Advanced Search

Indexed by SCI、CA、РЖ、PA、CSA、ZR、etc .

Volume 30 Issue 5
Oct.  2019
Article Contents
Turn off MathJax

Citation:

In-situ High-Temperature XRD and FTIR for Calcite, Dolomite and Magnesite: Anharmonic Contribution to the Thermodynamic Properties

  • Corresponding author: Yu Ye, yeyu@cug.edu.cn
  • Received Date: 2019-02-11
  • In-situ powder X-ray diffraction (XRD) and Fourier transform infrared (FTIR) spectra were measured on the natural crystals of calcite (Ca0.996Mg0.004CO3), dolomite (Ca0.497Mg0.454Fe0.046Mn0.003CO3) and magnesite (Mg0.988Ca0.010Fe0.002CO3), with a temperature up to 796 K. The thermal expansion coeffi-cients were evaluated for these carbonate minerals, resulting in the values of 2.7×10-5, 3.3×10-5 and 3.5×10-5 K-1 for calcite, dolomite and magnesite, respectively. The magnitude of these coefficients is in the same order as those for the isothermal and elastic moduli of these carbonates (e.g., calcite < dolomite < magnesite). The IR-active internal modes of the CO3 group systematically shift to lower frequencies at elevated temperature, and the isobaric (γiP) and isothermal (γiT) Grüneisen parameters for the internal modes are generally smaller than 0.5. The corresponding anharmonic parameters (ai) are typically within the range of -1.5-+1×10-5 K-1, which are significantly smaller in magnitude than those for the external modes. We also calculate the thermodynamic properties (internal energy, heat capacities and entropy) at high temperatures for these carbonates, and the anharmonic contribution to thermodynamics shows an order of calcite > dolomite > magnesite. The Debye model (harmonic approximation) would be valid for magnesite to simulating the thermodynamic properties and isotope fractionation β-factor at high P-T condition.
  • 加载中
  • [1] Adams, D. M., Williams, A. D., 1980. Vibrational Spectroscopy at very High Pressures. Part 26. An Infrared Study of the Metastable Phases of Ca[CO3]. Journal of the Chemical Society, Dalton Transactions, 8: 1482. https://doi.org/10.1039/dt9800001482 doi: 10.1039/dt9800001482
    [2] Andersen, F. A., Brečević, L., Beuter, G., et al., 1991. Infrared Spectra of Amorphous and Crystalline Calcium Carbonate. Acta Chemica Scandinavica, 45: 1018-1024. https://doi.org/10.3891/acta.chem.scand.45-1018 doi: 10.3891/acta.chem.scand.45-1018
    [3] Antao, S. M., Hassan, I., Mulder, W. H., et al., 2009. In-situ Study of the R3c-R3m Orientational Disorder in Calcite. Physics and Chemistry of Minerals, 36(3): 159-169. https://doi.org/10.1007/s00269-008-0266-y doi: 10.1007/s00269-008-0266-y
    [4] Antao, S. M., Mulder, W. H., Hassan, I., et al., 2004. Cation Disorder in Dolomite, CaMg(CO3)2, and Its Influence on the Aragonite+Magnesite↔Dolomite Reaction Boundary. American Mineralogist, 89(7): 1142-1147. https://doi.org/10.2138/am-2004-0728 doi: 10.2138/am-2004-0728
    [5] Biellmann, C., Gillet, P., 1992. High-Pressure and High-Temperature Behaviour of Calcite, Aragonite and Dolomite: A Raman Spectroscopic Study. European Journal of Mineralogy, 4(2): 389-394. https://doi.org/10.1127/ejm/4/2/0389 doi: 10.1127/ejm/4/2/0389
    [6] Biellmann, C., Gillet, P., Guyot, F., et al., 1993. Experimental Evidence for Carbonate Stability in the Earth's Lower Mantle. Earth and Planetary Science Letters, 118(1/2/3/4): 31-41. https://doi.org/10.1016/0012-821x(93)90157-5 doi: 10.1016/0012-821x(93)90157-5
    [7] Bigeleisen, J., Mayer, M. G., 1947. Calculation of Equilibrium Constants for Isotopic Exchange Reactions. The Journal of Chemical Physics, 15(5): 261-267. https://doi.org/10.1063/1.1746492 doi: 10.1063/1.1746492
    [8] Böttcher, M., Gehlken, P. L., Steele, D. F., 1997. Characterization of Inorganic and Biogenic Magnesian Calcites by Fourier Transform Infrared Spectroscopy. Solid State Ionics, 101-103: 1379-1385. https://doi.org/10.1016/s0167-2738(97)00235-x doi: 10.1016/s0167-2738(97)00235-x
    [9] Böttcher, M. E., Gehlken, P. L., Usdowski, E., 1992. Infrared Spectroscopic Investigations of the Calcite-Rhodochrosite and Parts of the Calcite-Magnesite Mineral Series. Contributions to Mineralogy and Petrology, 109(3): 304-306. https://doi.org/10.1007/bf00283320 doi: 10.1007/bf00283320
    [10] Boulard, E., Gloter, A., Corgne, A., et al., 2011. New Host for Carbon in the Deep Earth. Proceedings of the National Academy of Sciences of the United States of America, 108(13): 5184-5187. https://doi.org/10.1073/pnas.1016934108 doi: 10.1073/pnas.1016934108
    [11] Boulard, E., Menguy, N., Auzende, A. L., et al., 2012. Experimental Investigation of the Stability of Fe-Rich Carbonates in the Lower Mantle. Journal of Geophysical Research: Solid Earth, 117(B2): B02208. https://doi.org/10.1029/2011jb008733 doi: 10.1029/2011jb008733
    [12] Brenker, F. E., Vollmer, C., Vincze, L., et al., 2007. Carbonates from the Lower Part of Transition Zone or Even the Lower Mantle. Earth and Planetary Science Letters, 260(1/2): 1-9. https://doi.org/10.1016/j.epsl.2007.02.038 doi: 10.1016/j.epsl.2007.02.038
    [13] Bromiley, F. A., Ballaran, T. B., Langenhorst, F., et al., 2007. Order and Miscibility in the Otavite-Magnesite Solid Solution. American Mineralogist, 92(5/6): 829-836. https://doi.org/10.2138/am.2007.2315 doi: 10.2138/am.2007.2315
    [14] Catalli, K., Williams, Q., 2005. A High-Pressure Phase Transition of Calcite-Ⅲ. American Mineralogist, 90(10): 1679-1682. https://doi.org/10.2138/am.2005.1954 doi: 10.2138/am.2005.1954
    [15] Chang, L. L. Y., Howie, R. A., Zussman, J., 1996. Non-Silicates: Sulfates, Carbonates, Phosphates and Halides. The Geological Society, Longman, London. https://ci.nii.ac.jp/naid/10011703589/en/
    [16] Chen, P. F., Chiao, L. Y., Huang, P. H., et al., 2006. Elasticity of Magnesite and Dolomite from a Genetic Algorithm for Inverting Brillouin Spectroscopy Measurements. Physics of the Earth and Planetary Interiors, 155(1/2): 73-86. https://doi.org/10.1016/j.pepi.2005.10.004 doi: 10.1016/j.pepi.2005.10.004
