, KT0 the isothermal bulk modulus,K′T the pressure derivative of KT0, V0 the volume at zeropressure, and V the volume at high pressure. K′T was as-sumed to be constant. The temperature effect on KT andV0T are expressed as follows:

where (∂KT/∂T )P is the temperature derivative of the bulkmodulus, T0 the reference temperature (300 K), and α thevolume thermal expansion coefficient at atmosphericpressure. The volume thermal expansion is expressed asfollows:

The powder XRD data gave the unit–cell parametersas a0 = 4.9544(2) Å, b0 = 4.4594(3) Å, c0 = 2.9999(1)Å and V0 = 66.278(6) Å3 in good agreement with our pre-vious study (a0 = 4.954(1) Å, b0 = 4.4540(9) Å, c0 =3.0001(8) Å and V0 = 66.20(3) Å3; Suzuki, 2010). Thethermoelastic parameters derived by the fitting of P–V–Tdata to the HTBM EOS are listed in Table 2. When V0,T0 =66.278(6) Å3 is fixed, the fitting to the EOS gives KT0 =

135(3) GPa and K′T = 6.1(9). The compression curves at300, 400, 500, 600 and 700 K are shown in Figure 1.Because the bulk modulus KT and K′T are inversely corre-lated, these values are consistent with Suzuki (2010).Among the oxide hydroxides in Table 2, the compressi-bility of ε–FeOOH is similar to those of other oxide hy-droxides. However, CrOOH is remarkably less compres-sible than the others. Sano–Furukawa et al. (2012) showedthat the stiffening at high pressure occurs in InOOH–typeM3+OOH except for β–CrOOH. They suggested thatβ–CrOOH is already stiffened at ambient pressure. Thelarger K′ (6.1) of ε–FeOOH than that of β–CrOOH (3.5)implies that ε–FeOOH is stiffened at high pressure.

Figure 2 shows the pressure dependence of the rel-ative lattice constants of ε–FeOOH. The b axis was morecompressible than the a and c axes. Similar compressionbehavior was observed in InOOH (Sano–Furukawa et al.,2012). In contrast, in β–CrOOH (Sano–Furukawa et al.,2012), the c axis is the most compressible. In γ–MnOOH,the c axis is the least compressible (Suzuki, 2013). Thebulk modulus of γ–MnOOH was also smaller than that ofε–FeOOH (Table 2). It is suggested that the MnO6 octa-hedra in γ–MnOOH are distorted by the Jahn–Teller ef-fect. Although the data are scattered, the change in slopebetween 3 and 7 GPa can be recognized. One of the pos-sible reasons is the deviatoric stress on the sample. An-other possibility is the symmetrization of the hydrogenbond in oxide hydroxides with InOOH structure (Sano–Furukawa et al., 2008; 2009; 2012).

It can be suggested that δ–AlOOH, phase H, ε–FeOOH and their solid solution transport water to thedeep interior of the Earth. Terasaki et al. (2012) investi-gated the reaction between the Fe–Ni alloy and δ–AlOOHup to the pressure of the core–mantle boundary. Theyshowed that hydrogen is partitioned into the Fe–Ni alloyand suggested that the core was hydrogenated by the sub-ducting δ–AlOOH. Dobson and Brodholt (2005) pro-

Table 2. Thermoelastic parameters of oxide hydroxide with InOOH structure

* Fixed value.The number in parentheses represents the standard deviation.

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posed that during the late Archaean and early Proterozoiceras the banded iron formations along with the oceaniccrust subducted to the core–mantle boundary and stagnat-

ed there. They argue that such a relict of the banded ironformation may explain the observed features of the ultra-low–velocity zones of the seismic wave on the core–man-tle boundary. A recent theoretical study showed that theseismic wave velocity in the lower mantle can be ex-plained by the existence of ferric iron (Wang et al.,2015). It is expected that iron oxide hydroxide may beformed when the banded iron formations along with theoceanic crust subducted into the mantle. Then, hydrogenmay have been transported to the deep mantle by the sol-id solution of ε–Fe3+OOH, δ–AlOOH and phase H. Fur-ther experimental studies under high pressure and hightemperature conditions are required to understand themechanism of water transportation in the Earth’s interiorconsidering the oxidized conditions.

ACKNOWLEDGMENTS

The synchrotron XRD studies at the beamlines NE7Aand NE5C were performed with the approval of the Pho-ton Factory Advisory Committee (Proposals 2012G031,2015G524). This research was partially supported by theIto Science Foundation and by the Ministry of Education,Science, Sports and Culture, Grant–in–Aid for Scien-tific Research on Innovative Areas (no. 15H05828), andfor Challenging Exploratory Research (nos. 25610153,16K13901).

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Manuscript received July 19, 2016Manuscript accepted October 23, 2016

Manuscript handled by Tetsu Kogiso

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