CARBON AND NITROGEN IN EARTH AND PLANETARY INTERIORS By Mingda Lyu A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of Geological Sciences Doctor of Philosophy 2021 ABSTRACT CARBON AND NITROGEN IN EARTH AND PLANETARY INTERIORS By Mingda Lyu Volatile elements, such as carbon (C) and nitrogen (N), play an essential role on Earth in forming living organisms, maintaining a habitable climate, tracing geological p rocesses, and powering the core dynamo. Constraining the distribution and budgets of volatile elements on terrestrial planets, such as the Earth and Mars, holds the key to understanding their formation, evolution, dynamics, and habitability. In this disser tation, I performed a series of experiments to investigate the physical properties and chemical behavior of carbonates and iron nitrides at high pressure and temperature conditions to decipher the role of carbon and nitrogen in the Earth and planetary deep interior. governing long - term atmospheric CO 2 budget. Carbonates, including calcite (CaCO 3 ), magnesite (MgCO 3 ), and dolomite (CaMg(CO 3 ) 2 , are believed to be the maj or carriers to transport surface convecting lower mantle and the stable format of carbon at mantle conditions remain largely uncertain, due to lack of constraints on t hermodynamic properties of subducted carbonates and limited understanding of the fate of carbonates through subduction. In chapter 2, I measured the thermal equation of state of CaCO 3 - Pmmn , a stable polymorph of CaCO 3 through much of the lower mantle, usin - heated diamond - anvil cell up to 75 GPa and 2200 K. Using the newly determined thermodynamic parameters, I modeled the physical properties of CaCO 3 - Pmmn and (Ca,Mg) - carbonate - bearing eclogite, showing 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. In chapter 3, I examined the stability of MgCO 3 and CaCO 3 coexisting with the mantle s ilicates along mantle geotherm. With in - situ X - ray diffractions and ex - situ electron microscopic analysis, I showed if CaCO 3 can be transported to the deep lower mantle and even the core - mantle boundary, it can remain stable and coexist with the mantle sil icates, while MgCO 3 can only be stable at depth above ~1850 km. The observations indicate CaCO 3 the dominant host of oxidized carbon at the core - mantle boundary. The presence of light elements in the core are inferred by seismic and cosmochemical observat ions, and possible light elements are narrowed to Si, O, S, C, H. Recently, nitrogen has and other terrestrial planet cores. However, the physical propertie s, especially pressure - induced magnetic changes and effects on compressibility of iron nitrides remain poorly understood. In - Fe 7 N 3 and - Fe 4 N up to 60 GPa at 300 K, i ndicating the completion of magnetic transition induces elastic - Fe 7 N 3 by 22% at ~40 GPa, but has no resolvable effect on the compression behavior - Fe 4 N. I re - examined evidence for magnetic transition and effects on compressibility of o ther candidate components of terrestrial planet cores, Fe 3 S, Fe 3 P, Fe 7 C 3 , and Fe 3 C, showing the completion of magnetic transition of Fe 3 S, Fe 3 P and Fe 3 C induces elastic stiffening, whereas that of Fe 7 C 3 induces elastic softening. To sum up, this dissertation expands our understanding on the role of carbon and nitrogen in the properties of Earth and planetary interiors, by revealing the stability and fate of carbonate subducted to the lower mantle and the physical properties iron ni trides. Copyright by MINGDA LYU 2021 v This thesis is dedicated to my parents, my parents - in - law, and my wife. vi ACKNOWLEDGEMENTS First and foremost, I am tremendously grateful to my advisor, Prof. Susannah Dorfman, geophysics, geochemistry, and geodynamics. Prof. Dorfman trained me on ho w to conduct high - quality experiments, helped me to improve my writing and presentation skills, and provided a lot of advice on my career development. None of the work described in this dissertation could have been accomplished without the guidance and sup port of my advisor. I am deeply appreciative to my advisory committee, Profs. Allen McNamara, Tyrone Rooney, Matthew Schrenk, who pointed out my knowledge gap and weakness, and gave me conscientious suggestions from various perspectives throughout my journ ey. I am sincerely thankful for the inspiring and fruitful discussions in journal clubs, particularly with Profs. Min Chen, Jeffrey Freymueller, Dalton Hardisty, Seth Jacobson, Kevin Mackey, Michael Velbel, Songqiao Wei, and Warren Wood. I feel fortunate t o work under the supervision of these brilliant mentors in our department. I extremely appreciate my collaborators, in particular Drs. James Badro, Jie Li, Jiachao Liu, and Feng Zhu, who have been played an essential role in my research, gave me advice on my career development, and provided constructive comments to manuscripts. I greatly thank all the talented scientists who provided technical supports and training for my experiments, in particular Drs. Stephan Borensztajn, Eran Greenberg, Vitali Prakapenka , Yuming Xiao, Dongzhou Zhang, and Drs. Allen Hunter, Xudong Fan, Owen Neill. I want to thank my labmates and all the other colleagues, too many to be listed, who gave me endless help and support during the past five years. This dissertation was supported by new faculty startup funding from Michigan State - 2017 - 9954, and National vii Science Foundation (NSF) grants EAR - 1664332 and 1751664 to Prof. Dorfman. Parts of this dissertation were supporte d by IPGP multidisciplinary program PARI, and by Region Île - de - France SESAME Grant no. 12015908 to Dr. James Badro. Parts of this dissertation were supported disserta performed at GeoSoilEnviroCARS (The University of Chicago, Sector 13), Advanced Photon Source (APS), Argonne National Laboratory. GeoSoilEnviroCARS is supported by the Natio nal GSEC dissertation were performed at HPCAT (Sector 16), Advanced Photon Source (APS), Argonne National Laboratory. HPCAT operations are supported by DOE - l Sciences. This work 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 Finally and mo st importantly, I would like to express sincere gratitude to my parents, my parents - in - law, and my wife for their love, support, and encouragement throughout my life. viii TABLE OF CONTENTS LIST OF TABLE S ................................ ................................ ................................ .......................... x LIST OF FIGURES ................................ ................................ ................................ ....................... xi Chapter 1 Introduction ................................ ................................ ................................ .................... 1 Chapter 2 Thermal equation of state of post - aragonite CaCO 3 - Pmmn ................................ ......... 11 2.1 Abstract ................................ ................................ ................................ ............................... 11 2.2 Introduction ................................ ................................ ................................ ......................... 12 2.3 Experimental methods ................................ ................................ ................................ ......... 15 2.4 Results and discussion ................................ ................................ ................................ ......... 16 2.4.1 Synthesis and stability of CaCO 3 - Pmmn ................................ ................................ ...... 16 2.4.2 Compressibility of CaCO 3 - Pmmn at 300 K ................................ ................................ .. 18 2.4.3 Thermal equation of state of CaCO 3 - Pmmn ................................ ................................ . 20 2.5 Implications ................................ ................................ ................................ ......................... 23 Chapter 3 Reversal of carbonate - 43 3.1 Abstract ................................ ................................ ................................ ............................... 43 3.2 Introduction ................................ ................................ ................................ ......................... 43 3.3 Results ................................ ................................ ................................ ................................ . 46 3.3.1 Calcium carbonate reaction to form magnesium carbonate ................................ ......... 46 3.3.2 Magnesium carbonate reaction to form calcium carbonate. ................................ ......... 47 3.4 Discussion ................................ ................................ ................................ ........................... 49 3.5 Methods ................................ ................................ ................................ ............................... 52 3.5.1 Starting materials ................................ ................................ ................................ .......... 52 3.5.2 LHDAC experiments ................................ ................................ ................................ .... 53 3.5.3 In - situ XRD ................................ ................................ ................................ .................. 54 3.5.4 Ex - situ EDX ................................ ................................ ................................ ................. 55 3.6 Supporting Information ................................ ................................ ................................ ....... 56 - Fe 7 N 3 - Fe 4 N: implications for iron alloys in terrestrial planet cores ................................ ................................ ................................ .... 81 4.1 Abstract ................................ ................................ ................................ ............................... 81 4.2 Introduction ................................ ................................ ................................ ......................... 82 4.3 Experimental methods ................................ ................................ ................................ ......... 86 4.4 Results ................................ ................................ ................................ ................................ . 89 4.4.1 No structural transition of Fe 7 N 3 or Fe 4 N ................................ ................................ ..... 89 - Fe 7 N 3 - Fe 4 N ................................ ................................ ............... 89 - Fe 7 N 3 - Fe 4 N ................................ ............................ 90 4.5 Discussion ................................ ................................ ................................ ........................... 95 - Fe 7 N 3 - Fe 4 N ................................ ............................... 95 ix 4.5.2 Magneto - elastic coupling in Fe - light element alloys/compounds ................................ 98 ................................ ........ 101 4.6 Conclusions ................................ ................................ ................................ ....................... 102 BIBLIOGRAPHY ................................ ................................ ................................ ....................... 122 x LIST OF TABLES Table 2 - 1: Comparison of parameters of BM3 EoS of CaCO 3 - Pmmn at 300 K. ......................... 37 Table 2 - 2: Thermoelastic parameters of CaCO 3 , MgCO 3 , and major components in eclogite. ... 38 Table 2 - 3: Unit cell parameters of CaCO 3 - Pmmn at different P - T conditions. ............................ 39 Table 3 - 1: Starting materials, experimental conditions, and run products for all experiments. Starting materials for experiments were loaded in sandwich configu ration, with laser absorber layer between two thermal insulation layers. Pressures determined from Raman shift of the singlet peak of the diamond anvil at the culet surface (Akahama & emporal average of recorded temperatures over the heating duration rounded to the nearest 50 K. Temperature fluctuations over this time scale were less than the specified uncertainty, which is derived from a standard deviation of temperature measurements f rom both sides of the laser - heated sample (typically ±100 K below 2000 K and ±150 K above 2000 K). ................................ ................................ ................................ ....... 79 Table 3 - 2: Parameters for isot opic mass balance calculations (see Supplementary Note 1 for details). ................................ ................................ ................................ ....................... 80 Table 4 - - Fe 7 N 3 - Fe 4 N. ................................ .............. 116 Table 4 - 2: Volume and unit - - Fe 7 N 3 at 300 K. The uncertainties of pressures were propagated fro m uncertainties of unit cell volumes of Au and Ne, and uncertainties of their equation of state parameters (Fei et al., 2007), respectively. 117 Table 4 - 3: Volume and unit - - Fe 4 N at 300 K. The uncertainties of pressures were propagated from uncertainties of unit cell volumes of Au and Ne, and uncertainties of their equation of state parameters (Fei et al., 2007), res pectively. 118 Table 4 - 4: Volume and unit - cell parameters of Fe at 300 K. The uncertainties of pressures were propagated from uncertainties of unit cell volumes of Au and Ne, and uncertainties of their equation of state parameters (Fei et al., 2007), respectively. .......................... 119 Table 4 - iron. ................................ ................................ ................................ .......................... 120 xi LIST OF FIGURES Figure 1 - ................................ ..... 9 Figure 1 - . 10 Figure 2 - 1: Full - profile Le Bail refinement confirms the synthesis of CaCO 3 - 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 ti cks below). Le Bail fit (red curve) also includes expected peak positions for Au calibrant (yellow sticks) and Ne medium (blue ticks). One unknown peak at 2 around ~7° (marked by an asterisk) may be from the metastable CaCO 3 - P 2 1 / c - l due to kinetics. The w avelength of the monochromatic X - ray beam is 0.3344 Å. .............. 29 Figure 2 - 2: Representative in - situ X - ray diffraction patterns of CaCO 3 - Pmmn . (a) Representative in - situ X - ray diffraction patterns of CaCO 3 - Pmmn measured at high pressures and room temperature (black marker). (b) Representative high - temperature X - ray diffraction patterns of CaCO 3 - Pmmn at ~60 GPa (black marker) measured in - sit u 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. ................................ ............................ 30 Figure 2 - 3: Equation of state of CaCO 3 - pmmn . (a) Pressure - volume data for CaCO 3 - 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 m odeled by BM3 EoS using K T 0 = 162(±62) GPa, = 3.1 (±1.1), and V 0 = 96.6(±4.8) Å 3 . A brown dashed curve (Oganov et al., 2006) and a purple dashed curve (Marcondes et al., 2016) modeled by BM3 EoS constrained via DFT - GGA and LDA, respectively. (b) Isoth ermal bulk modulus ( K T ) 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 V 0 = 97.76 Å 3 and with reference pressure set at 50 GPa. ..................... 31 Figure 2 - 4: Volume Eulerian strain ( f ) - normalized pressure ( F ) plot of CaCO 3 - Pmmn . The dashed line represents the linear fit through the data, and a red envelope indicates 95% confidence interval. The V 0 was set as 96.6 Å 3 obtained by BM3 EoS fitting of experimental data at 300 K. ................................ ................................ ....................... 32 Figure 2 - 5: Measured pressure - volume - temperature data for CaCO 3 - Pmmn . Colorful curves are isotherms at 1300, 1600, 1900, 2200 K modeled by (a) HT - BM3 EoS and (b) MGD EoS, respectively, with parameters listed in Table 2 - 2. Black points and curve are at 300 K same as Figure 2 - 3. The lower panel of each figure shows fitting residuals. . 33 xii Figure 2 - 6: Modeled (a) density and (b) bulk sound velocity profiles of CaCO 3 and MgCO 3 from 30 to 80 GPa along mantle geotherm (Brown & Shankland, 1981) compared to PREM model (Dziewonski & Anderson, 1981) and eclogite (a ssumed to be composed by 27 mol.% bridgmanite [(Mg 0.9 ,Fe 0.1 )SiO 3 ], 24 mol.% Ca - perovskite (CaSiO 3 ), 20 mol.% stishovite (SiO 2 ), 29 mol.% Al - bearing calcium - ferrite - type silicate [(Mg 0.9 ,Fe 0.1 )Al 2 O 4 ]), using the thermoelastic parameters listed in Table 2 - 2. In order to clearly illustrate the density contrast of different carbonates, the phase transition of CaCO 3 - Pnma to CaCO 3 - Pmmn is assumed to occur at 45 GPa. ............................... 34 Figure 2 - 7: Modeled (a) bulk sound velocity and (b) density profiles of eclogite and carbonated - eclogite with the presence of CaCO 3 - MgCO 3 mixture as 2, 5 and 10 mol.%, respectively. The eclogite is assumed to be composed by 27 mol.% bridgmanite [(Mg 0.9 ,Fe 0.1 )SiO 3 ], 24 mol.% Ca - perovskite (CaSiO 3 ), 20 mol.% stishovite (SiO 2 ), 29 mol.% Al - bearing calcium - ferrite - type silicate [(Mg 0.9 ,Fe 0.1 )Al 2 O 4 ], and the thermoelastic parameters of these phases are listed in Table 2 - 2. The pressure is ranging from 30 to 80 GPa along cold geotherm (Syracuse et al., 2010). The CaCO 3 - Pnma to CaCO 3 - Pmmn transition is assumed to occur at 45 GPa. The PREM model (Dziewonski & Anderson, 1981) is plotted as a comparison of the averaged mantle. ................................ ................................ ................................ ................................ ... 35 Figure 2 - 8: The correlation between the fitted V 0 and K T 0 of CaCO 3 - Pmmn at 300 K using BM3 EoS. The red circle indicates the fitting result and black ellipsoid represents 95% confidence interval. ................................ ................................ ................................ .... 36 Figu re 3 - 1: Electron microscopic characterizations of recovered samples. Images of selected recovered sample cross - sections obtained using backscattered scanning electron microscopy (a, d, g), scanning transmitted electron microscopy (b, e, h) and energy - dispe rsive X - ray mapping (c, f, i) of the cross - section show the silicate layer sandwiched by two carbonate layers, with the reaction region along the contacting interface. (a - c) Ex - situ analysis of sample quenched from 33 GPa and 1650 K heated for 15 min (run #1) demonstrates reaction CaC - to - MgC: CaSiO 3 is not present in starting materials but is indicated in EDX map by colocation of Ca and Si, shown in magenta; (d - f) Ex - situ analysis of sample quenched from 88 GPa and 1800 K heated for 150 min (run #9) demonst rates reaction MgC - to - CaC: MgSiO 3 is not present in starting materials but is indicated in EDX map by colocation of Mg and Si, shown in blue - green. CaCO 3 also appears as red (Ca, but no Si) ribbon within CaSiO 3 starting material. (g - i) Ex - situ analysis of sample quenched from 133 GPa and 2000 K heated for 400 min (run #10) demonstrates reaction MgC - to - CaC: MgSiO 3 appears as Ca - depleted, Si - rich region (blue or blue - green) adjacent to CaSiO 3 starting material (magenta). ................................ ................................ ................................ .................. 60 Figure 3 - 2: Phase diagram for relative stability of the MgCO 3 + CaSiO 3 assemblage versus CaCO 3 + MgSiO 3 . The boundary sketched as a black dashed line with gray shadow as uncertainty inferred is based on experimental observations of carbonate - silicate exchange reactions CaC - to - MgC and MgC - to - CaC. Squares represent observations from this work starting with (Ca,Mg)CO 3 and (Mg,Fe)SiO 3 , looking for newly - synthesized C aSiO 3 to indicate the CaC - to - MgC reaction takes place. Circle symbols xiii represent observations from this work of experiments starting with (Mg,Fe)CO 3 + CaSiO 3 , looking for identification of newly - synthesized MgSiO 3 to indicate the MgC - to - CaC reaction takes p lace. Open symbols indicate nonreaction and filled for confirmed reaction, and blue and red colors correspond to the inferred stable phase assemblage based on reaction products. Triangles indicate the P - T conditions for CaC - to - MgC taking place reported by Seto et al. (2008), and blue shaded region indicates approximate conditions of four experiments conducted by Biellmann et al. (1993) using indirect methods for pressure and temperature calibration, which all produced the run products MgCO 3 + CaSiO 3 . The er ror bars indicate uncertainties of pressure and temperature measurements (see Methods for details). The boundaries proposed by previous theoretical predictions are illustrated by yellow shaded region (Santos et al., 2019; Yao et al., 2018b; Zhang et al., 2 018). ................................ ............................ 62 Figure 3 - 3: Pressure - temperature diagram of reactions between carbonate, silicates, and silica in the subducted oceanic crust to the lower mantle. The grey dotted line indicates the reversal boundary of the carbonate - silicate exchange reaction proposed by this study, whereas previous theoretical predictions are illustrated by yellow shaded region (Santos et al., 201 9; Yao et al., 2018b; Zhang et al., 2018). The cyan and orange lines indicate the decarbonation reactions of CaCO 3 + SiO 2 (Li et al., 2018) and MgCO 3 + SiO 2 (Drewitt et al., 2019), respectively. The black dashed line shows the melting curve of MgCO 3 - CaCO 3 system constrained by Thomson et al. (Thomson et al., 2014). Four typical mantle geotherms are modified from Maeda et al. (Maeda et al., 2017). The red shaded region indicates the transition boundary of CaCO 3 from sp 2 - to sp 3 structure predicted by density functional theory computations (Santos et al., 2020; Zhang et al., 2018). ................................ ................................ ................................ .... 64 Figure 3 - 4: Schematic illustration of the fate of carbonates in the oceanic crust (dark blue) subducted to the lower mantle. Through subduction, the carbonates may undergo melting (red arrow), redox freezing with metallic iron (purple arrow), decarbonation reaction with free silica (blue arrow), and excha nge reaction with lower mantle silicates (green arrow). Based on the observation of reversal of the carbonate - silicate cation exchange reaction at conditions relevant to cold subducted slabs at mid - lower - mantle depths, CaCO 3 is the potential stable phase t hat hosts oxidized carbon in the lowermost mantle. ................................ ................................ ................................ ...... 65 Figure 3 - 5: Schematic diagram of the laser - heated diamond - anvil cell (LHDAC) a nd sample loading design. The insulation layer (light gray region) and the laser absorber (black region) for different experimental runs are summarized in Table 3 - 1. ...................... 