Study on the High-Pressure Behavior of Goethite up to 32 GPa Using X-Ray Diffraction, Raman, and Electrical Impedance Spectroscopy

Abstract

Goethite is a major iron-bearing sedimentary mineral on Earth. In this study, we conducted in situ high-pressure x-ray diffraction, Raman, and electrical impedance spectroscopy measurements of goethite using a diamond anvil cell (DAC) at room temperature and high pressures up to 32 GPa. We observed feature changes in both the Raman spectra and electrical resistance at about 5 and 11 GPa. However, the x-ray diffraction patterns show no structural phase transition in the entire pressure range of the study. The derived pressure-volume (P-V) data show a smooth compression curve with no clear evidence of any second-order phase transition. Fitting the volumetric data to the second-order Birch–Murnaghan equation of state yields V₀ = 138.9 ± 0.5 ų and K₀ = 126 ± 5 GPa.

1. Introduction

Although both goethite (α-FeOOH) and hematite (Fe₂O₃) are major iron-bearing sedimentary minerals, goethite has received less attention in the research of Earth’s deep interior due to its instability at high temperatures. Upon heating, goethite decomposes into hematite and water [1,2]. The recent discovery of a pyrite-structure phase in FeOOH at lower mantle pressure and temperature conditions has led to more research on goethite [3,4,5,6]. There have been a few studies on its behavior at high pressures. In addition to its three other naturally occurring forms (akaganeite (β-FeOOH), lepidocrocite (γ-FeOOH), and feroxyhyte (δ-FeOOH)), two high-pressure phases (ε-FeOOH and pyrite-FeOOH) have been reported experimentally through heating at high pressures above 5 GPa [1,2,7] and 90 GPa [4,5,6,8], respectively. Before transforming to pyrite-FeOOH, ε-FeOOH experiences a second-order transition at 43 GPa with symmetry change from P21nm to Pnnm, accompanied by a sluggish high-spin to low-spin transition [9]. The spin transition also occurs in goethite at 45 GPa as an isostructural first-order phase transition [10,11]. Infrared and Raman spectroscopy indicate a few changes in the pressure range up to 45 GPa [10,12,13]. In a recent study, Liu et al. [12] reported two pressure-induced phase transitions at 7 and 20 GPa through Raman spectroscopy and electrical conductivity studies and attributed these two transitions to the structural transformation to ε-FeOOH (at 7 GPa) and an isostructural second-order transition (at 20 GPa). P-V equation of state (EOS) studies of goethite at room temperature are also very diverse; the measured bulk modulus (K₀) of ambient pressure and temperature ranges from 86 to 148 GPa [1,10,14,15,16,17,18]. Here, we report our high-pressure experimental studies of goethite using x-ray diffraction, Raman spectroscopy, and electrical impedance spectroscopy (EIS) up to 32 GPa in order to comprehend the discrepancies among observations of the high-pressure behavior of goethite from different studies in this pressure range. While we found similar phenomena in Raman spectroscopy and electrical impedance experiments to those reported by Liu et al. [12], the x-ray diffraction shows no structural phase transition in the pressure range studied. The analysis of the volumetric data as a function of pressure indicates that there is unlikely to be any second-order transition with a discontinuity of compressibility. The origin of the change in Raman spectra and electric conductivity remains unclear, although a sluggish magnetic state transition from antiferromagnetic (AFM) to ferromagnetic (FM) may be an explanation.

2. Materials and Methods

The starting material in our experiments was goethite (α-FeOOH) from Alfa Aesar with ≥99% purity. All measurements of x-ray diffraction (XRD), Raman, and electrical impedance spectroscopy (EIS) were conducted using a diamond anvil cell (DAC) (manufacture, city, country) with a 400 μm anvil culet and rhenium metal gasket for high-pressure generation. Inert neon gas and a mixture of 16:3:1 methanol-ethanol-water was used for pressure transmission in the XRD and Raman experiments, respectively, and no pressure transmission medium was used in EIS experiments. The goethite sample was loaded into a chamber 200 μm in diameter, together with small ruby spheres. The sample pressure was determined through in situ fluorescence measurement and the ruby pressure scale [19]. In situ x-ray diffraction was conducted at HPCAT of Advanced Photon Source (APS) (Lemont, IL, USA) with a wavelength of 0.4066 Å. The collected x-ray diffraction patterns were processed using the General Structure Analysis System (GSAS) software (manufacture, city, country) [20]. The P-V equations of state (EOS) were derived using EosFit7-GUI [21]. Raman spectroscopy was performed using a Micro-Raman Spectroscopy (inVia Reflex, Renishaw, KWotton-under-Edge, United Kingdom) System. A 532 nm diode-pumped solid-state laser was used to excite the sample, and Raman spectra were collected using a charge-coupled device (CCD)-spectrograph in the 150–5000 cm⁻¹ range.