    [17] Cynn, H., Hofmeister, A. M., Burnley, P. C., et al., 1996. Thermodynamic Properties and Hydrogen Speciation from Vibrational Spectra of Dense Hydrous Magnesium Silicates. Physics and Chemistry of Minerals, 23(6): 361-376. https://doi.org/10.1007/bf00199502 doi: 10.1007/bf00199502
    [18] Dasgupta, R., Hirschmann, M. M., 2010. The Deep Carbon Cycle and Melting in Earth's Interior. Earth and Planetary Science Letters, 298(1/2): 1-13. https://doi.org/10.1016/j.epsl.2010.06.039 doi: 10.1016/j.epsl.2010.06.039
    [19] Dorfman, S. M., Badro, J., Nabiei, F., et al., 2018. Carbonate Stability in the Reduced Lower Mantle. Earth and Planetary Science Letters, 489: 84-91. https://doi.org/10.1016/j.epsl.2018.02.035 doi: 10.1016/j.epsl.2018.02.035
    [20] Dorogokupets, P. I., 2007. Equation of State of Magnesite for the Conditions of the Earth's Lower Mantle. Geochemistry International, 45(6): 561-568. https://doi.org/10.1134/s0016702907060043 doi: 10.1134/s0016702907060043
    [21] Dorogokupets, P. T., Oganov, A. R., 2004. Intrinsic Anharmonicity in Equations of State of SOLIDS and Minerals. Doklady Earth Sciences, 395(2): 238-241
    [22] Dove, M. T., Powell, B. M., 1989. Neutron Diffraction Study of the Tricritical Orientational Order/disorder Phase Transition in Calcite at 1 260 K. Physics and Chemistry of Minerals, 16(5): 503-507. https://doi.org/10.1007/bf00197019 doi: 10.1007/bf00197019
    [23] Dove, M. T., Swainson, I. P., Powell, B. M., et al., 2005. Neutron Powder Diffraction Study of the Orientational Order-Disorder Phase Transition in Calcite, CaCO3. Physics and Chemistry of Minerals, 32(7): 493-503. https://doi.org/10.1007/s00269-005-0026-1 doi: 10.1007/s00269-005-0026-1
    [24] Effenberger, H., Mereiter, K., Zemann, J., 1981. Crystal Structure Refinements of Magnesite, Calcite, Rhodochrosite, Siderite, Smithonite, and Dolomite, with Discussion of some Aspects of the Stereochemistry of Calcite Type Carbonates. Zeitschrift für Kristallographie-Crystalline Materials, 156(3/4): 233-243. https://doi.org/10.1524/zkri.1981.156.3-4.233 doi: 10.1524/zkri.1981.156.3-4.233
    [25] Fahad, M., Iqbal, Y., Riaz, M., et al., 2016. Metamorphic Temperature Investigation of Coexisting Calcite and Dolomite Marble-Examples from Nikani Ghar Marble and Nowshera Formation, Peshawar Basin, Pakistan. Journal of Earth Science, 27(6): 989-997. https://doi.org/10.1007/s12583-015-0643-7 doi: 10.1007/s12583-015-0643-7
    [26] Fahad, M., Saeed, S., 2018. Determination and Estimation of Magnesium Content in the Single Phase Magnesium-Calcite[Ca(1-x)MgxCO3(S)] Using Electron Probe Micro-Analysis (EPMA) and X-Ray Diffraction (XRD). Geosciences Journal, 22(2): 303-312. https://doi.org/10.1007/s12303-017-0059-8 doi: 10.1007/s12303-017-0059-8
    [27] Falini, G., Fermani, S., Gazzano, M., et al., 1998. Structure and Morphology of Synthetic Magnesium Calcite. Journal of Materials Chemistry, 8(4): 1061-1065. https://doi.org/10.1039/a707893e doi: 10.1039/a707893e
    [28] Fei, Y., 1995. Thermal Expansion. In: Ahrens. T. J., ed., Mineral Physics & Crystallography: A Handbook of Physical Constants, Volume 2. American Geophysical Union, Washington, D.C. 29-44. https://doi.org/10.1029/rf002
    [29] Fiquet, G., Guyot, F., Itie, J. P., 1994. High-Pressure X-Ray Diffraction Study of Carbonates: MgCO3, CaMg(CO3)2, and CaCO3. American Mineralogist, 79(1-2): 15-23
    [30] Fiquet, G., Reynard, B., 1999. High-Pressure Equation of State of Magnesite; New Data and a Reappraisal. American Mineralogist, 84(5/6): 856-860. https://doi.org/10.2138/am-1999-5-619 doi: 10.2138/am-1999-5-619
    [31] Fiquet, G., Richet, P., Montagnac, G., 1999. High-Temperature Thermal Expansion of Lime, Periclase, Corundum and Spinel. Physics and Chemistry of Minerals, 27(2): 103-111. https://doi.org/10.1007/s002690050246 doi: 10.1007/s002690050246
    [32] Fujimori, H., Komatsu, H., Ioku, K., et al., 2002. Anharmonic Lattice Mode of Ca2SiO4: Ultraviolet Laser Raman Spectroscopy at High Temperatures. Physical Review B, 66(6): 064306. https://doi.org/10.1103/physrevb.66.064306 doi: 10.1103/physrevb.66.064306
    [33] Gong, Q., Deng, J., Wang, Q., et al., 2010. Experimental Determination of Calcite Dissolution Rates and Equilibrium Concentrations in Deionized Water Approaching Calcite Equilibrium. Journal of Earth Science, 21(4): 402-411. https://doi.org/ 10.1007/s12583-010-0103-3 doi: 10.1007/s12583-010-0103-3
    [34] Gillet, P., Guyot, F., Malezieux, J. M., 1989. High-Pressure, High-Temperature Raman Spectroscopy of Ca2GeO4 (Olivine Form): Some Insights on Anharmonicity. Physics of the Earth and Planetary Interiors, 58(2/3): 141-154. https://doi.org/10.1016/0031-9201(89)90050-2 doi: 10.1016/0031-9201(89)90050-2
    [35] Gillet, P., Biellmann, C., Reynard, B., et al., 1993. Raman Spectroscopic Studies of Carbonates Part Ⅰ: High-Pressure and High-Temperature Behaviour of Calcite, Magnesite, Dolomite and Aragonite. Physics and Chemistry of Minerals, 20(1): 1-18. https://doi.org/10.1007/bf00202245 doi: 10.1007/bf00202245
    [36] Gillet, P., McMillan, P., Schott, J., et al., 1996. Thermodynamic Properties and Isotopic Fractionation of Calcite from Vibrational Spectroscopy of 18O-Substituted Calcite. Geochimica et Cosmochimica Acta, 60(18): 3471-3485. https://doi.org/10.1016/0016-7037(96)00178-0 doi: 10.1016/0016-7037(96)00178-0
    [37] Grzechnik, A., Simon, P., Gillet, P., et al., 1999. An Infrared Study of MgCO3 at High Pressure. Physica B: Condensed Matter, 262(1/2): 67-73. https://doi.org/10.1016/s0921-4526(98)00437-2 doi: 10.1016/s0921-4526(98)00437-2
    [38] Hazen, R. M., Downs, R. T., Jones, A. P., et al., 2013. Carbon Mineralogy and Crystal Chemistry. Reviews in Mineralogy and Geochemistry, 75(1): 7-46. https://doi.org/10.2138/rmg.2013.75.2 doi: 10.2138/rmg.2013.75.2
    [39] Holland, T. J. B., Redfern, S. A. T., 1997. Unit Cell Refinement from Powder Diffraction Data: The Use of Regression Diagnostics. Mineralogical Magazine, 61(404): 65-77. https://doi.org/10.1180/minmag.1997.061.404.07 doi: 10.1180/minmag.1997.061.404.07
