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New thermoelastic parameters of natural C2/c omphacite

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Abstract

The compressibility at room temperature and the thermal expansion at room pressure of two disordered crystals (space group C2/c) obtained by annealing a natural omphacite sample (space group P2/n) of composition close to Jd56Di44 and Jd55Di45, respectively, have been studied by single-crystal X-ray diffraction. Using a Birch–Murnaghan equation of state truncated at the third order [BM3-EoS], we have obtained the following coefficients: V 0 = 421.04(7) Å3, K T0 = 119(2) GPa, K′ = 5.7(6). A parameterized form of the BM3 EoS was used to determine the axial moduli of a, b and c. The anisotropy scheme is β c  ≤ β a  ≤ β b , with an anisotropy ratio 1.05:1.00:1.07. A fitting of the lattice variation as a function of temperature, allowing for linear dependency of the thermal expansion coefficient on the temperature, yielded αV(1bar,303K) = 2.64(2) × 10−5 K−1 and an axial thermal expansion anisotropy of α b  ≫ α a  > α c . Comparison of our results with available data on compressibility and thermal expansion shows that while a reasonable ideal behaviour can be proposed for the compressibility of clinopyroxenes in the jadeite–diopside binary join [K T0 as a function of Jd molar %: K T0 = 106(1) GPa + 0.28(2) × Jd(mol%)], the available data have not sufficient quality to extract the behaviour of thermal expansion for the same binary join in terms of composition.

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References

  • Anderson OL, Isaak D, Oda HT (1992) High temperature elastic constant data on minerals relevant to geophysics. Rev Geophys 30:57–92

    Article  Google Scholar 

  • Angel RJ (2000) Equations of state. In Hazen RM, Downs RT (eds) High-temperature and high-pressure crystal chemistry. Rev Mineral Geochem, vol 41, pp 35–39

  • Angel RJ (2002) EOSFIT V5.2 program. Crystallography Laboratory, Virginia Tech, USA

    Google Scholar 

  • Angel RJ, Finger LW (2011) SINGLE: a program to control single-crystal diffractometers. J Appl Cryst 44:247–251

    Article  Google Scholar 

  • Angel RJ, Downs RT, Finger LW (2000) High-temperature high-pressure diffractometry. In: Hazen RM, Downs RT (eds) High-temperature and high-pressure crystal chemistry. Rev Mineral Geochem, vol 41, pp 559–596

  • Angel RJ, Allan DR, Miletich R, Finger LW (1997) The use of quartz as an internal pressure standard in high pressure crystallography. J Appl Cryst 30:461–466

    Article  Google Scholar 

  • Angel RJ, Bujak M, Zhao J, Gatta D, Jacobsen SD (2007) Effective hydrostatic limits of pressure media for high-pressure crystallographic studies. J Appl Cryst 40:26–32

    Article  Google Scholar 

  • Angel RJ, Jackson JM, Speziale S (2009) Elasticity measurements on minerals: a review. Eur J Mineral 21:525–550

    Article  Google Scholar 

  • Berman RG (1988) Internally-consistent thermodynamic data for minerals in the system Na2O-K2O-CaO-MgO-FeO-Fe2O3-Al2O3- SiO2-TiO2-H2O-CO2. J Petrol 29:445–522

    Google Scholar 

  • Bhagat SS, Bass JD, Smith JR (1992) Single-Crystal elastic proprieties of omphatice C2/c by brillouin scattering spectroscopy. J Geophys Res 97:6843–6848

    Article  Google Scholar 

  • Birch F (1947) Finite elastic strain of cubic crystals. Phys Rev 71:809–824

    Article  Google Scholar 

  • Blessing RH (1995) An empirical correction for absorption anisotropy. Acta Crystallographica 51:33–38

    Google Scholar 

  • Boffa Ballaran T, Carpenter MA, Domeneghetti MC, Tazzoli V (1998) Structural mechanisms of solid solution and cation ordering in augite-jadeite pyroxenes: I. A macroscopic perspective. Am Mineral 83:419–433

    Google Scholar 

  • Boffa Ballaran T, Nestola F, Tribaudino M, Ohashi H (2009) Bulk modulus variation along the diopside–kosmochlor solid solution. Eur J Mineral 21:591–597

    Article  Google Scholar 

  • Cámara F, Gatta D, Meven M, Pasqual D (2012) Thermal expansion and high temperature structure evolution of zoisite by single crystal X-ray and neutron diffraction. Phys Chem Minerals 39:27–45

    Article  Google Scholar 

  • Carpenter MA (1981) Time–temperature transformation (TTT) analysis of cation disordering in omphacite. Contrib Petrol Mineral 8:433–440

    Google Scholar 

  • Carpenter MA, Domeneghetti MC, Tazzoli T (1990) Application of Landau theory to cation ordering in omphacite I: equilibrium behavior. Eur J Mineral 2:7–18

    Google Scholar 

  • Fei Y (1995) Thermal expansion. In: Ahrens JA (ed) AGU reference shelf, vol 2, pp 29–44

  • Finger LW, Ohashi Y (1976) The thermal expansion of diopside to 800°C and a refinement of the crystal structure at 700°C. Am Mineral 61:303–310

    Google Scholar 

  • Gavrilenko P, Boffa Ballaran T, Kepler H (2010) The effect of Al and water on the compressibility of diopside. Am Mineral 95:608–616

    Article  Google Scholar 

  • Gottshalk M (1997) Internally consistent thermodynamic data forrock-forming minerals in the system SiO2-TiO2-Al2O3-Fe2O3-CaO-MgO-FeO-K2O-Na2O-H2O-CO2. Eur J Mineral 9:175–223