In the EIS measurement, a time (t)-dependent sinusoidal voltage was applied to the sample inside the DAC (Figure 1):

E(t) = E₀ sin (ωt),

(1)

where ω is the angular frequency (ω = 2πf, where f is the frequency). For a linear (or pseudolinear) sample, the current response to a sinusoidal voltage is a sinusoid at the same frequency, but shifted in phase by ϕ(ω), which is a function of frequency:

I(t) = I₀(ω) sin (ωt + ϕ(ω)).

(2)

The impedance of the sample is defined by the ratio of E(t)/I(t):

Z(ω) = E(t)/I(t) = (E₀/I₀(ω)) sin (ωt)/sin (ωt + ϕ(ω)).

(3)

when the applied voltage and its current response are expressed as a complex number,

E(t) = E₀ exp(jωt) and I(t) = I₀(ω) exp[j(ωt + ϕ(ω))],

the impedance is expressed by

Z(ω) = [E₀ exp(jωt)]/[I₀(ω) exp(jωt + jϕ(ω))]
= (E₀/I₀(ω)) exp(−jϕ(ω)) = Z₀(ω) [cos (ϕ(ω)) − (j)sinϕ(ω)]
= Z_R(ω) − Z_I(ω) j

(4)

where Z₀(ω) = E₀/I₀(ω) is the magnitude of impedance and Z(ω) is composed of a real part (Z_R(ω) = Z₀(ω) cos(ϕ(ω)) and an imaginary part (−Z_I(ω) = −Z₀(ω) sin (ϕ(ω)).

A simple sample system can be considered as an R-C circuit, i.e., a bulk resistance (R) and bulk capacitance (C) in parallel (Figure 2a). The impedance (Z) of this circuit follows

$$\frac{1}{\mathrm{Z}\left(\omega \right)}=\frac{1}{\mathrm{R}}+\frac{1}{1/\left(\mathrm{j}\omega \mathrm{C}\right)}$$

(5)

therefore,

$$\mathrm{Z}\left(\omega \right)=\frac{\mathrm{R}}{1+\mathrm{j}\omega \mathrm{C}\mathrm{R}}=\frac{\mathrm{R}}{1+{\left(\omega \mathrm{C}\right)}^2}-\mathrm{j}\frac{\omega \mathrm{C}{\mathrm{R}}^2}{1+{\left(\omega \mathrm{C}\right)}^2}.$$

(6)

let

$${\mathrm{Z}}_{\mathrm{R}}\left(\omega \right)= \frac{\mathrm{R}}{1+{\left(\omega \mathrm{C}\right)}^2} \mathrm{and} {\mathrm{Z}}_{\mathrm{I}}\left(\omega \right)=\frac{\omega \mathrm{C}{\mathrm{R}}^2}{1+{\left(\omega \mathrm{C}\right)}^2},$$

(7)

and eliminating ω from Z_R and Z_I, we get the relation between Z_R and Z_I:

$${({\mathrm{Z}}_{\mathrm{R}}\left(\omega \right)-\frac{\mathrm{R}}{2})}^2+{\mathrm{Z}}_{\mathrm{I}}{\left(\omega \right)}^2={(\frac{\mathrm{R}}{2})}^2.$$

(8)

Hence, the bulk resistance R can be obtained from the radius of the Z_I(ω) vs. Z_R(ω) semicircle (i.e., Nyquist plot [22]) of the EIS experiment with Z(ω) = Z_R(ω) − Z_I(ω)j (Figure 2b). In the Nyquist plot, the frequency (ω) does not appear in the equation, but the Z_R axis is the direction of decreasing ω. When ω = 0 (i.e., direct current), the impedance only has the real part with Z = R. As ω increases, Z_R(ω) decreases from R and Z_I(ω) increases from 0, following the semicircle. At the maximum point of the semicircle, Z_R(ω_m) = Z_I(ω_m) = R/2. Incorporating this into Equation (7), we get ω_mRC = 1. Therefore, ω_m = 1/(RC) = 1/τ (τ = RC is the time constant or relaxation time of the system).