    [40] Holland, T. J. B., Powell, R., 2004. An Internally Consistent Thermodynamic Data Set for Phases of Petrological Interest. Journal of Metamorphic Geology, 16(3): 309-343. https://doi.org/10.1111/j.1525-1314.1998.00140.x doi: 10.1111/j.1525-1314.1998.00140.x
    [41] Isshiki, M., Irifune, T., Hirose, K., et al., 2004. Stability of Magnesite and Its High-Pressure Form in the Lowermost Mantle. Nature, 427(6969): 60-63. https://doi.org/10.1038/nature02181 doi: 10.1038/nature02181
    [42] Koch-Müller, M., Jahn, S., Birkholz, N., et al., 2016. Phase Transitions in the System CaCO3 at High P and T Determined by in Situ Vibrational Spectroscopy in Diamond Anvil Cells and First-Principles Simulations. Physics and Chemistry of Minerals, 43(8): 545-561. https://doi.org/10.1007/s00269-016-0815-8 doi: 10.1007/s00269-016-0815-8
    [43] Lane, M. D., Christensen, P. R., 1997. Thermal Infrared Emission Spectroscopy of Anhydrous Carbonates. Journal of Geophysical Research: Planets, 102(E11): 25581-25592. https://doi.org/10.1029/97je02046 doi: 10.1029/97je02046
    [44] Lin, C. C., 2013. Elasticity of Calcite: Thermal Evolution. Physics and Chemistry of Minerals, 40(2): 157-166. https://doi.org/10.1007/s00269-012-0555-3 doi: 10.1007/s00269-012-0555-3
    [45] Litasov, K. D., Fei, Y. W., Ohtani, E., et al., 2008. Thermal Equation of State of Magnesite to 32 GPa and 2 073 K. Physics of the Earth and Planetary Interiors, 168(3/4): 191-203. https://doi.org/10.1016/j.pepi.2008.06.018 doi: 10.1016/j.pepi.2008.06.018
    [46] Liu, C. J., Zheng, H. F., Wang, D. J., 2017. Raman Spectroscopic Study of Calcite Ⅲ to Aragonite Transformation under High Pressure and High Temperature. High Pressure Research, 37(4): 545-557. https://doi.org/10.1080/08957959.2017.1384824 doi: 10.1080/08957959.2017.1384824
    [47] Liu, J., Lin, J. F., Mao, Z., et al., 2014. Thermal Equation of State and Spin Transition of Magnesiosiderite at High Pressure and Temperature. American Mineralogist, 99(1): 84-93. https://doi.org/10.2138/am.2014.4553 doi: 10.2138/am.2014.4553
    [48] Liu, L. G., Mernagh, T. P., 1990. Phase Transitions and Raman Spectra of Calcite at High Pressures and Room Temperature. American Mineralogist, 75(7-8): 801-806
    [49] Liu, Q., Tossell, J. A., Liu, Y., 2010. On the Proper Use of the Bigeleisen-Mayer Equation and Corrections to It in the Calculation of Isotopic Fractionation Equilibrium Constants. Geochimica et Cosmochimica Acta, 74(24): 6965-6983. https://doi.org/10.1016/j.gca.2010.09.014 doi: 10.1016/j.gca.2010.09.014
    [50] Mao, Z., Armentrout, M., Rainey, E., et al., 2011. Dolomite Ⅲ: A New Candidate Lower Mantle Carbonate. Geophysical Research Letters, 38(22): L22303. https://doi.org/10.1029/2011gl049519 doi: 10.1029/2011gl049519
    [51] Markgraf, S. A., Reeder, R. J., 1985. High-Temperature Structure Refinements of Calcite and Magnesite. American Mineralogist, 70(5-6): 590-600
    [52] Matas, J., Gillet, P., Ricard, Y., et al., 2000. Thermodynamic Properties of Carbonates at High Pressures from Vibrational Modelling. European Journal of Mineralogy, 12(4): 703-720. https://doi.org/10.1127/ejm/12/4/0703 doi: 10.1127/ejm/12/4/0703
    [53] Megaw, H. D., 1973. Crystal Structures: A Working Approach. Saunders, London. 563
    [54] Merlini, M., Sapelli, F., Fumagalli, P., et al., 2016. High-Temperature and High-Pressure Behavior of Carbonates in the Ternary Diagram CaCO3-MgCO3-FeCO3. American Mineralogist, 101(6): 1423-1430. https://doi.org/10.2138/am-2016-5458 doi: 10.2138/am-2016-5458
    [55] Oganov, A. R., Dorogokupets, P. I., 2004. Intrinsic Anharmonicity in Equations of State and Thermodynamics of Solids. Journal of Physics: Condensed Matter, 16(8): 1351-1360. https://doi.org/10.1088/0953-8984/16/8/018 doi: 10.1088/0953-8984/16/8/018
    [56] Oganov, A. R., Glass, C. W., Ono, S., 2006. High-Pressure Phases of CaCO3: Crystal Structure Prediction and Experiment. Earth and Planetary Science Letters, 241(1/2): 95-103. https://doi.org/10.1016/j.epsl.2005.10.014 doi: 10.1016/j.epsl.2005.10.014
    [57] Paquette, J., Reeder, R. J., 1990. Single-Crystal X-Ray Structure Refinements of Two Biogenic Magnesian Calcite Crystals. American Mineralogist, 75(9): 1151-1158
    [58] Pickard, C. J., Needs, R. J., 2015. Structures and Stability of Calcium and Magnesium Carbonates at Mantle Pressures. Physical Review B, 91(10): 104101 doi: 10.1103/PhysRevB.91.104101
    [59] Polyakov, V. B., 1998. On Anharmonic and Pressure Corrections to the Equilibrium Isotopic Constants for Minerals. Geochimica et Cosmochimica Acta, 62(18): 3077-3085. https://doi.org/10.1016/s0016-7037(98)00220-8 doi: 10.1016/s0016-7037(98)00220-8
    [60] Polyakov, V. B., Kharlashina, N. N., 1994. Effect of Pressure on Equilibrium Isotopic Fractionation. Geochimica et Cosmochimica Acta, 58(21): 4739-4750. https://doi.org/10.1016/0016-7037(94)90204-6 doi: 10.1016/0016-7037(94)90204-6
    [61] Redfern, S. A. T., Angel, R. J., 1999. High-Pressure Behaviour and Equation of State of Calcite, CaCO3. Contributions to Mineralogy and Petrology, 134(1): 102-106. https://doi.org/10.1007/s004100050471 doi: 10.1007/s004100050471
    [62] Reynard, B., Caracas, R., 2009. D/H Isotopic Fractionation between Brucite Mg(OH)2 and Water from First-Principles Vibrational Modeling. Chemical Geology, 262(3/4): 159-168. https://doi.org/10.1016/j.chemgeo.2009.01.007 doi: 10.1016/j.chemgeo.2009.01.007
    [63] Reeder, R. J., 1983. Crystal Chemistry of the Rhombohedral Carbonates. Reviews in Mineralogy and Geochemistry, 11(1): 1-47
    [64] Reeder, R. J., Markgraf, S. A., 1986. High-Temperature Crystal Chemistry of Dolomite. American Mineralogist, 71(5-6): 795-804
    [65] Ross, N. L., 1997. The Equation of State and High-Pressure Behavior of Magnesite. American Mineralogist, 82(7/8): 682-688. https://doi.org/10.2138/am-1997-7-805 doi: 10.2138/am-1997-7-805
    [66] Ross, N. L., Reeder, R. J., 1992. High-Pressure Structural Study of Dolomite and Ankerite. American Mineralogist, 77(3-4): 412-421