66 Figure 3 - 6: Microscope images of loaded sample for run #9. We loaded the Fe - bearing sample on top of the thermal insulation layer on the piston side of DAC (75/300 beveled anvil), then we loaded another insulation layer on the cylinder side of DAC together with Re gasket before we close and compress the DAC to the target pressure. (a) Samples are loaded at ambient conditions on the piston side before closing the cell. (b) Samples are compressed to target pressure before heating, and the dashed circle indicates the dark Fe - bearing sample. (c) The heating spot on the loaded sample during laser heating. 67 xiv Figure 3 - 7: X - ray diffraction patterns obtained from the starting material of CaC - to - MgC before heating (a) and products quenched from various P - T conditions: (b) run #1, (c) run #4, (d) run #5, and (e) run #7, and phase identifications are indicated by small ticks at the bottom. The wavelength of the incident X - ray beam was 0.3344 Å. ........................ 68 Figure 3 - 8: Representative u nrolled X - ray diffraction images (lower panel) corresponding to X - ray diffraction patterns (upper panel) obtained from the starting materials of CaC - to - MgC before heating and the products quenched from various P - T conditions: (a - b) run #4, (c - d) run #5. La rge spots in 2D diffraction patterns in (a) and (b) are from untransformed dolomite starting material. The wavelength of the incident X - ray beam was 0.3344 Å. ................................ ................................ ................................ ............ 69 Figure 3 - 9: Representative full - profile fitting for XRD of (a) run #1 and (b) run #5. Le Bail refinements (red curves) of observed XRD data (black dots) were ca rried out after background subtraction, demonstrating all the identified phases (vertical ticks below patterns) can account for the peaks and intensities of XRD patterns. Black curves are fitting residues. The wavelength of the incident X - ray beam was 0.33 44 Å. ............ 70 Figure 3 - 10: Ex - situ analysis of sample quenched from 33 GPa and 1650 K heated for 15 min (run #1) demonstrates CaC - to - MgC. (a) SEM - BSE image obtained during FIB milling. Sample was prepared as a (Mg,Fe)SiO 3 layer sandwiched by two (Ca,Mg)CO 3 layers; (b) dark - field STEM image reveals CaSiO 3 and MgCO 3 , as well as SiO 2 and FeO, formed by reaction between (Mg,Fe)SiO 3 and (Ca,Mg)CO 3 layers; (c) EDX spectrum and corresponding (d) chemical maps for calcium, silicon, magnesium, carbon, and iron. ................................ ................................ ................................ ............................ 71 Figure 3 - 11: Ex - situ analysis of sample quenched from 88 GPa and 1800 K heated for 150 min (run #9) demonstrates MgC - to - CaC. (a) SEM - BSE image obtained during FIB milling. Sample was prepared as an (Mg,Fe)CO 3 layer sandwiched by two CaSiO 3 layers; (b) dark - field STEM image reveals (Mg,Fe)SiO 3 and CaCO 3 formed by reaction of (Mg,Fe)CO 3 and CaSiO 3 layers; (c) STEM - EDX spectrum and corresponding (d) chemical maps for magnesium, silicon, calcium, and carbon. ................................ .. 72 Figure 3 - 12: Ex - situ analysis of sample quenched from 133 GPa and 2000 K heated for 400 min (run #10) demonstrates MgC - to - CaC. (a) SEM - BSE image obtaine d during FIB milling. Sample was prepared as a (Mg,Fe)CO 3 layer sandwiched by two CaSiO 3 layers; (b) dark - field STEM image reveals (Mg,Fe)SiO 3 and CaCO 3 formed by reaction of (Mg,Fe)CO 3 and CaSiO 3 layers; (c) EDX spectrum and corresponding (d) chemical map s for magnesium, silicon, calcium, and carbon. ................................ .. 73 Figure 3 - 13: Ex - situ analysis of sample quenched from 35 GPa and 1900 K heated for 20 min (run #8) demonstrates MgC - to - CaC. (a) SEM - BSE image obtained during FI B milling. Sample was prepared as a (Mg,Fe)CO 3 layer sandwiched by two CaSiO 3 layers; (b) STEM - EDX chemical maps for calcium, silicon, magnesium, carbon, iron and oxygen. ................................ ................................ ................................ ................................ ... 74 xv Figure 3 - 14: Typical temperature measurements of downstream (red squares) and upstream (blue circles) over heating duration of (a) run #5 for CaC - to - MgC and (b) run #9 for MgC - to - CaC, respectively. ................................ ................................ ................................ . 75 Figure 3 - 15: Representative temperature measurements and fitting profiles of upstream and downstream for run #9. Temperatures of the heated samples were determined by fitting the measured thermal radiation spectra using the Planck radiation function under the graybody approximation. ................................ ................................ ........................... 76 Figure 3 - 16: Calculated isotopic composition versus reaction rate after the reaction (a) CaC - to - MgC and (b) MgC - to - CaC. n represents the mole fraction of Mg in (Mg n Ca n - 1 )CO 3 . 44/40 26 Mg values in carbonates, respectively. ................................ ................................ ................................ ............... 77 Figure 3 - 17: Calculated isotopic composition of carbonated pyrolite after isotopic fractionation between carbonates and silicates for the reaction (a) CaC - to - MgC and (b) MgC - to - CaC. The horizontal axis represents the mole ratio of Mg/Ca in the carbonated pyrolite. k represents reaction rate. ................................ ................................ .......................... 78 Figure 4 - 1: (a) and (b) are representative X - - Fe 7 N 3 at 1 and 60 GPa at 30 0 K, respectively; (c) and (d) are representative X - - Fe 4 N at 1 and 60 GPa at 300 K, respectively. Le Bail refinements (red solid curves) of observed XRD data (black dots) were carried out after background subtraction, demonstr - Fe 7 N 3 - Fe 4 N, - Fe 7 N 3 - Fe 4 N (dark green), and the pressure calibrant, Au (orange). The wavelength of the incident X - r ay beam was 0.434 Å. ................................ ................................ 104 Figure 4 - 2: (a - b) Fe - K - Fe 7 N 3 - Fe 4 N up to 60.5 GPa at 300 K. The XES spectra were normalized to unity in integrated intensity. The top - left inset shows intensity difference of observed satellite emission peak ( K eV relative to the low - spin reference FeS 2 at 0 GPa (black dashed line). (c - d) High - spin - Fe 7 N 3 - Fe 4 N as a function of pressure derived from the XES measurements following integrated relative difference method (Mao et al., 2014). - Fe 7 N 3 - Fe 4 N at ~30 GPa. T he dashed line is fitted by Boltzmann function, and error bars determined by comparing results using FeS 2 vs. sample at 60 GPa as low - spin references. Pressures were determined by ruby fluorescence (Mao et al., 1986) before and after each XES collection, w hich differed by up to 10% due to relaxation of the sample or cell assembly. ................................ ................................ ................................ ................. 105 Figure 4 - - Fe 7 N 3 at 300 K. (a) Unit - - Fe 7 N 3 up to 60 GPa at 300 K determined from X - ray diffraction measurements in this work (solid circles), together with previous experimental results. The black and red curves represent the 3rd - order Birch - Murnaghan equa tion of state (BM3 - EoS) fits for the data for high spin (HS) and mixed spin (MS) / magnetic state (1 bar - 40 GPa), low spin (LS) / nonmagnetic state (40 - 60 GPa), respectively. (b) Normalized stress G as a function xvi of effective strain g . Solid black, gray, a nd red circles represent the results of high spin, mixed spin, and low spin state, respectively, as determined by XES. Black and red lines indicate fits of the high spin and low spin state G ( g ) data, respectively. The V 0 for the nonmagnetic state is obtain ed by extrapolating g to g 0 . ............................... 107 Figure 4 - - Fe 4 N at 300 K. (a) Unit - - Fe 4 N up to 60 GPa at 300 K determined from X - ray diffraction measurements in this work (dark green circles), together with previous experimental results. The black curve represents the 3rd - order Birch - Murnaghan equation of state (BM - EoS) fit of all pressure - v olume data from this study. (b) Normalized stress G as a function of effective strain g . Solid black, gray, and red circles represent the results of high spin, mixed spin, and low spin state, respectively, as determined by XES. The black solid line indicat es a linear fit for all data. The pressure of onset and completion of spin transition is indicated by XES, but no change in compressibility can be observed in either plot. ............................ 108 Figure 4 - 5: - Fe 7 N 3 - Fe 7 N 3 - Fe 4 N (dark green curve) at 300 K as a function of pressure, calculated from the fitted BM - EOS parameters ( Table 4 - 1 - Fe 7 N 3 induces +22% increase in incompressibility at 40 GPa. ................................ ....................... 109 Figure 4 - 6: Normalized stress G as a function of effective strain g for (a) Fe 3 S (Chen et al., 2007; Kamada et al., 2014; Seagle et al., 2006), (b) Fe 3 P (Lai et al., 2020), (c) Fe 7 C 3 (Chen et al., 2012; Liu et al., 2016), and (d) Fe 3 C (Li et al., 2002; Litasov et al., 2013; Ono & Mibe, 2010; Sata et al., 2010). Dashed lines are linear fits to g - G , and the discontinuity in compression behavior corresponds to the change of slope of the linearized g - G plot. ................................ ................................ ................................ .. 110 Figure 4 - 7: Compression behavior of pure Fe at 300 K. (a) Unit - - Fe (black circles) - Fe (red circles) up to 60 GPa at 300 K determined from X - ray diffraction measurements. The solid black curves and solid red curves represent the 3rd - order Birch - Murnaghan equation of state (BM - - Fe (1 - 15 GPa) and - Fe (15 - 60 GPa), r espectively. (b) Normalized stress G as a function of effective strain g - - Fe, respectively. - - Fe, respectively. The V 0 for - Fe is obtained by extrapolating g to g 0 . ................................ .......................... 111 Figure 4 - 8: Full width at half maximum (FWHM) for Au (111) normalized to 2 . Orange circles - Fe 4 N sample in the diamond anvil cell. The peak broadening induced by the onset of nonhydrostaticity of Ne medium (Klotz et al., 2009) in this study starts at ~17 GPa. The magnitude of peak broade ning remains small above this pressure, consistent with quasi - hydrostatic conditions in the sample chamber. ................................ ................................ ................................ ................... 112 Figure 4 - - Fe 7 N 3 - Fe 4 N (right) at ambient conditions. Gray spheres in polyhedra represent the N atoms and brown spheres represent Fe atoms. ................................ ................................ ................................ ................................ . 113 xvii Figure 4 - - Fe 7 N 3 at 300 K. ................................ ........................... 114 Figure 4 - - Fe 7 N 3 - Fe 7 N 3 - Fe 4 N - Fe 7 N 3 - Fe (light red) as a function of pressure at 300 K. The calculation is based on BM3 EoS with parameters of relevant phases summarized in Table 1 and 2. (b) Isothermal density profiles of nonmagnetic - Fe 7 N 3 (purple), Fe 7 C 3 (orange), Fe 3 C (brown), Fe 3 S (gray), Fe 3 P (pink) along a 5500 K isotherm. For comparison, a density profile of - Fe and seismologically constrained density profile (Preliminary Reference Earth Model, Dziewonski & equation of state with parameters of relevant phases listed in Tab le 4 - 5. ............... 115 1 Chapter 1 Introduction Earth is unique among the planets in our solar system in that it has a habitable climate fostering life on the surface, not only owing to the stabilization of hydrosphere and atmosphere, but also the presence of life - surface, such as carbon, nitrogen, hydrogen, oxygen, and sulfur (Bergin et al., 2015; Hirschmann, 2016; Marty, 2012) history, the surface inventory of life - essential volatile elements has been maintained by cycling of materials between the su rface and interior via outgassing and ingassing mechanisms induced by plate tectonics, which helps to stabilize the long - term moderation of the climate (Dasgupta, 2013; Shahar et al., 2019) . The storage and fluxes of life - essential volatile elements in and between several fields of Earth sciences, such as mantle and core dynamics, chemical differentiation and thermal evolution history, subduction and volcanism, we athering and sedimentation, climate change, and origin and evolution of life (Hazen & Schiffries, 2013) . In addition, it has been one of the most exciting puzzles in planetary science to search for a habitable exoplanet. A habitable planet must have the i ngredients necessary for the development of life, including the life - essential volatile elements on the surface. Assuming Earth - like concentration and distribution of volatile elements can sustain the habitability on an exoplanet, many efforts have been de dicated to constraining the origins, concentrations, and transportation of volatile elements in relevant reservoirs on Earth and planetary building blocks (Bergin et al., 2015; Hirschmann, 2016; Marty, 2012) . The abundance of volatile elements of cosmochem ical reservoirs can be directly constrained from chemical analysis of meteorites and samples returned by 2 ce, such as basalts, because of the unknown amounts of elements buried in inaccessible deep mantle and core reservoirs. Mantle - derived basalts along mid - ocean ridge and oceanic intraplate volcanoes contain volatile elements from the interior, but a conside rable amount of volatile elements have been lost during magma degassing due to their low solubility in silicate melts. Moreover, basalt generation only directly samples typically the top 100 - 200 km of the mantle, which results in large uncertainties when e xtrapolating the estimation to the bulk silicate Earth (Dasgupta & Hirschmann, 2010; Kelemen & Manning, 2015; Plank & Manning, 2019) . Therefore, indirect geochemical and geophysical observations, theoretical prediction, and dynamic modeling are necessary for understanding the storage of loss during primary planetary differentiation. Earth formation and origins of volatile elements. Earth is believ ed to be the product of a number of collisions between the proto - Earth and other planetary bodies (Carlson et al., 2014; Wood et al., 2006) . One of the final events during the accretion of Earth is believed to have been a large - scale collision with a Mars - moon around 4.5 billion years ago. This giant impact is thought to have generated enough energy to melt part or even all of the early Earth, creating planetary - scale volumes of molten rock tha t may form a magma ocean hundreds of kilometers in depth. The subsequent cooling of the planet from this molten state would have resulted in the segregation of iron - rich alloy from the magma ocean, and crystallization of the magma ocean into the solid mant le, which was a defining stage in early atmosphere (Carlson et al., 2014; Wood et al., 2006) . 3 The present - le and surface reservoirs are - rich materials, loss of volatile to space during accretion, and segregation of the metallic core and the silicate mantle (Bergin et al., 2 015; Hirschmann, 2016; Liu et al., 2019; Marty, 2012) . However, the processes of volatile acquisition into the early Earth remain poorly understood. One widely accepted model suggests that the Earth formed from chondritic material, but most of the volatile s were delivered by volatile - rich chondritic material in the form of late veneer after complete core - mantle segregation (e.g., Albarede, 2009; Wang & Becker, 2013) . Nevertheless, this model has been challenged by recent studies on partitioning behavior of carbon and sulfur, inferring their abundances do not formally require an accretion in a late veneer, and can be explained by a core - mantle equilibration alone (e.g., Boujibar et al., 2014; Fischer et al., 2020) . The distribution of volatile elements between the core - forming metallic melt, silicate melt, and atmosphere is controlled by partitioning between metal and silicate, and solubility in silicate melt in equilibrium with the overlying atmosphere (Hirschmann, 2016) . During core formation, some of the volatile elements entered the core, and some of them were trapped in the silicate mantle ( Figure 1 - 1 ). Some major uncertainties in how much, for example, carbon is in the mantle or nitrogen is in the core, relate to limited information on phase equilibria and physical properties of the minerals that host these volatiles at depth (see Chapter 2 and Chapter 4). Plate tectonics and volatile element cycling. The volatile elements in the mantle can be sampled by mantle - derived basalts, volcanic gases, and deep diamonds. Chemical analysis of species, concentration, and isotopic signatures of H, C, N, and S indicates they have been 4 minerals and conveyed into the mantle at subduction zones, where the hydrated and carbonated oceanic plates are plunging into the mantle. Some of the volatile elements are expelled during dehydration of plates and released back to the surface through arc magmatism, but a significant fraction of volatile elements survive dehydration and possibly co ntinue all the way down to the core - mantle boundary (Dasgupta & Hirschmann, 2010; Kelemen & Manning, 2015; Plank & Manning, 2019) ( Figure 1 - 2 ). The volatiles can return to the surface through volcanism and degassing at mid - ocean ridges and arcs, where volatile elements originally trapped in mantle minerals enter preferentially the magmas and degas to the atmosphere and hydrosphere during volcan ic eruptions (Dasgupta & Hirschmann, 2010; Kelemen & Manning, 2015; Plank & Manning, 2019) ( Figure 1 - 2 ). In addition, diamonds provide unique informatio most diamonds are thought to crystalize in the mantle roots of the continental lithosphere, the so - called superdeep diamonds and their inclusions are believed to crystalize in the convecting upper mantle, transition zone, and even lower mantle (Stachel & Luth, 2015) . The formation of superdeep diamonds itself is a key part of carbon cycling, since the r edox reactions between carbonates in subducting slabs and metallic iron in the ambient mantle have been proposed as an important mechanism to produce superdeep diamonds (e.g., Dorfman et al., 2018; Rohrbach & Schmidt, 2011; Thomson et al., 2016b) ( Figure 1 - 2 ). These diamonds may then carry to the surface traces of carbonates from great depth and reveal reactions that have taken place (see Chapters 2 and 3) . Carbon in the mantle. Carbon is the fourth most abundant element in the universe, which is the backbone for the chemistry of life and, in the form of CO 2 , combines with water to provide 5 the greenhouse needed for a habitable Earth. Although the surface carbon inventory has a key influence in building and sustaining a habitable planet, the specific physical, chemical and dynamic rbon inventory remain largely uncertain. One of the most debatable issues related to the carbon cycle is whether the global carbon (Dasgupta & Hirschmann, 2010; Kelemen & Manning, 2015; Plank & Manning, 2019) . Global carbon flux is difficult to constrain, since the mechanics of subduction (input) and carbonated melt production or CO 2 degassing (output) are dependent on multiple parameters. The fate and flux of car bon vary from trench to trench, as different subducting slab has a different mixture of carbon source (e.g., carbonate, organic carbon, sediment, serpentinite), temperature field, and geometry. The estimated carbon flux into the convecting mantle shows dis crepancies and uncertainties in the order of magnitudes by various studies (Dasgupta & Hirschmann, 2010; Kelemen & Manning, 2015; Plank & Manning, 2019) . Nonetheless, carbonates are the major source that conveys carbon into the deep Earth by subduction, an d deep subduction of oceanic crust introduces a considerable amount of carbon into the mantle. Therefore, several important questions have arisen in order to int erior? (Chapters 2 and 3) What are the physical and chemical properties of carbonates subducting to the lower mantle? (Chapter 2) Can carbonate remain stable until to the core - mantle boundary? (Chapter 3) Nitrogen in the core. The abundance of volatile ele respectively, less dense than pure, solid iron under the same pressure and temperature conditions. This density deficit i s primarily due to the presence of one or more light elements in the core, such 6 as Si, O, S, C, and H, although the identity of the light element(s) and abundance in the core is highly controversial (Hirose et al., 2013; Li & Fei, 2014) . In addition, nitro gen has been proposed as one of the light element candidates in the core. Nitrogen is the seventh most abundant element in the solar system, and is a key component of DNA, RNA, and proteins, while also present as the dominant constituent of our atmosphere, remain enigmatic. The abundance of nitrogen in the core can be constrained from geochemical and depe nds on whether it is siderophile (iron - loving) or lithophile (rock - loving) during the core - mantle segregation process, so the partitioning coefficient of nitrogen between metal and silicate at relevant core formation conditions can be a key parameter to co nstrain the nitrogen in the core. - rich alloys at the pressure - phase relations, etc.) a nd comparing them to seismological measurements of core properties (Hirose et al., 2013; Li & Fei, 2014) . Therefore, several important questions have arisen to better constrain the nitrogen in the core: what are the physical and chemical properties of iron - nitrogen alloys (iron nitride) at core conditions? How does nitrogen affect the physical properties of iron in the core? (Chapter 4). Dissertation outline. In this dissertation, I have investigated the physical and chemical behavior of carbonates and iron nitrides to decipher the role of carbon and nitrogen within the Earth and planetary deep interior. In chapter two, I report the results of in - situ high pressure and temperature X - ray diffraction measurements to study the stability and physical properties of CaCO 3 at lower mantle conditions. It has been shown that CaCO 3 7 subducting to the mantle, CaCO 3 undergoes a series of phase transitions at high pressures, and six high - pressure polymorphs of CaCO 3 corresponding to the mantle conditions have been reported, i.e., same composition with different crystal structures (e.g., Lobanov et al., 2017; Oganov et al., 2013; Pickard & Needs, 2015) . I focused on studying one of the CaCO 3 polymorphs, post - ara gonite, which is believed to be the dominant stable phase along mantle geotherm from 25 to 135 GPa and 2000 to 2500 K. In chapter three, I examine the stability of carbonates, MgCO 3 and CaCO 3 , coexisting with the lower mantle minerals. Previous studies sho w carbon has limited solubility in mantle silicates, and therefore resides chiefly in carbon - rich accessory phases in the deep mantle, such as carbonates, carbonate melts, carbon - bearing fluids, graphite, diamond, and/or iron carbides (Oganov et al., 2013) . One question that scientists have dedicated efforts to answer is what are forms of carbon in addition to constraining the stability of the single carbonate phase as chapter two did, I designed a series of high pressure and temperature experiments to investigate the stability and phase equilibrium between carbonate and silicates. In chapter four, I focus on the spin/magnetic transition and its effect on the in compressibility of iron nitrides, which provide new constraints on the role of nitrogen and other volatile elements in the core. Iron is the most abundant transition metal within the Earth and the major component of the core. Iron has its 3 d electronic she lls partially filled, leading to a series of possible energy configurations that depend on its atomic environment: iron adopts different valences, namely metallic (Fe 0 ), ferrous (Fe 2+ ), and ferric (Fe 3+ ) iron, and different electronic configurations, such as high - spin and low - spin states. The spin transitions of iron in silicates, oxides, and alloys have been reported, which revealed the role of spin transitions on physical, 8 chemical, and transport properties of the deep Earth (Badro, 2014; Lin et al., 2013 ). Here I study the pressure - driven spin transition of iron nitrides, and compared the effects of nitrogen with other volatile elements. 