In a polycrystalline sample, an equivalent circuit can be composed through a simplified series two-phase model [23], taking the grain interior (intra-grain) as phase 1 and the grain boundary (inter-grain) as phase 2 (Figure 2c). In reality, the bulk capacitance (C) is replaced by the constant phase element (CPE) with Z_CPE = Z_C/(jω)ⁿ, where 0 ≤ n ≤ 1. When n = 0, Z_C = R (pure resistance); when n = 1, Z_C = 1/C (pure capacitance). The Nyquist plot for the polycrystalline sample consists of two semicircles (Figure 2d). For porous polycrystals, the resistance of the grain boundary is larger and, therefore, its Z_I(ω) vs. Z_R(ω) semicircle has a larger radius than that of the grain interior, according to Equation (8).

The EIS measurements were conducted using a Solartron 1260 Phase-Gain-Analyzer equipped with a Solartron 1296 dielectric interface. A sinusoidal voltage signal with a 1.0 V magnitude was applied to the sample in a DAC (Figure 1). The signal frequency ranged from 0.1 Hz to 10 MHz.

3. Results

3.1. Raman Spectroscopy

Figure 3a shows the in situ Raman spectra of goethite in the wavenumber range 150–1300 cm⁻¹ during compression up to 32 GPa at room temperature. The spectra above 1300 cm⁻¹ up to 5000 cm⁻¹ are not shown as there is no significant feature detected in this wavenumber range. The spectrum near ambient pressure is consistent with data previously reported. The assignments of the observed Raman peaks are listed in

Table 1. Assignments of the observed Raman peak of goethite at ambient conditions.

Label	ν1	ν2	ν3	ν4	ν5	ν6
Wavenumber	250	302	391	486	556	687
Assignment [30]	Fe–O stretching symmetric	Fe–O Hbending symmetric	Fe–O–Fe/–OH stretching symmetric	Fe–OH stretching asymmetric	Fe–OH stretching asymmetric	Fe–O stretching symmetric

. There are some unassigned weak peaks, i.e., 209, 399, 420, 887, 1020, and 1117 cm⁻¹ (at ambient conditions). These peaks were also present in previously reported Raman spectra [10,12,24,25,26]. Peaks above 800 cm⁻¹ are associated with OH bonding, and, therefore, are difficult to observe in some Raman experiments. The total number of Raman active modes calculated using the SMODES module of ISOTROPY Software Suite (Version 1.2.4, Brigham Young University, Provo, USA) [27] is 24, which is consistent with that of diaspore (α-AlOOH), an isostructural mineral of goethite with the space group Pbnm [28]. Upon compression, the Raman peak at 302 cm⁻¹ shows an obvious splitting at 5.2 GPa, and the main peak at about 391 cm⁻¹ loses one of its two shoulder peaks on the high wavenumber side at about the same pressure. These shoulder peaks are theoretically predicted by the density functional theory (DFT) calculation for goethite [29]. A new peak at about 260 cm⁻¹ appears when the pressure is increased from 10.6 to 11.7 GPa, and the peak at 302 cm⁻¹ further yields a small shoulder peak. Both of these new peaks are very weak. When the positions of all the observed peaks are plotted as a function of pressure (Figure 3b,c), more features become visible. As the pressure increases, all peaks show smooth blueshifts as a function of pressure due to shortening of the bond distances. At about 5 GPa, where the peak at 302 cm⁻¹ splits, discontinuities in the peak shift as a function of pressure occurring at most peaks, and the slopes of the shifts also change across this pressure. Distinctly, the new peak split at 302 cm⁻¹ shows a redshift in contrast to all other peaks. At 11.7 GPa, where two weak peaks appear (at 260 and 302 cm⁻¹), only subtle changes in the slopes of the shifts are observed. Such a subtle change appears to occur at 20 GPa for the ν₄ and ν₅ peaks. Upon decompression to ambient pressure, the original Raman spectrum of the starting sample is recovered, indicating that all the changes during compression are reversible.