    [67] Santillán, J., 2005. An Infrared Study of Carbon-Oxygen Bonding in Magnesite to 60 GPa. American Mineralogist, 90(10): 1669-1673. https://doi.org/10.2138/am.2005.1703 doi: 10.2138/am.2005.1703
    [68] Santillán, J., Williams, Q., 2004. A High-Pressure Infrared and X-Ray Study of FeCO3 and MnCO3: Comparison with CaMg(CO3)2-Dolomite. Physics of the Earth and Planetary Interiors, 143-144: 291-304. https://doi.org/10.1016/j.pepi.2003.06.007 doi: 10.1016/j.pepi.2003.06.007
    [69] Santillán, J., Williams, Q., Knittle, E., 2003. Dolomite-Ⅱ: A High-Pressure Polymorph of CaMg(CO3)2. Geophysical Research Letters, 30(2): 1054. https://doi.org/10.1029/2002gl016018 doi: 10.1029/2002gl016018
    [70] Stekiel, M., Nguyen-Thanh, T., Chariton, S., et al., 2017. High Pressure Elasticity of FeCO3-MgCO3 Carbonates. Physics of the Earth and Planetary Interiors, 271: 57-63. https://doi.org/10.1016/j.pepi.2017.08.004 doi: 10.1016/j.pepi.2017.08.004
    [71] Suito, K., Namba, J., Horikawa, T., et al., 2001. Phase Relations of CaCO3 at High Pressure and High Temperature. American Mineralogist, 86(9): 997-1002. https://doi.org/10.2138/am-2001-8-906 doi: 10.2138/am-2001-8-906
    [72] Thomson, A. R., Walter, M. J., Kohn, S. C., et al., 2016. Slab Melting as a Barrier to Deep Carbon Subduction. Nature, 529(7584): 76-79. https://doi.org/10.1038/nature16174 doi: 10.1038/nature16174
    [73] Titschack, J., Goetz-Neunhoeffer, F., Neubauer, J., 2011. Magnesium Quantification in Calcites [(Ca, Mg)CO3] by Rietveld-Based XRD Analysis: Revisiting a Well-Established Method. American Mineralogist, 96(7): 1028-1038. https://doi.org/10.2138/am.2011.3665 doi: 10.2138/am.2011.3665
    [74] Urey, H. C., 1947. The Thermodynamic Properties of Isotopic Substances. Journal of the Chemical Society (Resumed), 562-581. https://doi.org/10.1039/jr9470000562 doi: 10.1039/jr9470000562
    [75] Valenzano, L., Noël, Y., Orlando, R., et al., 2007. Ab Initio Vibrational Spectra and Dielectric Properties of Carbonates: Magnesite, Calcite and Dolomite. Theoretical Chemistry Accounts, 117(5/6): 991-1000. https://doi.org/10.1007/s00214-006-0213-2 doi: 10.1007/s00214-006-0213-2
    [76] Wang, A. L., Pasteris, J. D., Meyer, H. O. A., et al., 1996. Magnesite-Bearing Inclusion Assemblage in Natural Diamond. Earth and Planetary Science Letters, 141(1/2/3/4): 293-306. https://doi.org/10.1016/0012-821x(96)00053-2 doi: 10.1016/0012-821x(96)00053-2
    [77] Wang, G., Wang, J., Wang, Z., et al., 2017. Carbon Isotope Gradient of the Ediacaran Cap Carbonate in the Shennongjia Area and Its Implications for Ocean Stratification and Palaeogeography. Journal of Earth Science. 28(2): 42-56. https://doi.org/10.1007/s12583-016-0923-x doi: 10.1007/s12583-016-0923-x
    [78] Wang, M. L., Shi, G. H., Qin, J. Q., et al., 2018. Thermal Behaviour of Calcite-Structure Carbonates: A Powder X-Ray Diffraction Study between 83 and 618 K. European Journal of Mineralogy, 30(5): 939-949. https://doi.org/10.1127/ejm/2018/0030-2768 doi: 10.1127/ejm/2018/0030-2768
    [79] Wang, X., Ye, Y., Wu, X., et al., 2019. High-Temperature Raman and FTIR Study of Aragonite-Group Carbonates. Physics and Chemistry of Minerals, 46(1): 51-62. https://doi.org/10.1007/s00269-018-0986-6 doi: 10.1007/s00269-018-0986-6
    [80] Wei, S. H., Xu, X. X., 2018. Boosting Photocatalytic Water Oxidation Reactions over Strontium Tantalum Oxynitride by Structural Laminations. Applied Catalysis B: Environmental, 228: 10-18. https://doi.org/10.1016/j.apcatb.2018.01.071 doi: 10.1016/j.apcatb.2018.01.071
    [81] Weir, C. E., Lippincott, E. R., van Valkenburg, A., et al., 1959. Infrared Studies in the 1- to 15-Micron Region to 30, 000 Atmospheres. Journal of Research of the National Bureau of Standards Section A: Physics and Chemistry, 63A(1): 55-62. https://doi.org/10.6028/jres.063a.003 doi: 10.6028/jres.063a.003
    [82] White, W. B., 1974. The Carbonate Minerals. In: Farmer, V. C., ed., The Infrared Spectra of Minerals. Mineralogical Society of Great Britain and Ireland, London. 227-284
    [83] Yang, J., Mao, Z., Lin, J.-F., et al., 2014. Single-Crystal Elasticity of the Deep-Mantle Magnesite at High Pressure and Temperature. Earth and Planetary Science Letters, 392: 292-299. https://doi.org/10.1016/j.epsl.2014.01.027 doi: 10.1016/j.epsl.2014.01.027
    [84] You, X. L., Jia, W. Q., Xu, F., et al., 2018. Mineralogical Characteristics of Ankerite and Mechanisms of Primary and Secondary Origins. Earth Science, 43(11): 4046-4055 (in Chinese with English Abstract). https://doi.org/ 10.3799/dqkx.2018.152 doi: 10.3799/dqkx.2018.152
    [85] Zhang, J., Martinez, I., Guyot, F., et al., 1997. X-Ray Diffraction Study of Magnesite at High Pressure and High Temperature. Physics and Chemistry of Minerals, 24(2): 122-130. https://doi.org/10.1007/s002690050025s doi: 10.1007/s002690050025s
    [86] Zhang, J., Reeder, R., 1999. Comparative Compressibilities of Calcite-Structure Carbonates: Deviations from Empirical Relations. American Mineralogist, 84(5-6): 861-870. https://doi.org/10.2138/am-1999-5-620 doi: 10.2138/am-1999-5-620
    [87] Zhang, X., Yang, S. Y., Zhao, H., et al., 2019. Effect of Beam Current and Diameter on Electron Probe Microanalysis of Carbonate Minerals. Journal of Earth Science, 30(4): 834-842. https://doi.org/10.1007/s12583-017-0939-x doi: 10.1007/s12583-017-0939-x
    [88] Zheng, R., Pan, Y., Zhao, C., et al., 2013. Carbon and Oxygen Isotope Stratigraphy of the Oxfordian Carbonate Rocks in Amu Darya Basin. Journal of Earth Science, 24(1): 42-56. https://doi.org/10.1007/s12583-013-0315-4 doi: 10.1007/s12583-013-0315-4
    [89] Zhu, Y. F., Ogasawara, Y., 2002. Carbon Recycled into Deep Earth: Evidence from Dolomite Dissociation in Subduction-Zone Rocks. Geology, 30(10): 947-950. https://doi.org/10.1130/0091-7613(2002)030%3c0947:cridee%3e2.0.co; 2 doi: 10.1130/0091-7613(2002)030%3c0947:cridee%3e2.0.co;2
  • 加载中
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Figures(9) / Tables(3)

