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BY-NC-ND 4.0 license Open Access Published by De Gruyter September 20, 2020

Thermal equation of state of post-aragonite CaCO3-Pmmn

Mingda Lv ORCID logo , Jiachao Liu , Eran Greenberg ORCID logo , Vitali B. Prakapenka and Susannah M. Dorfman ORCID logo
From the journal American Mineralogist

Abstract

Calcium carbonate (CaCO3) is one of the most abundant carbonates on Earth’s surface and transports carbon to Earth’s interior via subduction. Although some petrological observations support the preservation of CaCO3 in cold slabs to lower mantle depths, the geophysical properties and stability of CaCO3 at these depths are not known, due in part to complicated polymorphic phase transitions and lack of constraints on thermodynamic properties. Here we measured thermal equation of state of CaCO3-Pmmn, the stable polymorph of CaCO3 through much of the lower mantle, using synchrotron X‑ray diffraction in a laser-heated diamond-anvil cell up to 75 GPa and 2200 K. The room-temperature compression data for CaCO3-Pmmn are fit with third-order Birch-Murnaghan equation of state, yielding KT0 = 146.7 (±1.9) GPa and K0 = 3.4(±0.1) with V0 fixed to the value determined by ab initio calculation, 97.76 Å3. High-temperature compression data are consistent with zero-pressure thermal expansion αT = a0 + a1T with a0 = 4.3(±0.3)×10-5 K-1, a1 = 0.8(±0.2)×10-8 K-2, temperature derivative of the bulk modulus (∂KT/∂T)P = –0.021(±0.001) GPa/K; the Grüneisen parameter γ0 = 1.94(±0.02), and the volume independent constant q = 1.9(±0.3) at a fixed Debye temperature θ0 = 631 K predicted via ab initio calculation. Using these newly determined thermodynamic parameters, the density and bulk sound velocity of CaCO3-Pmmn and (Ca,Mg)-carbonate-bearing eclogite are quantitatively modeled from 30 to 80 GPa along a cold slab geotherm. With the assumption that carbonates are homogeneously mixed into the slab, the results indicate the presence of carbonates in the subducted slab is unlikely to be detected by seismic observations, and the buoyancy provided by carbonates has a negligible effect on slab dynamics.

Introduction

Calcium carbonate (CaCO3) in the form of calcite is one of the most abundant carbonates on Earth’s surface (reviewed by Luth 1999) and an important vector of carbon to Earth’s interior. Calcite can be sequestered in the oceanic crust by hydrothermal alteration and biological activity and transferred to the mantle in subducting slabs (Dasgupta and Hirschmann 2010; Kelemen and Manning 2015; Staudigel 2014). However, four major chemical processes have been argued to block the transport of CaCO3 transport to the lower mantle: (1) melting of carbonate and carbonated peridotite or eclogite (e.g., Dasgupta and Hirschmann 2006; Ghosh et al. 2014; Kiseeva et al. 2013; Thomson et al. 2016); (2) reduction of carbonate solid or melt through reaction with iron or other reduced phases, generating diamond (e.g., Dorfman et al. 2018; Palyanov et al. 2013; Rohrbach and Schmidt 2011); (3) carbonate-silicate exchange consuming CaCO3 to form Caperovskite and MgCO3 (e.g., Biellmann et al. 1993; Seto et al. 2008); and (4) decarbonation of CaCO3 with free silica phase to form Ca-perovskite, CO2, or C (e.g., Drewitt et al. 2019; Li et al. 2018). Whether the energetics and kinetics of these reactions lead to complete loss of CaCO3 from very cold and/or fast subducting slabs has been controversial (e.g., Martirosyan et al. 2016 though superdeep diamonds with CaCO3 inclusions coexisting with lower mantle phases such as CaSiO3 (Brenker et al. 2007; Bulanova et al. 2010) prove the existence of CaCO3 in at least some regions of the transition zone and lower mantle. To determine the conditions needed to preserve CaCO3 in these regions and its fate during subduction to the mantle, experimental constraints on thermodynamic behavior of CaCO3 are needed at lower-mantle conditions.

At mantle pressure and temperature (P-T) conditions, multiple polymorphic phase transitions of CaCO3 have recently been discovered and debated, with potentially important effects on melting and other chemical reactions in the mantle. Calcite is stable up to ~3 GPa and then transforms to aragonite with space group Pnma (CaCO3-Pnma), which remains stable through the transition zone and shallow lower mantle (e.g., Litasov et al. 2017). The reported melting curves of CaCO3-Pnma and a mixture of CaCO3-MgCO3 are higher than a hot slab geotherm (Li et al. 2017; Thomson et al. 2014), suggesting that subducted CaCO3 may survive melting in the transition zone and travel to the lower mantle. At lower mantle pressures, the post-aragonite structures have been a subject of active recent research, and experimental studies from ~40 to 50 GPa have identified a transition to an orthorhombic structure, or transitions to an intermediate monoclinic structure then an orthorhombic structure. The orthorhombic structure is most commonly termed “post-aragonite” (CaCO3-Pmmn), which was first identified by Ono et al. (2005) at ~40 GPa and confirmed by computational structure simulations (Oganov et al. 2006). More recently, a monoclinic P21/c structure (CaCO3-P21/c-1, “-l” = low-pressure) was predicted to be an intermediate stable phase from ~40 to 50 GPa between CaCO3-Pnma and CaCO3-Pmmn (Gavryushkin et al. 2017; Pickard and Needs 2015; Smith et al. 2018). CaCO3-P21/c-1 was observed experimentally (Gavryushkin et al. 2017; Li et al. 2018; Smith et al. 2018), but the transition from monoclinic to CaCO3-Pmmn was found to be kinetically challenging (Smith et al. 2018). Near the base of Earth’s mantle, CaCO3 is expected to transform from one of these sp2-hybridized post-aragonite structures to one of multiple proposed sp3-hybridized post-post-aragonite structures. The first sp3-hybridized post-post-aragonite to be identified was a pyroxene-structured C2221 phase (CaCO3-C2221) observed at pressures higher than 130 GPa, corresponding to conditions near the core-mantle boundary (Oganov et al. 2006, 2008; Ono et al. 2007). A second monoclinic P21/c structure with sp3-hybridization, termed CaCO3-P21/c-h (“-h” = high-pressure, to distinguish it from the lower-pressure “-1” polymorph), was predicted to be more favorable than CaCO3-C2221 (Pickard and Needs 2015) and observed at pressures as low as ~105 GPa (Lobanov et al. 2017). Although the stable forms of CaCO3 at the top and bottom of the lower mantle and conditions of the sp2- to sp3-hybridization transition in CaCO3 remain controversial, CaCO3-Pmmn is thought to be the stable phase of CaCO3 throughout most of the lower mantle (see phase diagram of CaCO3 proposed by Gavryushkin et al. 2017; Smith et al. 2018; Zhang et al. 2018).