    Google Scholar 

  • Hawthorne FC, Ungaretti L, Oberti R (1995) Site populations in minerals: terminology and presentation of results of crystal-structure refinement. Can Mineral 33:907–911

    Google Scholar 

  • Holland TJB, Powell R (1998) An internally consistentthermodynamic data set for phases of petrological interest. J Metamorph Geol 16:309–343

    Article  Google Scholar 

  • King HE, Finger LW (1979) Diffracted beam crystal centering and its application to high-pressure crystallography. J Appl Cryst 12:374–378

    Article  Google Scholar 

  • Knight KS (1996) A neutron powder diffraction determination of the thermal expansion tensor of crocoite (PbCrO4) between 60 K and 290 K. Mineral Mag 60:963–972

    Article  Google Scholar 

  • McCormick TC, Hazen RM, Angel RJ (1989) Compressibility of omphacite to 60 kbar: role of vacancies. Am Mineral 74:1287–1292

    Google Scholar 

  • Miletich R, Allan DR, and Kuhs WF (2000) High-pressure single-crystal techniques. In: Hazen RM, Downs RT (eds) High-temperature and high-pressure crystal chemistry. Rev Min Geochem, vol 41, pp 445–519

  • Nestola F, Tribaudino M, Ballaran Boffa T (2004) High pressure behavior transformation and crystal structure of synthetic iron-free pigeonite. Am Mineral 89:189–196

    Google Scholar 

  • Nestola F, Boffa Ballaran T, Liebske C, Bruno M, Tribaudino M (2006) High-pressure behaviour along the jadeite NaAlSi2O6–aegirine NaFeSi2O6 solid solution up to 10 GPa. Phys Chem Mineral 33:417–425

    Article  Google Scholar 

  • Nestola F, Longo M, McCammon C (2007) Crystal-structure refinement of Na-bearing clinopyroxenes from mantle-derived eclogite xenoliths. Am Mineral 92:1242–1245

    Article  Google Scholar 

  • Nestola F, Boffa Ballaran T, Liebske C, Thompson R, Downs RT (2008) The effect of the hedenbergitic substitution on the compressibility of jadeite. Am Mineral 93:1005–1013

    Article  Google Scholar 

  • Nestola F, Nimis P, Ziberna L, Longo M, Marzoli A, Harris JW, Manghnani MH, Fedortchouk Y (2011) First crystal-structure determination of olivine in diamond: composition and implications for provenance in the Earth’s mantle. Earth Planet Sci Lett 305:249–255

    Article  Google Scholar 

  • Nishihara Y, Takahashi E, Matsukage K, Kikegawa T (2003) Thermal equation of state of omphacite. Am Mineral 88:80–86

    Google Scholar 

  • Pandolfo F, Nestola F, Cámara F, Domeneghetti MC (2012) High-pressure behavior of P2/n omphacite. Am Mineral (in press)

  • Pavese A, Bocchio R, Ivaldi G (2000) In situ high temperature single crystal X-ray diffraction study of a natural omphacite. Mineral Mag 64:983–993

    Article  Google Scholar 

  • Pavese A, Diella V, Levy D, Hanfland M (2001) Syncrotron X-ray powder diffraction study of natural P2/n omphacities at high pressure conditions. Phys Chem Minerals 28:9–16

    Google Scholar 

  • Pouchou JL, Pichoir F (1991) Quantitative analysis of homogeneous or stratified microvolumes applying the model “PAP”. In: Heinrich KFJ, Newbury DE (eds) Electron probe quantitation. Plenum Press, New York, pp 31–75

    Google Scholar 

  • Ralph RL, Finger LW (1982) A computer program for refinement of crystal orientation matrix and lattice constraints from diffractometer data with lattice symmetry constraints. J Appl Cryst 15:537–539

    Article  Google Scholar 

  • Redhammer GJ, Cámara F, Alvaro M, Nestola F, Tippelt G, Prinz S, Simmons J, Roth G, Amthauer G (2010) Thermal expansion and high-temperature P21/c-C2/c phase transition in clinopyroxene-type LiFeGe2O6 and comparison to NaFe(Si, Ge)2O6. Phys Chem Min 37:685–704

    Article  Google Scholar 

  • Sheldrick GM (1996) SADABS, a program for absorption correction with the siemens SMART system. University of Gottingen, Gottingen

    Google Scholar 

  • Sheldrick GM (1997) SHELX, programs for crystal structure analysis (Release 97-2). Institüt für Anorganische Chemie der Universität, Tammanstrasse 4, D-3400 Göttingen, Germany

  • Tribaudino M, Nestola F, Bruno M, Boffa Ballaran T, Liebske C (2008) Thermal expansion along the NaAlSi2O6–NaFe3+Si2O6 and NaAlSi2O6–CaFe2+Si2O6 solid solutions. Phys Chem Minerals 35:241–248

    Google Scholar 

  • Wilson AJC (1995) International tables for crystallography, vol C. Kluwer, Dordrecht

    Google Scholar 

Download references

Acknowledgments

Roberto Gastoni CNR-Pavia is thanked for sample preparation for EMPA analyses, and R. Carampin of CNR-Padova is thanked for help with the WDS electron microprobe facilities. This work was funded by the Italian Ministry of University and Research (MIUR) and by F.A.R. of the University of Pavia. The paper benefited from the critical reviews of two anonymous reviewers.

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Correspondence to Francesco Pandolfo.

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Pandolfo, F., Nestola, F., Cámara, F. et al. New thermoelastic parameters of natural C2/c omphacite. Phys Chem Minerals 39, 295–304 (2012). https://doi.org/10.1007/s00269-012-0484-1

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  • DOI: https://doi.org/10.1007/s00269-012-0484-1

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