Article Metrics

Article views(22) PDF downloads(0) Cited by()

Related
Proportional views

In-situ High-Temperature XRD and FTIR for Calcite, Dolomite and Magnesite: Anharmonic Contribution to the Thermodynamic Properties

    Corresponding author: Yu Ye, yeyu@cug.edu.cn
  • 1. State Key Laboratory of Geological Processes and Mineral Resources, China University of Geosciences, Wuhan 430074, China
  • 2. Shanghai Key Lab of Chemical Assessment and Sustainability, School of Chemical Science and Engineering, Tongji University, Shanghai 200092, China

Abstract: In-situ powder X-ray diffraction (XRD) and Fourier transform infrared (FTIR) spectra were measured on the natural crystals of calcite (Ca0.996Mg0.004CO3), dolomite (Ca0.497Mg0.454Fe0.046Mn0.003CO3) and magnesite (Mg0.988Ca0.010Fe0.002CO3), with a temperature up to 796 K. The thermal expansion coeffi-cients were evaluated for these carbonate minerals, resulting in the values of 2.7×10-5, 3.3×10-5 and 3.5×10-5 K-1 for calcite, dolomite and magnesite, respectively. The magnitude of these coefficients is in the same order as those for the isothermal and elastic moduli of these carbonates (e.g., calcite < dolomite < magnesite). The IR-active internal modes of the CO3 group systematically shift to lower frequencies at elevated temperature, and the isobaric (γiP) and isothermal (γiT) Grüneisen parameters for the internal modes are generally smaller than 0.5. The corresponding anharmonic parameters (ai) are typically within the range of -1.5-+1×10-5 K-1, which are significantly smaller in magnitude than those for the external modes. We also calculate the thermodynamic properties (internal energy, heat capacities and entropy) at high temperatures for these carbonates, and the anharmonic contribution to thermodynamics shows an order of calcite > dolomite > magnesite. The Debye model (harmonic approximation) would be valid for magnesite to simulating the thermodynamic properties and isotope fractionation β-factor at high P-T condition.

0.   INTRODUCTION
1.   EXPERIMENTAL METHODS
  • We adopted natural samples of calcite, dolomite and magnesite for our high-temperature X-ray diffraction (XRD) and Fourier transform infrared spectroscopy (FTIR) experiments. The compositions of these natural samples were measured by a JEOL JXA-8100 electron probe micro analyzer (EPMA) equipped with four wavelength-dispersive spectrometers (WDS), operated at an accelerating voltage of 15 kV, with a beam current of 5 nA, and a spot size of 10 m to reduce the fluctuations of X-ray intensity, and minimize sample damage (Zhang et al., 2019). The certified mineral standards (wollastonite for Ca, olivine for Mg, and garnet for Fe and Mn) were adopted for quantification using ZAF wavelength-dispersive corrections. In total, eight to ten points were selected for measurements on each sample, and averaged values for the weight percentages of oxides are listed in Table S1 with standard deviations. These compositions can be summarized as: Ca0.996Mg0.004CO3 for calcite, Ca0.994Mg0.908Fe0.092Mn0.006(CO3)2 for dolomite, and Mg0.988Ca0.010Fe0.002CO3 for magnesite. In addition, we confirmed the phases of these natural minerals by Raman spectroscopy (Fig. 1), with results which are consistent with the previous studies (Liu et al., 2017; Gillet et al., 1993; Liu and Mernagh, 1990).

    Figure 1.  Raman spectra of calcite, dolomite and magnesite at ambient condition.

    In-situ high-temperature powder XRD experiments were conducted on a Bruker D8 Focus diffractometer with a Cu-anode X-ray generator (Kα1=1.540 6 Å and Kα2=1.544 4 Å; Wei and Xu, 2018). The XRD patterns for each sample were collected in the 2 range from 20° to 90° with a step size of 0.02°. Measurements were collected at 50 K intervals, from 296 K up to 796 K, using a heating rate of 20 K/min. Each target temperature was held for 5 minutes for thermal equilibrium before the XRD pattern was collected at each temperature step. Silicon powder (purity > 99.99%) was used as the reference for calibrating the X-ray diffractometer.

    Mid-FTIR spectra were obtained using a Nicolet iS50 FTIR coupled with a Continum microscope and a KBr beam-splitter. The MCT-A detector was cooled by liquid-nitrogen. Ground sample powder was wiped on a platinum plate, which was loaded in an INSTEC mK2000 heating stage. FTIR spectra in the reflection mode were collected in the frequency range of 650-2 000 cm-1 with a resolution of 4 cm-1 and an accumulation of 128 scans. The experimental temperature range was from 296 K up to 796 K, with measurements collected at temperature increments of 50 K, and temperature uncertainties less than 5 K. The target temperatures were controlled by an automatic temperature controlling unit with a heating rate of 20 K/min.

2.   RESULTS AND DISCUSSIONS
  • The representative XRD patterns for calcite, dolomite and magnesite at elevated temperatures are shown in Figs. 2a-2c, and the unit-cell parameters are refined by the "unit cell" software (Holland and Redfern, 1997), and are listed in Table S2. The unit-cell parameters at ambient condition are a=4.998 2(1) Å, c=17.073 2(7) Å and V=369.38(2) Å3 for calcite; a=4.808 7(7) Å, c=16.027 8(5) Å and V=320.97(1) Å3 for dolomite; while a=4.645 3(1) Å, c=15.087 1(6) Å and V=281.94(2) Å3 for magnesite, which are consistent with the previous studies (Fahad and Saeed, 2018; Titschack et al., 2011; Falini et al., 1998; Effenberger et al., 1981). The a and c axes, as well as V, decrease in the order of calcite > dolomite > magnesite, with an increase of Mg percentage (Mg/(Mg+Ca)) in the compositions.

    Figure 2.  Selected powder XRD patterns at elevated temperature for (a) calcite, (b) dolomite and (c) magnesite, with the reflection peaks indexed.

    Variations of the unit-cell parameters with temperature for these carbonate samples are plotted in Figs. 3a-3c. The thermal expansion coefficient (K-1) is defined as

    Figure 3.  Variations of the unit-cell parameters (a, c and V) with temperature for (a) calcite, (b) dolomite and (c) magnesite, which have been normalized to the ones at room temperature (a0, c0, and V0). Uncertainties of the unit-cell parameters are smaller than the sizes of the symbols.

    The averaged thermal expansion coefficients for the axes (αa, αc) and volume (αV) are calculated in Table 1, and the volumetric thermal expansion coefficients are also fit for a linear function of temperature (α=a1×T+a0). Several high-temperature XRD experiments have been conducted on calcite, dolomite and magnesite (Wang et al., 2018; Merlini et al., 2016; Antao et al., 2009; Fei, 1995; Reeder and Markgraf, 1986; Markgraf and Reeder, 1985), however, the thermal expansion coefficients reported in these studies vary as a function of the temperatures range fit in each study. Therefore, to enable the direct comparison of these literature values with the present study, we recalculated the average volumetric thermal expansion coefficients from these earlier studies using the temperature range of this study (296-796 K), as shown in Fig. 4. The volumetric thermal expansion coefficients for calcite and dolomite measured in this study were consistent with previous measurements: 2.1×10-5-2.8×10-5 K-1 for calcite (Merlini et al., 2016; Antao et al., 2009; Fei, 1995; Markgraf and Reeder, 1985), 3.3×10-5-3.8×10-5 K-1 for dolomite (Merlini et al., 2016; Fei, 1995; Reeder and Markgraf, 1986) and 3.5(1)×10-5 K-1 for magnesite (Litasov et al., 2008).

    Axial (10-5·K-1) Volumetric
    αa αc αV a1 (10-8·K-2) a0 (10-5·K-1)
    Calcite 0.09(3) 2.52(12) 2.71(9) 3.4(8) 1.2(5)
    Dolomite 0.64(3) 2.03(13) 3.30(14) 5.4(12) 0.4(6)
    Magnesite 0.67(3) 2.17(7) 3.51(10) 3.5(11) 1.6(6)

    Table 1.  The mean thermal expansion coefficients (10-5·K-1) for the axes and volume, the volumetric thermal expansion coefficients are also expressed in the form of α=a1×T+a0

    Figure 4.  Comparison among the mean thermal expansion coefficients for calcite, dolomite and magnesite of different studies.