3.2. Electrical Impedance Spectroscopy

In situ EIS measurements were conducted up to 31 GPa at room temperature. Figure 4 shows the Nyquist plots of the EIS data collected at different pressures. Resistances of grain-interior and grain-boundary contributions were derived from the first and second semicircles of the Nyquist plots and are shown in Figure 5, together with some of the previously reported results [10,12]. Since the starting sample was pre-pressed into a pallet to minimize the void space in the grain boundaries, the resistance contribution from the grain boundary started at a value comparable to that from the grain interior. Upon compression, the grain boundaries were further reduced, and, therefore, the grain-boundary resistance became much smaller than the grain-interior resistance (about one order of magnitude smaller at the peak pressure, 31 GPa). The pressure influences on the grain-interior resistance and grain-boundary resistance are well-correlated. Two significant changes can be recognized in the total resistance as a function of pressure. Upon compression, the total resistance initially decreases with pressure. At about 5 GPa, the resistance begins to increase with pressure and then decreases with pressure again at 11 GPa. These changes are also well-correlated with those observed in Raman spectroscopy.

3.3. In Situ X-Ray Diffraction

Figure 6 shows the sequence of in situ synchrotron x-ray diffraction patterns at high pressures up to 32 GPa at room temperature. No diffraction feature change was observed in the entire pressure range, except for the peak shift due to compression. A peak showing a dramatic shift in contrast to the rest of the diffraction pattern was obtained from the solidified neon pressure transmission medium. The volumetric data (Figure 7) derived from the diffraction patterns were fitted to the third-order Birch–Murnaghan equation of state (BM EOS):

P = 3K₀f(1 + 2f)^5/2(1 + (3/2)(K’ − 4)f),

(9)

where K₀ and K’ are the bulk modulus at ambient pressure and its pressure derivative, respectively, and f = ((V₀/V)^2/3 − 1)/2 is the Eulerian strain. The EOS fitting yields V₀ = 138.8 ± 0.8 ų, K₀ = 129 ± 19 GPa, and K‘ = 3.8 ± 1.2.

4. Discussion

Although solidification of the pressure medium (mixture of 16:3:1 methanol-ethanol-water) at about 11 GPa in the Raman experiments may give rise to the change in the slope of peak-shift as a function of pressure, the change in the EIS experiment at the same pressure is independent of the solidification because no pressure medium was used in the EIS measurement. Similar phenomena have been observed in other in situ high-pressure Raman spectroscopy studies [10,12]. Xu et al. [10] resolved the peak at 300 cm⁻¹ as three peaks at ambient pressure, whereas we recognized only one peak initially, a splitting at about 5 GPa, and a second splitting at about 11 GPa. On the other hand, they did not observe the shoulder peak on the high wavenumber side of the main peak at 400 cm⁻¹ at ambient pressure. Instead, they observed a splitting of the peak at 5 GPa and changes in the slope of peak-shift with pressure at 16 GPa in some of the peaks (i.e., at 250 and 300 cm⁻¹). No discontinuity of peak-shift with pressure was reported throughout the entire pressure range (up to 40 GPa) they studied. In their Raman study, Liu et al. [12] did not focus their attention on weak peaks, such as the shoulder peak from the second splitting of the peak at 300 cm⁻¹ and the shoulder peaks on the high wavenumber side of the main peak at 400 cm⁻¹. Their observation of the peak-shift discontinuities with pressure at 7 GPa is approximately consistent with our current study (5 GPa). The second slope-change they reported is at a higher pressure (20 GPa) compared to what we observed in this study (11 GPa), except for the ν₄ and ν₅ peak, which change their slopes at 20 GPa. Discrepancies among these in situ high-pressure Raman spectroscopy results seem to originate from the instrumental resolution, stress environment, and experimentalist’s attention.