9 Figure 1 - 1 : Origins and behavior of volatile elements in 10 Figure 1 - 2 11 Chapter 2 Thermal equation of state of post - aragonite CaCO 3 - Pmmn This chapter has been published as Lv et al. (2020a) . 2.1 Abstract Calcium carbonate (CaCO 3 observations support preservation of CaCO 3 in cold slabs to lower mantle depths, the geophysical properties and stability of CaCO 3 at these depths are not known, due in part to complicated polymorphic phase transitions and lack of constraints on thermodyna mic properties. Here we measured thermal equation of state of CaCO 3 - Pmmn , the stable polymorph of CaCO 3 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 CaCO 3 - Pmmn are fit with third - order Birch - Murnaghan equation of state, yielding K T 0 = 146.7 (±1.9) GPa and = 3.4(±0.1) with V 0 fixed to the value determined by ab initio calculation, 97.76 Å 3 . High - temperature compression data are consistent with zero - pressure thermal expansion T = a 0 + a 1 T with a 0 = 4.3(±0.3)×10 - 5 K - 1 , a 1 = 0.8(±0.2)×10 - 8 K - 2 K T T ) P = - 0.021(±0.001) GPa/K; the Grüneisen paramete r 0 = 1.94(±0.02), and the volume independent constant q = 1.9(±0.3) at a fixed Debye temperature 0 = 631 K predicted via ab initio calculation. Using these newly determined thermodynamic parameters, the density and bulk sound velocity of CaCO 3 - 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 subducted slab is unlikely to be detected by seismic 12 observations, and the source of buoyancy provided by carbonates is negligible to affect slab dynamics. 2.2 Introduction Calcium carbonate (CaCO 3 ) in the form of calcite is one of the most abundant carbonates surface (reviewed by Luth, 1999) Calcite can be sequestered in the oceanic crust b y hydrothermal alteration and biological activity, and transferred to the mantle in subducting slabs (Dasgupta & Hirschmann, 2010; Kelemen & Manning, 2015; Staudigel, 2014) . However, four major chemical processes have been argued to block transport of CaCO 3 transport to the lower mantle: 1) melting of carbonate and carbonated peridotite or eclogite (e.g., Dasgupta & Hirschmann, 2006; Ghosh et al., 2014; Kiseeva et al., 2013; Thomson et al., 2016b) , 2) reduction of carbonate solid or melt through reaction wi th iron or other reduced phases, generating diamond ( e.g., Dorfman et al., 2018 ; Palyanov et al., 2013 ; Rohrbach & Schmidt, 2011 ) , 3) carbonate - silicate exchange consuming CaCO 3 to form Ca - perovskite and MgCO 3 (e.g., Biellmann et al., 1993 ; Seto et al., 20 08 ) , 4) decarbonation of CaCO 3 with free silica phase to form Ca - perovskite, CO 2 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 CaCO 3 from very cold and/or fast subducting slabs has been controversial (e.g., Martirosyan et al., 2016; Zhu et al., 2019) , though s uperdeep diamonds with CaCO 3 inclusions coexisting with lower mantle phases such as CaSiO 3 perovskite ( Brenker et al., 2007 ; Bul anova et al., 2010 ; Tschauner et al., 2018 ) prove the existence of CaCO 3 in at least some regions of the transition zone and lower mantle. To determine the conditions needed to preserve CaCO 3 in these regions and its fate during subduction to the 13 mantle, e xperimental constraints on thermodynamic behavior of CaCO 3 are needed at lower - mantle conditions. At mantle pressure and temperature ( P - T ) conditions, multiple polymorphic phase transitions of CaCO 3 have recently been discovered and debated, with potentia lly 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 (CaCO 3 - Pnma ), which remains stable through the transition zone and shallow lower mantle (e.g. , Litasov et al., 2017a) . The reported melting curve of CaCO 3 - Pnma and a mixture of CaCO 3 - MgCO 3 are higher than a hot slab geotherm ( Li et al., 2017 ; Thomson et al., 2014 ) , suggesting that subducted CaCO 3 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 1 transition to an orthorhombic structure, or transitions to an intermediate monoclinic structure then an orthorhombic structure. The orthorhombic structure is most - 3 - 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 P 2 1 /c structure (CaCO 3 - P 2 1 /c - - - pressure) was predicted to be an intermediate stable phase from ~40 to 50 GPa between CaCO 3 - Pnma and CaCO 3 - Pm mn (Gavryushkin et al., 2017; Pickard & Needs, 2015; Smith et al., 2018) . CaCO 3 - P 2 1 /c - 1 was observed experimentally by (Gavryushkin et al., 2017; Li et al., 2018; Smith et al., 2018) , but the transition from monoclinic to CaCO 3 - Pmmn was found to be kinetic ally challenging (Smith et al., 2018) 3 is expected to transform from one of these sp 2 - hybridized post - aragonite structures to one of multiple proposed sp 3 - hybridized post - post - aragonite structures. The first sp 3 - hybridized post - post - aragonite to be identified was a pyroxene - 14 structured C 222 1 phase (CaCO 3 - C 222 1 ) observed at pressures higher than 130 GPa, corresponding to conditions near the core - mantle bounda ry ( Oganov et al., 2006 ; Oganov et al., 2008 ; Ono et al., 2007 ) . A second monoclinic P 2 1 /c structure with sp 3 - hybridization, termed CaCO 3 - P 2 1 /c - - = high - pressure, to distinguish it from the lower - - more fav orable than CaCO 3 - C 222 1 (Pickard & Needs, 2015) and observed at pressures as low as ~105 GPa ( Lobanov et al., 2017 ) . Although the stable forms of CaCO 3 at the top and bottom of the lower mantle and conditions of the sp 2 - to sp 3 - hybridization transition in CaCO 3 remain controversial, CaCO 3 - Pmmn is thought to be the stable phase of CaCO 3 throughout most of the lower mantle (see phase diagram of CaCO 3 proposed by Gavryushkin et al., 2017; Smith et al., 2018; Zhang et al., 2018) . The stability an d abundance of CaCO 3 - Pmmn can be modeled in the Earth using constraints on thermoelastic behavior, including accurate thermal equation of state (TEoS) measurements and corresponding thermoelastic parameters bulk modulus , its pressure and temperature deriva tives, and thermal expansion coefficient. However, in contrast to the relatively well - known thermoelastic behavior of CaCO 3 - Pnma (Li et al., 2015; Litasov et al., 2017a; Palaich et al., 2016; Ye et al., 2012) , experimental and computational constraints on the equation of state (EoS) of CaCO 3 - 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. In order to accurately model the phase equili brium and physical properties of CaCO 3 at lower mantle conditions, the TEoS study on CaCO 3 - Pmmn is required. In this study, we investigate the structural stability of CaCO 3 - Pmmn , and establish its TEoS up to 75 GPa and 2200 K using synchrotron X - ray diffraction in a laser - heated diamond anvil cell (LHDAC). The physical properties of CaCO 3 along cold subducting slab geotherm are calculated 15 using the TEoS parameters, which are compared with the other major endmember carbonate, MgCO 3 . By combining the ne wly obtained parameters with literature thermodynamic parameters of mineral phases in the subducted slab, we model the effect of the presence of CaCO 3 - MgCO 3 mixture on the density and bulk sound velocity of the carbonate - rich subducting slab at lower mantl e conditions. 2.3 Experimental methods CaCO 3 - 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% micron - scale Au powder (99 .95%, Goodfellow), which serves as a laser absorber and pressure calibrant. The mixture was mechanically ground under ethanol for 1 hour, then dried in an oven at 120 °C overnight to remove moisture contamination. The powder was slightly compressed to form a ~10 - - thick disc for loading into the DAC. We use a symmetric DAC equipped with a pair of 150 - - indented to ~25 - - in the center of the indentation, serving as the sample chamber. To separate the sample disc from the diamond anvils, we loaded a sample disc into the sample chamber supported by three small ~5 - thick calcite spacers. T o achieve quasi - hydrostatic condition s 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 TEoS of CaCO 3 - Pmmn was determined using synchrotron X - ray diffraction with in - situ laser he ating carried out at beamline 13 - ID - D of the GeoSoilEnviroCARS sector of the Advanced Photon Source (APS), Argonne National Laboratory (ANL). The monochromatic X - 16 2 on the sample. E ach two - dimensional X - ray diffraction image was recorded on a CdTe 1M Pilatus detector for 30 s, and subsequently integrated using Dioptas software (Prescher & 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 LaB 6 powder at ambient conditions. The sample was heated using a double - sided Nd:YLF laser heating system ( Prakapenka et al., 2008 ) . Two 20 - diameter on both sides of the sample, and co - axially 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. Press ures were calculated using the TEoS of the Au standard ( Fei et al., 2007 ) , with uncertainties propagating from that of temperatures, unit - cell volumes of Au, and TEoS parameters of Au, and the unit - cell volumes of Au were derived from diffraction lines (1 1 1), (2 0 0), (2 2 0) and (3 1 1) ( Figure 2 - 1 and Figure 2 - 2 ). 2.4 Results and discussion 2.4.1 Synthesis and stability of CaCO 3 - 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 CaCO 3 . During heating at 1800 K and after quench to 300 K, CaCO 3 - Pmmn was confirmed by full - p rofile refinement XRD using the Le Bail method (Le Bail et al., 1988) as implemented in the GSAS/EXPGUI program 17 (Toby, 2001) ( Figure 2 - 1 ). In contrast, s ome previous studies which attempted synthesis from CaCO 3 - Pnma or CaCO 3 - P 2 1 /c - l (Gavryushkin et al., 2017; Smith et al., 2018) failed to obtain complete transformation to CaCO 3 - 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 ( Figure 2 - 1 and Figure 2 - 2 ). An additional diffraction peak is observed at d - spacing of 2.6 Å, which broadens with increasing pressure and disappears above 60 GPa, probably representing metastable CaCO 3 - P 2 1 /c - l retained due to phase transition kinetics (Bayarjargal et al., 2018; Gavryushkin et al., 2017; Li et al., 2018; Smith et al., 2018 ) . T he unit - cell parameters of CaCO 3 - Pmmn at 300 K and 49 GPa are consistent with previous observations (Gavryushkin et al., 2017; Ono et al., 2005) within the uncertainty of pressure calibration ( Figure 2 - 1 ). As pressure and temperature increased, in - situ XRD exhibits no splitting or broadening of CaCO 3 - Pmmn peaks, indicating no melting, dissociation or phase transition occurred ( Figure 2 - 1 and Figure 2 - 2 ). This study concurs with other previous studies (e.g., Gavryushkin et al., 2017; Oganov et al., 2006; Ono et al., 2005) that CaCO 3 - Pmmn is the stable form of CaCO 3 up to 75 GPa and 2200 K. After synthesis of CaCO 3 - Pmmn , we further compressed the sample at ~2 - 3 GPa 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 tar get pressure, we collected XRD patterns of the sample at 300 K before and after heating, and collected high - temperature patterns while the temperature was increasing at ~50 - 100 K intervals from ~1000 to 2200 K ( Figure 2 - 2 ). The lattice parameters of CaCO 3 - Pmmn were obtained by least - squares fitting of diffraction lines (1 1 1), (0 2 0), (2 0 0) and (0 2 1) by using PDIndexer software (Seto et al., 2010) , and are provided in the Table 2 - 3 . 18 To directly compare volumes observed at 300 K for CaCO 3 - 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 ( Figure 2 - 3 a). With this correction, all P - V data are consistent within uncertainty over the pressure range examined in this work. 2.4.2 Compressibility of CaCO 3 - Pmmn at 300 K Because all previous compression data for CaCO 3 - 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 CaCO 3 - Pmmn . P - V data of CaCO 3 - 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 unit - cell volume ( V 0 ), bulk modulus ( K T 0 ) and its pressure derivative ( ) ( Figure 2 - 3 a and Table 2 - 1 ). We first fit the data using BM3 EoS without constraints on parameters, y ielding V 0 = 96.6(±4.8) Å 3 , K T 0 = 162(±62) GPa, = 3.1(±1.1). The large uncertainties in fitted parameters reflect the long extrapolation from high - pressure data to 1 bar for this unquenchable phase, but compressibility at mantle - relevant pressures is well - constrained. 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 , 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 high relative to our extrapolated EoS even w ith pressures corrected to match the pressure scale in this study ( Figure 2 - 3 a), corresponding to a relatively high 19 incompressibility at mantle pressures. However, the incompressibility K T 0 reported by both previous studies is relatively low compared to our unconstrained fit. This parameter trades off with relatively high V 0 and in these studies. Since CaCO 3 - Pmmn i s 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 set ting 50 GPa as the reference pressure and obtain K 50 = 302(±15) GPa, = 2.1(±1.7) and V 50 = 77.526(±0.046) Å 3 . 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 K 50 ( Figure 2 - 3 b). 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 CaCO 3 - Pmmn supports the low from the BM3 EoS. P - V data can be described by the normalized stress ( f E = [( V 0 / V ) 2/3 - 1]/2) versus the finite Eulerian strain ( F E = P/ [3 f E (1+2 f E ) 5/2 ]) plot ( Figure 2 - 4 ), where F E = K T 0 + 1.5 K T 0 f E ( - 4 ) . The intercept value, F E (0) = 162(±2) GPa, agrees with K T 0 obtained from the fit to the BM3 EoS, and the negative slope indicates is smaller than 4 (Angel, 2000) , which is consistent with our fitting results. The EoS obtained by DFT - GGA ( Oganov et al., 2006 ) and DFT - LDA ( Marcondes et al., 2016 ) serve as uppe r and lower bounds of experimental measurements, respectively ( Figure 2 - 3 a). ( Marcondes et al., 2016 ) provide the only previous predictions of the elastic shear properties of CaCO 3 - Pmmn , which are necessary to directly compare our results for thermoelastic parameter s derived by MGD EoS (discussed in the following section). We thus provide an additional fit to our 300 K P - V data with V 0 fixed to 97.76 Å 3 as predicted by DFT - LDA, y ielding K T 0 = 146.7 (±1.9) 20 GPa and = 3.4(±0.1) . Smaller K T 0 and larger relative to the unconstrained BM3 EoS are mainly due to the tradeoffs between V 0 , K T 0 , and ( Figure 2 - 8 ) . The modeled K T at pressures from 50 - 80 GPa (black dashed line in Figure 2 - 3 b) are cons istent with the fits without a fixed V 0 . 2.4.3 Thermal equation of state of CaCO 3 - Pmmn To constrain the TEoS, unit - cell volumes for CaCO 3 - Pmmn are collected up to 75 GPa and 2200 K ( Table 2 - 3 ), with temperature determined by spectroradiometry and pressure measured using the TEoS of Au ( Fei et al., 2007 ) . We use two approaches to constrain high - temperature behavior: 1) obtaining thermal expansion coefficient ( T ) from fitting P - V - T data to a high - temperature BM3 EoS (HT - BM3 EoS) (Birch, 1952; Fei, 1995) ( Figure 2 - 5 a), and 2) obtaining Grüneisen parameter ( 0 ) from a Mie - Grüneisen - Debye equation of state (MGD EoS) (Jackson, 1998; Jackson & Rigden, 1996) ( Figure 2 - 5 b). Both the MGD EoS and HT - BM3 EoS models can mathematically describe our experimental measurements well ( Figure 2 - 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 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 mo dels have been widely applied to materials in Earth sciences with thermodynamic databases used in geophysical studies, such as ( Fabrichnaya et al., 2004 ) based on HT - BM3 EoS, and (Stixrude & Lithgow - Bertelloni, 2011) based on MGD EoS. We present both model s 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. 21 The HT - BM3 EoS is given by the following expression for P ( V , T ): , where K T denotes isothermal bulk modulus at ambient pressure and a given high temperature, V T , 0 is the ambient pressure volume, V is the high - pressure and temperature volume, and is the pressure derivative of K T 0 at ambient pressure, neglecting higher - order pressure derivatives of the bulk modulus and assuming that is a constant in the temperature range of our study, i. e., . The temperature effect on K T can be expressed as a linear function of temperature, with the K T T ) P and K T 0 as follow: , where T 0 K T T ) P is assumed to be a constant within the temperature range of our study. The temperature dependence of the volume at ambient pressure, V T , 0 , can be expressed as a function of the thermal expansion at zero pressure: . The thermal expansion coefficient T is expressed as T = (1/ V V T ) P . At atmospheric pressure, T can be approximated to a linear function of temperature: , where a 0 and a 1 are constants. By least - squares fitting with the parameters V 0 , K T 0 and fixed from the 300 K BM3 EoS, we obtained a 0 , a 1 K T T ) P . We further fit the P - V - T data with a fixed V 0 to 97.76 Å 3 alone, yielding K T 0 , , a 0 , a 1 K T T ) P , which are consistent with the first fitting within uncertainties ( Table 2 - 2 ). The isothermal compression curves for temperatures from 1300 to 2200 K at 300 K intervals were calculated from these thermoelastic parameters ( Figure 2 - 5 a). The fitting residuals indicate the discrepancies between measured and calculated 22 pressure are ranging from - 1.7 to 1.4 GPa within the investigated pressure and temperature range ( Figure 2 - 5 a), 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 , T 0 ), and the thermal pressure, P th ( V , T ): , where P ( V , T 0 ) is fixed by BM3 EoS at 300 K, and the thermal pressure P t h ( V , T ) is a function of the Grüneisen parameter and the thermal energy E th ( V , T ), that can be estimated using a Debye model: , , where is the Debye temperature, n = 5 is the number of atoms in the formula unit, and R is the - 1 K - 1 ). The volume dependence of the and are described by: , , where q is the dimensionless power m ode parameter, 0 and 0 are Grüneisen parameter and Debye temperature at 300 K, respectively. As above, V 0 , K T 0 , are fixed from the 300 K EoS. The 0 vibration model ( Poirier, 2000 ) . With self - consistent elastic parameters at zero pressure K S0 = 122 GPa, G 0 = 56 GPa and 0 = 3.4 g/cm 3 reported by ( Marcondes e t al., 2016 ) , the 0 for CaCO 3 - Pmmn was estimated to be 631 K. Due to strong correlations between the three high - temperature parameters 0 , 0 and q , we fixed 0 and obtained the fitted 0 = 1.94(±0.02) and q = 1.9(±0.3). To 23 investigate the tradeoff between 0 and q , we further fix q = 1 as a common assumption, yielding 0 =1.53(±0.01). We also fit the P - V - T data with a fixed V 0 to 97.76 Å 3 and 0 to 631 K alone, yielding K T 0 = 151(±4) GPa, = 3.2(±0.2), 0 = 1.6(±0.5) and q = 1.3(±0.9), which are in agreement with the first fitting within uncertainties ( Table 2 - 2 ). These thermoelastic parameters produce isothermal compression curves ( Figure 2 - 5 b) cons istent with those obtained from HT - BM3 EoS ( Figure 2 - 5 a). The fitting residuals indicate the discrepancies between measured and calculated pressure are r anging from - 1.7 to 1.7 GPa within the investigated pressure and temperature range ( Figure 2 - 5 b). In summary, both HT - BM3 EoS and MGD EoS results here comprise the first characterization of high - temperature properties of CaCO 3 - Pmmn and can be used to model the chemical and physical prop erties of CaCO 3 in the lower mantle. Neither of EoS yields a superior or significantly different fit to the experimental data ( Figure 2 - 5 ) and the resul ts for density and bulk sound velocity of CaCO 3 - Pmmn are not significantly affected by the choice of EoS. Calculated densities and velocities follow geotherms from 45 to 80 GPa ( Figure 2 - 6 and Figure 2 - 7 ), which does not extrapolate our experimental P - T conditions significantly and minimizes the potential errors produced by extrapolation of the thermal equation of state. 2.5 Implications Due to the substantially lower density of carbonates than the principal constituents of the lower mantle ( Figure 2 - 6 ), sufficient amounts of carbonates may be expected to affect the buoyancy of the subducting slab and its seismic signature, which would be the main manifestations that could be used to constrain the survival and behavior of carbonates subducted into Earth lower mantle. Calcite/aragonite is one of the most abundant carbonates at shallow depths, along 24 with dolomite (CaMg(CO 3 ) 2 ) and magnesite (MgCO 3 ) (Luth, 1999) . During subduction, CaMg(CO 3 ) 2 breaks down to MgCO 3 and CaCO 3 above 5 GPa ( Luth, 2004 ) . The two end - member carbonates, CaCO 3 and MgCO 3 , 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 - d eep 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 o f 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 understan d the dynamics and seismic signatures of subducting carbonate - bearing slabs, density ( ) and bulk sound velocity ( V ) of CaCO 3 and MgCO 3 at relevant P - T conditions are firstly modeled based on the thermal equations of state. The bulk sound velocity is calc ulated by V = ( K S / ) 1/2 , where K S = K T 0 (1+ ), which are determined by HT - BM3 EoS and MGD EoS. Because the thermoelastic parameters of CaCO 3 - P 2 1 /c - 1 have not been constrained experimentally or theoretically, we cannot address the physical properties change due to phase transition from CaCO 3 - P 2 1 /c - 1 to CaCO 3 - Pmmn . We assume the phase transition from CaCO 3 - Pnma to CaCO 3 - Pmmn occurred at 45 GPa. The thermoelastic parameters used in the modeling of CaCO 3 - Pnma (Litasov et al., 2017a) , CaCO 3 - Pmmn (this study) and magnesite (MgCO 3 - R c) (Litasov et al., 2008) are summarized in Table 2 - 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 du ring subduction. The calculated and V of CaCO 3 and MgCO 3 from 30 to 80 GPa are plotted in Figure 2 - 6 , and both HT - BM3 EoS and MGD EoS of 25 CaCO 3 and MgCO 3 provide similar results. The phase transition of CaCO 3 - Pnma to CaCO 3 - Pmmn in our model leads to an increase in by ~4.5% but a decrease in V by ~0.8%, consistent with previous modeled results (Bayarjargal et al., 2018; Litasov et al., 2017a) . At mid - lower mantle conditions, the density of CaCO 3 - Pmmn is higher than MgCO 3 - R c by ~10 - 12%, whereas the V is lower by ~9 - Preliminary Reference Earth Model (Dziewonski & Anderson, 1981) , pure CaCO 3 in the lower mantle exhibits V ~15% lower, while MgCO 3 has V closer to PREM ( Figure 2 - 6 b). As a result, slow seismic anomalies in the mid - lower mantle may be more likely to be associated with local enrichment in CaCO 3 than MgCO 3 . More realistically, CaCO 3 and MgCO 3 are components of carbonated mantle lithologies (Poli & 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 d etermine 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 & Schmidt, 2002) . It is likely that the carbonate content o f 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 & Teagle, 1999; Shilobreeva et al., 2011) . The basalt part of the subducting sla b transforms at lower mantle conditions to a mixture of bridgmanite, Ca - perovskite, stishovite and Al - bearing calcium - ferrite - type (cf - ) silicate (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 and V 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 c onstituents of subducted slab ( Stixrude & Lithgow - Bertelloni, 2011 ) 26 and a mixture CaCO 3 - MgCO 3 used in the model are summarized in Table 2. CaCO 3 and MgCO 3 are added into the metamorphosed basalt assemblages as a 1:1 molar ratio in proportions of 0 (i.e., e clogite), 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 V of eclogite can be decreased by at most ~2.0 % with the presence of 10 mol.