The stability and abundance of CaCO3-Pmmn can be modeled in the Earth using constraints on thermoelastic behavior, including accurate thermal equation of state (EoS) measurements and corresponding thermoelastic parameters such as bulk modulus, its pressure and temperature derivatives, and thermal expansion coefficient. However, in contrast to the relatively well-known thermoelastic behavior of CaCO3-Pnma (Li et al. 2015; Litasov et al. 2017; Palaich et al. 2016; Ye et al. 2012), experimental and computational constraints on the EoS of CaCO3-Pmmn have been limited to 300 K (Lobanov et al. 2017; Ono et al. 2005) and 0 K (Oganov et al. 2006), respectively, without addressing high-temperature expansion behavior. To accurately model the phase equilibrium and physical properties of CaCO3 at lower mantle conditions, the thermal EoS of CaCO3-Pmmn is required.

In this study, we investigate the structural stability of CaCO3-Pmmn and establish its thermal EoS up to 75 GPa and 2200 K using synchrotron X‑ray diffraction in a laser-heated diamond-anvil cell (LHDAC). The physical properties of CaCO3 along a cold subducting slab geotherm are calculated using the thermal EoS parameters, which are compared with the other major end-member carbonate, MgCO3. By combining the newly obtained parameters with literature thermodynamic parameters of mineral phases in the subducted slab, we model the effects of the presence of CaCO3-MgCO3 mixture on the density and bulk sound velocity of the carbonate-rich subducting slab at lower mantle conditions.

Experimental methods

CaCO3-Pmmn was synthesized from calcite under high-pressure and temperature conditions using a LHDAC. Sample material was prepared by mixing calcite powder (99.95%, Alfa Aesar) with 5 wt% micrometer-scale Au powder (99.95%, Goodfellow), which serves as a laser absorber and pressure calibrant. The mixture was mechanically ground under ethanol for 1 h, then dried in an oven at 120 °C overnight to remove moisture contamination. The powder was slightly compressed to form a ~10 μm thick disk for loading into the DAC. We used a symmetric DAC equipped with a pair of 150 μm culet beveled anvils to generate high pressures. A rhenium gasket 250 μm thick was pre-indented to ~25 μm, and a hole with 75 μm diameter was drilled in the center of the indentation, serving as the sample chamber. To separate the sample disk from the diamond anvils, we loaded a sample disk into the sample chamber supported by three small ~5 μm thick calcite spacers. To achieve quasi-hydrostatic conditions in the sample chamber, Ne was loaded as pressure transmitting medium and thermal insulator using the COMPRES/ GSECARS gas-loading system (Rivers et al. 2008).

The thermal EoS of CaCO3-Pmmn was determined using synchrotron X‑ray diffraction with in situ laser heating carried out at beamline 13-ID-D of the Geo-SoilEnviroCARS sector of the Advanced Photon Source (APS), Argonne National Laboratory (ANL). The monochromatic X‑ray beam with a wavelength of 0.3344 Å was focused on an area of ~2.5 × 3 μm2 on the sample. Each two-dimensional X‑ray diffraction image was recorded on a CdTe 1M Pilatus detector for 30 s, and subsequently integrated using Dioptas software (Prescher and Prakapenka 2015). The sample-to-detector distance, tilt, and rotation of the detector relative to the incident X‑ray beam were calibrated using the diffraction pattern of LaB6 powder at ambient conditions. The sample was heated using a flat-top double-sided laser heating system (Prakapenka et al. 2008). Two 1.064 μm laser beams were focused to 20 μm diameter on both sides of the sample, and coaxially aligned with the incoming X‑ray beam by using the X‑ray-induced luminescence on the sample. Temperatures during heating were determined by fitting the measured thermal radiation spectra using the Planck radiation function under the graybody approximation (Prakapenka et al. 2008). The uncertainty of temperatures is ±100 K up to 2000 K and ±150 K higher than 2000 K based on multiple temperature measurements from both sides of the laser-heated sample. Pressures were calculated using the thermal EoS of the Au standard (Fei et al. 2007), with uncertainties propagating from those of temperatures, unit-cell volumes of Au, and thermal EoS parameters of Au, and the unit-cell volumes of Au were derived from diffraction lines (111), (200), (220), and (311) (Figs. 1 and 2).

Figure 1 
          Full-profile Le Bail analysis confirms the synthesis of CaCO3-Pmmn. Measured XRD data for the quenched sample after heating at 49 GPa and 300 K (black dots) are consistent with orthorhombic post-aragonite structure (space group Pmmn with Z = 2) (black ticks below). Le Bail fit (red curve) also includes expected peaks for Au calibrant (yellow sticks) and Ne medium (blue ticks). One unknown peak around ~7° (marked by an asterisk) may be from the metastable CaCO3-P21/c-l due to slow kinetics. The wavelength of the monochromatic X‑ray beam is 0.3344 Å. (Color online.)
Figure 1

Full-profile Le Bail analysis confirms the synthesis of CaCO3-Pmmn. Measured XRD data for the quenched sample after heating at 49 GPa and 300 K (black dots) are consistent with orthorhombic post-aragonite structure (space group Pmmn with Z = 2) (black ticks below). Le Bail fit (red curve) also includes expected peaks for Au calibrant (yellow sticks) and Ne medium (blue ticks). One unknown peak around ~7° (marked by an asterisk) may be from the metastable CaCO3-P21/c-l due to slow kinetics. The wavelength of the monochromatic X‑ray beam is 0.3344 Å. (Color online.)

