Physics and Chemistry of Minerals

, Volume 37, Issue 6, pp 343–351 | Cite as

Compressibility of nanocrystalline forsterite

  • Hélène CouvyEmail author
  • Jiuhua Chen
  • Vadym Drozd
Original Paper


We established an equation of state for nanocrystalline forsterite using multi-anvil press and diamond anvil cell. Comparative high-pressure and high-temperature experiments have been performed up to 9.6 GPa and 1,300°C. We found that nanocrystalline forsterite is more compressible than macro-powder forsterite. The bulk modulus of nanocrystalline forsterite is equal to 123.3 (±3.4) GPa whereas the bulk modulus of macro-powder forsterite is equal to 129.6 (±3.2) GPa. This difference is attributed to a weakening of the elastic properties of grain boundary and triple junction and their significant contribution in nanocrystalline sample compare to the bulk counterpart. The bulk modulus at zero pressure of forsterite grain boundary was determined to be 83.5 GPa.


Equation of state Nanocrystalline mineral High-pressure high-temperature experiments Subducting slab 



Research is supported by NSF research grant EAR-0711321. The authors would like to gracefully thank S-I. Karato for his useful comments. H.C. would like to thank V. Musaramthota for his help in the synthesis of nc-Fo sample. Use of the National Synchrotron Light Source, Brookhaven National Laboratory, was supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under Contract No. DE-AC02-98CH10886. Use of the X17B2 and X17B3 beamlines were supported by COMPRES, the Consortium for Materials Properties Research in Earth Sciences under NSF Cooperative Agreement EAR 01-35554 and by the Mineral Physics Institute, Stony Brook University.