% carbonates in the case of maximum carbonate enr ichment and zero loss of carbonate during subduction. Even for this extreme upper bound, the effect of CaCO 3 phase transition on the seismic velocity of the slab, increased by ~0.1%, is invisible ( Figure 2 - 7 a). In the case of typical 0.5 mol.% carbonates presence in the subducting slab, the V of eclogite would decrease by less than 0.1 %. Comparing to the ambient mantle profile (PREM), the subduc ting slabs exhibit high V 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. 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 CaCO 3 - P 2 1 /c - l to CaCO 3 - Pmmn phase transition (Bayarjargal et al., 2018) , and largely localized anisotropy due to small shear modulus of MgCO 3 (Yao et al., 2018a) . Although the region with >1% seismic velocity anomaly is detectable by seismic tomography (e.g., French & 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. 27 The contrast between carbonates and surrounding phases at lower mantle conditions is a source o f 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 the higher density of eclogite helps drive subduction in the lower m antle. However, the model results indicate the density of highly carbonated eclogite with maximum carbonate enrichment 10 mol.% carbonates are lower than the ambient lower mantle by ~0.6 % ( Figure 2 - 7 b), 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 alter ed 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 meta stable olivine (Rubie & Ross, 1994) and pyroxene (van Mierlo et al., 2013) . Thermoelastic properties of CaCO 3 - Pmmn provide useful geochemical constraints necessary for modeling the phase equilibria of carbonates with mantle phases at lower mantle conditi ons. Reactions that control the presence of CaCO 3 in the slab include melting, decarbonation and redox interactions with ambient mantle phases. For example, recent experimental studies suggest the CaCO 3 decarbonation occurs in the presence of silica at low er mantle conditions forming Ca - perovskite and CO 2 ( Drewitt et al., 2019 ; Li et al., 2018 ) , and the redox reaction between CaCO 3 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 28 boundaries of both reactions are essential to understanding the fate of subducted CaCO 3 and equilibr ium between CaCO 3 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 & Lithgow - Bertelloni, 2011) . The newly determined thermoelastic parameters of CaCO 3 - Pmmn combined with those of other mantle phases will contribute to more quan titative constraints on phase equilibria in the carbonate - silicate system at lower mantle conditions. 29 Figure 2 - 1 : Full - profile Le Bail refinement confirms the synthesis of CaCO 3 - 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 peak posi tions for Au calibrant (yellow sticks) and Ne medium (blue ticks). One unknown peak at 2 around ~7° (marked by an asterisk) may be from the metastable CaCO 3 - P 2 1 / c - l due to kinetics. The wavelength of the monochromatic X - ray beam is 0.3344 Å. 30 Figure 2 - 2 : Representative in - situ X - ray diffraction patterns of CaCO 3 - Pmmn . (a) Representative in - situ X - ray diffraction patterns of CaCO 3 - Pmmn measured at high pressures and room temperature (black mark er). (b) Representative high - temperature X - ray diffraction patterns of CaCO 3 - 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. 31 Figure 2 - 3 : Equation of state of CaCO 3 - pmmn . (a) Pressure - volume data for CaCO 3 - 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 squa re) were recalculated using Pt pressure scale ( Fei et al., 2007 ) . Black solid curve (this study) is modeled by BM3 EoS using K T 0 = 162(±62) GPa, = 3.1 (±1.1), and V 0 = 96.6(±4.8) Å 3 . A brown dashed curve ( Oganov et al., 2006 ) and a purple dashed curve ( Marcondes et al., 2016 ) modeled by BM3 EoS constrained via DFT - GGA and LDA, respectively. (b) Isothermal bulk modulus ( K T ) 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 V 0 = 97.76 Å 3 and with reference pressure set at 50 GPa. 32 Figure 2 - 4 : Volume Eulerian strain ( f ) - normalized pressure ( F ) plot of CaCO 3 - Pmmn . The dashed line represents the linear fit through the data, and a red envelope indicates 95% confidence interval. The V 0 was set as 96.6 Å 3 obtained by BM3 EoS fitting of experimental data at 300 K. 33 Figure 2 - 5 : Measured pressure - volume - temperature data for CaCO 3 - Pmmn . Colorful curves are isotherms at 1300, 1600, 1900, 2200 K modeled by (a) HT - BM3 EoS and (b) MGD EoS, respectively, with parameters listed in Table 2 - 2 . Black points and curve are at 300 K same as Figure 2 - 3. The lower panel of each figure shows fitting residuals. 34 Figure 2 - 6 : Modeled (a) density and (b) bulk sound velocity profiles of CaCO 3 and MgCO 3 from 30 to 80 GPa along mantle geotherm (Brown & Shankland, 1981) compared to PREM model (Dziewonski & Anderson, 1981) and eclogite (assumed to be composed by 27 mol.% bridgmanite [(Mg 0.9 ,Fe 0.1 )SiO 3 ], 24 mol.% Ca - perovskite (CaSiO 3 ), 20 mol.% stishovite (SiO 2 ), 29 mol.% Al - bearing calcium - ferrite - type silicate [(Mg 0.9 ,Fe 0.1 )Al 2 O 4 ]), using the thermoelastic parameters listed in Table 2 - 2 . In order to clearly illustrate the density contrast of different carbonates, the phase transi tion of CaCO 3 - Pnma to CaCO 3 - Pmmn is assumed to occur at 45 GPa. 35 Figure 2 - 7 : Modeled (a) bulk sound velocity and (b) density profiles of eclogite and carbonated - eclogite with the presence of CaCO 3 - MgCO 3 mixture as 2, 5 and 10 mol.%, respectively. The eclogite is assumed to be composed by 27 mol.% bridgmanite [(Mg 0.9 ,Fe 0.1 )SiO 3 ], 24 mol.% Ca - perovskite (CaSiO 3 ), 20 mol.% stishovite (SiO 2 ), 29 mol.% Al - bearing calcium - ferrite - type silicate [(Mg 0.9 ,Fe 0.1 )Al 2 O 4 ], and the thermoelastic parameters of these phases are listed in Table 2 - 2 . The pressure is ranging from 30 to 80 GPa along cold geotherm (Syra cuse et al., 2010) . The CaCO 3 - Pnma to CaCO 3 - Pmmn transition is assumed to occur at 45 GPa. The PREM model (Dziewonski & Anderson, 1981) is plotted as a comparison of the averaged mantle. 36 Figure 2 - 8 : The correlation between the fitted V 0 and K T 0 of CaCO 3 - Pmmn at 300 K using BM3 EoS. The red circle indicates the fitting result and black ellipsoid represents 95% confidence interval. 37 Table 2 - 1 : Comparison of parameters of BM3 EoS of CaCO 3 - Pmmn at 300 K. V 0 (Å 3 ) K T 0 (GPa) Method References 99.4(20) 118(14) 4 (fixed) XRD (PM 2 : NaCl) Ono et al. (2005) 3 97.3(16) 135(12) 4 (fixed) XRD (No PM) Lobanov et al. (2017) 3 109.74 65.4 4.94 DFT - GGA 4 Oganov et al. (2006) 97.76 122 3.732 DFT - LDA 4 Marcondes et al. (2016) 96.6(48) 162(62) 3.1(11) XRD (PM: Ne) 5 This study 97.76 (fixed) 146.7(19) 3.4(1) XRD (PM: Ne) 5 This study 1 Numbers in parentheses are uncertainties on the last digits. 2 PM: pressure medium 3 Refitted by the pressure scale of Pt ( Fei et al., 2007 ) . 4 Results are from 0 K. 5 Using the pressure scale of Au ( Fei et al., 2007 ) . 38 Table 2 - 2 : Thermoelastic parameters of CaCO 3 , MgCO 3 , and major components in eclogite. Sample V 0 (Å 3 ) K T 0 (GPa) K T T - 1 ) a 0 (10 - 5 K - 1 ) a 1 (10 - 8 K - 2 ) 0 (K) 0 q CaCO 3 - Pmmn 1 97.76 5 146.7(19) 5 3.4(1) 5 - 0.021(1) 4.3(3) 0.8(2) 631 5 1.94(2) 1.9(3) CaCO 3 - Pmmn 1 97.76 5 146(5) 3.4(2) - 0.022(8) 4.4(5) 0.9(8) - - - CaCO 3 - Pmmn 1 97.76 5 151(4) 3.2(2) - - - 631 5 1.6(5) 1.3(9) CaCO 3 - Pmmn 1 97.76 5 146.7(19) 5 3.4(1) 5 - - - 631 5 1.53(1) 1 5 CaCO 3 - Pnma 2 227.11(3) 6 67.0(8) 4.74(12) - 0.016(1) 4.95(22) 2.77(40) 516 5 1.39(1) 1 5 MgCO 3 - R c 3 279.55(2) 97.1(5) 5.44(7) - 0.013(1) 4.03(7) 0.49(10) 747 5 1.38(1) 1 5 MgSiO 3 (perovskite) 4 162.40 251(3) 4.1(1) 905(5) 1.57(5) 1.1(3) FeSiO 3 (perovskite) 4 169.31 272(40) 4.1(10) 871(26) 1.57(30) 1.1(10) MgAl 2 O 4 (cf) 4 480.63 211(1) 4.1(1) 838(16) 1.31(30) 1.0(10) FeAl 2 O 4 (cf) 4 494.97 211 (10) 4.1(10) 804(69) 1.31(30) 1.0(10) CaSiO 3 (perovskite) 4 45.58 236 (4) 3.9 (2) 796 (44) 1.89 (7) 0.9 (16) SiO 2 (stishovite) 4 46.56 314(8) 3.8(1) 1108(13) 1.37(17) 2.8(22) 1 This study. 2 Litasov et al. (2017). 3 Litasov et al. (2008). 4 Stixrude and Lithgow - Bertelloni (2011). 5 Fixed during fitting. 6 Numbers in parentheses are uncertainties on the last digits 39 Table 2 - 3 : Unit cell parameters of CaCO 3 - Pmmn at different P - T conditions. T (K) P (GPa) V (Å 3 ) a (Å) b (Å) c (Å) 298 49.9(1) a 77.55(7) 4.182(5) 4.600(6) 4.031(4) 298 52.2(1) 76.89(2) 4.155(2) 4.611(2) 4.014(5) 298 55.4(1) 76.23(6) 4.132(4) 4.594(5) 4.016(9) 298 56.1(2) 75.99(7) 4.127(5) 4.589(5) 4.013(9) 298 56.8(2) 75.77(9) 4.121(7) 4.589(7) 4.008(9) 298 59.1(2) 75.22(9) 4.104(6) 4.574(7) 4.007(9) 298 60.6(2) 74.95(7) 4.102(5) 4.576(6) 3.994(9) 298 66.1(2) 73.70(4) 4.075(3) 4.558(3) 3.967(9) 298 67.5(3) 73.36(3) 4.066(2) 4.548(2) 3.968(6) 1308(100) 60.3(5) 76.36(6) 4.144(4) 4.595(5) 4.010(9) 1317(100) 60.1(5) 76.35(4) 4.145(3) 4.597(3) 4.007(9) 1319(100) 72.3(7) 73.63(4) 4.076(2) 4.554(3) 3.967(9) 1320(100) 61.6(5) 76.17(5) 4.135(4) 4.592(4) 4.012(9) 1322(100) 72.6(6) 73.58(3) 4.073(2) 4.553(3) 3.967(9) 1326(100) 60.8(5) 76.30(7) 4.143(5) 4.597(6) 4.007(9) 1340(100) 73.1(6) 73.57(3) 4.073(2) 4.552(2) 3.968(9) 1348(100) 64.0(6) 75.62(8) 4.117(5) 4.578(6) 4.013(9) 1353(100) 64.0(5) 75.67(8) 4.118(5) 4.578(6) 4.015(9) 1354(100) 63.8(5) 75.72(9) 4.119(6) 4.578(7) 4.015(9) 1358(100) 73.3(6) 73.57(5) 4.072(4) 4.552(4) 3.970(9) 1360(100) 57.8(5) 77.04(5) 4.155(3) 4.606(4) 4.025(9) 1360(100) 57.4(5) 77.11(4) 4.158(3) 4.607(3) 4.026(9) 1360(100) 61.3(5) 76.22(4) 4.140(3) 4.594(3) 4.007(9) 1362(100) 69.2(6) 74.41(1) 4.103(1) 4.564(1) 3.974(3) 1366(100) 69.4(6) 74.28(2) 4.102(1) 4.565(2) 3.967(4) 1366(100) 69.0(6) 74.40(6) 4.103(1) 4.565(1) 3.972(5) 1368(100) 72.6(7) 73.60(2) 4.075(2) 4.554(2) 3.966(9) 1369(100) 60.1(5) 76.45(6) 4.147(4) 4.597(4) 4.010(9) 1369(100) 64.1(6) 75.61(8) 4.117(5) 4.577(6) 4.013(9) 1372(100) 63.6(5) 75.74(7) 4.119(5) 4.578(6) 4.016(9) 1374(100) 58.2(5) 76.96(5) 4.155(3) 4.605(4) 4.022(9) 1378(100) 64.6(6) 75.50(8) 4.115(6) 4.577(6) 4.009(9) 1381(100) 64.5(6) 75.60(8) 4.115(5) 4.576(6) 4.015(9) 1392(100) 64.5(6) 75.61(8) 4.116(6) 4.577(6) 4.013(9) 1393(100) 69.7(6) 74.22(4) 4.100(3) 4.565(3) 3.965(8) 1396(100) 72.5(7) 73.65(2) 4.076(2) 4.554(2) 3.968(9) 1402(100) 69.0(6) 74.49(3) 4.104(1) 4.565(2) 3.976(6) 1405(100) 69.9(6) 74.18(3) 4.100(2) 4.565(3) 3.963(7) 1414(100) 64.9(6) 75.51(8) 4.113(6) 4.576(6) 4.012(9) 1415(100) 58.8(5) 76.90(4) 4.154(3) 4.605(3) 4.021(9) 1422(100) 65.1(6) 75.51(9) 4.113(6) 4.575(7) 4.013(9) 1429(100) 59.5(5) 76.79(4) 4.151(3) 4.603(3) 4.019(8) 40 Table 2 - 1430(100) 65.8(6) 75.40(9) 4.109(7) 4.574(7) 4.011(9) 1431(100) 72.8(7) 73.64(2) 4.077(1) 4.554(1) 3.967(3) 1438(100) 62.0(5) 76.24(5) 4.139(4) 4.593(4) 4.011(9) 1440(100) 70.3(6) 74.13(3) 4.100(2) 4.565(2) 3.961(6) 1445(100) 70.3(6) 74.10(2) 4.098(1) 4.564(2) 3.962(4) 1448(100) 73.9(6) 73.53(5) 4.071(3) 4.552(4) 3.968(9) 1456(100) 57.5(5) 77.17(4) 4.163(3) 4.609(3) 4.022(8) 1463(100) 72.8(7) 73.69(2) 4.079(1) 4.554(1) 3.967(4) 1467(100) 70.6(6) 74.15(2) 4.098(1) 4.564(1) 3.965(3) 1467(100) 69.3(6) 74.55(1) 4.105(1) 4.565(1) 3.979(3) 1471(100) 55.3(5) 78.42(4) 4.199(3) 4.619(3) 4.044(9) 1472(100) 60.6(5) 76.53(5) 4.147(3) 4.596(4) 4.015(9) 1479(100) 59.4(5) 76.85(4) 4.152(3) 4.604(3) 4.020(7) 1485(100) 56.9(6) 77.98(6) 4.185(4) 4.616(4) 4.036(9) 1485(100) 69.5(6) 74.55(4) 4.105(1) 4.565(3) 3.979(7) 1489(100) 69.5(6) 74.48(3) 4.104(1) 4.565(3) 3.975(3) 1490(100) 65.9(6) 75.37(7) 4.111(5) 4.576(6) 4.007(9) 1492(100) 57.3(5) 77.26(5) 4.164(3) 4.609(3) 4.025(9) 1492(100) 64.3(6) 75.79(7) 4.122(5) 4.579(5) 4.016(9) 1495(100) 54.6(5) 78.49(3) 4.200(2) 4.619(2) 4.046(6) 1500(100) 56.4(5) 78.24(3) 4.193(2) 4.616(3) 4.042(7) 1506(100) 64.5(6) 75.75(7) 4.121(5) 4.579(5) 4.014(9) 1507(100) 62.9(5) 76.18(6) 4.134(4) 4.591(5) 4.014(9) 1509(100) 65.9(6) 75.49(9) 4.112(7) 4.575(7) 4.013(9) 1511(100) 64.6(6) 75.74(7) 4.121(4) 4.579(5) 4.013(9) 1516(100) 66.2(6) 75.48(9) 4.111(7) 4.575(8) 4.014(9) 1521(100) 69.4(6) 74.65(4) 4.105(1) 4.566(3) 3.984(8) 1522(100) 62.9(5) 76.20(7) 4.136(5) 4.593(5) 4.011(9) 1523(100) 72.5(7) 73.80(4) 4.082(3) 4.555(3) 3.970(9) 1526(100) 70.9(6) 74.12(3) 4.098(2) 4.564(3) 3.963(7) 1529(100) 57.1(6) 78.09(6) 4.187(4) 4.615(4) 4.041(9) 1532(100) 64.9(6) 75.73(6) 4.121(4) 4.580(5) 4.013(9) 1533(100) 57.1(6) 78.08(5) 4.187(4) 4.615(4) 4.041(9) 1538(100) 66.0(6) 75.44(8) 4.112(5) 4.576(6) 4.010(9) 1542(100) 60.7(5) 76.54(6) 4.149(4) 4.597(4) 4.013(9) 1542(100) 66.3(6) 75.37(8) 4.110(6) 4.575(6) 4.008(9) 1543(100) 64.9(6) 75.74(8) 4.120(5) 4.578(6) 4.015(9) 1544(100) 64.5(6) 75.77(7) 4.122(5) 4.580(5) 4.013(9) 1582(100) 71.5(6) 74.11(2) 4.097(1) 4.564(1) 3.963(4) 1594(100) 60.6(5) 76.76(2) 4.151(2) 4.604(2) 4.016(5) 1615(100) 58.9(5) 77.11(4) 4.159(3) 4.609(3) 4.022(9) 1620(100) 58.1(6) 77.91(7) 4.184(5) 4.616(5) 4.035(9) 1629(100) 64.8(6) 75.86(6) 4.127(4) 4.581(5) 4.013(9) 41 Table 2 - 1648(100) 61.4(6) 76.72(2) 4.149(2) 4.601(2) 4.019(5) 1648(100) 72.0(5) 74.05(4) 4.096(3) 4.564(3) 3.961(9) 1655(100) 61.5(6) 76.71(3) 4.147(2) 4.600(2) 4.021(6) 1656(100) 73.6(7) 73.77(3) 4.082(1) 4.555(2) 3.968(4) 1661(100) 70.0(6) 74.67(2) 4.105(1) 4.565(1) 3.985(3) 1673(100) 61.6(5) 76.56(4) 4.149(3) 4.597(3) 4.014(9) 1701(100) 61.5(5) 76.65(4) 4.151(3) 4.598(3) 4.016(8) 1704(100) 73.8(7) 73.82(2) 4.082(2) 4.555(2) 3.970(5) 1705(100) 56.0(5) 78.36(3) 4.201(2) 4.622(3) 4.036(7) 1728(100) 65.4(6) 75.80(6) 4.126(4) 4.581(5) 4.010(9) 1731(100) 65.5(6) 75.86(7) 4.126(5) 4.581(6) 4.014(9) 1734(100) 64.6(6) 76.10(5) 4.133(4) 4.591(4) 4.011(9) 1736(100) 65.6(6) 75.81(7) 4.125(5) 4.581(6) 4.011(9) 1740(100) 58.7(6) 77.31(4) 4.165(3) 4.609(3) 4.027(9) 1748(100) 65.5(6) 75.81(7) 4.127(5) 4.582(5) 4.009(9) 1785(100) 65.7(6) 75.83(6) 4.127(4) 4.581(5) 4.010(9) 1790(100) 65.8(6) 75.85(6) 4.127(4) 4.582(5) 4.011(9) 1792(100) 58.5(6) 77.27(5) 4.168(3) 4.612(4) 4.020(9) 1798(100) 70.6(6) 74.68(4) 4.105(1) 4.566(4) 3.985(4) 1813(100) 74.7(7) 73.74(2) 4.080(1) 4.555(1) 3.968(3) 1814(100) 62.1(6) 76.67(2) 4.153(1) 4.595(1) 4.017(4) 1816(100) 65.9(6) 75.85(6) 4.127(4) 4.581(5) 4.012(9) 1819(100) 66.0(6) 75.87(7) 4.127(5) 4.581(5) 4.013(9) 1820(100) 74.8(7) 73.78(1) 4.082(1) 4.554(1) 3.969(3) 1824(100) 62.8(6) 76.72(3) 4.147(2) 4.601(2) 4.021(6) 1832(100) 75.0(7) 73.77(3) 4.083(3) 4.554(3) 3.967(8) 1835(100) 63.0(6) 76.51(5) 4.147(4) 4.597(4) 4.013(9) 1840(100) 66.4(6) 75.82(7) 4.126(5) 4.581(5) 4.012(9) 1866(100) 62.8(6) 76.61(4) 4.150(3) 4.598(3) 4.015(8) 1873(100) 65.9(6) 75.87(7) 4.128(5) 4.583(6) 4.011(9) 1897(100) 71.1(6) 74.54(4) 4.105(1) 4.567(1) 3.976(2) 1937(100) 63.4(6) 76.75(3) 4.147(2) 4.601(3) 4.023(7) 1956(100) 62.8(6) 76.84(4) 4.152(3) 4.605(3) 4.019(8) 1962(100) 67.0(6) 75.74(6) 4.128(4) 4.582(4) 4.004(9) 1992(100) 67.5(6) 75.83(6) 4.126(4) 4.582(5) 4.011(9) 1999(100) 71.8(6) 74.47(2) 4.105(2) 4.567(2) 3.972(5) 2015(150) 66.9(7) 75.87(6) 4.128(4) 4.583(5) 4.010(9) 2029(150) 57.8(6) 78.03(2) 4.192(1) 4.623(1) 4.026(1) 2037(150) 67.3(7) 75.86(6) 4.128(4) 4.582(5) 4.010(9) 2054(150) 60.0(7) 77.20(2) 4.170(1) 4.611(2) 4.015(4) 2061(150) 67.8(7) 75.78(5) 4.128(4) 4.583(4) 4.006(9) 2069(150) 58.4(6) 77.96(2) 4.190(2) 4.624(2) 4.024(5) 2080(150) 67.7(7) 75.79(5) 4.127(4) 4.582(4) 4.008(9) 42 Table 2 - 2103(150) 72.7(8) 74.52(4) 4.106(1) 4.567(1) 3.974(2) 2139(150) 64.2(7) 76.64(3) 4.151(2) 4.598(2) 4.015(5) 2160(150) 61.1(7) 77.18(1) 4.166(1) 4.609(1) 4.019(2) a Numbers in parentheses are uncertainties on the last digits. 43 Chapter 3 Reversal of carbonate - mantle This chapter has been published as Lv et al. (2021) . 3.1 Abstract the planet over geologic time, impacting the surface climate as well as carrying rec ords of geologic processes in the form of diamond inclusions. However, current estimates of the distribution of carbonates through subduction, the main mechanism th to its interior. Oxidized carbon carried by subduction has been found to reside in MgCO 3 throughout much of the mantle. Experiments in this study demonstrate that at deep mantle conditions MgCO 3 reacts with silicates to form CaCO 3 . In combination with previous work indicating that CaCO 3 is more stable than MgCO 3 mantle, these observations allow us to predict that the signature of surface carbon reach lowermost mantle may include CaCO 3 . 3.2 Introduction geological processes of subduction, partial melting, degassing, and metasomatism, providing ( Hazen & Schiffries, 2013 ) . Over the history of the planet, carbon transport between surface and deep reservoirs has impacted the atmospheric, oceanic and 44 crustal CO 2 ( Kelemen & Manning, 2015 ; Plank & Manning, 2019 ) . to its interior mainly as carbonate minerals in subduction zones, and is returned in carbon - bearing gas/fluid through volcanic degassing ( Kelemen & Manning, 2015 ; Plank & Manning, 2019 ) . These processes leave sig natures in the mantle including depletion of incompatible elements ( Stachel et al., 2004 ; Thomson et al., 2016a ) , diamond formation (and inclusions) ( Palyanov et al., 2013 ; Rohrbach & Schmidt, 2011 ) , and isotopic abundances ( Cartigny et al., 2014 ; Teng, 201 7 ) . Carbon flux via subduction to the deep mantle remains uncertain, with estimated magnitudes ranging from 0.0001 to 52 megatons/year ( Dasgupta & Hirschmann, 2010 ; Kelemen & Manning, 2015 ) . The wide range of these estimates is due in part to limited under standing of the physical and chemical responses of carbonates to mantle pressures, temperatures, and compositional environments. The dominant carbonates carried into the mantle by subducting slabs, dolomite CaMg(CO 3 ) 2 , magnesite MgCO 3 , and calcite CaCO 3 (Poli & Schmidt, 2002) , undergo changes in crystal structure or state and chemical reactions at depth. Carbonates are likely to be retained as solid minerals in subducting ocean crust until/unless the solidus of carbonated peridotite (Dasgupta & Hirschmann , 2006; Ghosh et al., 2014) or eclogite (Kiseeva et al., 2012; Thomson et al., 2016b) intersects with mantle geotherms, initiating melting. These slab - derived carbonatite melts will segregate to the overlying mantle due to low viscosity and density (Sun & Dasgupta, 2019) , or be reduced to diamonds at depths greater than ~250 km via redox freezing (Rohrbach & Schmidt, 2011; Stagno et al., 2013; Thomson et al., 2016b) . However, carbonates are present in the mantle transition zone and possibly lower mantle depths in some regions, based on direct evidence provided by carbonate minerals found in deep - sourced diamond inclusions (Brenker et al., 2007; Wirth et al., 2009) . Additional evidence from thermodynamic mod eling of devolatilization of 45 carbonate - bearing subducting slab (Kerrick & Connolly, 2001; Poli et al., 2009) , and melting experiments on carbonates in the MgCO 3 - CaCO 3 system up to 80 GPa (Thomson et al., 2014) supports preservation of solid carbonates alon g low - temperature geotherms in subducting slabs in the lower mantle. However, temperature is not the only control on the fate of subducted carbonates: carbonates may also interact chemically with the major phases of the ambient mantle or basalt - rich subduc ted crust. In these compositions in the lower mantle, the silicates potentially reacting with carbonates are bridgmanite (bdg), post - perovskite (pPv), and Ca - perovskite (Ca - Pv). The presence of the end - member carbonates, MgCO 3 and CaCO 3 (note that (Mg,Ca)( CO 3 ) 2 dolomite breaks down to these end - members above 5 GPa and 1200 K (Luth, 2004 ) ), together with lower mantle silicates depends on the thermodynamics and kinetics of the carbonate - silicate exchange reaction: CaCO 3 + MgSiO 3 3 + CaSiO 3 (1) Previou s experiments (Biellmann et al., 1993; Seto et al., 2008) indicate CaCO 3 reacts with silicates to form MgCO 3 via the forward reaction up to 80 GPa and 2300 K, i.e. at least to the mid - lower mantle. Theoretical studies further predict that MgCO 3 + CaSiO 3 ar e enthalpically favored over CaCO 3 + MgSiO 3 throughout the lower mantle pressure and temperature regime (Oganov et al., 2008; Pickard & Needs, 2015; Santos et al., 2019; Yao et al., 2018b; Zhang et al., 2018) . However, although many studies have addressed the stability of individual carbonates up to higher pressures (Binck et al., 2020; Boulard et al., 2011; Isshiki et al., 2004) , no experiments examined the carbonate - silicate cation exchange reaction up to core - mantle boundary conditions. In this work, to assess the stability of MgCO 3 and CaCO 3 coexisting with lower mantle silicates, we conduct a series of experiments on the carbonate - silicate reaction along the lower mantle geotherm. Thin disks of carbonates and silicates were loaded together in l aser - heated 46 diamond - anvil cells (LHDAC, Table 3 - 1 , see Methods for details). Laser heating at 1600 - 2800 K and 33 - 137 GPa was applied for 10 - 400 mins. Ru n products were examined by in - situ synchrotron X - ray diffraction (XRD) and ex - situ energy - dispersive X - ray spectroscopy (EDX) analysis with a scanning transmission electron microscope (STEM, see Methods for details). 