Figure 2 
          ( a ) Representative in situ XRD patterns of CaCO3-Pmmn measured at high pressures and room temperature (black marker). (b) Representative high-temperature XRD patterns of CaCO3-Pmmn at ~60 GPa (black marker) measured in situ in a laser-heated diamond-anvil cell. In all XRD patterns, Au was used as the internal pressure calibrant (Fei et al. 2007) and laser-absorber (orange marker), while Ne was used as the thermal insulator and pressure medium (blue marker). The wavelength of the monochromatic X‑ray beam is 0.3344 Å. (Color online.)
Figure 2

( a ) Representative in situ XRD patterns of CaCO3-Pmmn measured at high pressures and room temperature (black marker). (b) Representative high-temperature XRD patterns of CaCO3-Pmmn at ~60 GPa (black marker) measured in situ in a laser-heated diamond-anvil cell. In all XRD patterns, Au was used as the internal pressure calibrant (Fei et al. 2007) and laser-absorber (orange marker), while Ne was used as the thermal insulator and pressure medium (blue marker). The wavelength of the monochromatic X‑ray beam is 0.3344 Å. (Color online.)

Results and discussion

Synthesis and stability of CaCO3-Pmmn

The starting material calcite was directly compressed in a DAC to the target pressure of 49 GPa before laser heating to synthesize the stable lower-mantle form of CaCO3. Upon heating at 1800 K and then quenching to 300 K, CaCO3-Pmmn was confirmed by full-profile analysis of XRD pattern using the Le Bail method (Le Bail et al. 1988) as implemented in the GSAS/EXPGUI program (Toby 2001) (Fig. 1). In contrast, some previous studies that attempted synthesis from CaCO3-Pnma or CaCO3-P21/c-l (Gavryushkin et al. 2017; Smith et al. 2018) failed to obtain complete transformation to CaCO3-Pmmn, perhaps due to thermal gradients during laser heating and/or high kinetic barriers to transitions between these structures. Sharp diffraction peaks of Au after annealing and intense diffraction from Ne pressure medium support quasi-hydrostatic stress conditions in the sample chamber (Figs. 1 and 2). An additional diffraction peak is observed at a d-spacing of 2.6 Å, which broadens with increasing pressure and disappears above 60 GPa, probably representing metastable CaCO3-P21/c-l retained due to phase transition kinetics (Bayarjargal et al. 2018; Gavryushkin et al. 2017; Li et al. 2018; Smith et al. 2018). The unit-cell parameters of CaCO3-Pmmn at 300 K and 49 GPa are consistent with previous observations (Gavryushkin et al. 2017; Ono et al. 2005) within uncertainties (Fig. 1). As pressure and temperature increased, in situ XRD patterns exhibited no splitting or broadening of CaCO3-Pmmn peaks, indicating no melting, dissociation or phase transition occurred (Figs. 1 and 2). This study concurs with other previous studies (e.g., Gavryushkin et al. 2017; Oganov et al. 2006; Ono et al. 2005) that CaCO3-Pmmn is the stable form of CaCO3 up to 75 GPa and 2200 K.

After synthesis of CaCO3-Pmmn, we further compressed the sample Figure at ~2–3 GPa 1 intervals from 50 to 75 GPa, the minimum range of stability of this phase (Gavryushkin et al. 2017; Smith et al. 2018; Zhang et al. 2018). At each target pressure, we collected XRD patterns of the sample at 300 K before and after heating, and we collected high-temperature patterns while the temperature was increasing at ~50–100 K intervals from ~1000 to 2200 K (Fig. 2). The lattice parameters of CaCO3-Pmmn were obtained by least-squares fitting of diffraction lines (111), (020), (200), and (021) using PDIndexer software (Seto et al. 2010), and are provided in the Supplemental[1] Table S1.

To directly compare unit-cell volumes observed at 300 K for CaCO3-Pmmn to previous studies (Lobanov et al. 2017; Ono et al. 2005), we recalculated previously reported pressures using the Pt scale of Fei et al. (2007) for consistency with Au scale applied in this study (Fig. 3a). With this correction, all P-V data are consistent within uncertainty over the pressure range examined in this work.

Figure 3 
            (a) Pressure-volume data for CaCO3-Pmmn at room temperature from this study (black circle) and previous studies. Data from Ono et al. (2005) (red square) and Lobanov et al. (2017) (blue square) were recalculated using Pt pressure scale (Fei et al. 2007). Black solid curve (this study) is modeled by BM3 EoS using KT0 = 162(±62) GPa, K0 = 3.1 (±1.1), and V0 = 96.6(±4.8) Å3. A brown dashed curve (′Oganov et al. 2006) and a purple dashed curve (Marcondes et al. 2016) modeled by BM3 EoS are constrained via DFT-GGA and LDA, respectively. (b) Isothermal bulk modulus (KT) at 300 K calculated by BM3 EoS. The black solid line, dashed line and short-dashed line represent the BM3 EoS fittings without constraint, with a fixed V0 = 97.76 Å3 and with reference pressure set at 50 GPa. (Color online.)
Figure 3

(a) Pressure-volume data for CaCO3-Pmmn at room temperature from this study (black circle) and previous studies. Data from Ono et al. (2005) (red square) and Lobanov et al. (2017) (blue square) were recalculated using Pt pressure scale (Fei et al. 2007). Black solid curve (this study) is modeled by BM3 EoS using KT0 = 162(±62) GPa, K0 = 3.1 (±1.1), and V0 = 96.6(±4.8) Å3. A brown dashed curve (′Oganov et al. 2006) and a purple dashed curve (Marcondes et al. 2016) modeled by BM3 EoS are constrained via DFT-GGA and LDA, respectively. (b) Isothermal bulk modulus (KT) at 300 K calculated by BM3 EoS. The black solid line, dashed line and short-dashed line represent the BM3 EoS fittings without constraint, with a fixed V0 = 97.76 Å3 and with reference pressure set at 50 GPa. (Color online.)