  1. Ahuja R, Osorio-Guillen MJ, Souza de Almeida J, Holm B et al (2004) Electronic and optical properties of γ-Al2O3 from ab initio theory. J Phys Condens Matter 16:2891–2900CrossRefGoogle Scholar
  2. Anderson OL, Isaak DG (1995) Elastic constants of mantle minerals at high temperature. In: Ahrens TJ (ed) Mineral physics and crystallography: a handbook of physical constants. American Geophysical Union, Washington DC, pp 64–97Google Scholar
  3. Andrault D, Bouhifd MA, Itié JP, Richet P (1995) Compression and amorphization of (Mg, Fe)2SiO4 olivines: an X-ray diffraction study up to 70 GPa. Phys Chem Miner 22(2):99–107CrossRefGoogle Scholar
  4. Angel RJ (2001) EOS-FITv5.2. Crystallography laboratory. Virginia Tech, BlackburgGoogle Scholar
  5. Baldwin K (1990) Plot85. Mineral Physics Institute, Stony Brook University, NYGoogle Scholar
  6. Brodholt J, Patel A, Refson K (1996) An ab initio study of the compressional behavior of forsterite. Amer Miner 81:257–260Google Scholar
  7. Burnley PC, Green HW II, Prior DJ (1991) Faulting associated with the olivine to spinel transformation in Mg2GeO4 and its implications for deep-focus earthquakes. J Geophys Res 96(B1):425–443CrossRefGoogle Scholar
  8. Chen J, Schmidt N, Chen JH, Wang LP et al (2005) Yield strength enhancement of MgO by nanocrystals. J Mater Sci 40(21):5763–5766CrossRefGoogle Scholar
  9. Decker DJ (1965) Equation of state of NaCl and its use as a pressure gauge in high-pressure research. J Appl Phys 36(1):157–161CrossRefGoogle Scholar
  10. Decker DL (1971) High-pressure equation of state for NaCl, KCl and CsCl. J Appl Phys 42(8):3239–3244CrossRefGoogle Scholar
  11. Ehm L, Michel FM, Antao SM, Martin CD et al (2009) Structural changes in nanocrystalline mackinawite (FeS) at high pressure. J Appl Cryst 42:15–21CrossRefGoogle Scholar
  12. Erb U (1995) Electrodeposited nanocrystals: synthesis, properties and industrial applications. Nanostruct Mater 6:533–538CrossRefGoogle Scholar
  13. Fei Y (1995) Thermal expansion. In: Ahrens TJ (ed) Mineral physics and crystallography: a handbook of physical constants. American Geophysical Union, Washington DC, pp 29–44Google Scholar
  14. Frost HJ, Ashby MF (1982) Deformation-mechanism map. Pergamon Press, OxfordGoogle Scholar
  15. Gerward L, Morup S, Topsoe H (1976) Particle size and strain broadening in energy-dispersive X-ray powder patterns. J Appl Phys 47(3):822–825CrossRefGoogle Scholar
  16. Green HW II, Burnley PC (1989) A new self-organizing mechanism for deep-focus earthquakes. Nature 341:733–737CrossRefGoogle Scholar
  17. Hochella MF, Lower SK, Maurice PA, Penn RL et al (2008) Nanominerals, mineral nanoparticles, and earth systems. Science 319:1631–1635CrossRefGoogle Scholar
  18. Isaak DG, Anderson OL, Goto T (1989) Elasticity of single-crystal forsterite measured to 1700 K. J Geophys Res 94(B5):5895–5906CrossRefGoogle Scholar
  19. Karato S-I (1998) Seismic anisotropy in the deep mantle, boundary layers and the geometry of mantle convection. Pure Appl Geophys 151:565–587CrossRefGoogle Scholar
  20. Karato S-I, Dupas-Bruzek C, Rubie DC (1998) Plastic deformation of silicate spinel under the transition-zone conditions of the earth’s mantle. Nature 395:266–269CrossRefGoogle Scholar
  21. Katsura T, Shatskiy A, Manthilake MAGM, Zhai S et al (2008) Thermal expansion of forsterite at high pressures determined by in situ X-ray diffraction: the adiabatic geotherm in the upper mantle. Phys Earth Planet Inter 174:86–92CrossRefGoogle Scholar
  22. Kerschhofer L, Sharp TG, Rubie DC (1996) Intracrystalline transformation of olivine to wadsleyite and ringwoodite under subduction zone conditions. Science 274(5284):79–81CrossRefGoogle Scholar
  23. Kerschhofer L, Dupas C, Liu M, Sharp TG et al (1998) Polymorphic transformations between olivine, wadsleyite and ringwoodite: mechanisms of intracrystalline nucleation and the role of elastic strain. Miner Mag 62(5):617–638CrossRefGoogle Scholar
  24. Klotz S, Chervin J-C, Munsch P, Le Marchand G (2009) Hydrostatic limits of 11 pressure transmitting media. J Phys D Appl Phys 42Google Scholar
  25. Knittle E (1995) Static compression measurements of equations of state. In: Ahrens TJ (ed) Mineral physics and crystallography: a handbook of physical constants. American Geophysical Union, Washington DC, pp 98–142Google Scholar