3.3 Results 3.3.1 Calcium carbonate r eaction to form magnesium carbonate Experiments assessed thermodynamic stability by using as reactants either (Mg,Ca)CO 3 + (Mg,Fe)SiO 3 (reactants for the forward reaction, hereafter referred to CaC - to - MgC) and (Mg,Fe)CO 3 + CaSiO 3 (reactants for the reverse reaction, hereafter referred to MgC - to - CaC). For reaction CaC - to - MgC, the criterion for determining whether the reaction takes place is the presence of newly - synthesized CaSiO 3 - perovskite in the run product. For reaction MgC - to - CaC, newly - synthesized MgSi O 3 and CaCO 3 indicate the reaction is favorable. The silicate reaction products are easier to observe through diffraction than carbonates due to higher diffraction intensity. Experiments with CaC - to - MgC reactants indicate the forward reaction takes place in runs condu cted below 83 GPa (runs #1 - 4), as determined via both EDX and XRD. For example, ex - situ electron microscopic analysis of the sample recovered from 33 GPa and 1650 K (run #1) ( Figure 3 - 1 a - c) reveals a ~1 - - thick layer of CaSiO 3 between the silicate layer and the carbonate layer, coexisting with SiO 2 , FeO, MgSiO 3, and MgCO 3 . These observations are consistent with in - situ XRD patterns of run products after heating ( Figure 3 - 7 , Figure 3 - 9 ), which exhibit several new sharp peaks compared to the pattern before heating ( Figure 3 - 7 a). The diffraction pattern of run products is consistent with the pres ence of Ca - Pv, magnesite, bdg, wüstite, stishovite, and 47 monoclinic dolomite III (previously observed at presure above 36 GPa (Mao et al., 2011a) ). Ca - Pv can be observed in the run products of CaC - to - MgC up to 83 GPa ( Figure 3 - 7 c, Figure 3 - 8 a - b), in agreement with previous experimental observations (Biellmann et al., 1993; Seto et al., 2008) . At higher pressures from 91 to 137 GPa, however, we observe no evidence of carbonate - silicate exchange reaction in experiments with CaC - to - MgC reactants. Ca - Pv is not identified in the run products (runs #5 - 7) through either in - situ ( Figure 3 - 7 d - e, Figure 3 - 8 c - d, Figure 3 - 9 b) or ex - situ analysis. New, sharp peaks from bdg and pPv can be observed in - situ in XRD patterns ( Figure 3 - 7 d - e), indicating the sample was sufficiently heated to transform starting materials to high - pressure silicate structures, but no carbonate - silicate exchange reaction occurs. Two hypotheses can explain these observations: (1) in contrast to theoretical predictions that the reversal of the carbonate - exchange reaction takes place at higher pressures and lower temperatures (Oganov et al., 2008; Pickard & Needs, 2015; Santos et al., 2019; Yao et al., 2018b; Zhang et al., 2018) , CaCO 3 + MgSiO 3 become more favorable than MgCO 3 + CaSiO 3 from 91 - 137 GPa and 2100 - 2800 K; (2) the reaction CaC - to - MgC is hindered by reaction kinetics, and metastable starting materials are observed. 3.3.2 Magnesium carbonate reaction to form calcium carbonate. In order to resolve the thermodynamically stable phase assemblage, three separate sets of experiments on the backward reaction (MgC - to - CaC, runs #8 - 11) were conducted at 35 - 133 GPa and 1800 - 2000 K. Elemental mapping of the run products of experiments at 88 GPa (run #10, Figure 3 - 1 d - f) and 133 GPa (run #11, Figure 3 - 1 g - i) indicates that MgSiO 3 layers formed along the carbonate - silicate interface, and newly - formed CaCO 3 can be observed as well. At 35 GPa, neither EDX nor XRD shows MgSiO 3 formed from MgC - to - CaC reactants (run #8, Figure 3 - 13 ). 48 Observations of the reversal of the reaction confirm that MgCO 3 is unstable and reacts with CaSiO 3 producing CaCO 3 and MgSiO 3 at pressures higher than 88 GPa along a lower mantle geotherm. Our results agree with previous experimental constraints ( Figure 3 - 2 ) below 80 GPa showing: dolomite is unstable relative to CaCO 3 and MgCO 3 at lower mantle conditions (Biellmann et al., 1993; Dorfman et al., 2018; Luth, 2004; Seto et al., 2008 ) ; neither CaO nor MgO are observed in run products, indicating no decomposition of CaCO 3 and MgCO 3 into oxides plus CO 2 ( Oganov et al., 2008; Pickard & Needs, 2015; Santos et al., 2019) ; MgCO 3 is more favorable in the lower mantle than CaCO 3 up to ~80 GPa due to the CaC - to - MgC reaction (Biellmann et al., 1993; Seto et al., 2008) . Since similar previous studies were limited to pressures below 80 GPa, they did not observe the reversal reaction (MgC - to - CaC). Combining our new results with previous results (Biellmann et al., 1993; Seto et al., 2008) and theoretical predictions indicating a positive Clapeyro n slope for this reaction (Santos et al., 2019; Yao et al., 2018b; Zhang et al., 2018) , we suggest a reaction boundary above 80 GPa with a positive slope (black dashed line in Figure 3 - 2 ). We note that the experimental data allow for significant uncertainty in this boundary, but are inconsistent with theoretical predictions (Santos et al., 2019; Yao et al., 2018b; Zhang et al., 2018) (yellow region, Figure 3 - 2 ). This discrepancy may have been produced by theoretical approximations at higher temperatures. If density functional pertur bation theory and quasi - harmonic approximation have misestimated the volumes of the carbonate phases expected to be stable at ~80 GPa and higher pressures, this could lead to the systematic overestimation of Gibbs free energy of CaCO 3 + MgSiO 3 relative to MgCO 3 + CaSiO 3 at higher temperatures. 49 3.4 Discussion The pressure/temperature conditions of the reversal reaction as constrained by these experiments are similar to those of polymorphic phase transitions associated with sp 2 - sp 3 bonding changes in both MgCO 3 and CaCO 3 , which suggests these transitions are related to the stabilization of a CaCO 3 + MgSiO 3 assemblage. The transition from sp 2 - to sp 3 - bonds in MgCO 3 has been identified at ~80 GPa with the stabilization of the C 2/ m structure (Binck et al., 2020; Boulard et al., 2011; Maeda et al., 2017) , and the resulting densification of MgCO 3 supports the forward reaction to MgCO 3 + CaSiO 3 . The transition in CaCO 3 from sp 2 - to sp 3 - bonds in the P 2 1 / c - h structure was experimentally observed at ~105 GPa and 2000 K (Lobanov et al., 2017) . Computation al studies predicted this boundary at ~70 (Zhang et al., 2018) and ~100 GPa (Santos et al., 2020) at mantle - relevant temperatures (red shaded region in Figure 3 - 3 ). While an earlier study that did not include the sp 3 CaCO 3 - P 2 1 / c - h structure predicted a crossover in silicate - carbonate exchange reaction at 135 GPa and 0 K (Oganov et al., 2008) , a later st udy that predicted the sp 3 CaCO 3 - P 2 1 / c - h structure found a silicate - carbonate reaction reversal at 84 GPa and 0 K (Santos et al., 2019) . This would correspond to sp 2 - sp 3 crossover and stabilization of CaCO 3 + MgSiO 3 in the mid - lower mantle. Whether a crossover in the carbonate - silicate exchange reaction takes place in the deep depth. Previous studies have identified barrier s to carbon subduction and stability in the lower mantle, particularly melting (Kiseeva et al., 2013; Thomson et al., 2016b) and reduction (Drewitt et al., 2019; Kakizawa et al., 2015; Li et al., 2018) . If carried in cold subducting slabs, MgCO 3 and CaCO 3 may avoid melting as their melting temperatures (Thomson et al., 2014) are higher than some predicted cold slab geotherms (Maeda et al., 2017) . Any solid carbonate in the mantle will 50 be in contact and may equilibrate with silicates in all mantle environmen ts and with free silica in basalt - rich compositions. MgCO 3 and CaCO 3 have been observed in experiments (Drewitt et al., 2019; Kakizawa et al., 2015; Li et al., 2018) to undergo decarbonation reactions with free silica over a pressure range of ~40 to 60 GPa . However, the Clapeyron slope of CaCO 3 + SiO 2 3 + CO 2 is positive and takes place at pressure/temperature conditions warmer than the coolest slab geotherms (Li et al., 2018) . Observations that MgCO 3 is less thermally stable than CaCO 3 support the s urvival of CaCO 3 rather than MgCO 3 along a cold subducted slab geotherm to the lowermost mantle (Drewitt et al., 2019; Maeda et al., 2017) ( Figure 3 - 3 ). In this study, we report a reversal in the Mg - Ca silicate - carbonate cation exchange reaction at ~90 GPa, making MgCO 3 + CaSiO 3 favorable in the upper part of the lower mantle, while CaCO 3 + MgSiO 3 is preferred in the lower part of the lower mantle ( Figure 3 - 3 ). However, the question of whether any carbonate persists to these depths in the c oldest subducting slabs remains unresolved. If MgCO 3 remains present in cold slabs, and the reaction CaC - to - MgC proceeds throughout most of the mantle eliminating CaCO 3 , the reversal MgC - to - CaC reaction may transform MgCO 3 back to CaCO 3 in the lowermost ma ntle ( Figure 3 - 4 ). CaCO 3 could thus be found in the lowermost mantle coexisting with silicates and reduced iron. - wüstite buffer in the transition zone and greater depths (Frost & McCammon, 2008) , stabilizes diamond or Fe - carbide as long - term hosts of carbon, owing to their chemical refractoriness and dynamic immobility (Shirey et al., 2013) . Similarly, our experimental observations support CaCO 3 as a refractory, stable host for oxidized car bon in the middle to lowermost mantle, in particular, the high - pressure polymorph of CaCO 3 (CaCO 3 - P 2 1 / c - h) with tetrahedral bonds (Lobanov et al., 2017) . Experimental observations also suggest CaCO 3 is more resistant to redox breakdown 51 reaction with iron u nder reduced conditions than MgCO 3 (Dorfman et al., 2018) . In addition, due to the cation exchange between carbonate and silicate, the relative stability of MgCO 3 or CaCO 3 will change in the lowermost mantle, and depending on conditions one of these phases may buffer the redox state of the mantle through an influx of oxidized carbon in the form of solid carbonate (Stagno et al., 2019) . The Mg - Ca silicate - carbonate exchange reactions along subduction pressure - temperature ( P - T ) conditions may impact observabl e signatures of Mg and Ca isotopes in mantle silicates under certain special conditions, or in carbonate inclusions in diamonds. Subducting carbonates carry low - 44/40 Ca and low - 26 Mg signatures relative to the heavier mantle ratios, but although previous studies have observed heterogeneity in the Ca and Mg isotope signatures in basalts and mantle peridotites, these studies determined that lighter ratios cannot be simply interpreted as evidence of recycled marine carbonates (Ionov et al., 2019; Wang et al., 2014) . The Mg - Ca silicate - carbonate exchange reactions along subduction P - T conditions may contribute to these variable Mg and Ca isotopic compositions. The reaction CaC - to - MgC in the transition zone and upper part of the lower mantle would transfer light Ca isotopes from subducted CaCO 3 to CaSiO 3 (Ca - Pv) ( Figure 3 - 1 6 ). Isotopically light Ca - Pv can then be trapped in diamond inclusions and return to the surface (Nestola et al., 2018) , while the Ca isotopic signature of upwelling rocks would remain variable, as it undergoes continuous fractionation within peridotitic mantle lithologies (Amsellem et al., 2020; Chen et al., 2018b; Ionov et al., 2019; Kang et al., 2017) . The modification of carbonate - silicate phase equilibria observed in this study provides a ne w process that could alter Mg and Ca isotopic composition in such lithologies ( Figure 3 - 1 6 ). While the isotope signature of MgSiO 3 produced by reaction M gC - to - CaC would not be observable due to the small masses involved relative to the vast lower mantle reservoir of MgSiO 3 , any CaCO 3 produced in the deep lower 52 44/40 Ca signature that would distinguish it from surface - derived carbonate. If preserved in diamond inclusions and returned to the surface, heavy CaCO 3 could be used to trace the presence of oxidized carbon in the lowermost mantle. The potential of CaCO 3 to be a signature of an ultrad eep carbon cycle reaching the core - mantle - boundary region may help to reveal other mysteries of the deep mantle, such as heat budget related to radioactive elements stored in Ca - bearing silicates (Corgne et al., 2005) , and compositions of heterogeneities t (Howell et al., 2020; Nestola et al., 2018) . 3.5 Methods 3.5.1 Starting materials To investigate phase equilibria in the carbonate - control for effects of reaction kinetics, b oth CaC - to - MgC and MgC - to - CaC experiments were carried out in symmetric diamond anvil cells (DAC) with flat - top double - sided laser heating (Prakapenka et al., 2008) . For CaC - to - MgC, natural dolomite with homogeneous composition of (Mg 0.38 Ca 0.59 Fe 0.03 )CO 3 wa s used as a carbonate reactant, the composition and structure of which has been characterized by X - ray fluorescence spectroscopy and X - ray diffraction, respectively (Dorfman et al., 2018) . Fe - bearing enstatite synthesized at École Polytechnique Fédérale de Lausanne with a composition of (Mg 0.5 Fe 0.5 )SiO 3 was used as a silicate reactant (Dorfman et al., 2020) . For MgC - to - CaC, natural ferromagnesite (sample from Princeton University) was used as a carbonate reactant, with composition determined to be (Mg 0.87 Fe 0. 13 )CO 3 by wavelength dispersive X - ray spectroscopy in a Cameca SX100 Electron Probe Microanalyzer at University of Michigan. Pure calcium silicate (CaSiO 3 , Alfa Aesar) was used as a silicate reactant. The chief advantages to the abovementioned starting com positions are that recognition of a carbonate - silicate exchange 53 reaction only requires identification of the presence of newly synthesized silicates in quenched run products, i.e., Ca - perovskite (Ca - Pv) in CaC - to - MgC and bridgmanite (bdg) in MgC - to - CaC; an d Fe - bearing enstatite and ferromagnesite can serve as laser absorber during the forward CaC - to - MgC and reversal MgC - to - CaC experiments, respectively. 3.5.2 LHDAC experiments The dolomite, enstatite, and calcium silicate samples were separately ground und er acetone in an agate mortar for ~2 hours each to achieve homogenous, finely powdered samples with grain size typically less than ~2 µm. A single ferromagnesite crystal was double - side polished to ~10 - micron thickness. All starting materials were dried in an oven at 120 °C overnight before loading, and the powder samples were subsequently pressed in a DAC to form thin foils approximately ~8 - 10 µm thick. The enstatite foils and ferromagnesite crystals were sandwiched between iron - free dolomite and calcium s ilicate, respectively, serving as thermal insulators in symmetric DACs for CaC - to - MgC and MgC - to - CaC ( Figure 3 - 5 and Figure 3 - 6 ). No other pressure standard or medium was loaded to prevent reactions wit h other components and contamination of the chemical system. The sample sandwiches were loaded in sample chambers with diameters approximately halves of the anvil culet sizes drilled into Re gaskets pre - indented to a thickness of laser drilling system at HPCAT (Sector 16) of the Advanced Photon Source (APS), Argonne National Laboratory (ANL) (Hrubiak et al., 2015) ts under 100 GPa, Before laser heating, each sample was compressed to the target pressure at 300 K, and after heating each sample was quenched to ambient pressure at 300 K to limit and preserv e reactions at 54 target conditions. Pressures were determined from the Raman shift of the singlet peak of the diamond anvil at the culet surface (Akahama & Kawamura, 2006) , and post - heating pressures were typically within 3% of the pre - heating pressure. Ther mal pressure during heating may be estimated to be ~10% GPa higher than the pre - heating pressure at the modest temperatures (Fiquet et al., 2010; Nomura et al., 2014) . High - temperature conditions were achieved by using a double - sided ytterbium fiber laser heating system at beamline 13 - ID - D (GeoSoilEnviroCars) of APS, ANL (Prakapenka et al., 2008) - top spot with a diameter of 10 - det ermined by fitting the measured thermal radiation spectra using the Planck radiation function under the graybody approximation (Prakapenka et al., 2008) . The temperature reported in Table 3 - 1 is the temporal average of multiple temperature measurements over the heating duration. Temperature fluctuations over this time scale were less than the specified uncertainty, which is derived from a standard deviation of temperature measurements from bot h sides of the laser - heated sample (typically ±100 K below 2000 K and ±150 K above 2000 K) ( Figure 3 - 14 and Figure 3 - 15 ). Experiments were held at temperatures between 1600 and 2800 K for ~30 min in CaC - to - MgC experiments and up to 400 min in MgC - to - CaC experiments. 3.5.3 In - situ XRD Phases synthesized at high P / T and achievement of chemical steady - state were determined by in - situ angle - dispersive X - ray diffraction (XRD) measurements performed before, during and after heating at beamline 13 - ID - D (GeoSoilEnviroCars) of APS, ANL. The incident X - ray beam w 2 X - rays were recorded using a MAR 165 detector or Pilatus 1M CdTe pixel array detector. NIST 55 standard LaB 6 was used to calibrate the detector distance, tilt angle, and rotation angle of the image plane relative to the incident X - ray beam. Exposure times were typically 30 s. The XRD patterns were integrated to produce 2 plots using the software DIOPTAS (Presch er & Prakapenka, 2015) . 3.5.4 Ex - situ EDX After complete pressure release, each sample was recovered from the LHDAC, and then sectioned along the compression axis through the laser - heated spot and over the entire thickness of the DAC sample (~5 - ing a focused ion beam (FIB) coupled with a field emission scanning electron microscope (FE - SEM) at IPGP (Paris, France) or the Michigan Center for Materials Characterization at the University of Michigan (Ann Arbor, USA). A ~30 - nm - thick Au layer was coate d on each sample to reduce charging in the scanning electron microscope, and a 2 - - thick Pt layer was deposited across the center of each heated spot to protect the sample from damage by the Ga + ion beam. Thin sections of each heated spot were extracted a nd polished to electron transparency ( 100 nm thickness). Textural and chemical characterization of recovered samples was performed with scanning transmission electron microscopy (STEM) and energy - dispersive X - ray spectroscopy (EDX) in a JEOL 2200FS field emission TEM (Center for Advanced Microscopy, MSU), operated at 200 kV to image the sample in Bright - Field. EDX maps were scanned over 512 ×384 pixel areas with a pixel dwell time of 50 microseconds. Typical count rates were ~2,000 counts per second. Chemi cal mapping rather than point measurement approach prevents migration of elements due to damage by the electron beam. Uncertainties in compositions were determined from standard deviations of EDX measurements obtained from selected regions within multiple grains. 56 3.6 Supporting Information To assess whether observations of Ca and Mg isotopes in mantle silicates or diamond inclusions can be used to detect the presence of carbonates in the deep mantle, we estimate the potential effects of carbonate - silicate cation exchange on isotope signature s based on available constraints and mass balance. Subducting carbonates carry low - 44/40 Ca (reported relative to NIST SRM 915a standard, 44/40 Ca = [( 44 Ca/ 40 Ca) sample /( 44 Ca/ 40 Ca) standard - 1]×1,000) and low - 26 Mg (relative to the Dead Sea metal Mg standar d (DSM - 26 Mg = [( 26 Mg/ 24 Mg) sample /( 26 Mg/ 24 Mg) standard - 1]×1,000) signatures, while reported mantle ratios are heavier (Fantle & Tipper, 2014; Kang et al., 2017; Teng et al., 2010; Wombacher et al., 2011) ( Table 3 - 2 ). Based on both our observations and previous experimental studies (Biellmann et al., 1993; Seto et al., 2008) , CaCO 3 is unstable relative to MgCO 3 in the shallow lower mantle due to the reaction CaC - to - MgC, so the light Ca isotopes brought by CaCO 3 may be transferred to CaSiO 3 in the slab and surrounding ambient shallow lower mantle. Conversely, our experiments obtain the new result that in the deep lower mantle, MgCO 3 is unstable relative to CaCO 3 due to the reaction MgC - to - CaC, so the light Mg isotopes brought by MgCO 3 may be transferred to the surrounding ambient deep lower mantle in MgSiO 3 , and deep mantle CaCO 3 would form with the Ca isotope signature of the mantle silicate. These reactions, their stable isotope equilibrium fractionation factors, and the masses of carbonate and silicate that reach equilibrium may moderate isotope ratios in cold carbonated subduc ting slabs and their surroundings. The reaction CaC - to - 44/40 26 Mg of carbonate: ( f Ca_pyro + k f Ca_carb 44/40 Ca pyro = f Ca_pyro 44/40 Ca pyro i + k f Ca_carb 44/40 Ca carb i (1) ( f Mg_carb + k f Ca_carb 26 Mg carb = f Mg _carb 26 Mg carb i + k f Ca_carb 26 Mg pyro i (2) 57 and the reaction MgC - to - 26 44/40 Ca of carbonate: ( f Mg_pyro + k f Mg_carb 26 Mg pyro = f Mg_pyro 26 Mg pyro i + k f Mg_carb 26 Mg carb i (3) ( f Ca_carb + k f Mg_carb 44/40 Ca carb = f Ca_carb 44/40 Ca carb i + k f Mg_carb 44/40 Ca pyro i (4) where f Ca_pyro , f Ca_carb , f Mg_pyro , f Mg_carb represent the mole fraction of Ca and Mg contributed by pyrolitic mantle and carbonate, respectively. i represents the initial status before the reaction. k is reaction rate ranging from 0 to 1, representing the mole fraction of carbonate that undergoes c ation exchange reaction with silicate in pyrolitic mantle. In this model, we fixed the weight ratio of carbonate and surrounding pyrolitic mantle to 1/10 based on previous work applied to upper mantle conditions (Wang et al., 2014) . For a subducting slab i n the lower mantle, this ratio represents a generous upper bound on the amount of carbonate available to react with silicates. We varied the composition of subducted carbonate by changing the n in (Mg n Ca n - 1 )CO 3 from 0 to 1. Parameters used in the calculati on are listed in Table 1, and the calculated results are plotted in Figure 3 - 1 6 . We assume equilibrium isotope fractionation between carbonates and mant le silicates, occurring after the cation exchange reaction, i.e., carbonates are well mixed and equilibrium with 44/40 26 Mg of this carbonated pyrolite are governed by the following equations according to Wang et a l. (2014) , respectively: ( f Ca_pyro + k f Ca_carb 44/40 Ca pyro f = ( f Ca_pyro + k f Ca_carb 44/40 Ca pyro + 44/40 Ca carb i 44/40 Ca pyro - carb f Ca_carb - k f Ca_carb ) (5) ( f Mg_pyro + k f Mg_carb 26 Mg pyro f = ( f Mg_pyro - k f Ca_carb 26 Mg pyro i + 26 Mg carb 26 Mg pyro - carb f Mg_carb + k f Ca_carb ) (6) similarly, after the reaction MgC - to - 44/40 26 Mg of mantle are governed by the following equations, respectively: ( f Mg_pyro + k f Mg_carb 26 Mg pyro f = ( f Mg_pyro + k f Mg_carb 26 Mg pyro + 58 26 Mg carb i 26 Mg pyro - carb f Mg_carb - k f Mg_carb ) (7) ( f Ca_pyro + k f Ca_carb 44/40 Ca pyro f = ( f Ca_pyro - k f Mg_carb 44/40 Ca pyro i + 44/40 Ca carb 44/40 Ca pyro - carb f Ca_carb + k f Mg_carb ) (8) 44/40 Ca pyro - carb 26 Mg pyro - carb 44/40 Ca pyro - carb 26 Mg pyro - carb listed in Table 3 - 2 represent constraints measured at ~Earth surface conditions. Fractionation may be expected to depend on pressure and temperature as well as the high - pressure polymorphism in the carbonate and silicate systems. However, due to the lack of available measurements at deep mantle conditions, we assume fractionation values remain constant throughout the mantle. The calculated results are plotted in Figure 3 - 17 . To use isotope fractionation to identify carbonates at depth, isotope ratios in subducted carbonate cation exchange scenarios must be significantly different from the scenario where no subduc ted carbonate reaches the deep mantle. If no carbonate reaches the lower mantle in subducted slabs, lower - mantle - 44/40 26 Mg, and there would be no lower - mantle - derived carbonate. If some carbonate reaches the shall ow lower mantle in subducted slabs, lower - mantle - 44/40 Ca due to reaction of persistent metastable CaCO 3 with MgSiO 3 to produce CaSiO 3 (reaction CaC - MgC). The mass balance calculation indicates that a gener ous upper bound on the masses involved could locally enrich mantle CaSiO 3 44/40 Ca ( Figure 3 - 1 6 26 Mg of the silicates in the mantle, the CaC - 26 Mg in the carbonate relatively heavy ( Figure 3 - 1 6 a) and would no longer appear to have a sub duction source. If some carbonate continues to the deeper lower mantle where the reaction MgC - CaC becomes favorable, the much 26 Mg of silicates would not be 59 significantly impacted by the breakdown of MgCO 3 ( Figure 3 - 1 6 44/40 Ca in CaCO 3 produced by this reaction would reflect the heavy mantle source ( Figure 3 - 1 6 b) and could be distinguished by CaCO 3 with a surface origin. The exchange reactions potentially overwrite the isotope signals in subducted carbonates with heavy isotopes, and could not significantly affect mantle silicate isotope ratios in the deep lower mantle. Mg and Ca isotope composition of carbonated pyrolite after the equi librium isotopic fractionation between carbonate and surrounding pyrolitic mantle depends on the mole ratio of Mg and Ca of the subducted carbonates, but less strongly depends relies on the reaction completion ( Figure 3 - 17 ). In summary, carbonate - silicate cation exchange reactions only produce potentially observable heterogeneity in silicate cation isotopes relative to the null case in the CaC - MgC regime, 44/40 Ca. CaCO 3 formed by a cation exchange reaction between MgCO 3 and CaSiO 3 in the lower mantle can be expected to have a different isotope signature relative to subducted CaCO 3 formed 3 formed in the deep lower mantle would contain Ca isotopes that sample d carbonate source. This could provide a test for shallow vs. ultradeep origin of carbonate inclusions. This is the motivation for future systematic study of the isotope signatures of diamond inclusions. 