Phase diagram and thermoelastic property of iron oxyhydroxide across the spin crossover under extreme conditions

Bo Gan (甘波), Gang Jiang (蒋刚), Yuqian Huang (黄钰倩), Hong Zhang (张红), Qingyang Hu (胡清扬), and Youjun Zhang (张友君)

Phys. Rev. B 107, 064106 – Published 28 February 2023

Abstract

Spin transition and its effect on the physical properties of iron-bearing minerals at high pressure-temperature $(P − T)$ are of great importance for understanding the structural heterogeneity of Earth's mantle. Here, we investigate the phase diagram and thermoelastic properties of iron oxyhydroxide (FeOOH) across the spin crossover using dynamic high $P − T$ experiments and theoretical simulations. The Hugoniot equation of state in FeOOH has been measured up to $\sim 90$ GPa and $\sim 2100$ K in a two-stage light-gas gun and exhibits a density discontinuity between 47 GPa (∼950 K) and 61 GPa (∼1150 K) due to the high-low spin transition of ${Fe}^{3 +}$ , which is consistent with our first-principles calculations. The $P − T$ phase diagram indicates that the shock-elevated temperature shifts the spin transition to a higher pressure and broadens the pressure range of mixed spins. The large volume collapse of FeOOH during its spin crossover leads to remarkable elastic anomalies, with ∼60% softening of adiabatic bulk modulus and a negative Poisson's ratio (−0.1) of abnormal auxeticity in the mixed-spin phase. Our results suggest that FeOOH undergoes an unselective spin transition of ferric iron at the corresponding $P − T$ conditions of the Earth's 1400–1800 km depth and exhibits drastic softening in sound velocities and elastic modulus which may be detected as seismic heterogeneities in subducting slabs of the lower mantle.

Received 31 August 2022
Revised 5 February 2023
Accepted 10 February 2023

DOI:https://doi.org/10.1103/PhysRevB.107.064106

Physics Subject Headings (PhySH)

First-principles calculations Geophysics High-pressure studies Phase diagrams Spin state transition

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Bo Gan (甘波)^1,2, Gang Jiang (蒋刚)¹, Yuqian Huang (黄钰倩)¹, Hong Zhang (张红)³, Qingyang Hu (胡清扬)^4,*, and Youjun Zhang (张友君)^1,5,†

¹Institute of Atomic and Molecular Physics, Sichuan University, Chengdu 610065, China
²Institute for Integrated Radiation and Nuclear Science, Kyoto University, Kumatori, Osaka 590-0494, Japan
³College of Physics, Sichuan University, Chengdu 610065, China
⁴Center for High Pressure Science and Technology Advanced Research, Beijing 100094, China
⁵International Center for Planetary Science, College of Earth Sciences, Chengdu University of Technology, Chengdu 610059, China

^*qingyang.hu@hpstar.ac.cn
^†zhangyoujun@scu.edu.cn

Article Text (Subscription Required)

Click to Expand

Supplemental Material (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 107, Iss. 6 — 1 February 2023