A comparison of our EIS data with the resistance data from Xu et al. [10] and the resistivity (reciprocal of conductivity) data from Liu et al. [12] in the same pressure range is shown in Figure 5. Since the resistance value highly depends on the geometries of the sample and electrodes, the data from Xu et al. [10] are about one order of magnitude lower than the result of this study. However, the trend of reducing resistance with pressure is consistent with the current study, and a notable discontinuity of resistance as a function of pressure can be recognized in their data (dashed lines), although the pressure step in their experiment is too large to unveil any details due to their primary interest in the higher pressure range. The resistivity data as a function of pressure from Liu et al. [12] show two changes at pressures similar to those observed in this study. Nevertheless, we did not observe the resistance increase at a higher pressure (20 GPa) reported by Liu et al. [12], and neither did Xu et al. [10].

Although both Raman spectroscopy (Figure 3) and EIS (Figure 5) indicate feature changes at about 5 and 11 GPa in this study, the observation of in situ x-ray diffraction (Figure 6) rules out the possibility of any first-order structural transition at these pressures. Xu et al. [10] reported a change in the bulk modulus at 16 GPa, based on their x-ray diffraction data, from 120 to 197 GPa. When we break our volumetric data into two groups at 16 GPa and fit the two datasets separately to the third-order BM EOS, we get V₀ = 138.8 ų, K₀ = 129 GPa, and K‘ = 3.7 for data below 16 GPa, and V₀ = 136.1 ų, K₀ = 175 GPa, and K‘ = 2.1 for data above 16 GPa. An increase in bulk modulus appears to be present across the breaking pressure. However, the confidence ellipses (at a 1σ level) in K₀ and K′ (Figure 8) of the two datasets indicate that the fitting results of K₀ and K′ in each dataset are highly correlated and both datasets can be fitted almost equally well with K₀ and K′ located in the intersection area of the two ellipses [31], e.g., K’ = 4. In addition, fitting the entire data with single EOS yields a much smaller confidence ellipse lying within the intersection area of the two ellipses, indicating an improvement in the quality of fitting. Therefore, we fitted the two datasets using the second-order BM EOS, and got V₀ = 138.8 ų and K₀ = 127 GPa, and V₀ = 139.0 ų and K₀ = 125 GPa for the data below and above 16 GPa, respectively. The difference between the results of the two datasets is negligible. Therefore, the current volumetric data from x-ray diffraction indicates no second-order phase transition. The final fitting of the entire data into the second-order BM EOS yields V₀ = 138.9 ± 0.5 ų and K₀ = 126 ± 5 GPa. To validate the final choice of the entire data for the EOS fitting, we made a plot of normalized stress F = P/[3f(1+2f)^5/2] vs. Eulerian strain f, i.e., f-F plot (Figure 9). Substituting P in Equation. (9) with F, the third-order BM EOS is expressed as

F = K₀ + (3/2)K₀(K’ − 4)f.

(10)

A linear fit of the f-F plot (Figure 9) yields K₀ = 125.6 GPa and K’= 4.07, which indicates that the second-order BM EOS is an appropriate estimate. A comparison of the EOS parameters for goethite from published reports is given in

Table 2. Comparison of EOS parameters for goethite.

Reference	V0	K0	K’*	Method**	Pressure Medium***	Pressure Calibrant	Pressure Range (GPa)
This study	138.9(5)	126(5)	4	DAC, AD	Ne	Ruby	0–32
Suzuki [16]	138.96(7)	85.9(15)	12.6(8)	LVP, ED	NaCl	NaCl	0–7.55
Xu et al. [10]	138.4(3)	120(3)	4	DAC, AD	He, Ne	Au	0–16
Gleason et al. [1]	138.75(2)	140.3(37)	4.6(4)	DAC, AD	ME(4:1)	Au	0–29.4
Kim et al. [14]	138.8	131.1(58)	4	LVP, ED	ME(4:1)	NaCl	0–9.54
Nagai et al. [15]	140.45(1)	111(2)	4	DAC, AD	ME(4:1)	Ruby	0–24.5
Kim et al. [18]	139.3	147.9	4	DAC, ED	MEW(16:3:1)	MgO	0–27.6
Tunega [32]	138.70	93.5	4	spDFT	-	-	-
	140.86	118.7	4	spDFT+U	-	-	-
Guo et al. [33]	141.49	114.1	-	PW-GGA+U	-	-	-
Otte et al. [34]	144.4	108.8	5.9	GGA+U	-	-	-