60 Figure 3 - 1 : Electron microscopic characterizations of recovered samples. Images of selected recovered sample cross - sections obtained using backscattered scanning electron microscopy (a, d, g), scanning transmitted electron microscopy ( b, e, h) and energy - dispersive X - ray mapping (c, f, 61 i) of the cross - section show the silicate layer sandwiched by two carbonate layers, with the reaction region along the contacting interface. (a - c) Ex - situ analysis of sample quenched from 33 GPa and 1650 K heated for 15 min (run #1) demonstrates reaction CaC - to - MgC: CaSiO 3 is not present in starting materials but is indicated in EDX map by colocation of Ca and Si, shown in magenta; (d - f) Ex - situ analysis of sample quenched from 88 GPa and 1800 K heated for 150 min (run #9) demonstrates reaction MgC - to - CaC: MgSiO 3 is not present in starting materials but is indicated in EDX map by colocation of Mg and Si, shown in blue - green. CaCO 3 also appears as red (Ca, but no Si) ribbon within CaSiO 3 starting material. ( g - i) Ex - situ analysis of sample quenched from 133 GPa and 2000 K heated for 400 min (run #10) demonstrates reaction MgC - to - CaC: MgSiO 3 appears as Ca - depleted, Si - rich region (blue or blue - green) adjacent to CaSiO 3 starting material (magenta). 62 Figure 3 - 2 : Phase diagram for relative stability of the MgCO 3 + CaSiO 3 assemblage versus CaCO 3 + MgSiO 3 . The boundary sketched as a black dashed line with gray shadow as uncertainty inferred is based on experimental observations of carbonate - silicate exchange reactions CaC - to - MgC and MgC - to - CaC. Squares represent observations from this work starting with (Ca,Mg)CO 3 and (Mg,Fe)SiO 3 , looking for newly - synthesized CaSiO 3 to indicate the CaC - to - MgC reaction takes place. Circle symbols represent observations from this work of experiments starting with (Mg,Fe)CO 3 + CaSiO 3 , looking for identification of newly - synthesized MgSiO 3 to indicate the MgC - to - CaC reaction takes place. Open symbols indicate nonreaction and filled for confirmed reaction, and blue and red colors correspond to the inferred stable phase assemblage based on reaction products. Triangles indicate the P - T conditions for CaC - to - MgC taking place reported by Seto et al. (2008) , and blue shaded region indicates approximate conditions of four experiments conducted by Biellmann et al. (1993) using indirect methods for pressure and temperature calibration, which all produced the run products MgCO 3 + CaSiO 3 . The error b ars indicate uncertainties of pressure and temperature measurements (see Methods for details). The boundaries 63 proposed by previous theoretical predictions are illustrated by yellow shaded region (Santos et al., 2019; Yao et al., 2018b; Zhang et al., 2018). 64 Figure 3 - 3 : Pressure - temperature diagram of reactions between carbonate, silicates, and silica in the subducted oceanic crust to the lower mantle. The grey dotted line indicates the reversal boundary of the carbonate - silicate exchange reaction proposed by this study, whereas previous theoretical predictions are illustrated by yellow shaded region (Santos et al., 2019; Yao et al., 2018b; Zhang et al., 2018) . The cyan and orange lines indicate the decarbona tion reactions of CaCO 3 + SiO 2 (Li et al., 2018) and MgCO 3 + SiO 2 (Drewitt et al., 2019) , respectively. The black dashed line shows the melting curve of MgCO 3 - CaCO 3 system constrained by Thomson et al. (Thomson et al., 2014) . Four typical mantle geotherms are modified from Maeda et al. (Maeda et al., 2017) . The red shaded region indicates the transition boundary of CaCO 3 from sp 2 - to sp 3 structure predicted by density functional theory computations (Santos et al., 2020; Zhang et al., 2018) . 65 Figure 3 - 4 : Schematic illustration of the fate of carbonates in the oceanic crust (dark blue) subd ucted to the lower mantle . Through subduction, the carbonates may undergo melting (red arrow), redox freezing with metallic iron (purple arrow), decarbonation reaction with free silica (blue arrow), a nd exchange reaction with lower mantle silicates (green arrow). Based on the observation of reversal of the carbonate - silicate cation exchange reaction at conditions relevant to cold subducted slabs at mid - lower - mantle depths, CaCO 3 is the potential stable phase that hosts oxidized carbon in the lowermost mantle. 66 Figure 3 - 5 : Schematic diagram of the laser - heated diamond - anvil cell (LHDAC) and sample loading design. The insulation layer (light gray region) and the laser absorber (black region) for different experimental runs are summarized in Table 3 - 1 . 67 Figure 3 - 6 : Microscope images of loaded sample for run #9. We loaded the Fe - bearing sample on top of the thermal insulation layer on the piston side of DAC (75/300 beveled anvil), then we loaded another insulation layer on the cylinder side of DAC together with Re gasket before we close and compress the DAC to the target pressure. (a) Samples are loaded at ambient co nditions on the piston side before closing the cell. (b) Samples are compressed to target pressure before heating, and the dashed circle indicates the dark Fe - bearing sample. (c) The heating spot on the loaded sample during laser heating. 68 Figure 3 - 7 : X - ray diffraction patterns obtained from the starting material of CaC - to - MgC before heating (a) and products quenched from various P - T conditions: (b) run #1, (c) run #4, (d) run #5, and (e) run #7, and phase identifications are indicated by small ticks at the bottom. The wavelength of the incident X - ray beam was 0.3344 Å. ( a ) ( b ) ( c ) ( d ) ( e ) 69 Figure 3 - 8 : Representative unrolled X - ray diffraction images (lower panel) corresponding to X - ray diffraction patterns (upper panel) obtained from the starting materials of CaC - to - MgC before heating and the products quenched from various P - T conditions: (a - b) run #4 , (c - d) run #5. Large spots in 2D diffraction patterns in (a) and (b) are from untransformed dolomite starting material. The wavelength of the incident X - ray beam was 0.3344 Å. ( a ) ( b ) ( c ) ( d ) 70 Figure 3 - 9 : Representative full - profile fitting for XRD of (a) run #1 and (b) run #5. Le Bail refinements (red curves) of observed XRD data (black dots) were carried out after background subtraction, demonstrating all the identified ph ases (vertical ticks below patterns) can account for the peaks and intensities of XRD patterns. Black curves are fitting residues. The wavelength of the incident X - ray beam was 0.3344 Å. (a) ( b ) 71 Figure 3 - 10 : Ex - situ analysis of sample quenched from 33 GPa and 1650 K heated for 15 min (run #1) demonstrates CaC - to - MgC. (a) SEM - BSE image obtained during FIB milling. Sample was prepared as a (Mg,Fe)SiO 3 layer s andwiched by two (Ca,Mg)CO 3 layers; (b) dark - field STEM image reveals CaSiO 3 and MgCO 3 , as well as SiO 2 and FeO, formed by reaction between (Mg,Fe)SiO 3 and (Ca,Mg)CO 3 layers; (c) EDX spectrum and corresponding (d) chemical maps for calcium, silicon, magnes ium, carbon, and iron. ( a ) ( b ) ( c ) ( d ) 72 Figure 3 - 11 : Ex - situ analysis of sample quenched from 88 GPa and 1800 K heated for 150 min (run #9) demonstrates MgC - to - CaC. (a) SEM - BSE image obtained during FIB milling. Sample was prepared as an (Mg,Fe)CO 3 layer sandwiched by two CaSiO 3 layers; (b) dark - field STEM image reveals (Mg,Fe)SiO 3 and CaCO 3 formed by reaction of (Mg,Fe)CO 3 and CaSiO 3 layers; (c) STEM - EDX spectrum and corresponding (d) chemical maps for magnesium, silicon, calcium, and carbon. ( a ) ( b ) ( c ) ( d ) 73 Figure 3 - 12 : Ex - situ analysis of sample quenched from 133 GPa and 2000 K heated for 400 min (run #10) demonstrates MgC - to - CaC. (a) SEM - BSE image obtained during FIB milling. Sample was prepared as a (Mg,Fe)CO 3 layer sandwiched by two CaSiO 3 layers; (b) dark - field STEM image reveals (Mg,Fe)SiO 3 and CaCO 3 formed by reaction of (Mg,Fe)CO 3 and CaSiO 3 layers; (c) EDX spectrum and corresponding (d) chemical maps for magnesium, silicon, calcium, and carbon. ( a ) ( b ) ( c ) ( d ) 74 Figure 3 - 13 : Ex - situ analysis of sample quenched from 35 GPa and 1900 K heated for 20 min (run #8) demonstrates MgC - to - CaC. (a) SEM - BSE image obtained during FIB milling. Sample was prepared as a (Mg,Fe)CO 3 layer sandwiched by two CaSiO 3 layers; (b) STEM - EDX chemical maps for calcium, silicon, magnesium, carbon, iron and oxyge n. ( a ) ( b ) 75 Figure 3 - 14 : Typical temperature measurements of downstream (red squares) and upstream (blue circles) over heating duration of (a) run #5 for CaC - to - MgC and (b) run #9 for MgC - to - CaC, respectivel y. 76 Figure 3 - 15 : Representative temperature measurements and fitting profiles of upstream and downstream for run #9. Temperatures of the heated samples were determined by fitting the measured thermal radi ation spectra using the Planck radiation function under the graybody approximation. 77 Figure 3 - 1 6 : Calculated isotopic composition versus reaction rate after the reaction (a) CaC - to - MgC and (b) MgC - to - CaC. n represents the mole fraction of Mg in (Mg n Ca n - 1 )CO 3 . Black dashed 44/40 26 Mg values in carbonates, respectively. (a) ( b ) 78 Figure 3 - 17 : Calculated isotopic composition of carbonated pyrolite after isotopic fractionation between carbonates and silicates for the reaction (a) CaC - to - MgC and (b) MgC - to - CaC. The horizontal axis represents the mole ratio of Mg/C a in the carbonated pyrolite. k represents reaction rate. ( a ) ( b ) 79 Table 3 - 1 : Starting materials, experimental conditions, and run products for all experiments. Starting materials for experiments were loaded in sandwich configuration, with laser absorber layer between two thermal insulation layers. Pressures determined from Raman shift of the singlet peak of the diamond anvil at the culet surface (Akahama & Kawamura, 2006) reported is the temporal average of recorded temperatures over the heating duration rounded to the nearest 50 K. Temperatu re fluctuations over this time scale were less than the specified uncertainty, which is derived from a standard deviation of tem perature measurements from both sides of the laser - heated sample (typically ±100 K below 2000 K and ±150 K above 2000 K). Run # Insulation Laser absorber P (GPa) T (K) Heating duration (min) Phases observed after heating 1 (Mg,Ca)CO 3 (Mg,Fe)SiO 3 33(2) a 1650(100) 15 CaSiO 3 + SiO 2 + FeO + MgSiO 3 + MgCO 3 2 (Mg,Ca)CO 3 (Mg,Fe)SiO 3 45(2) 1600(100) 20 CaSiO 3 + MgSiO 3 + MgCO 3 3 (Mg,Ca)CO 3 (Mg,Fe)SiO 3 66(3) 1900(100) 11 CaSiO 3 + MgSiO 3 + MgCO 3 4 (Mg,Ca)CO 3 (Mg,Fe)SiO 3 83(4) 2500(150) 20 CaSiO 3 + MgSiO 3 + MgCO 3 5 (Mg,Ca)CO 3 (Mg,Fe)SiO 3 91(5) 2100(150) 24 MgSiO 3 + CaCO 3 6 (Mg,Ca)CO 3 (Mg,Fe)SiO 3 106(5) 2000(150) 10 MgSiO 3 + CaCO 3 7 (Mg,Ca)CO 3 (Mg,Fe)SiO 3 137(7) 2800(150) 15 MgSiO 3 + CaCO 3 8 CaSiO 3 (Mg,Fe)CO 3 35(2) 1900(100) 20 CaSiO 3 + MgCO 3 9 CaSiO 3 (Mg,Fe)CO 3 88(4) 1800(100) 150 MgSiO 3 + CaCO 3 + CaSiO 3 + MgCO 3 10 CaSiO 3 (Mg,Fe)CO 3 133(7) 2000(150) 400 MgSiO 3 + CaCO 3 + CaSiO 3 + MgCO 3 a Numbers in parenthesis are uncertainties on the last digits. 80 Table 3 - 2 : Parameters for isotopic mass balance calculations (see Supplementary Note 1 for details). Parameter Value Reference 44/40 Ca pyro i Kang et al. (2017) 44/40 Ca carb i - Fantle and Tipper (2014) 26 Mg pyro i - Teng et al. (2010) 26 Mg carb i - Wombacher et al. (2011) CaO abundance in pyrolite 3.17 % Workman and Hart (2005) MgO abundance in pyrolite 38.73 % Workman and Hart (2005) 44/40 Ca pyro - carb - Amsellem et al. (2020) 26 Mg pyro - carb Macris et al. (2013) 81 Chapter 4 - Fe 7 N 3 - Fe 4 N: implications for iron alloys in terrestrial planet cores This chapter has been published as Lv et al. (2020b) . 4.1 Abstract Iron nitrides are possible constituents of the cores of Earth and other terrestrial planets. Pressure - induced magnetic changes in iron nitrides and effe cts on compressibility remain poorly understood. Here we report synchrotron X - ray emission spectroscopy (XES) and X - ray diffraction - Fe 7 N 3 - Fe 4 N up to 60 GPa at 300 K. The XES spectra reveal completion of high - to low - spin - Fe 7 N 3 - Fe 4 N at 43 and 34 GPa, respectively. The - Fe 7 N 3 by 22% at ~40 - Fe 4 N. Fitting pressure - v olume data to the Birch - Murnaghan equation of state yields V 0 = 83.29±0.03 (Å 3 ), K 0 = 232±9 GPa, K 0 ' - Fe 7 N 3 above the spin transition completion pressure, and V 0 = 54.82±0.02 (Å 3 ), K 0 = 152±2 GPa, K 0 - Fe 4 N over t he studied pressure range. By re - examining evidence for spin transition and effects on compressibility of other candidate components of terrestrial planet cores, Fe 3 S, Fe 3 P, Fe 7 C 3 , and Fe 3 C based on previous XES and XRD measurements, we located the complet ion of high - to low - spin transition at ~67, 38, 50, and 30 GPa at 300 K, respectively. The completion of spin transitions of Fe 3 S, Fe 3 P and Fe 3 C induces elastic stiffening, whereas that of Fe 7 C 3 induces elastic softening. Changes in compressibility at comp letion of spin transitions in iron - and planetary cores. 82 4.2 Introduction The Fe - both geophysical observations ( Birch, 1952 ) and compositions of planetary building blocks ( Mcdonough & Sun, 1995 ), with potential implications for volatile storage and cycling within our sulfur, carbon, and hydrogen ( Poirier, 1994 ); in addition to a possible mixture of these, nitrogen has been more recently proposed as a candidate light element in the core (e.g., Kusakabe et al., 2019 ; Minobe et al., 2015 ) based on structural stability and - Fe 7 N 3 ) extrapolated to core conditions. Additional support for the presence of iron nitrides in planetary interiors is provided by observations of iron nitrides in iron meteorites ( Rubin & Ma, 2017 ) and in inclusion - mantle boundary region ( Kaminsky & Wirth, 2017 ) ( Zedgenizov & Litasov, 2017 ) . The behavior of nitrogen - bearing iron alloys and co mpounds at conditions relevant to both accretion and the modern core is thus important to evaluate the potential (e.g., Kusakabe et al., 2019 ; Litasov et al., 2017b ; Liu et al., 2019 ; Minobe et al., 2015 ) . The few constraints on the identities and abundances of core light particularly ~4 - 7% density deficit of the core relative to properties of Fe - Ni noted since ( Birch, 1952 ) . Av ailable constraints on thermoelasticity of solid iron nitrides from previous studies (e.g., Adler & Williams, 2005 ; Breton et al., 2019 ; Kusakabe et al., 2019 ; Litasov et al., 2017b ) can be ends on stability and electronic/magnetic properties of these materials under high pressure conditions which remain poorly understood. 83 A wide range of stable iron nitride compounds with varying stoichiometries are stabilized by different conditions ( De Wae le et al., 2019 ; Wriedt et al., 1987 ). Stable iron nitrides at 1 bar - Fe 3 N x (0.75 < x < 1.4) with iron atoms arranged in a hexagonal - close - - Fe 4 N adopting a cubic - close - packed structure ( Wide nmeyer et al., 2014 ; Wriedt et al., 1987 ). Previous studies have identified additional structures in the Fe - N system stabilized by high pressure (e.g., De Waele et al., 2019 ; Wetzel et al., 2019 ; Widenmeyer et al., 2014 - Fe 7 N 3 structure (same stoich iometry as Fe 3 N x =1.3 , space group 6 3 22) remains stable up to 51 GPa and 300 K ( Adler & Williams, 2005 ), and was observed - Fe 7 N 3 above 41 GPa and ~1000 K ( Minobe et al., 2015 - Fe 4 N (space group Pm m ) is predicted to decompose to - Fe 7 N 3 - Fe at ~56 GPa and 300 K based on thermodynamic analysis ( Breton et al., 2019 - Fe 4 N was observed to - Fe 4 N above 1373 K and 8.5 GPa ( Guo et al., 2013 - Fe 7 N 3 above 41 GPa at ~1000 K ( Minobe et al., 2015 - Fe 7 N 3 was observed to remain stable up to 3100 Kusakabe et al., 2019 ). In addition, a new crystal structure of Fe 7 N 3 with space group C 2/ m was predicted to be st able under ( Sagatov et al., 2019 ) . However, due to the complex stoichiometries and structural variations in iron nitrides at high pressure and temperature conditions, understanding of high - pressure phase stability in this system rem ains incomplete. The effects of incorporating nitrogen in iron alloys and compounds include not only modifying stable crystalline structure, but also the arrangement and bonding style of electrons in d orbitals around iron atoms that control magneto - elast ic properties (e.g., Sifkovits et al., 1999 ; Widenmeyer et al., 2014 ). Electronic structure of iron nitrides have been investigated by first principles calculations and experimental measurements, which indicate that the chemical bonding 84 - Fe 7 N 3 ( e.g., Z hang et al., 2012 ) - Fe 4 N ( e.g., dos Santos & Samudio Pérez, 2016 ) are complex mixtures of metallic, covalent, and ionic characters. Additionally, iron nitrides undergo pressure - induced magnetic transitions, which may affect thermodynamics and elastici ties of Fe - N alloys and compounds at high pressures ( e.g., dos Santos & Samudio Pérez, 2016 ; Ishimatsu et al., 2003 ; Popov et al., 2015 ) . At 1 bar, the d - orbital electrons in Fe in all known Fe - N compounds adopt a high - spin ferromagnetic arrangement and are remarkable for high saturation of magnetism - Fe 3 N x ranges from B per Fe atom as N concentration increases from x = 1 to 1.48 ( Leineweber et al., 2001 ) , - Fe 4 B per Fe atom ( Dirba et al., 2015 ). Only a few high - pressure studies on magnetism of the Fe - N system exist, and the magnetic transition pressures of iron nitrides and their effects on elasticities are largely unknown. Experiments on pressure - induced - Fe 3 N x - Fe 4 N undergoes a ferromagnetic to paramagnetic transition at 24 GPa an d 300 K as resolved by X - ray magnetic circular dichroism (XMCD) measurements ( Ishimatsu et al., 2003 ) , while first - principles calculations predicted the - Fe 4 N occurs at 250 GPa ( Popov et al., 2015 ). Systematic experi mental constraints on pressure - - Fe 3 N x - Fe 4 N from ferromagnetic to paramagnetic or nonmagnetic state and the coupling between these electronic arrangements and elasticities and phase stability are necessary for an improved understanding of the physical properties of iron nitrides. The identification of magneto - elastic coupling behavior in other iron alloy systems such as Fe - C, Fe - S, and Fe - P ( recently reviewed by Caracas, 2016 ) provides additional motivation to tes t whether the Fe - N system behaves similarly. In the electronically - and structurally - similar Fe - C system, ferromagnetic (FM) Fe - C compounds undergo transitions first to a paramagnetic (PM) 85 state, and then to a low - spin non - magnetic (NM) state, and these tr ansitions have been proposed to significantly affect compressibility of Fe - C materials (e.g., Chen et al., 2012 ; Chen et al., 2018a ; Lin et al., 2004b ; Mookherjee et al., 2011 ; Prescher et al., 2012 ) . The pressure - induced magnetic transition of Fe - S (e.g., Chen et al., 2007 ; Lin et al., 2004a ) and Fe - P compounds (e.g., Gu et al., 2014 , 2016 ; Lai et al., 2020 ) have also been reported as well to affect compressibility and sound velocities. Due to the lack of characterization of electronic states at high press ures in previous studies of compression and phase transitions of iron nitrides (e.g., Adler & Williams, 2005 ; Breton et al., 2019 ; Litasov et al., 2017b ) candidate light elements remains poorly co nstrained. Magnetic transitions at high pressures have been experimentally detected using methods that directly characterize electronic states, as well as methods that indirectly assess magnetism through its effects on elasticity and compression behavior. The total spin moment of Fe, ranging from high to low spin, can be characterized by X - ray emission spectroscopy (XES). The appearance of the satellite emission peak K located at the lower energy relative to the main emission peak K is a result of th e 3 p - 3 d core - hole exchange interaction in the final state of the emission process. That is, the intensity of the satellite peak depends on the spin polarization of the 3 d shell and is sensitive to the net magnetic spin state. The collapse of the magnetization of Fe is characterized by the disappearance of the low - energy satellite due to the loss of 3 d magnetic moment (e.g., Badro et al., 2003 ; Badro et al., 2004 ). Therefore, the local spin moment change of iron atoms revealed by XES can distinguish between high - sp in (FM or PM) states vs. low - spin (NM) states. XES spectroscopy performed at high pressures using a synchrotron X - ray source has been used to study magnetic spin transitions in Fe - C, Fe - S, and Fe - P compounds (e.g., Chen et al., 2018a ; Chen et al., 2014 ; Gu et al., 2016 ; Lin et al., 2004b ; Shen et al., 2003 ) . Characterizing 86 magneto - elastic coupling requires complementary information provided by spectroscopic methods such as X - ray emission and structural/elastic methods such as X - ray diffraction to confirm ma gnetic transitions and discontinuous compression behavior operate in tandem ( e.g., Chen et al., 2014 ) . However, no such study has been conducted in the Fe - N system. Here we present a systematic study of magnetic transitions and compressibility of iron - nitr - Fe 7 N 3 - Fe 4 N, using synchrotron XES and XRD measurements up to 60 GPa at 300 K. Compression behavior of both compounds is monitored by dense pressure - volume ( P - V ) data coverage, combined with total spin moment indicated by XES, to determine an y effects of magnetic transitions on the incompressibility of iron nitrides. Observed behavior is compared to the effect of magneto - elastic coupling in other Fe alloys studied using the same protocol. 