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
Hugoniot equation of state for the natural goethite under shock compression. (a) The relation between the shock velocity and particle velocity $(U_{s} - u_{p})$ . (b) The relation between the Hugoniot pressure and specific volume ( $P - V$ ). The red circles and blue diamonds are experimental data determined by forward and reverse impacts in this paper and reanalyzed from the previous data [12], respectively; the orange and green lines are fitted (or calculated) results for the high- and low-spin states, respectively; the light-shaded area represents the spin crossover region with the mixed-spin state; the dashed violet line is to guide the eye.
Reuse & Permissions
Figure 2
Equation of state of FeOOH across the spin crossover at high pressure-temperature. (a) The density of FeOOH under static and shock compression. (b) Hugoniot temperature of FeOOH under shock compression. The solid red circles are Hugoniot density determined by using natural goethite in this paper; the open violet triangles [5] and blue inverted triangles [13] are densities determined by in situ x-ray diffraction (XRD) at high pressures and 300 K; the solid red line is the pressure-density ( $P$ -ρ) Hugoniot relation of the natural goethite; the red dashed and dotted dashed lines are Hugoniot densities of the high-spin (HS) and low-spin (LS) states from our density functional theory (DFT) calculations, respectively; the blue dashed and dotted dashed lines are isothermal pressure-density relations of the HS and LS states from DFT calculations by Ref. [13], respectively; the carmine line and solid black line (circles) are shock temperatures determined from our DFT calculations and the thermodynamic equation, respectively.
Reuse & Permissions
Figure 3
Phase diagram of the spin crossover of ${Fe}^{3 +}$ in $ɛ − FeOOH$ at high pressure-temperature. The gray circles (this paper), diamonds [5], and triangles [13] represent the high-spin state; the black circles (this paper), diamonds [5], and triangles [13] represent the low-spin (LS) state; the carmine circles are $ɛ − FeOOH$ in the mixed-spin state observed by this paper. Colors in the horizontal column on the bottom right represent fractions of the LS ${Fe}^{3 +}, n_{LS}$ (%), in $ɛ − FeOOH$ . The area surrounded by the black dotted line in (a) is enlarged into (b), which shows that the onset of the spin transition of ${Fe}^{3 +}$ observed in our shock experiments is in good agreement with our first-principles calculations. The double dots and dotted dashed lines represent the proposed mantle [83] and subducting slab geotherms [84], respectively.
Reuse & Permissions
Figure 4
(a) Sound velocities, (b) elastic parameters, and (c) Poisson's ratio of $ɛ − FeOOH$ as a function of pressure. The solid red squares are longitudinal sound velocity $(V_{P})$ measured using a reverse impact method under shock compression [12]; the solid blue squares and circles are $V_{P}$ and shear sound velocity $(V_{S})$ measured using an ultrasonic pulse-echo-overlap method at high pressures and 300 K [30]; the solid wine lines are bulk sound velocity $(V_{B})$ of the high- and low-spin $ɛ − FeOOH$ calculated using the Hugoniot equation of state in this paper; the wine dashed line is $V_{B}$ of the mixed-spin (MS) $ɛ − FeOOH$ estimated using the Hugoniot data in the spin crossover region; the open red circles are the $V_{S}$ calculated based on a combination of our determined $V_{B}$ and the $V_{P}$ from Ref. [12]; the open green triangles, blue inverted triangles, and orange diamonds are adiabatic bulk modulus $(K_{S})$ , shear modulus (μ), and Poisson's ratio (ν) obtained in this paper, respectively; the solid gray line represents the $V_{P}$ of seismic observations from the preliminary reference Earth model (PREM) [87]; the light-shaded area (47–61 GPa) is the spin crossover region with the MS state; all dotted dashed lines are guides to the eye. The uncertainties in the $V_{S}, K_{S}$ , μ, and ν are estimated from the errors in $ρ_{H}, V_{P}$ , and $V_{B}$ by using error propagation.
Reuse & Permissions
Figure 5
Comparisons of (a) longitudinal sound velocity and (b) adiabatic bulk modulus between typical hydrous phases and other lower-mantle minerals at the conditions relevant to the lower mantle. Data sources: $ɛ − FeOOH$ (solid red squares), this study, and Ref. [12]; δ-AlOOH (green curves), Ref. [104]; Phase H (cyan curves), Ref. [105]; $NaAlSi O_{4}$ (blue curves) and $Mg {Al}_{2} O_{4}$ (carmine curves), Ref. [107]; $CaSi O_{3}$ (orange curves), Ref. [106]; solid black curves are preliminary reference Earth model (PREM) values [87]. The dotted dashed lines are used to guide the eye, and the light-shaded area shows the spin crossover region of ${Fe}^{3 +}$ in $ɛ − FeOOH$ .
Reuse & Permissions

Physical Review B

covering condensed matter and materials physics