* K’ = 4 indicates a fitting with the second-order Birch–Murnaghan equation of state (BM EOS). ** DAC: diamond anvil cell experiment; LVP: large volume press experiment; AD/ED: angle/energy dispersive x-ray diffraction; spDFT: spin-polarized density functional theory; U: the on-site Coulomb repulsion parameter in density functional theory (DFT); PW: plane-wave basis; GGA: generalized gradient approximation in DFT. *** ME: mixture of methanol and ethanol; MEW: mixture of methanol, ethanol, and water.

.

Ruling out the possibilities of a first-order structural transition and a second-order compressibility transition, the origin for the changes observed in Raman spectroscopy and EIS remains unjustified [11]. A theoretical calculation [34] once predicted a pressure-induced structural phase transformation to the high-pressure ε-FeOOH at 6–7 GPa, followed by a high-spin to low-spin transition at 7.7 GPa, using first-principle generalized gradient approximation (GGA). However, experimental studies have indicated that the ε-FeOOH phase only forms at an elevated temperature [1,2], and the predicted spin transition is shifted to a much higher pressure (56 GPa) if the on-site Coulomb repulsion term (U) is included in the GGA calculation [34]. Xu et al. [10] experimentally observed high-spin to low-spin transition in goethite at 45 GPa. Therefore, the transformation to ε-FeOOH phase and the spin transition cannot be responsible for the changes observed in Raman spectroscopy and EIS at 5 and 11 GPa. The theoretical calculation using spDFT by Tunega [32] indicates that a high-spin ferromagnetic (FM) state of goethite may become energetically favorable at about 15 GPa, whereas the high-spin antiferromagnetic (AFM) state is stable at ambient pressure. The GGA+U calculation [34] shows that the FM state at high pressure has a wider bandgap over the AFM state, and, therefore, is expected to have a higher resistance. If we follow these theoretical results, we may speculate that the FM state (higher resistance phase) becomes stable at 5 GPa, and the transition from an AFM to FM state is a sluggish process. Following this speculation, the electrical resistance behavior of goethite from EIS (Figure 5) can be illustrated as a pure AFM state (lower resistance phase) before 5 GPa, a pure FM state (higher resistance phase) above 11 GPa, and a transition stage from AFM to FM between 5 and 11 GPa, resulting in a slow increase of resistance. The pressure-induced AFM to FM transition has been experimentally observed in many other materials, e.g., Au₂Mn [35], EuTe [36], USb₂ [37], SrFeO₃, and CaFeO₃ [38]. The electrical resistance behavior observed in USb₂ is very similar to what we observed here in goethite. Upon compression, the resistance decreases within the AFM phase, increases during the AFM-FM transition, and finally decreases again in the FM phase [37]. The AFM-FM transition pressure assumed here (5 GPa) in goethite is lower than that of the spDFT prediction (15 GPa). Since the major changes in Raman spectra at 11 GPa (delayed to 20 GPa for ν₄ and ν₅ peaks) are exhibited on the slope of the peak shifts with pressure, they are consistent with the AFM-FM transition assumption as well. Further theoretical simulation of the influence of AFM-FM transition on phonon vibrations will be interesting. No apparent crystallographic signature is observed to accompany this transition in our x-ray diffraction data. Suzuki [16] reported an anomaly in the compression behavior along the unit-cell axes at about 5 GPa, but this was not observed in either our compression data (Figure 10) or other published data (except for the effect of pressure-medium solidification) [1,3,10,14,15].

FeOOH was recently found to be stable in a pyrite-type structure in deep mantle conditions [5,6]. If the mineral presents at shallower depths where goethite (a-FeOOH) is stable, its influence on the magnetic properties of Earth’s mantle needs to be considered when understanding the magnetism of Earth’s interior, which is a matter still the subject of much debate [39,40]. Further studies on this may be worthwhile.