Compressibility of CaCO3-Pmmn at 300 K

Because all previous compression data for CaCO3-Pmmn were obtained at room temperature only, and the room-temperature isotherm provides a useful constraint on the P-V-T EoS, we first address the 300 K P-V EoS of CaCO3-Pmmn. P-V data of CaCO3-Pmmn obtained at 300 K were fit to a third-order Birch-Murnaghan equation of state (BM3 EoS) (Birch 1952) using the error-weighted least squares method to constrain zero-pressure parameters including unit-cell volume (V0), bulk modulus (KT0), and its pressure derivative (K0')(Fig. 3a and Table 1). We first fit the data using BM3 EoS without constraints on parameters, V0=96.6(±4.8)Ao3,KT0=162(±62)GPa,K0'=3.1(±1.1).yielding The large uncertainties in fitted parameters reflect the long extrapolation from high-pressure data to 1 bar for this unquenchable phase, but the compressibility at mantle-relevant pressures is well-constrained.

Table 1

Comparison of parameters of BM3 EoS of CaCO3-Pmmn at 300 K

V 03) K T0 (GPa) K0 Method References
99.4(20) 118(14) 4 (fixed) XRD (PM[a]: NaCl) Ono et al. (2005) [b]
97.3(16) 135(12) 4 (fixed) XRD (No PM) Lobanov et al. (2017) [b]
109.74 65.4 4.94 DFT-GGA[c] Oganov et al. (2006)
97.76 122 3.732 DFT-LDA[c] Marcondes et al. (2016)
96.6(48) 162(62) 3.1(11) XRD (PM: Ne)[d] This study
97.76 (fixed) 146.7(19) 3.4(1) XRD (PM: Ne)[d] This study
  1. Note: Numbers in parentheses are uncertainties on the last digits.

Previous experimental studies (Ono et al. 2005; Lobanov et al. 2017) reported EoS parameters that may differ due to different scales used to determine pressure, extrapolation to 1 bar, and the choice ′to fix K0 = 4, as well as differences in hydrostatic conditions due to choice of pressure media. Experimental volumes obtained by Lobanov et al. (2017) without a pressure medium above ~90 GPa are large relative to our extrapolated EoS even with pressures corrected to match the pressure scale in this study (Fig. 3a), corresponding to a relatively high incompressibility at mantle pressures. However, the incompressibility KT0 reported by both previous studies is relatively low compared to our unconstrained fit. This parameter trades off with relatively high V0 and K0 in these studies. Since CaCO3-Pmmn is an unquenchable phase and reverts to calcite upon decompression (Ono et al. 2005), the unit-cell volume at ambient pressure cannot be measured directly, which leads to large uncertainties on the 1 bar parameters. We therefore also fit our 300 K data setting 50 GPa as the reference pressure and obtain K50 = 302(±15) GPa, K50'=2.1(±1.7),and V50 = 77.526(±0.046) Å3. A fit to the 300 K data from Ono et al. (2005) and Lobanov et al. (2017) setting 50 GPa as the reference pressure yields larger K50 (Fig. 3b). This difference is consistent with less hydrostatic conditions in the sample chamber provided by NaCl medium in Ono et al. (2005) and no pressure medium in Lobanov et al. (2017) relative to the quasi-hydrostatic conditions provided by Ne medium and frequent annealing in this study.

Analysis of the finite Eulerian strain corresponding to compression behavior of CaCO3-Pmmn supports the low K0'from the BM3 EoS. P-V data can be described by the normalized stress {fE = [(V0/V)2/3 – 1]/2} vs. the finite Eulerian strain {FE = P/[3fE(1 + 2fE)5/2]} plot (Fig. 4), where FE=KT0+1.5KT0fE(K0'4).The intercept value, FE(0) = 162(±2) GPa, agrees with KT0 obtained from the fit to the BM3 EoS, and the negative slope indicates K0 is smaller than 4 (Angel 2000), which is consistent with our fitting results.

Figure 4 
            Volume Eulerian strain (f) to normalized pressure (F) plot of CaCO3-Pmmn. The dashed line represents the linear fit through the data, and a red envelope indicates 95% confidence interval. The V0 was set as 96.6 Å3 obtained by BM3 EoS fitting of experimental data at 300 K. (Color online.)
Figure 4

Volume Eulerian strain (f) to normalized pressure (F) plot of CaCO3-Pmmn. The dashed line represents the linear fit through the data, and a red envelope indicates 95% confidence interval. The V0 was set as 96.6 Å3 obtained by BM3 EoS fitting of experimental data at 300 K. (Color online.)

The EoS obtained by DFT-GGA (Oganov et al. 2006) and DFT-LDA (Marcondes et al. 2016) serve as upper and lower bounds of experimental measurements, respectively (Fig. 3a). Marcondes et al. (2016) provide the only previous predictions of the elastic shear properties of CaCO3-Pmmn, which are necessary to directly compare our results for thermoelastic parameters derived by MGD EoS (discussed in the following section). We thus provide an additional fit to our 300 K P-V data with V0 fixed to 97.76 Å3 as predicted by DFT-LDA, yielding KT0 = 146.7 (±1.9) GPa and K0'=3.4(±0.1).Smaller KT0 and larger K0 relative to the unconstrained BM3 EoS are mainly due to the tradeoffs between V0,KT0,andK0'(Supplemental[1] Fig. S1). The modeled KT at pressures from 50–80 GPa (black dashed line in Fig. 3b) are consistent with the fits without a fixed V0 (black solid line in Fig. 3b).