    Our high-temperature XRD results support the general trend that the thermal expansivities (αV) increase in the order of calcite < dolomite < magnesite, at ambient pressure. The same trend of calcite < dolomite < magnesite was also observed for the isothermal bulk moduli (KT0) (Merlini et al., 2016; Redfern and Angel, 1999; Fiquet et al., 1994), as well as for the elastic bulk (KS0) and shear (G0) moduli (Yang et al., 2014; Lin, 2013; Chen et al., 2006). Thus, in the pressure range before any phase transitions at ambient temperature, the compressibilities for these three minerals show the order of calcite > dolomite > magnesite, which is opposite to the order of the thermal expansivity. In the crystal structures of calcite and magnesite (R3c) (Antao et al., 2009; Bromiley et al., 2007), both Ca2+ and Mg2+ cations are coordinated with six O2- anions, and the radii ratio of RCa2+: RO2- is equal to 0.707 at ambient condition, which is close to the upper limit (0.732) of the cation-to-anion radii ratio for the 6-fold coordination. Therefore the calcite structure is relatively unstable at high pressure conditions, and transforms to aragonite (9-fold coordination for Ca2+) at pressures as low as 2 GPa (above 550 K) (Suito et al., 2001); while the magnesite structure is stable up to more than 80 GPa (~1 700 km depth in the lower mantle) (Pickard and Needs, 2015; Boulard et al., 2011; Oganov et al., 2006; Isshiki et al., 2004). The more stable MgO6 octahedron of magnetite may contribute to its smaller compressibility with larger thermal expansion.

    vi (∂vi/∂T)P γip (∂vi/∂P)T γiT ai
    (cm-1) (10-2·cm-1·K-1) (cm-1/GPa) (10-5·K-1)
    Calcite
    v4 711.2 -0.56(2) 0.29(2) 5.66a 0.58(2) 0.65(2)
    v2 873.4 -0.82(5) 0.35(2) 3.77a 0.31(1) -0.50(4)
    v3 1 397.9 -1.89(10) 0.50(3) 6.17b 0.32(1) 0.09(6)
    Dolomite
    v4 726.8 -0.91(5) 0.38(3) 1.31c 0.17(1) -0.69(9)
    v2 879.7 -1.20(5) 0.42(3) 0.27c 0.03(1) -1.27(10)
    v3 1 410.6 -2.35(7) 0.51(3) 3.36c 0.22(1) -0.94(10)
    Magnesite
    v4 756.2 -1.10(6) 0.41(3) 2.64(4)d 0.40(1) -0.05(7)
    v2 885.7 -1.25(7) 0.42(2) 1.16(7)d 0.15(1) -0.96(5)
    v3 1 422.0 -2.74(15) 0.55(3) 4.23(7)d 0.34(1) -0.73(10)
    a. Adams et al. (1980); b. Weir et al. (1959); c. Santillán and Williams (2004); d. Grzechnik et al. (1999).

    Table 2.  The IR internal modes Grüneisen parameters γiP, γiT and the anharmonic parameters ai of the calcite, dolomite and magnesite.

    On the other hand, the c axis of these carbonate crystals shows significantly larger thermal expansivity (this study, Merlini et al., 2016; Anto et al., 2009; Zhang et al., 1997) and compressibility (Merlini et al., 2016; Redfern and Angel, 1999; Zhang and Reeder, 1999; Fiquet et al., 1994), as compared to the a axis. These phenomena could be explained by the internal structure of these phases in which the coplanar CO3 groups, serving as rigid bodies, stack perpendicular to the c axis (Antao et al., 2009, 2004; Bromiley et al., 2007). In this study, we observed a slightly positive thermal expansion coefficient for the a axis (αa) of calcite (+0.09×10-5 K-1), which is significantly smaller than that of dolomite and magnesite (0.64×10-5-0.67×10-5 K-1). However, previous studies have reported a negative coefficient of αa (-0.05×10-5- -0.01×10-5 K-1) for the calcite samples with high purity (Antao et al., 2009; Dove et al., 2005; Dove and Powell, 1989; Markgraf and Reeder, 1985), therefore, this discrepancy is likely due to some impurity (Mg/(Mg+Ca)=0.4%) in our natural calcite sample. Even a small amount of Mg or Fe content in the carbonate structures could have significant effect on the thermo-elastic properties, such as thermal expansion and compressibility (Merlini et al., 2016).

  • According to the mode distribution and selection rules (Falini et al., 1998; Böttcher et al., 1997, 1992; White, 1974), there are 30 vibrational modes total for calcite and magnesite (space group R3c), as well as for dolomite (space group R3). These vibrational modes include 3 acoustics modes and 27 optical modes (Raman-active, IR-active, and inactive). Among these optical modes, there are 15 lattice vibrational modes (external modes) and 12 internal modes for the CO3 groups, while the internal modes for magnesite and calcite can be divided into four groups: the v1 (symmetric stretching) modes contain 1A1g (Raman active)+1A1u (inactive); the v2 (out-of-plane bending) modes contain 1A2g(inactive)+1A2u (IR active); while the v3 (asymmetric stretching) and v4 (in-plane bending) modes are constituted of 2Eg (Raman active)+2Eu (IR active).

    The representative mid-FTIR spectra of these three carbonates obtained at elevated temperatures from this study are shown in Figs. 5a-5c, which are in good agreement with the previous IR measurements (Lane and Christensen, 1997; Böttcher et al., 1992; Andersen et al., 1991; White, 1974). Three internal modes of CO3 groups were observed in this FTIR measurement: v4 (711-756 cm-1), v2 (873-885 cm-1) and v3 (1 397-1 422 cm-1), while in this Raman spectra, the internal vibrations of v4 (710-740 cm-1), v1 (1 085-1 097 cm-1) and v3 (1 431-1 446 cm-1) were detected and shown in Fig. 1. The FTIR and Raman spectra show that both the external (< 400 cm-1) and the internal Raman modes (> 700 cm-1) shift to higher frequency when comparing magnesite versus calcite. The structure refinements by single-crystal XRD (Markgraf and Reeder, 1985) show that the C-O covalent bond length (dC-O) for calcite (1.290 1(5) Å) is slightly longer than that for magnesite (1.289(1) Å), with the libration correction applied.

    Figure 5.  Typical FTIR spectra for (a) calcite, (b) dolomite and (c) magnesite at high temperatures.

    The variations of the frequencies for the internal modes at elevated temperature are plotted in Fig. 6 with linear regression, and the fitted slopes ((∂vi/∂T)P, cm-1·K-1) are listed in Table 2. The internal vibration modes shift to lower frequency at elevated temperature, and for each carbonate, the magnitude for the temperature-dependence increases as the frequency increases: v4 (in-plane bending) < v2 (out-of-plane bending) < v3 (asymmetric stretching), which is consistent with the observations fo aragonite-group carbonates (aragonite, strontianite, cerussite and witherite) by high-temperature Raman and FTIR spectra (Wang et al., 2019).

    Figure 6.  Variations of FTIR modes with temperature for calcite, dolomite and magnesite, and the uncertainties are smaller than the sizes of the symbols.

  • Two contributions should be considered for the frequency shift of a given mode (vi): (1) a pure volume contribution due to compression or thermal expansion (quasi-harmonicity); (2) a volume independent contribution due to the intrinsic anharmonicity (Fujimori et al., 2002; Gillet et al., 1989). Thus, the isobaric (γiP) and isothermal (γiT) Grüneisen parameters, as well as the anharmonic parameters (ai) need to be calculated to separate these two contributions, as shown in Eqs. 2-4 below

    where νi is the wavenumber of a given vibrational mode, ρ is the density, while α and KT are the thermal expansion coefficient and isothermal bulk modulus, respectively.