4.3 Experimental methods High purity nonstoichiometric - Fe 7 N 3 and - Fe 4 N powders (99.9%, Kojundo Chemical Lab. Co. Ltd., average grain size ~1 m) were used as starting materials. XRD for both samples at ambient conditions confirms unit cell volumes in good agreement with previous studies of - Fe 7 N 3 (Adler & Williams, 2005; Kusakabe et al., 2019; Litasov et al., 2017b; Minobe et al., 2015) and - Fe 4 N (Adler & Williams, 2005; Guo et al., 2013) . For the nonstoichiometric - Fe 7 N 3 , the ambient volume measured for our sample V 0 = 86.32(±0.01) Å 3 is consistent with a linear relationship between unit - - Fe 3 N x , V = 10.637x + 72.858 (Litasov et al., 2017b) when x is 1.27. XES of - Fe 7 N 3 and - Fe 4 N was measured up to 60 GPa at intervals of ~5 GPa. Compression in the diamond anvil cell (DAC) wa s performed using two pairs of diamond anvils with 200 - - Fe 7 N 3 3 ) or - Fe 4 N (~ 15 × 87 3 ) sample was loaded in a 100 - - indented Be gasket. The sample chamber was drilled in the center of the Be gasket with pre - indented vanced Photon Source (APS), Argonne National Laboratory (ANL) (Hrubiak et al., 2015) . Silicone oil (Alfa Aesar) served as the pressure - transmitting medium and a 5 - chamber as the pressure standard. Pressures were dete rmined by ruby fluorescence (Mao et al., 1986) before and after each XES collection, and differed by up to 10% due to relaxation of the sample or cell assembly. The XES measurements were performed at 300 K at beamline 16 - ID - D of the APS, ANL. The incident X - ray beam was focused to 5×7 2 full width at half maximum at the sample position. The fluorescence signal was observed through the Be gasket. The incident X - ray energy was 11.3 keV with a bandwidth of ~1 eV was used for the experiments. Fe K emission w as selected by silicon analyzer and reflected to a silicon detector with an energy step of about 0.3 eV. Each spectrum was recorded for about 40 min and 3 spectra were taken to accumulate at least 30,000 counts at the Fe K main peak at each pressure. All spectra were normalized to area and aligned to the position of the Fe K main peak ( Figure 4 - 2 ). The high - spin reference is the sample spectrum at 1 bar, and low - spin references are the spectrum of FeS 2 at 1 bar collected using the same setup and the sample spectrum at 60 GPa. Intensity difference between the sample and references was integrated over the energy range of the satellite K - 7053.0 eV) using the integrated relative difference method (Mao et al., 2014) . Uncertainty in total spin moment was determined based on diffe rence in calculations using FeS 2 vs. pressurized sample as low - spin references. XRD measurements were carried out at 300 K up to 60 GPa with 1 - 2 GPa steps. The sample flakes of - Fe 7 N 3 3 ) and - Fe 4 N 3 ) were loaded side - by - 88 side in the sample chamber of a DAC with a pair of 300 - µm - culet diamonds. The sample chamber was drilled in the center of the Re gasket with a pre - drilling system at HPCAT (Hrubiak et al., 2015) . Au powder (>99.95%, Goodfellow) was spread on top of the samples to serve as the pressure calibrant (Fei et al., 2007) . Because the Au (111) peak overlapped with of - Fe 7 N 3 (110) peak, we use the pressure calculated from Au at the position of the - Fe 4 N sample to represent the pressure at all sample positions. A flake of pure Fe 3 was loaded alongside the samples as a secondary reference to monitor the hydrostaticity of stress conditions in the sample chamber (Liu et al., 2016) . Ne was loaded into the sample chamber as the pressure - transmitting medium using the COMPRES/GSECARS gas - loading system (Rivers et al., 2008) . The uncertainties in pressures were propagated from the standard deviation of t he unit - cell volumes of Au and Ne (if applicable). Angle - dispersive X - ray diffraction measurements were performed at beamline 13 - BM - C of the APS, ANL. The incident X - ray beam had a monochromatic wavelength of 0.434 Å and was 2 . Two - di mensional X - ray diffraction images were recorded on a MAR165 CCD detector and the sample - to - detector distance and the tilt angle of the detector relative to the incident X - ray beam were calibrated using 1 - bar diffraction of the NIST 660a LaB 6 standard. X - r ay diffraction images of - Fe 7 N 3 , - Fe 4 N, and Fe w ere exposed for 60 s. At each pressure, the XRD patterns were integrated using Dioptas software (Prescher & Prakapenka, 2015) . For selected pressures (lowest, highest, and one intermediate pressure), crystal structures were confirmed from XRD data using the full spectrum Le Bail fitting technique ( Le Bail, 2012 ) implemented in the EXPGUI/GSAS software package (Toby, 2001) . 89 4.4 Results 4.4.1 No structural transition of Fe 7 N 3 or Fe 4 N XRD patterns for both iron nitrides within the investigated pressure range at 300 K show sharp and intense peaks from the sample, Au, Ne, and Re, and no new diffraction lines nor splitting of lines w ere observed. The lattice parameters of - Fe 7 N 3 were obtained by fitting diffraction lines - Fe 4 N was fit from diffraction lines (111) and (200) using PDIndexer (Seto et al., 2010) . The uncertainty in the lattice parame ters corresponds to one standard deviation obtained in fit using multiple XRD peaks. The pressure at each step was calculated from the lattice parameters of Au by fitting the diffraction lines (111) and (200), and from Ne by fitting (111) and (200) peaks a t ~19 - 60 GPa as well ( Table 4 - 2 , Table 4 - 3 , Table 4 - 4 ). The uncertainties of pressures were propagated from uncertainties of unit cell volumes of Au and Ne, and uncertainties of their equation of state parameters (Fei et al., 2007) . Diffraction data - Fe 7 N 3 were refined using a 6 3 22 space group (averaged wRp = 2.2 %, representatives shown in Figure 4 - 1 a and b) up to 60 GPa. L e Bail refinements of the structure of - Fe 4 N were performed with the Pm m space group (averaged wRp = 1.8 %, representatives shown in Figure 4 - 1 c and d ) up to 60 GPa. Note that previous work indicates that - Fe 7 N 3 is metastable above ~40 GPa (Minobe et al., 2015) , and - Fe 4 N is metastable above ~56 GPa (Breton et al., 2019) . Both samples continue to adopt the initial structures without dissociation or phase transi tion up to 60 GPa at 300 K, but above 40 GPa we assume that - Fe 7 N 3 is structurally metastable . - Fe 7 N 3 - Fe 4 N The net magnetic spin state of 3 d - Fe 7 N 3 and - Fe 4 N can be probed by XES spectra of the K fluorescence lines. At ambient conditions, the XES spectra for both iron 90 nitrides are composed of a dominant K peak and a lower - energy satellite K of the 3 p core - hole - 3 d exchange interaction i n the final state of the emission process, consistent with iron entirely in the high - spin state ( Figure 4 - 2 a and b). The intensity of the satellite peak in the magnetic/high spin state is lower than that of iron oxides such as FeO and Fe 2 O 3 (Badro et al., 2003; Badro et al., 2002) , but similar to th at of pure iron and iron alloys (such as Fe - C, Fe - P, Fe - S alloys). As pressure increases, the integrated K decrease demonstrates that the onsets of spin transitions in both compounds are nearly immediate up - Fe 7 N 3 and 5 GPa in - Fe 4 N . The integrated K - Fe 7 N 3 and - Fe 4 N disappears at 43 and 34 GPa, respectively, with no further change up to 60 GPa ( Figure 4 - 2 c and d ) . The decrease of total spin moment of Fe as a function of pressure - Fe 7 N 3 and - Fe 4 N undergo a gradual spin - pairing transition from high to low - - Fe 7 N 3 and - Fe 4 N fully in low - spin state at pressures higher than 43 and 34 GPa, respectively ( Figure 4 - 2 c and d ) . Spin transition pressures are expected to be upper bounds due to possible effects of pressure hysteresis and non - hydrostatic stress on the spin crossover upon compression (Lin et al., 2013) - Fe 7 N 3 and - Fe 4 N correspond to magnetic to nonmagnetic (high to low spin) transitions, but the ferromagnetic to paramagnetic transition, depending on the relative orientations of the individual spins, cannot be detected by XES. However, both ferromagnetic - paramagnetic and magnetic - n onmagnetic transitions may be detected via XRD if they take place and affect compressibility. - Fe 7 N 3 - Fe 4 N Pressure - volume ( P - V ) data obtained from XRD of - Fe 7 N 3 and - Fe 4 N at 300 K demonstrate smooth compression without discontinuity in volume ( Figure 4 - 3 a and Figure 4 - 4 a). Second - order and order - disorder transitions such as magnetic transitions may be continuous in 91 volume but discontinuous in the higher - order derivatives of P ( V ) (Vocadlo et al., 2002) . Subtle effects on the unit cell volume with abrupt changes in incompressibility may be emphasized by the relationship between the Eulerian finite strain ( f E = [( V 0 / V ) 2/3 - 1]/2) versus the normalized stress ( F E = P/ [3 f E (1+2 f E ) 5/2 ]) (Angel, 2000) as in previous studies (Chen et al., 2012; Liu et al., 2016) . However, it is important to note that the calculation of both F E and f E requires priori knowledge of the 1 - bar volume ( V 0 ), and using an incorrect value of V 0 produces an anomalous curvature in the f - F plot (Angel, 2000) . Thus, to avoid the bias caused by V 0 of the unquenchable nonmagnetic phase, we plot the effective strain ( g = [( V 0 / V ) 2/3 - 1]/2), same as f E , versus the normalized stress ( G = P /[3(1 + 2 g ) 3/2 ]) following the formalism (Jeanloz, 1981) for - Fe 7 N 3 and - Fe 4 N ( Figure 4 - 3 b and Figure 4 - 4 b ), respectively. As is shown in Figure 4 - 3 b , the g - G plot of - Fe 7 N 3 reveals that the pressure - dependent stress exhibits a linear response to applied strain up to 40 GPa within the established errors. Above 40 GPa, the slope of linearized g - G increases, implying a discontinuity of compression behavior and an increase in the incompressibility given that dG / dg is positively correlated with ( K 0 + P ). This pressure is within the uncertainty of the completion of the magnetic t o nonmagnetic transition (i.e., completion of spin transition) pressure of ~40 GPa determined independently by XES, indicating the elastic stiffening coincides with the magnetic collapse of Fe in - Fe 7 N 3 . In addition, this change of compressibility is similar to the pressure of - - Fe 7 N 3 transition (Minobe et al., 2015) observed with laser - heating to promot e equilibrium phase transitions. Due to the low pressure of the onset of the spin transition observed by XES, with upper bound ~10 GPa, and gradual, broad pressure range of the transition, it is difficult to resolve a transition from high to mixed spin sta te in the compression behavior. The compression behavior up to 40 GPa may thus represent the mixed - spin state. The crossing point of the g axis (i.e., G = 0) and the fitted curve constrain the 92 zero - pressure volume of the nonmagnetic (or low spin state) phase to 83.29 ± 0.03 Å 3 , with the error propagated from the error of linear fitting and volume at ambient conditions. No stiffening is observed at pressur es lower than the spin transition pressure, so no clear evidence is available for any ferromagnetic - paramagnetic transition in - Fe 7 N 3 . In contrast, the calculated G of - Fe 4 N can be linearized as a function of g within the investigated pressure range, a nd no discontinuity is observed ( Figure 4 - 4 b). That is, both onset and - Fe 4 N, and no anomalous compressibility behavior needs to be explained by any ot her magnetic transition such as a ferromagnetic - paramagnetic transition. Discontinuities in higher derivatives of compression behavior can also be generated by nonhydrostatic stress in the sample chamber. To rule out this effect on iron nitrides, we consi der the pressure gradient observed in Ne medium, microstrain in Au calibrant as determined by peak width, and the behavior of the Fe foil relative to previous measurements under quasi - hydrostatic conditions. The pressure difference determined from the Ne m edium at positions of the two iron nitride samples is remains less than ~0.5 GPa up to the peak pressure of 60 GPa ( Table 4 - 2 , Table 4 - 3 ), consistent with the low strength of Ne. Nonhydrostatic stress generally resu lts in diffraction peak broadening due to microstrain (e.g., Takemura & Dewaele, 2008) . We choose the Au (111) peak obtained at the - Fe 4 N sample position ( Figure 4 - 1 c and d) to examine changes in diffraction peak width as a function of pressure . The normalized FWHM of the Au peak and its trend with pressure are comparable to previous measurements of Au foi l and powder in He pressure medium (Takemura & Dewaele, 2008) ( Figure 4 - 8 ), indicating hydrostatic conditions up to 17 GPa and quasi - hydrostatic conditions at higher pressures, in agreement with previous characterization of the stress gradient sustained by the pressure medium Ne (Klotz et al., 2009) . In addition, 93 compression of both phases of pure Fe remains smooth over the entire pressure range and the condition of the phase transition and compressibility are in agreement with previous studies conducted under quasi - hydrostatic stress (e.g., Dewaele et al., 2006) ( Figure 4 - 7 ). We investigated the P - V data and g - G plot of pure Fe loaded in the same sample chamber as a reference ( Figure 4 - 7 ). The discontinuities of both compression curve and g - G plot of Fe at ~15 GPa reflect a phase - - Fe, which is in good agree ment with previous studies ( Dewaele et al., 2006 ) . Therefore, the change in hydrostaticity of Ne at ~17 GPa ( Figure 4 - 8 ) was not manifested in the compression behavior of the samples, and the change in G - g at ~40 GPa of - Fe 7 N 3 is not associated with nonhydrostaticity. Relative to previous studies (Adler & Williams, 2005; Litasov et al., 2017b) , the design of this study provides greater sensitivity to discontinuities in the compression behavior of - Fe 7 N 3 due to denser data cover age with pressure intervals of ~1 GPa ( Figure 4 - 3 a) and quasi - hydrostatic medium. Given the compression and magnetic behaviors described above , we separately fit the P - V data of - Fe 7 N 3 using third - order Birch - Murnaghan equation of state (BM3 - EoS) over two distinct pressure ranges above and below 40 GPa , and that of - Fe 4 N with a single curve for the entire data range in order to better describe the compressibility. Below 40 GPa - Fe 7 N 3 has a continuously - evolving, mixed - spin state, and the resulting EoS parameters are expected to be anomalously soft relative to the high - spin state. The parameters of the BM3 - EoS, isothermal bulk modulus, K 0 , its pressure derivative, K 0 , and volume at 1 bar V 0 , obtained in the present study and previous studies are summarized in Table 4 - 1 . The BM3 - EoS parameters of magnetic, mixed spin - Fe 7 N 3 obtained by fitting the P - V data from 1 bar and 40 GPa to BM3 - EoS are compared with previous experimental constraints on the same stoichiometry (Adler & Williams, 2005; Litasov et al., 2017b) ( Table 4 - 1 ), showing 94 consistenc y with t he parameters obtained by (Litasov et al., 2017b) within uncertainties, whereas 5% (or higher given the tradeoff between K 0 and K 0 ) elastic softer than that constrained by (Adler & Williams, 2005) . Figure 4 - 3 a shows our measured P - V data are in good agreement with data obtained by (Litasov et al., 2017b) from 1 bar to 31 GPa using a multi - anvil pres s, supporting a quasi - hydrostatic conditions in this study. However, the volume data reported by Adler and Williams (2005) deviate from our measurements at pressures higher than 30 GPa, likely due to the nonhydrostatic stress supported by methanol:ethanol: water pressure transmitting medium. Properties predicted for magnetic - Fe 3 N 1.25 by density functional theory (Popov et al., 2015) are significantly offset, with V 0 lower by 6% and K 0 higher by 38% compared to experimental constraints. For nonmagnetic, low spin - Fe 7 N 3 , EoS fit for the data from 40 GPa to 60 GPa with a fixed V 0 [ 83.28(±2) Å 3 ] constrained by g - G plot ( Figure 4 - 3 b) yields K 0 45% higher than that of magnetic phase (22% increase in bulk modulus at 40 GPa, Figure 4 - 5 ), indicating a significant elastic stiffening associated with the magnetic collapse. Popov et al. (2015) predicted a magnetic - nonmagnetic transition of - Fe 7 N 3 completed at 130 GPa, inducing a 35% difference in K 0 , but both the transition pressure and bulk modulus are much higher than our constraints ( Table 4 - 1 ). An increase in incompressibility induced by the collapse of magnetic momentum has been observed in other Fe - alloys such as Fe 3 C (Prescher et al., 2012) and Fe 3 P (Lai et al., 2020) . These all oys are also not observed to soften during the spin transition, in contrast to pressure - induced Invar behavior of Fe alloys such as Fe - Ni (Dubrovinsky et al., 2001) and Fe 7 C 3 (Chen et al., 2012) which undergo elastic softening during the transition followe d by reaching a stiffer nonmagnetic state. The EoS parameters of - Fe 4 N derived by fitting the measured P - V data up to 60 GPa to BM3 - EoS agree with the parameters reported by Adler and Williams (2005) and (Guo et al., 2013) 95 within uncertainties ( Table 4 - 1 ). However, the K 0 reported by Breton et al. (2019) , 169(±6) GPa, is 13% higher than our result, and the measured volumes deviate from our measurements as illustrated in Figure 4 - 4 a. This discrepancy can be attributed to nonhydrostatic conditions in the sample chamber produced using KCl as the pressure transmitting medium, and lack of data at 0 - 20 GPa regime may cause a fitting bias when fixing the V 0 constrained by (Adler & William s, 2005) . K 0 computed by density functional theory with generalized gradient approximation studies (Niewa et al., 2009b; Popov et al., 2015) spans a range from 0 to 9% higher than that constrained by experiments, whereas the K 0 calculated from single - cryst al elastic constants by first - principles total - energy method is 26% higher than that constrained by experiments. Popov et al. (2015) predicted a magnetic - nonmagnetic transition of - Fe 4 N completed at 250 GPa, inducing an +87.5% jump of K 0 , in contrast to our observation of this transition at much lower pressure with no - Fe 4 N is also less incompressible than both magnetic and - Fe 7 N 3 , which leads to its destabilization at pressures above 60 GPa (Br eton et al., 2019) . 4.5 Discussion - Fe 7 N 3 - Fe 4 N Both - Fe 7 N 3 - Fe 4 N adopt a ferromagnetic state at 1 bar with Curie temperatures of 400 K ( Leineweber et al., 2001 ) and 750 K ( Wriedt et al., 1987 ) , respectively. Based on the XES observations described above, these compounds have fully reached a non - magnetic state by 43 and 34 GPa, respectively. Iron - light element compounds and alloys in Fe - P, Fe - C, Fe - S and other systems typically undergo a transit ion from ferromagnetic to paramagnetic state before the transition to a fully non - magnetic state (Chen et al., 2018a; Chen et al., 2014; Gu et al., 2016; Lin 96 et al., 2004a) , so it can be inferred that an additional FM - PM transition may take place in Fe - N c ompounds below the completion of the spin transition. The only previous experimental investigation of pressure - induced magnetic transitions of iron nitrides was conducted by ( Ishimatsu et al., 2003 ) on - Fe 4 N using XMCD, and showed the spin polarization w as suppressed by pressure and finally vanished at 24 GPa. This loss of spin polarization was interpreted as a ferromagnetic to paramagnetic transition. This combined with our XES results indicates that - Fe 4 N has completely transitioned to th e nonmagnetic state by 34 GPa. However, the pressure of any FM - PM transition in - Fe 7 N 3 has not been directly observed by experiments, due to the lack of studies using Mössbauer spectroscopy or XMCD . Indirect measurement of a FM - PM transition in Fe - N comp ounds through compression behavior has been inconclusive, and in iron - light element compounds more broadly, effects of FM - PM transitions on compressibility are either not observed or controversial. For example, the pressure of the FM - PM transition in Fe 3 C was determined at ~8 - 10 GPa using Mössbauer spectroscopy, and no effect on the compression behavior was observed (Prescher et al., 2012) ; whereas Litasov et al. (2013) observed this transition at ~7 - 9 GPa by based on anomalous compression behavior of the a - axis , and proposed an elastic stiffening. Conditions of FM - PM - Fe 7 N 3 - Fe 4 N do not correspond to any significant changes in incompressibility. In contrast, most Fe - light element compounds and alloys do exhibit stiffening after completing the transition to nonmagnetic state. Comparison between compression behavior and spin transition of - Fe 7 N 3 reveals elastic stiffening associated with magnetic - n onmagnetic (i.e., high to low spin) transition at ~40 GPa. Similar behaviors have been observed and predicted in iron alloys, such as Fe - C, Fe - P, Fe - S systems (see section 4.2 for more discussion), which 97 consistently show that the PM - NM transition induces elastic stiffening, whereas elastic softening of Fe 7 C 3 is due to Invar behavior (Chen et al., 2012; Chen et al., 2014; Mookherjee et al., 2011) . - Fe 4 N is unique among the Fe - light element compounds and alloys discussed here: while the pressure of the PM - NM transition is constrained through complementary spectroscopic methods, it has no significant effect on compression behavior. Ab initio calculations of magnetic states of Fe - N compounds have predicted magnetic transition pressures much higher than those observed in experiments. T he transitions from magnetic to non - - Fe 3 N 1.25 - Fe 4 N at 0 K were predicted to complete at 130 GPa and 250 GPa, respectively (Popov et al., 2015) . Popov et al. (2015) also predicted significant volume collapse of iron nitrides due to the changes in the magnetic moment, which is in contrast to experimental observations, and not reported in previous ab initio calculations on iron carbides (Mookherjee et al., 2011; Vocadlo et al., 2002) although both stud ies used the generalized gradient approximation (GGA). The difference in magneto - elastic coupling behavior between - Fe 7 N 3 - Fe 4 N may be attributed to the difference in strengths of Fe - N bonds associated with the crystal structures. In the idealized m - Fe 3 N, the iron atoms are distributed according to - Fe) and nitrogen atoms occupy one - third of octahedral voids between the iron layers in an ordered manner ( Figure 4 - 9 - Fe 3 N x (0.75 < x < 1.4) exhibits a broad homogeneity range together with some entropy - driven transfer of nitrogen to further octahedral voids (Niewa et al., 2009a ) - Fe 4 N are distributed according - Fe) and nitrogen atoms occupy one - fourth of octahedral voids ( Figure 4 - 9 ). The resulting different 3 d band structure affected by stronger 3 p - 3 d hybridization of Fe and N in - Fe 7 N 3 leads to a magnetic to nonmagnetic transition pressure of - Fe 7 N 3 ~10 GPa higher 98 - Fe 4 N ( Figure 4 - 2 ) . The difference in transition pressures may also be due to the relationship between anisotropic compressibility and the orientation of the ma gnetic moment relative to the crystal structure. For - Fe 7 N 3 , a collinear ferromagnetic arrangement of moments was determined to be parallel to the c - axis by neutron diffraction measurements (Robbins & White, 1964) , and c - axis is more incompressible than a - axis (Shi et al., 2013) ( c / a ratio increases with pressure, Figure 4 - 10 - Fe 4 N, magnetic arrangement of moments was proposed to be parallel to the a - axis (Costa - Krämer et al., 2004) , which is the stiffest direction (Gressmann et al., 2007) . To better understand the effect of spin transition on elastic anisotropy of both iron nitrides, further measurements o n elastic constants up to spin transition pressures are necessary. 