Thermal equation of state of CaCO3-Pmmn

To constrain the thermal EoS unit-cell volumes for CaCO3-Pmmn are determined up to 75 GPa and 2200 K (Supplemental[1] Table S1), with temperature measured by spectroradiometry and pressure using the thermal EoS of Au (Fei et al. 2007). We use two approaches to constrain high-temperature behavior: (1) obtaining thermal expansion coefficient (αT) from fitting P-V-T data to a high-temperature BM3 EoS (HT-BM3 EoS) (Birch 1952; Fei 1995) (Fig. 5a), and (2) obtaining Grüneisen parameter (γ0) from a Mie-Grüneisen-Debye equation of state (MGD EoS) (Jackson 1998; Jackson and Rigden 1996) (Fig. 5b). Both the MGD EoS and HT-BM3 EoS models can mathematically describe our experimental measurements well (Fig. 5), but have complementary strengths and weaknesses in terms of fitting tradeoffs, assumptions, and sensitivity to physically meaningful quantities. To be more specific, the MGD EoS formulation is based on statistical mechanics, i.e., Debye’s approximation, but is not directly comparable to experiments; whereas the HT-BM3 EoS formulation is based on finite strain theory to empirically express experimental measurements, but can lead to poor extrapolation beyond experimental conditions (Poirier 2000). Both models have been widely applied to Earth materials with thermodynamic databases used in geophysical studies, such as the study of Fabrichnaya et al. (2004) based on HT-BM3 EoS, and that of Stixrude and Lithgow-Bertelloni (2011) based on MGD EoS. We present both models to allow the reader to assess the effects of tradeoffs, and to directly use and compare our results to the previous results in these thermodynamic databases.

Figure 5 
            Measured pressure-volume-temperature data for CaCO3-Pmmn. Colorful curves are isotherms at 1300, 1600, 1900, and 2200 K modeled by (a) HT-BM3 EoS and (b) MGD EoS, with parameters listed in Table 2. Black points and curve are at 300 K same as Figure 3. The lower panel of each figure shows fitting residuals. (Color online.)
Figure 5

Measured pressure-volume-temperature data for CaCO3-Pmmn. Colorful curves are isotherms at 1300, 1600, 1900, and 2200 K modeled by (a) HT-BM3 EoS and (b) MGD EoS, with parameters listed in Table 2. Black points and curve are at 300 K same as Figure 3. The lower panel of each figure shows fitting residuals. (Color online.)

Table 2

Thermoelastic parameters of CaCO3, MgCO3, and major components in eclogite

Sample V 03) K T0 (GPa) K 0 KT/∂T (GPa×K–1) a 0 (10–5K–1) a 1 (10–8K–2) θ0 (K) γ0 q
CaCO3-Pmmn[a] 97.76[e] 146.7(19)[e] 3.4(1)[e] –0.021(1) 4.3(3) 0.8(2) 631[e] 1.94(2) 1.9(3)
CaCO3-Pmmn[a] 97.76[e] 146(5) 3.4(2) –0.022(8) 4.4(5) 0.9(8)
CaCO3-Pmmn[a] 97.76[e] 151(4) 3.2(2) 631[e] 1.6(5) 1.3(9)
CaCO3-Pmmn[a] 97.76[e] 146.7(19)[e] 3.4(1)[e] 631[e] 1.53(1) 1[e]
CaCO3-Pnma[b] 227.11(3)[f] 67.0(8) 4.74(12) –0.016(1) 4.95(22) 2.77(40) 516[e] 1.39(1) 1[e]
MgC O 3 R 3 ¯ c [c] 279.55(2) 97.1(5) 5.44(7) –0.013(1) 4.03(7) 0.49(10) 747[e] 1.38(1) 1[e]
MgSiO3 (perovskite)[d] 162.40 251(3) 4.1(1) 905(5) 1.57(5) 1.1(3)
FeSiO3 (perovskite)[d] 169.31 272(40) 4.1(10) 871(26) 1.57(30) 1.1(10)
MgAl2O4 (cf )[d] 480.63 211(1) 4.1(1) 838(16) 1.31(30) 1.0(10)
FeAl2O4 (cf )[d] 494.97 211(10) 4.1(10) 804(69) 1.31(30) 1.0(10)
CaSiO3 (perovskite)[d] 45.58 236(4) 3.9(2) 796(44) 1.89(7) 0.9(16)
SiO2 (stishovite)[d] 46.56 314(8) 3.8(1) 1108(13) 1.37(17) 2.8(22)

The HT-BM3 EoS is given by the following expression for P(V,T):

P ( V , T ) = ( 3 2 ) K T [ ( V T , 0 V ) 7 3 ( V T , 0 V ) 5 3 ] { 1 + 3 4 ( K T ' 4 ) [ ( V T , 0 V ) 2 3 1 ] }

where KT denotes isothermal bulk modulus at ambient pressure and a given high temperature, VT,0 is the ambient pressure volume, V is the high-pressure and temperature volume, and KT is the pressure derivative of KT0 at ambient pressure, neglecting higher-order pressure derivatives of the bulk modulus and assuming that KT is a constant in the temperature range of our study, i.e., K0. The temperature effect on KT can be expressed as a linear function of temperature, with the temperature derivative at ambient pressure (∂KT/∂T)P and KT0 as follow:

K T = K T0 + ( K T / T ) P ( T T 0 )

where T0 is the reference temperature, 300 K. (∂KT/∂T)P is assumed to be a constant within the temperature range of our study. The temperature dependence of the volume at ambient pressure, VT,0, can be expressed as a function of the thermal expansion at zero pressure:

V T, 0 = V 0 exp ( T 0 T α T d T )