    With the adoption of the thermal expansion coefficients, we calculated the IR-active mode Grüneisen parameters (γiP) for calcite, dolomite and magnesite, which are listed in Table 2. In addition, high-temperature Raman spectra were also measured for these three minerals (Gillet et al., 1993; Biellmann and Gillet, 1992; Liu and Mernagh, 1990). Here, we selected detailed datasets from Gillet et al. (1993) and Liu and Mernagh (1990) to calculate the isobar Grüneisen parameters for the Raman-active modes (please refer to Table S3), and the γiP parameters from both FTIR (this study, solid symbols) and Raman (Gillet et al., 1993; Liu and Mernagh, 1990, open symbols) measurements, as shown in Fig. 7a.

    Figure 7.  (a) Isobaric (γiP) and (b) isothermal (γiT) modes Grüneisen parameters of calcite, dolomite and magnesite, and the solid and open symbols represent the datasets from FTIR and Raman spectra, respectively (This study for high-T FTIR; Gillet et al. (1993) and Liu and Mernagh (1990) for high-T and high-P Raman; while Santillán and Williams (2004), Grzechnik et al. (1999), Adams and Williams (1980) and Weir et al. (1959) for high-P FTIR). The vertical error bars stand for the estimated uncertainties of the Grüneisen parameters, if larger than the sizes of the symbols.

    High-pressure FTIR (Santillán and Williams, 2004; Grzechnik et al., 1999; Adams and Williams, 1980; Weir et al., 1959) and Raman (Gillet et al., 1993; Biellmann and Gillet, 1992; Liu and Mernagh, 1990) spectra of calcite, dolomite and magnesite have been well studied. Using the reported isothermal bulk moduli of KT0=73.4(2) GPa for calcite (Redfern and Angel, 1999), KT0=94(1) for dolomite (Merlini et al., 2016) for dolomite, and KT0=115(1) GPa for magnesite (Fiquet and Reynard, 1999), we calculated the isothermal Grüneisen parameters (γiT) for the IR-active (Table 2) and Raman-active (Table S3) internal modes, which are also plotted in Fig. 7b. Due to the uncertainties and discrepancies among different experiments, we could not draw any clear trends for these internal vibrations. But generally, the γiP and γiT mode Grüneisen parameters for the internal modes of CO3 group are in the range of 0-0.5, which are significantly smaller than those for the external modes (lattice modes) (Wang et al., 2019; Gillet et al., 1993).

    Based on the derived Grüneisen parameters γiP and γiT, we evaluated the intrinsic anharmonic parameters (ai) for these IR-active (Table 2) and Raman-active (Table S3) modes (Fig. 8). The ai values are in the range of -0.96- +0.65×10-5 K-1 for the v4 (in-plane bending) modes; -1.27- -0.50×10-5 K-1 for the v2 (out-of-plane bending) modes; -0.35-+0.22×10-5 K-1 for the v1 (symmetric stretching) modes; while -0.94- +0.09×10-5 K-1 for the v3 (asymmetric stretching) modes. Similarly, for the aragonite-group carbonates (aragonite, strontianite, cerussite and witherite), the ai parameters for the internal modes are also in the range of -1.5-1.5×10-5 K-1 (Wang et al., 2019). The ai parameters of the vibrational modes are summarized in Table 3 for the phases of calcite, magnesite, and dolomite, and the ai parameters for the external modes in significant larger magnitudes (Matas et al., 2000; Gillet et al., 1993), as compared with those for the internal modes.

    Figure 8.  The intrinsic anharmonic parameters (ai), and the solid and open symbols represent the datasets from the FTIR and Raman spectra, respectively. The vertical error bars stand for the estimated uncertainties of the anharmonic parameters, if larger than the sizes of the symbols.

  • In this discussion, we provide robust evaluations of the anharmonic contribution to the thermodynamic properties (internal energy, heat capacities and entropy) of the calcite, dolomite and magnesite at high temperatures, on the basis of the intrinsic anharmonic parameters ai for the vibrational modes as summarized in Table 3. In the harmonic approximation, the internal energy (U), isochoric (CV) and isobaric (CP) heat capacities, as well as entropy (S) can be simulated as a function of temperature

    Modes TypeCalcite Magnesite Dolomite
    Number of Oscillators Frequency (cm-1) ai (10-5·K-1) Frequency (cm-1) ai (10-5·K-1) Modes Type Number of Oscillators Frequency (cm-1) ai (10-5·K-1)
    A2u Acoustics 1 173a -15a 273a -2a Au Acoustics 1 203a -7.8a
    Eu Acoustics 2 98a -15a 139a -2a Eu Acoustics 2 104a -7.8a
    Eu Infrared 2 92c -15a 225c -2a Eu Infrared 2 150c -7.8a
    A2u Infrared 1 102c -15a 230c -2a Au Infrared 1 146c -7.8a
    Eg Raman 2 155.9b -16.9b 213b 0.3b Eg Raman 2 178b -8.4b
    A2g Inactive 1 190d -15a 311d -2a Ag Raman 1 235d -7.8a
    Eu Infrared 2 223c -15a 301c -2a Eu Infrared 2 255c -7.8a
    Eg Raman 2 276b -13b 329b -2.5b Eg Raman 2 300b -7.3b
    Eu Infrared 2 297c -15a 356c -2a Eu Infrared 2 345c -7.8a
    A1u Inactive 1 289d -15a 365d -2a Au Infrared 1 314c -7.8a
    A2u Infrared 1 303c -15a 362c -2a Au Infrared 1 361c -7.8a
    A2g Inactive 1 311d -15a 359d -2a Ag Raman 1 335b, c -3.7b
    Eg Raman 2 711b -0.3b 738b 0.44b Eg Raman 2 724b 0.2b
    Eu Infrared 2 711.2* 0.65* 756.2* -0.05* Eu Infrared 2 726.8* -0.69*
    A2u Infrared 1 873.4* -0.5* 885.7* -0.96* Au Infrared 1 879.7* -1.27*
    A2g Inactive 1 882d -0.5* 888d -0.96* Ag Raman 1 879b -1.27*
    A1g Raman 1 1 088.4b -0.1b 1 094b 0.21b Ag Raman 1 1 097b 0b
    A1u Inactive 1 1 088d -0.1b 1 099d 0.21b Au Infrared 1 1 096d 0b
    Eu Infrared 2 1 397.9* 0.09* 1 422* -0.73* Eu Infrared 2 1 410.6* -0.94*
    Eg Raman 2 1 432.4b -1.3b 1 444b -1.42b Eg Raman 2 1 439b -1.9b
    *. This study; superscript: a. Matas et al. (2000); b. Gillet et al. (1993); c. White (1974); d. Valenzano et al. (2007).

    Table 3.  The frequencies and intrinsic anharmonic parameters (ai) for the vibrational modes of calcite, magnesite and dolomite

    where N is the total number of atoms inside a unit cell of a mineral phase (N=10 for these three carbonates), and vi is the fundamental frequency of the i-th vibrational mode. While Uvih and Cvih are the internal energy and isochoric heat capacity of the i-th vibration, in the quasi-harmonic case.