4.5.2 Magneto - elastic coupling in Fe - light element alloys/compounds Previous studies have identified multiple candidate Fe alloys and light element compounds (reviewed by Hirose et al., 2013; Li & Fei, 2014) , and many of them undergo pressure - induce d magnetic transitions with effects on elasticity (reviewed by Caracas, 2016) . As a result, the extrapolation of density and velocity of ambient or low - experiments at higher pressures and temp eratures are critical. However, the pressure of magnetic collapse and its coupling with elastic properties were inconsistent in previous results: for example, the pressure of PM to NM transition for Fe 3 C from different studies spans a large range of 22 to 68 GPa (reviewed by Chen & Li, 2016) . This inconsistency is partially caused by different criteria for magnetic transitions constrained using different methods. T he spin transition (or PM - NM transition) of ionic or covalent materials is usually accompan ied by a change in interatomic distance due to a decrease in the size of the Fe atom, 99 which results in a volume collapse (Lin et al., 2013) . In Fe alloys, the effect of the spin transition on structure and volume is subtle, leading to difficulties in detec tion. For direct comparison to this work on - Fe 7 N 3 - Fe 4 N , in which complementary methods determine the collapse of magnetic momentum and changes in compression behavior, we re - examine evidence for magnetic collapse and its effect on the compression behavior of other Fe - light element compounds Fe 3 S, Fe 3 P, Fe 7 C 3 , and Fe 3 C, for which previous authors have obtained both XES measurements and dense P - V data coverage up to ~150 GPa. Fe 3 S remains in the tetragonal structure up to at least 200 GPa, with the completion of magnetic - nonmagnetic transition determined to occur at ~25 GPa by XES (Shen et al., 2003) . A previous study argued that the magnetic transition did not affect the structure or compression behavior of Fe 3 S (Kamada et al., 2014) . However, a g - G plot ( Figure 4 - 6 a) of the compression measurements from (Chen et al., 2007; Kamada et al., 2014; Seagle et al., 2006) illustrates a discontinuity in compression behavior at ~67 GPa, which could have been induced by a magnetic collapse. The spin transition pressure may be underestimated by XES (Shen et al., 2003) , due to the limitations of the spectral analysis method (no low spin reference applied) and the limited pressure range (up to 30 GPa) of the study. Fe 3 P is isostructural with the Fe 3 S tetragonal phase at ambient conditions, and in - situ XRD patterns suggest no structural phase transition up to 111 GPa (Lai et al., 2020) , although the structural evolution of Fe 3 P upon compression remains controversial (Gu et al., 2014; Sagatov et al., 2020; Scott et al., 2007) . The g - G plot based on the P - V measurements by (Lai et al., 2020) shows an increase in incompressibility at ~38 GPa ( Figure 4 - 6 b), which coincides with the pressure of magnetic spin momentum collapse determined by XES (Gu et al., 2016) . Lai et al. (2020) propose the completion of magnetic - nonmagnetic transition occurre d at 21 GPa based on t he 100 disappearance of fast oscillation in Mössbauer spectra, which can be attributed to a ferromagnetic to paramagnetic transition. Fe 7 C 3 adopts a hexagonal structure from ~7 - 8 GPa to 167 GPa (Chen et al., 2012; Lord et al., 2009) , and its magneto - elastic coupling effects have been thoroughly studied. By plotting the measurements from (Chen et al., 2012; Liu et al., 2016) as a g - G relation, an elastic stiffening occurs at 16 GPa and a softening occurs at 50 GPa ( Figure 4 - 6 c). These discontinuities in the compression behavior can be explained by a noncollinear to paramagnetic transition proposed by (Liu et al., 20 16) and a magnetic collapse determined by XES (Chen et al., 2014) , respectively. Fe 3 C, known as the mineral cohenite, has an orthorhombic structure with Pnma space group, and no structural change in Fe 3 C was observed up to 187 GPa (Sata et al., 2010) . The - to low - spin) transition in Fe 3 C determined by XES has ranged widely from ~25 GPa by (Lin et al., 2004b) to ~50 GPa by (Chen et al., 2018a) . The g - G plot of P - V measurements c ombined from (Li et al., 2002; Litasov et al., 2013; Ono & Mibe, 2010; Sata et al., 2010) indicates an elastic stiffening occurring at ~30 GPa ( Figure 4 - 6 d), which is consistent with the decreasing of the emission satellite peak intensity until 30 GPa observed by (Lin et al., 2004b) . We thus interpret the discontinuity in compression behavior of Fe 3 C at ~30 GPa is induced by the completion of the spin transition. In summary, XES and g - G plots generally reveal the collapse of magnetic moment and effects on the compression behavior of Fe - light element alloys and compounds, which are candidate cons - nonmagnetic transitions may be common throughout Fe - light element compound systems, whereas the effects from FM - PM transition on compression are not significant for most compoun 101 spin/nonmagnetic thermodynamic parameters should be used, and the effects of temperature should be considered. It has been shown that the pressure range for mixed - spin ferropericlase [(Mg 0.75 Fe 0.25 )O] is broadened by 30 GPa as the temperature increases from 300 to 2000 K (Mao et al., 2011b) . The thermal equations of state of Fe - conditions await further investigation. Our results suggest that although magnetic - to - nonmagnetic transitions do not produce sharp discontinuities in the compression behavior of Fe 7 N 3 , Fe 3 S, Fe 3 P, Fe 7 C 3 , and Fe 3 C, their effect is non - negligible and additional tools, such as XES experiments and an analysis of g - G plots, are required to accurately determine the pre ssure range of the magnetic transitions. Consequently, the effect of magnetic transitions on the compression behavior of other light - element - bearing iron compounds may have been overlooked in previous experiments based only on an analysis of the pressure - v olume data (e.g., Kamada et al., 2014) . The effects of magnetic transitions should not conditions. For example, distribution of iron isotopes in the Earth , which has been used to trace planetary differentiation processes, is dependent on isotope fractionation between various candidate host phases for iron in planetary cores and silicate melts under different pressure, temperature, composition, and oxygen fu gacity conditions (Dauphas et al., 2017) . Pressure effects on iron isotope fractionation determined by nuclear resonant inelastic X - ray scattering spectroscopy measurements have been different for different alloys, which is explained by differences in bond strength between combinations of iron with different alloying elements (Liu 102 et al., 2017; Shahar et al., 2016) . Considering the effects of magnetic transitions on bond lengths and strengths of iron alloys presented in this study, magnetic transitions of i ron alloys may impact the pressure dependence of the 57/54 The pressure conditions of the magnetic transitions in - Fe 7 N 3 , Fe 3 S, Fe 3 P, Fe 7 C 3 , and Fe 3 C revealed by this study overlap with the moderate P - T range of the cores of relatively small planets, such as Mercury ( 8 to 40 GPa, 1700 to 2200 K) (Chen et al., 2 008) and Mars ( 24 to 42 GPa, 2000 to 2600 K) (Fei & Bertka, 2005) . Whether Mercury and Mars have fully molten cores (Margot et al., 2007; Yoder et al., 2003) or include solid inner cores (Genova et al., 2019; Stevenson, 2001) is under debate. In either case, planetary cooling may entail a present and/or past - - rich solids nucleate at the liquidus and sink or rise based on buoyancy. Minor solid iron alloys may thus significantly affect planetary core dynamics through powering magnetic dynamos (Breuer et al., 2015 and references therein) . The effects of magnetic transition on physical properties [such as incompressibility and density ( Figure 4 - 11 )] of these candidate constituents of planetary cores may play an important role in deciphering the potential role of N, C, S, and P in these planetary cores. 4.6 Conclusions In this work, we report spin/ magnetic transitions and compressibility of - Fe 7 N 3 - Fe 4 N, the two stable iron nitrides at ambient conditions. Synchrotron XES and XRD measurements were carried out up to 60 GPa at 300 K using DAC. The completion of magnetic collapse in - Fe 7 N 3 - Fe 4 N is observed at 43 and 34 GPa, respectively, indicated b y the completion of high - to low - spin state transition. Comparing spin transition and discontinuities in compression behavior 103 monitored by g - G - Fe 7 N 3 by 22% at ~40 GPa, but has no resol - Fe 4 N. Accordingly, fitting P - V data to BM3 - EoS yields: V 0 = 86.55±0.02 (Å 3 ), K 0 = 160 ± 2 GPa, and K 0 ' = 4.3 ± 0.2 for magnetic, mixed spin - Fe 7 N 3 ; V 0 = 83.29 ± 0.03 (Å 3 ), K 0 = 232 ± 9 GPa, and K 0 ' = 4.1 ± 0.5 for nonmagnetic, low spin - Fe 7 N 3 ; V 0 = 54.82 ± 0.02 (Å 3 ), K 0 = 152 ± 2 GPa, and K 0 ' = 4.0 ± 0.1 for - Fe 4 N within the investigated pressure range. Using the same protocol, we re - examine evidence for magnetic collapse and its effect on the compression behavior of other Fe - light element compounds as candidate components of 3 S, Fe 3 P, Fe 7 C 3 , and Fe 3 C. We summarize previous reported dense P - V data up to ~150 GPa and comparing with XES m easurements, which indicate the completion of the magnetic transition in Fe 3 S, Fe 3 P, and Fe 7 C 3 is at about 67, 38, 50, and 30 GPa, respectively. The completion of the magnetic transition of Fe 3 S and Fe 3 P induces elastic stiffening, whereas that of Fe 7 C 3 in duces elastic softening. The changes of incompressibility induced by magnetic - nonmagnetic transition may have potential implications in deciphering the role of iron - light 104 Figure 4 - 1 : (a) and (b) are representative X - - Fe 7 N 3 at 1 and 60 GPa at 300 K, respectively; (c) and (d) are representative X - - Fe 4 N at 1 and 60 GPa at 300 K, respectively. Le Bail refinements (red solid curves) of observed XRD data (black dots) were carried out after background subtraction, demonstrating all sample peaks - Fe 7 N 3 - Fe 4 N, respectively, within the investigated pressure - Fe 7 N 3 - Fe 4 N (dark green), and the pressure calibrant, Au (orange). The wavelength of the incident X - ray beam was 0.434 Å. 105 Figure 4 - 2 : (a - b) Fe - K - Fe 7 N 3 - Fe 4 N up to 60.5 GPa at 300 K. The XES spectra were normalized to unity in integrated intensity. The top - left inset shows intensity difference of observed satellite emission peak ( K to the low - spin reference FeS 2 at 0 GPa (black dashed line). (c - d) High - - Fe 7 N 3 - Fe 4 N as a function of pressure derived from the XES measurements following integrated relative diffe rence method (Mao et al., 2014) - Fe 7 N 3 - Fe 4 N at ~30 GPa. The dashed line is fitted by Boltzmann function, and error bars determined by comparing results using FeS 2 vs. sample at 60 GPa as low - spin references. Pressures were determined by ruby fluorescence (Mao et al., 1986) before 106 and after each XES collection, which differed by up to 10% due to relaxation of the sample or cell assembly. 107 Figure 4 - 3 - Fe 7 N 3 at 300 K. (a) Unit - - Fe 7 N 3 up to 60 GPa at 300 K determined from X - ray diffraction measurements in this work (solid circles), together with previous experim ental results. The black and red curves represent the 3rd - order Birch - Murnaghan equation of state (BM3 - EoS) fits for the data for high spin (HS) and mixed spin (MS) / magnetic state (1 bar - 40 GPa), low spin (LS) / nonmagnetic state (40 - 60 GPa), respectivel y. (b) Normalized stress G as a function of effective strain g . Solid black, gray, and red circles represent the results of high spin, mixed spin, and low spin state, respectively, as determined by XES. Black and red lines indicate fits of the high spin an d low spin state G ( g ) data, respectively. The V 0 for the nonmagnetic state is obtained by extrapolating g to g 0 . 108 Figure 4 - 4 - Fe 4 N at 300 K. (a) Unit - cell volume of - Fe 4 N up to 60 GPa at 300 K determined from X - ray diffraction measurements in this work (dark green circles), together with previous experimental results. The black curve represents the 3rd - order Birch - Murnaghan equation of state (BM - EoS) fit of all pres sure - volume data from this study. (b) Normalized stress G as a function of effective strain g . Solid black, gray, and red circles represent the results of high spin, mixed spin, and low spin state, respectively, as determined by XES. The black solid line i ndicates a linear fit for all data. The pressure of onset and completion of spin transition is indicated by XES, but no change in compressibility can be observed in either plot. 109 Figure 4 - 5 : - Fe 7 N 3 - Fe 7 N 3 - Fe 4 N (dark green curve) at 300 K as a function of pressure, calculated from the fitted BM - EOS parameters ( Table 4 - 1 ). - Fe 7 N 3 induces +22% increase in incompressibility a t 40 GPa. 110 Figure 4 - 6 : Normalized stress G as a function of effective strain g for (a) Fe 3 S (Chen et al., 2007; Kamada et al., 2014; Seagle et al., 2006) , (b) Fe 3 P (Lai et al., 2020) , (c) Fe 7 C 3 (Chen et al., 2012; Liu et al., 2016) , and (d) Fe 3 C (Li et al., 2002; Litasov et al., 2013; Ono & Mibe, 2010; Sata et al., 2010) . Dashed lines are linear fits to g - G , and the discontinuity in compression behavior corresponds to the change of slope of the l inearized g - G plot. 111 Figure 4 - 7 : Compression behavior of pure Fe at 300 K. (a) Unit - - Fe (black circles) - Fe (red circles) up to 60 GPa at 300 K determined from X - ray diffraction measurements. The solid black curves and solid red curves represent the 3rd - order Birch - Murnaghan equation of state (BM - - Fe (1 - - Fe (15 - 60 GPa), respectively. (b) Normalized stress G as a function of effective strain g . Solid black and red circles represent the - - - - Fe, respectively. The V 0 - Fe is obtained by extrapolating g to g 0 . 112 Figure 4 - 8 : Full width at half maximum (FWHM) for Au (111) normalized to 2 . Orange circles - Fe 4 N sample in the diamond anvil cell. The peak broadening induced by the onset of nonhydrostaticity of Ne medium (Klotz et al., 2009) in this study starts at ~17 GPa. The magnitude of peak broadening remains small above this pressure, consistent with quasi - hydrostatic conditions in the sample chamber. 113 Figure 4 - 9 - Fe 7 N 3 - Fe 4 N (right) at ambient conditions. Gray spheres in polyhedra represent the N atoms and brown spheres represent Fe atoms. 114 Figure 4 - 10 - Fe 7 N 3 at 300 K. 115 Figure 4 - 11 - Fe 7 N 3 - Fe 7 N 3 - Fe 4 N - Fe 7 N 3 - Fe (light red) as a function of pressure at 300 K. The calculation is based on BM3 EoS with parameters of relevant phases summarized in - Fe 7 N 3 (purple), Fe 7 C 3 (orange), Fe 3 C (brown), Fe 3 S (gray), Fe 3 P (pink) along a 5500 K isotherm. For comparison, a density profile - Fe and seismologically constrained density profile (Preliminary Reference Earth Model, Dziewonski & Anderson, 1981) Debye equation of state with parameters of relevant phases listed in Table 4 - 5 . 116 Table 4 - 1 - Fe 7 N 3 - Fe 4 N. Phase Magnetism P (GPa) V 0 (Å 3 ) K 0 K 0 ' Method Reference - Fe 7 N 3 Magnetic (mixed spin) 0 - 40 86.55(2) a 160(2) 4.3(2) DAC c This study - Fe 7 N 3 Nonmagnetic (low spin) 40 - 60 83.29(3) 232(9) 4.1(5) DAC This study - Fe 7 N 3 - 0 - 51 86.04(10) 168(10) 5.7(2) DAC Adler and Williams (2005) - Fe 3 N 1.26 - 0 - 31 86.18(3) 163(2) 5.3(2) MA d Litasov et al. (2017) - Fe 3 N 1.25 Magnetic (mixed spin) 0 - 100 81.35 224(1) 4.30(5) DFT - GGA e Popov et al. (2015) - Fe 3 N 1.25 Nonmagnetic 0 - 500 77.44 303(1) 4.38(1) DFT - GGA Popov et al. (2015) - Fe 4 N - 0 - 60 54.82(2) 152(2) 4.0(1) DAC This study - Fe 4 N - 0 - 31 54.95(22) 155(3) 4 b DAC Adler and Williams (2005) - Fe 4 N - 0 - 33 54.81 154(3) 5.3(1) DAC Guo et al. (2013) - Fe 4 N - 22 - 60 54.95 b 169(6) 4.1(4) DAC Breton et al. (2019) - Fe 4 N - - - 166(1) 4.2(1) DFT - GGA Niewa et al. (2009) - Fe 4 N Magnetic - 54.64 192(1) - FP - TEC f Gressmann et al. (2007) - Fe 4 N Magnetic (mixed spin) 0 - 200 54.10 152(4) 5.41(17) DFT - GGA Popov et al. (2015) - Fe 4 N Nonmagnetic 0 - 500 49.25 285(3) 4.38(1) DFT - GGA Popov et al. (2015) a Numbers in parentheses are uncertainties on the last digits. b Fixed value c Diamond anvil cell d Multi - anvil press e Density functional theory - generalized gradient approximation f First - principles total - energy calculations 117 Table 4 - 2 : Volume and unit - - Fe 7 N 3 at 300 K. The uncertainties of pressures were propagated from uncertainties of unit cell volumes of Au and Ne, and uncertainties of their equation of state parameters (F ei et al., 2007), respectively. P (Au, GPa) P (Ne, GPa) V (Å 3 ) a (Å) c (Å) 0.4(1) - 86.31(2) 4.756(1) 4.407(1) 1.0(1) - 86.01(2) 4.750(1) 4.402(1) 1.9(1) - 85.54(2) 4.741(1) 4.395(1) 3.3(1) - 84.90(2) 4.728(1) 4.385(1) 4.6(1) - 84.27(3) 4.716(1) 4.375(1) 4.8(1) - 84.19(4) 4.715(1) 4.374(1) 5.6(1) - 83.82(4) 4.707(1) 4.369(1) 6.6(1) - 83.36(2) 4.698(1) 4.362(1) 7.7(1) - 82.91(5) 4.689(1) 4.355(1) 8.8(1) - 82.44(5) 4.680(1) 4.347(1) 9.9(1) - 81.93(7) 4.670(1) 4.340(1) 11.2(1) - 81.41(7) 4.659(1) 4.332(1) 12.4(1) - 80.95(7) 4.650(1) 4.325(1) 13.5(1) - 80.52(7) 4.642(2) 4.318(1) 14.8(1) - 80.09(7) 4.632(1) 4.312(1) 15.6(1) - 79.69(6) 4.624(1) 4.306(1) 17.1(1) - 79.20(9) 4.614(2) 4.298(1) 18.2(1) 19.2(2) 78.72(8) 4.604(1) 4.291(1) 20.6(1) 21.4(2) 78.02(2) 4.589(1) 4.279(1) 21.7(2) 22.8(3) 77.64(4) 4.581(1) 4.273(1) 23.3(2) 24.7(3) 77.09(4) 4.569(1) 4.264(1) 24.9(2) 26.3(3) 76.66(3) 4.560(1) 4.257(1) 27.2(2) 28.2(3) 76.18(2) 4.550(1) 4.249(1) 28.4(2) 29.7(3) 75.79(1) 4.541(1) 4.243(1) 30.4(3) 31.8(4) 75.32(2) 4.531(1) 4.236(1) 33.9(3) 35.3(4) 74.52(9) 4.511(2) 4.226(1) 35.8(3) 37.5(4) 74.00(4) 4.498(1) 4.219(1) 38.1(3) 40.1(5) 73.51(1) 4.491(1) 4.208(1) 40.0(4) 41.5(5) 73.11(3) 4.479(1) 4.206(1) 44.9(4) 45.6(5) 72.13(5) 4.458(1) 4.191(1) 46.9(4) 48.0(5) 71.73(3) 4.446(1) 4.184(1) 49.2(5) 49.9(6) 71.41(4) 4.441(1) 4.180(1) 51.6(5) 52.7(6) 70.95(7) 4.432(1) 4.172(1) 54.1(5) 55.4(6) 70.56(7) 4.420(1) 4.167(1) 56.2(5) 57.6(7) 70.22(9) 4.412(2) 4.161(1) 58.2(5) 60.1(7) 69.84(1) 4.404(1) 4.156(1) Numbers in parentheses are uncertainties on the last digits. 118 Table 4 - 3 : Volume and unit - - Fe 4 N at 300 K. The uncertainties of pressures were propagated from uncertainties of unit cell volumes of Au and Ne, and uncertainties of their equation of state parameters (Fei et al., 2007), respectively. P (Au, GPa) P (Ne, GPa) V (Å 3 ) a (Å) 0.3(1) - 54.71(1) 3.796(1) 1.0(1) - 54.49(1) 3.791(1) 1.9(1) - 54.14(1) 3.783(1) 3.3(1) - 53.69(1) 3.773(1) 4.6(1) - 53.30(1) 3.763(1) 4.7(1) - 53.25(1) 3.762(1) 5.7(1) - 52.95(1) 3.755(1) 6.7(1) - 52.66(1) 3.748(1) 7.7(1) - 52.35(1) 3.741(1) 8.8(1) - 52.03(1) 3.733(1) 10.0(1) - 51.71(2) 3.725(1) 11.2(1) - 51.38(3) 3.717(1) 12.4(1) - 51.08(4) 3.710(1) 13.6(1) - 50.77(2) 3.702(1) 14.7(1) - 50.50(6) 3.695(1) 15.9(1) - 50.23(6) 3.689(1) 17.2(2) - 49.93(6) 3.681(1) 18.7(2) 19.3(2) 49.58(6) 3.672(1) 20.6(2) 21.3(2) 49.15(7) 3.662(1) 22.0(2) 22.8(3) 48.87(8) 3.655(1) 23.8(2) 24.6(3) 48.54(8) 3.646(1) 25.4(2) 26.2(3) 48.25(9) 3.639(1) 27.0(2) 28.0(3) 47.93(8) 3.631(1) 28.6(2) 29.6(3) 47.66(8) 3.624(1) 30.5(2) 31.5(4) 47.33(7) 3.615(1) 33.6(2) 34.8(4) 46.78(8) 3.602(1) 35.6(2) 36.9(4) 46.42(8) 3.594(1) 38.2(3) 39.6(4) 46.02(8) 3.584(1) 40.1(3) 41.6(5) 45.72(8) 3.576(1) 44.8(3) 46.2(5) 45.05(7) 3.558(1) 46.9(3) 48.3(5) 44.75(8) 3.550(1) 48.9(3) 50.3(6) 44.46(8) 3.542(1) 51.2(3) 52.6(6) 44.13(8) 3.530(1) 53.7(4) 55.1(6) 43.79(8) 3.521(1) 55.8(4) 57.2(7) 43.50(7) 3.514(1) 58.1(4) 59.6(7) 43.23(8) 3.506(1) Numbers in parentheses are uncertainties on the last digits. 119 Table 4 - 4 : Volume and unit - cell parameters of Fe at 300 K. The uncertainties of pressures were propagated from uncertainties of unit cell volumes of Au and Ne, and uncertainties of their equation of state parameters (Fei et al., 2007), respectively. P (GPa) V (Å 3 ) a (Å) c (Å) 0.4(1) a 23.47(4) 2.863(1) - 1.0(1) a 23.39(4) 2.860(1) - 2.0(1) a 23.25(4) 2.854(1) - 3.4(2) a 23.06(4) 2.846(1) - 4.6(2) 1 22.92(3) 2.841(1) - 4.8(2) a 22.90(4) 2.840(1) - 5.8(2) a 22.77(4) 2.834(1) - 6.8(2) a 22.65(3) 2.829(1) - 7.9(2) a 22.52(3) 2.824(1) - 9.0(2) a 22.40(3) 2.819(1) - 10.2(2) a 22.25(5) 2.813(1) - 11.4(2) a 22.13(3) 2.808(1) - 12.7(2) a 22.01(3) 2.802(1) - 13.9(2) a 21.88(3) 2.797(1) - 15.3(2) a 21.76(3) 2.792(1) - 16.7(2) b 20.68(4) 2.460(1) 3.945(1) 18.0(2) b 20.56(4) 2.454(1) 3.943(1) 19.6(3) b 20.40(4) 2.449(1) 3.927(1) 21.7(3) b 20.26(4) 2.442(1) 3.922(1) 23.2(3) b 20.14(3) 2.438(1) 3.913(1) 25.0(3) b 20.00(4) 2.432(1) 3.904(1) 26.7(3) b 19.88(4) 2.428(1) 3.895(1) 28.4(3) b 19.76(4) 2.423(1) 3.887(1) 30.0(3) b 19.66(3) 2.419(1) 3.879(1) 32.2(3) b 19.52(3) 2.413(1) 3.870(1) 35.8(4) b 19.31(5) 2.405(1) 3.855(1) 38.1(4) b 19.17(3) 2.399(1) 3.846(1) 40.9(4) b 19.01(3) 2.392(1) 3.836(1) 43.1(4) b 18.88(3) 2.387(1) 3.828(1) 45.6(4) b 18.71(3) 2.380(1) 3.814(1) 47.9(5) b 18.61(4) 2.376(1) 3.806(1) 50.1(5) b 18.52(4) 2.373(1) 3.799(1) 52.7(5) 2 18.41(3) 2.368(1) 3.791(1) 55.5(5) b 18.27(4) 2.362(1) 3.783(1) 57.8(5) b 18.16(4) 2.357(1) 3.776(1) 60.6(6) b 18.03(4) 2.351(1) 3.768(1) a - Fe 120 b - Fe Numbers in parentheses are uncertainties on the last digits. Table 4 - 5 iron. Phase P (GPa) V 0 (Å 3 ) K 0 (GPa) K 0 ' 0 (K) 0 q - Fe 7 N 3 a - 181.4(5) c 316(5) 3.2 430 2.1(3) 4.5(9) Fe 3 S 67 - 197 348.2(32) 224(5) 4.2(2) 417 d 1.01(3) d 1 d Fe 3 P 38 - 110 350.2(17) 260(5) 4.0(2) 417 d 1.01(3) d 1 d Fe 7 C 3 50 - 167 188.7(11) 223(2) 4.1(1) 920(140) e 2.57(5) e 2.2(5) e Fe 3 C 30 - 186.6 151.24(25) 264(3) 4.0(1) 490(120) f 2.09(4) f - 0.1(3) f - Fe b - 22.14(19) 185(2) 4.94(12) 1173(62) 3.2(2) 0.8(3) a Data from (Kusakabe et al., 2019) b Data from (Sakai et al., 2014) c Numbers in parentheses are uncertainties on the last digits. d Data from (Thompson et al., 2020) e Data from (Nakajima et al., 2011) f Data from (Litasov et al., 2013) 121 BIBLIOGRAPHY 122 BIBLIOGRAPHY Adler, J. F., & Williams, Q. (2005). A high - pressure X - ray diffraction study of iron nitrides: Implications for Earth's core. Journal of Geophysical Research - Solid Earth, 110 (B1). http://10.1029/2004jb003103 Akahama , Y., & Kawamura, H. (2006). 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