The thermal expansion coefficient αT is expressed as αT = (1/V) (∂V/∂T)P. At atmospheric pressure, αT can be approximated to a linear function of temperature:

α T = a 0 + a 1 T

where a0 and a1 are constants. By least-squares fitting with the parameters V0,KT0,andK0fixed from the 300 K BM3 EoS, we obtained a0, a1, and (∂KT/∂T)P. We further fit the P-V-T data with a fixed V0 to 97.76 Å3 alone, yielding KT0,K0',a0,a1,and(KT/T)P,which are consistent with the first fitting within uncertainties (Table 2). The isothermal compression curves for temperatures from 1300 to 2200 K at 300 K intervals were calculated from these thermoelastic parameters (Fig. 5a). The fitting residuals indicate the discrepancies between measured and calculated pressure are ranging from –1.7 to 1.4 GPa within the investigated pressure and temperature range (Fig. 5a), indicating the fitted HT-BM3 EoS can describe our experimental measurements well.

In the MGD EoS, the total pressure P(V,T) is expressed as the sum of the static pressure at room temperature, P(V,T0), and the thermal pressure, Pth(V,T):

P ( V , T ) = P ( V , T 0 ) + P th ( V , T )

where P(V,T0) is fixed by BM3 EoS at 300 K, and the thermal pressure Pth(V,T) is a function of the Grüneisen parameter γ and the thermal energy Eth(V,T), that can be estimated using a Debye model:

P th ( V , T ) = γ ( V , T ) V [ E th ( V , T ) E th ( V , T 0 ) ] , E th ( V , T ) = 9 nR T ( θ / T ) 3 0 θ / T x 3 e x 1 d x ,

where θ is the Debye temperature, n = 5 is the number of atoms in the formula unit, and R is the gas constant [8.314 J/(mol∙K)]. The volume dependences of θ and γ are described by:

θ = θ 0 exp ( γ 0 γ q ) γ = γ 0 ( V V 0 ) q

where q is the dimensionless power mode parameter, γ0 and θ0 are Grüneisen parameter and Debye temperature at 300 K, respectively. As above, V0, KT0, and K0 are fixed from the 300 K EoS. θ0 can be evaluated more precisely from sound velocities using equations based on Debye’s lattice vibration model (Poirier 2000). With self-consistent elastic parameters at zero pressure KS0 = 122 GPa, G0 = 56 GPa, and ρ0 = 3.4 g/cm3 reported by (Marcondes et al. 2016), the θ0 for CaCO3-Pmmn was estimated to be 631 K. Due to strong correlations between the three high-temperature parameters θ0, γ0, and q, we fixed θ0 and obtained the fitted γ0 = 1.94(±0.02) and q = 1.9(±0.3). To investigate the tradeoff between γ0 and q, we further fix q = 1 as a common assumption, yielding γ0 = 1.53(±0.01). We also fit the P-V-T data with a fixed V0 to 97.76 Å3 and θ0 to 631 K alone, yielding KT0 = 151(±4) GPa, K0 = 3.2(±0.2), γ0 = 1.6(±0.5), and q = 1.3(±0.9), which are in agreement with the first fit within uncertainties (Table 2). These thermoelastic parameters produce isothermal compression curves (Fig. 5b) consistent with those obtained from HT-BM3 EoS (Fig. 5a). The fitting residuals indicate the discrepancies between measured and calculated pressure range from –1.7 to 1.7 GPa within the investigated pressure and temperature range (Fig. 5b). In summary, both HT-BM3 EoS and MGD EoS results here comprise the first characterization of high-temperature properties of CaCO3-Pmmn and can be used to model the chemical and physical properties of CaCO3 in the lower mantle.

Neither of EoS yields a superior or significantly different fit to the experimental data (Fig. 5) and the results for density and bulk sound velocity of CaCO3-Pmmn are not significantly affected by the choice of EoS. Calculated densities and velocities follow geotherms from 45 to 80 GPa (Figs. 6 and 7), which does not extrapolate from our experimental P-T conditions significantly and minimizes the potential errors produced by extrapolation of the thermal equation of state.

Figure 6 
            Modeled (a) density and (b) bulk sound velocity profiles of CaCO3 and MgCO3 from 30 to 80 GPa along mantle geotherm (Brown and Shankland 1981) compared to PREM model (Dziewonski and Anderson 1981) and eclogite (assumed to be composed by 27 mol% bridgmanite [(Mg0.9,Fe0.1)SiO3], 24 mol% Ca-perovskite (CaSiO3), 20 mol% stishovite (SiO2), 29 mol% Al-bearing calcium-ferrite-type silicate [(Mg0.9,Fe0.1)Al2O4]), using the thermoelastic parameters listed in Table 2. To clearly illustrate the density contrast of different carbonates, the phase transition of CaCO3-Pnma to CaCO3-Pmmn is assumed to occur at 45 GPa. (Color online.)
Figure 6

Modeled (a) density and (b) bulk sound velocity profiles of CaCO3 and MgCO3 from 30 to 80 GPa along mantle geotherm (Brown and Shankland 1981) compared to PREM model (Dziewonski and Anderson 1981) and eclogite (assumed to be composed by 27 mol% bridgmanite [(Mg0.9,Fe0.1)SiO3], 24 mol% Ca-perovskite (CaSiO3), 20 mol% stishovite (SiO2), 29 mol% Al-bearing calcium-ferrite-type silicate [(Mg0.9,Fe0.1)Al2O4]), using the thermoelastic parameters listed in Table 2. To clearly illustrate the density contrast of different carbonates, the phase transition of CaCO3-Pnma to CaCO3-Pmmn is assumed to occur at 45 GPa. (Color online.)