    However, such harmonic approximation becomes inaccurate at elevated temperatures, as the anharmonic contribution becomes more severe (Dorogokupets and Oganov, 2004; Oganov and Dorogokupets, 2004). Therefore, at high temperatures the incorporation of an anharmonic correction is increasingly paramount. The anharmonic corrections to the internal energy and heat capacity CV are expressed below

    Based on the equations above, we derived the thermodynamic properties U(T)-U(0K), CV, CP and S(T)-S(0K) for the phases of calcite, magnesite as well as dolomite. The results for the harmonic approximation are shown in Figs. 9a, 9c, 9e, 9g), while the anharmonic corrections (the differences calculated between the anharmonic and harmonic cases) are shown in Figs. 9b, 9d, 9f, 9h). The trends of the internal energies decrease in the order of calcite > dolomite > magnesite, since the frequencies of the vibrational modes systematically increase in the order of calcite < dolomite < magnesite. The internal energy is inversely correlating with the frequency vi of the i-th microscopic vibration (Eq. 5). For each carbonate phase in this study, the molar heat capacity, CV should approach the limit of 3nR at extremely high temperature (R is the molar gas constant, and n=5 for these carbonates).

    Figure 9.  The thermodynamic properties of internal energy U (a), (b); heat capacities CV (c), (d); and CP (e), (f) as well as entropy S (g), (h), as a function of temperature, for the phases of calcite, magnesite and dolomite. The models from harmonic approximation are shown on the left (a), (c), (e), (g), while the anharmonic corrections (differences between the anharmonic and harmonic cases) are plotted on the right (b), (d), (f), (h).

    The anharmonic contributions to the thermodynamic properties are positive (Eqs. 9, 10), because nearly all the ai parameters are in negative values. At the high temperature of 800 K, the anharmonic contributions are 11.5%, 6.5% and 1.8% to the internal energy of calcite, dolomite and magnesite, respectively; 16%, 8.4% and 2.1% to the heat capacities, individually; while 7.9%, 4.2% and 1.0% to the entropies, respectively. The anharmonic parameters from the external modes (in the frequency range below 400 cm-1) play more important role than those from the internal modes (700-1 450 cm-1), and the high-pressure and high-temperature Raman studies (Matas et al., 2000; Gillet et al., 1993) indicate that the absolute values of ai parameters for the external vibrations shows the order of calcite (-17×10-5- -15×10-5 K-1) > Dolomite (-9×10-5- -7×10-5 K-1) > magnesite (-3×10-5- -2×10-5 K-1).

    On the other hand, the intrinsic anharmonicity is also important and responsible for some isotope phenomena such as pressure effects on isotope equilibrium fractionations between minerals. Polyakov (1998) and Gillet et al., (1996) constrained the reduced isotopic partition function ratios (β-factor) for oxygen isotope (18O/16O) in calcite with the anharmonic correction: the anharmonic correction to the value of 103·lnβ decreases from 0.60 at 300 K to 0.37 at 1 200 K, which is comparable to the typical values of the anharmonic correction in gas molecules. This calculation method has been well established and accepted for evaluating the equilibrium isotope fractionation β-factor of various isotopes, such as O, C, Mg and Ca, etc. Our calculation above reveals that the anharmonic contribution to the thermodynamic properties for calcite is 7-8 times of that for magnesite. Hence, the anharmonic correction to 103·lnβ should be of much smaller values for magnesite at elevated temperatures.

    A rigorous relationship between pressure-dependence and temperature-dependence of the β-factor is established (Polyako, 1998; Polyakov and Kharlashina, 1994) as

    The Grüneisen parameter, γ, with the anharmonic correction is expressed below

    where the dimensionless frequency ui=h·vi/(kB·T), γi and ai are the isothermal Grüneisen parameter and intrinsic anharmonic parameter, respectively, while * denotes for the heavier isotopes. According to Eq. 12, the external modes at lower frequencies account for larger weights in determination of the anharmonic contribution to the γ parameter (Reynard and Caracas, 2009). For the case of calcite, the anharmonic correction to the pressure-dependence of β-factor (103·∂lnβ/P)T is less than 0.02 GPa-1, in the temperature range up to 1 200 K (Polyakov, 1998). Hence, such anharmonic correction for magnesite would be no more than 0.003 GPa-1. Even when extrapolated to 80 GPa, which is close to the phase transition boundary of magnesite, the anharmonic correction to 103·lnβ is about 0.25, which is also smaller than that for the typical value of the anharmonic correction in gas.

  • Carbonate cycle has drawn lots of attention from the whole society of Earth sciences, which has important implication to the composition and evolution history of the Earth. The calcite-group carbonates, including calcite, dolomite and magnesite, are the most abundant carbon-bearing minerals in the crust, which serves as carriers of carbon from the Earth's surface to the deep interior (Dasgupta and Hirschmann, 2010). Hence, evaluations of the thermodynamic properties (such as P-V-T Equations of State, elasticities, capacities, and equilibrium isotope fractionation) are essential for constraining the physical and chemical behaviors of the carbonate in the deep Earth. However, such thermodynamic properties at the P-T conditions in the mantle are not measurable at low-pressure conditions in the laboratory, while calculations provide us with good way for such simulation. In addition, the widely used Debye model, which only considered the vibrations of atoms inside the crystal structure in harmonic approximation, should be inaccurate especially in high-T conditions, and then the anharmonic correction is necessary and important for such thermodynamic modeling (Dorogokupets and Oganov, 2004; Polyakov, 1998; Gillet, 1996). This study provides robust and detailed evaluation of the anharmonic contribution to the thermodynamics of the calcite-group minerals at high-temperature condition

3.   CONCLUSIONS
  • We have conducted in-situ powder XRD and FTIR measurements on the calcite, dolomite and magnesite, with a temperature range of 296-796 K at ambient pressure. The averaged thermal expansivity (αV) shows an order of calcite < dolomite < magnesite, which is consistent with the order of the isothermal bulk modulus (KT): calcite < dolomite < magnesite. The c axis in all three carbonates has much larger thermal expansivity and compressibility, compared with the a axis, since the rigid coplanar CO3 groups are stacked in the planes perpendicular to the c axis.

    The isobar Grüneisen parameters (γiP) are evaluated for the internal IR modes (v4, v2, v3) of CO3 group, and a similar trend is also observed for the values of these microscopic Grüneisen parameters: calcite < dolomite < magnesite. For the internal modes of CO3 group (710-1 450 cm-1, including both IR-active and Raman-active ones), the mode Grüneisen parameters (γiP and γiT) range from 0 to 0.5, and the absolute values for the ai are typically less than 1.3×10-5 K-1, which are also significantly smaller than those for the external modes (< 400 cm-1).

    We also simulate the thermodynamic properties (internal energy, heat capacities CV and CP, as well as entropy) as a function of temperature for these three carbonates, in both harmonic and anharmonic cases. The intrinsic anharmonicity shows positive contribution to the thermodynamics with the order of calcite > dolomite > magnesite, and the anharmonic correction for calcite is 78 times of that for magnesite. Hence, the classic Debye model (harmonic approximation) could be a proper and valid framework for simulating the isotope fractionation β-factor (for Mg, C and O isotopes) for the phase of magnesite, which is one of the most abundant carbonate minerals and the important carbon reservoir in the lower mantle.

ACKNOWLEDGMENT
  • Many thanks to Profs. Kurt Leinenweber and Joseph Smyth for helpful and constructive discussion and revision on this manuscript. This work was supported by the National Key Research and Development Program of China (No. 2016YFC0600204), and the National Natural Science Foundation of China (Nos. 41590621, 41672041). EPMA and in-situ high-T FTIR experiments were carried out at the State Key Laboratory of Geological Processes and Mineral Resources, China University of Geosciences (Wuhan), while in-situ high-T powder XRD measurements were conducted at School of Chemical Science and Engineering, Tongji University. The final publication is available at Springer via https://doi.org/10.1007/s12583-019-1236-7.

    Electronic Supplementary Materials: Supplementary materials (Tables S1, S2, S3) are available in the online version of this article at https://doi.org/10.1007/s12583-019-1236-7.

Reference (89)

Catalog

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return