Figure 7 
            Modeled (a) bulk sound velocity and (b) density profiles of eclogite and carbonated-eclogites with the presence of CaCO3-MgCO3 mixtures of 2, 5, and 10 mol%. The eclogite is assumed to be composed by 27 mol% bridgmanite [(Mg0.9,Fe0.1)SiO3], 24 mol% Ca-perovskite (CaSiO3), 20 mol% stishovite (SiO2), 29 mol% Al-bearing calcium-ferrite-type silicate [(Mg0.9,Fe0.1)Al2O4], and the thermoelastic parameters of these phases are listed in Table 2. The pressure ranges from 30 to 80 GPa along cold geotherm (Syracuse et al. 2010). The CaCO3-Pnma to CaCO3-Pmmn transition is assumed to occur at 45 GPa. The PREM model (Dziewonski and Anderson 1981) is plotted as a comparison of the averaged mantle. (Color online.)
Figure 7

Modeled (a) bulk sound velocity and (b) density profiles of eclogite and carbonated-eclogites with the presence of CaCO3-MgCO3 mixtures of 2, 5, and 10 mol%. The eclogite is assumed to be composed by 27 mol% bridgmanite [(Mg0.9,Fe0.1)SiO3], 24 mol% Ca-perovskite (CaSiO3), 20 mol% stishovite (SiO2), 29 mol% Al-bearing calcium-ferrite-type silicate [(Mg0.9,Fe0.1)Al2O4], and the thermoelastic parameters of these phases are listed in Table 2. The pressure ranges from 30 to 80 GPa along cold geotherm (Syracuse et al. 2010). The CaCO3-Pnma to CaCO3-Pmmn transition is assumed to occur at 45 GPa. The PREM model (Dziewonski and Anderson 1981) is plotted as a comparison of the averaged mantle. (Color online.)

Implications

Due to the substantially lower density of carbonates relative to the principal constituents of the lower mantle (Fig. 6a), sufficient amounts of carbonates may be expected to affect the buoyancy of the subducting slab and its seismic signature, which manifestations could be used to constrain the survival and behavior of carbonates subducted into Earth’s lower mantle. Calcite/aragonite is one of the most abundant carbonates at shallow depths, along with dolomite [CaMg(CO3)2] and magnesite (MgCO3) (Luth 1999). During subduction, CaMg(CO3)2 breaks down to MgCO3 and CaCO3 above 5 GPa (Luth 2004). The two end-member carbonates, CaCO3 and MgCO3, have melting points above typical slab geotherms and thus have been suggested to remain stable in the lower mantle (Li et al. 2017; Solopova et al. 2014; Thomson et al. 2014), where they may be trapped in super-deep diamonds (Brenker et al. 2007; Bulanova et al. 2010; Tschauner et al. 2018). However, as these diamonds provide only samples of local composition that may not be typical of the mantle, geophysical methods may provide useful bounds on the abundance of these carbonates in the deep Earth. Key questions include what maximum amounts of each carbonate or mixture are consistent with observed behaviors and properties of subducting carbonate-bearing slabs in the transition zone and lower mantle.

To understand the dynamics and seismic signatures of sub-ducting carbonate-bearing slabs, density (ρ) and bulk sound velocity (VF) of CaCO3 and MgCO3 at relevant P-T conditions are first modeled based on the thermal equations of state. The bulk sound velocity is calculated by VF = (KS/ρ)1/2, where KS = KT0 (1 + αγT), which are determined by HT-BM3 EoS and MGD EoS. Because the thermoelastic parameters of CaCO3-P21/c-1 have not been constrained experimentally or theoretically, we cannot address the change in physical properties due to phase transition from CaCO3-P21/c-1 to CaCO3-Pmmn. We assume the phase transition from CaCO3-Pnma to CaCO3-Pmmn occurs at 45 GPa. The thermoelastic parameters used in the modeling of CaCO3-Pnma (Litasov et al. 2017), CaCO3-Pmmn (this study) and magnesite (MgCO3-Rc) (Litasov et al. 2008) are summarized in Table 2. A cold slab temperature profile [600 K cooler than normal mantle geotherm (Syracuse et al. 2010)] is considered in the model as a typical scenario most likely to retain carbonate minerals during subduction. The calculated ρ and VF of CaCO3 and MgCO3 from 30 to 80 GPa are plotted in Figure 6, and both HT-BM3 EoS and MGD EoS of CaCO3 and MgCO3 provide similar results. The phase transition of CaCO3-Pnma to CaCO3-Pmmn in our model leads to an increase in ρ by ~4.5% but a decrease in VF by ~0.8%, consistent with previous modeled results (Bayarjargal et al. 2018; Litasov et al. 2017). At mid-lower mantle conditions, the density of CaCO3-Pmmn is higher than that of MgCO3-Rc by ~10–12%, whereas the VF is lower by ~9–11%. In comparison to surrounding “average” mantle represented by the Preliminary Reference Earth Model (PREM) (Dziewonski and Anderson 1981), pure CaCO3 in the lower mantle exhibits VF ~15% lower, while MgCO3 has VF closer to PREM (Fig. 6b). As a result, slow seismic anomalies in the mid-lower mantle may be more likely to be associated with local enrichment in CaCO3 than MgCO3.

More realistically, CaCO3 and MgCO3 are components of carbonated mantle lithologies (Poli and Schmidt 2002), and the role of these carbonates in changing properties of the subducting slabs may provide a way to estimate bounds on amounts of these carbonates. To determine the physical properties of carbon-bearing rocks in the lower mantle, we must account for geologically relevant mixtures of carbonates with the major mantle silicate and oxide phases (Poli and Schmidt 2002). It is likely that the carbonate content of subducted rocks varies substantially, from a typical value of ~0.5 mol% for altered oceanic basalts, ranging up to ~10 mol% due to local enrichment of carbonates (e.g., Alt and Teagle 1999; Shilobreeva et al. 2011). The basalt part of the subducting slab transforms at lower mantle conditions to a mixture of bridgmanite, Ca-perovskite, stishovite, and Al-bearing calcium-ferrite-type (cf-) silicate (e.g., Dorfman 2016). Mixing this assemblage with carbonates will affect not only the chemical behavior of the rock but also its geophysical behavior. We thus model ρ and VF profile of carbonated basalt in the lower mantle from 30 to 80 GPa along a cold slab geotherm (Syracuse et al. 2010) as a typical scenario. Thermoelastic parameters of relevant phases, including constituents of subducted slab (Stixrude and Lithgow-Bertelloni 2011) and a CaCO3-MgCO3 mixture used in the model are summarized in Table 2. CaCO3 and MgCO3 are added into the metamorphosed basalt assemblages as a 1:1 molar ratio in proportions of 0 (i.e., eclogite), 2, 5, and 10 mol%, respectively. The bulk properties of carbonated basalt are calculated based on MGD EoS by using a Hashin-Shtrikman averaging scheme (Cottaar et al. 2014).

The comparison of the bulk sound velocity profile between eclogite and carbonated-eclogite illustrates the effects of carbonate on seismic signatures of the subducting slab. The modeled results show VF of eclogite can be decreased by at most ~2.0% with the presence of 10 mol% carbonates in the case of maximum carbonate enrichment and zero loss of carbonate during subduction. Even for this extreme upper bound, the effect of CaCO3 phase transition on the seismic velocity of the slab, increased by ~0.1%, is invisible (Fig. 7a). In the case of typical 0.5 mol% carbonates present in the subducting slab, the VF of eclogite would decrease by less than 0.1%. Comparing to the ambient mantle profile (PREM), the subducting slabs exhibit high VF zones, which cannot be changed by adding carbonates. Therefore, the presence of carbonates in the lower mantle is unlikely to be detected by seismic observation of the slab. Previous studies proposed that the presence of sufficient amounts (i.e., 10 mol%) of carbonates would cause shear velocity discontinuities (decreased by 7%) due to CaCO3-P21/c-l to CaCO3-Pmmn phase transition (Bayarjargal et al. 2018), and largely localized anisotropy due to small shear modulus of MgCO3 (Yao et al. 2018). Although the region with >1% seismic velocity anomaly is detectable by seismic tomography (e.g., French and Romanowicz 2015), considering the typical concentration and thickness of carbonate depositions on the oceanic crust, even the localized shear velocity anomaly or anisotropy caused by the presence of carbonates is unlikely detectable due to the limit of spatial resolution of seismic tomography.

The ρ contrast between carbonates and surrounding phases at lower mantle conditions is a source of buoyancy that impedes the downward motion of the slab. In comparison to the average mantle density profile (PREM), eclogite is denser than the ambient lower mantle by ~0.8%, indicating that the higher density of eclogite helps drive subduction in the lower mantle. However, the model results indicate the density of highly carbonated eclogite with maximum carbonate enrichment 10 mol% is lower than that of the ambient lower mantle by ~0.6% (Fig. 7b), and thus will not sink. The maximum amount of carbonate stored in eclogite that will not contribute to slab stagnation is 5 mol%. This is also much greater than the typical 0.5% carbonate content in altered oceanic crust. The temperature effects on the density of subducting slab are negligible, i.e., the calculated density of eclogite decreases by ~1% when changing the reference geotherm from cold slab to hot slab [300 K cooler than normal mantle geotherm (Syracuse et al. 2010)]. In addition, the buoyancy of carbonates is not expected to significantly affect the dynamics of subducting slabs relative to other metastable components of cold slabs potentially present in far greater abundance, particularly metastable olivine (Rubie and Ross 1994) and pyroxene (van Mierlo et al. 2013).

Thermoelastic properties of CaCO3-Pmmn provide useful geochemical constraints necessary for modeling the phase equilibria of carbonates with mantle phases at lower mantle conditions. Reactions that control the presence of CaCO3 in the slab include melting, decarbonation, and redox interactions with ambient mantle phases. For example, recent experimental studies suggest the CaCO3 decarbonation occurs in the presence of silica at lower mantle conditions forming Ca-perovskite and CO2 (Drewitt et al. 2019; Li et al. 2018), and the redox reaction between CaCO3 and metallic iron in the ambient mantle is proposed to be a mechanism of deep diamond formation (Martirosyan et al. 2016; Palyanov et al. 2013). The P-T boundaries of both reactions are essential to understanding the fate of subducted CaCO3 and equilibrium between CaCO3 and mantle phases. However, both boundaries are not well constrained by experiments, mainly due to the kinetic barriers in reactions and uncertainties in pressure and temperature measurements. For other lower mantle phases, thermodynamic modeling has begun to be used to construct physically consistent phase diagrams (e.g., Stixrude and Lithgow-Bertelloni 2011). The newly determined thermoelastic parameters of CaCO3-Pmmn combined with those of other mantle phases will contribute to more quantitative constraints on phase equilibria in the carbonate-silicate system at lower mantle conditions.


† Present address: Applied Physics Department, Soreq Nuclear Research Center (NRC), Yavne 81800, Israel.


Acknowledgments

We acknowledge the editor for handling our manuscript, and two anonymous reviewers for their constructive and thoughtful feedback.

  1. Funding

    This work was supported by the Sloan Foundation’s Deep Carbon Observatory Grant G-2017-9954, NSF grant (EAR-1751664), and startup fund to S.M.D. GeoSoilEnviroCARS is supported by the NSF-Earth Sciences (EAR-1634415) and DOE-GeoSciences (DE-FG02-94ER14466). Use of the COMPRES-GSECARS gas loading system was supported by COMPRES under NSF Cooperative Agreement EAR-1606856 and by GSECARS through NSF grant EAR-1634415 and DOE grant DE-FG02-94ER14466. This research used resources of the Advanced Photon Source, a U.S. Department of Energy (DOE) Office of Science User Facility operated for the DOE Office of Science by Argonne National Laboratory under Contract No. DE-AC02-06CH11357.

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Received: 2019-09-05
Accepted: 2020-02-17
Published Online: 2020-09-20
Published in Print: 2020-09-25

© 2020 Walter de Gruyter GmbH, Berlin/Boston

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