  26. Kudoh Y, Takeuchi Y (1985) The crystal structure of forsterite Mg2SiO4 under high pressure up to 149 kb. Z Kristallogr 171:291–302Google Scholar
  27. Latapie A, Farkas D (2003) Effect of grain size on the elastic properties of nanocrystalline α-iron. Scripta Mater 48:611–615CrossRefGoogle Scholar
  28. Lutterotti L, Matthies S, Wenk HR (1999) MAUD: a friendly java program for material analysis using diffraction. IUCr: Newsletter of the CPD 21(14–15)Google Scholar
  29. Mao H-K, Bell PM, Dunn KJ, Chrenko RM et al (1979) Absolute pressure measurements and analysis of diamonds subjected to maximum static pressures of 1.3–1.7 Mbar. Rev Sci Instrum 50:1002CrossRefGoogle Scholar
  30. Mao H-K, Xu J, Bell PM (1986) Calibration of the ruby pressure gauge to 800 kbar under quasi-hydrostatic conditions. J Geophys Res 91:4673–4676CrossRefGoogle Scholar
  31. Mayo MJ, Siegel RW, Narayanasamy A, Nix WD (1990) Mechanical properties of nanophase TiO2 as determined by nanoindentation. J Mater Res 5(5):1073–1082CrossRefGoogle Scholar
  32. Mueller HJ, Schilling FR, Lauterjung J, Lather C (2003) A standard-free pressure calibration using simultaneous XRD and elastic property measurements in a multi-anvil device. Eur J Miner 15:865–873CrossRefGoogle Scholar
  33. Paul B (1960) Prediction of elastic constants of multiphase materials. Trans AIME 218:36–41Google Scholar
  34. Ricoult DL, Kohlstedt DL (1983) Structural width of low-angle grain boundaries in olivine. Phys Chem Miner 9:133–138CrossRefGoogle Scholar
  35. Riedel MR, Karato S-I (1997) Grain-size evolution in subducted oceanic lithosphere associated with the olivine-spinel transformation and its effects on rheology. Earth Planet Sci Lett 148:27–43CrossRefGoogle Scholar
  36. Rubie DC (1984) The olivine-spinel transformation and the rheology of subducting lithosphere. Nature 308:505–508CrossRefGoogle Scholar
  37. Saberi A, Alinejad B, Negahdari Z, Kazemi F et al (2007) A novel method to low temperature synthesis of nanocrystalline forsterite. Mater Res Bull 42:666–673CrossRefGoogle Scholar
  38. Shen TD, Koch CC, Tsui TY, Pharr GM (1995) On the elastic moduli of nanocrystalline Fe, Cu, Ni and Cu-Ni alloys prepared by mechanical milling/alloying. J Mater Res 10(11):2892–2896CrossRefGoogle Scholar
  39. Shen Y, Kumar RS, Pravica M, Nicol MF (2004) Characteristics of silicone fluid as a pressure transmitting medium in diamond anvil cells. Rev Sci Instrum 75(11):4450–4454CrossRefGoogle Scholar
  40. Van Swygenhoven H, Caro A (1998) Plastic behavior of nanophase metals studied by molecular dynamics. Phys Rev B 58(17):11246–11251CrossRefGoogle Scholar
  41. Vaughan PJ, Coe RS (1981) Creep mechanism in Mg2GeO4: effects of a phase transition. J Geophys Res 86(B1):389–404CrossRefGoogle Scholar
  42. Wang Y, Weidner DJ, Meng Y (1998) Advances in equation of state measurements in SAM-85. In: Manghnani MH, Yagi T (eds) Properties of earth and planetary materials at high pressure and temperature, geophysical monograph 101. American Geophysical Union, Washington DC, pp 365–372Google Scholar
  43. Wang Y, Zhang J, Zhao Y (2007) Strength weakening by nanocrystals in ceramic materials. Nano Lett 7(10):3196–3199CrossRefGoogle Scholar
  44. Weidner DJ, Vaughan MT, Ko J, Wang Y (1992) Characterization of stress, pressure and temperature in SAM85, a dia type high pressure apparatus. In: Syono Y, Manghnani MH et al (eds) High-pressure research; application of the earth and planetary sciences, geophysical monograph 67. American Geophysical Union, Washington DC, pp 13–17Google Scholar
  45. Weidner DJ, Wang Y, Vaughan MT (1994) Yield strength at high pressure and temperature. Geophys Res Lett 21(9):753–756CrossRefGoogle Scholar
  46. Wentzcovitch RM, Stixrude L (1997) Crystal chemistry of forsterite: a first-principles study. Amer Miner 82:663–671Google Scholar
  47. Will G, Hoffbauer W, Hinze E, Laurejung J (1986) The compressibility of forsterite up to 300 kbar measured with synchrotron radiation. Physica 139 and 140B: 193–197Google Scholar
  48. Willets FW (1965) An analysis of X-ray diffraction line profiles using standard deviation as a measure of breadth. Brit J Appl Phys 16:323–333CrossRefGoogle Scholar
  49. Wilson B, Dewers T, Reches Z, Brune J (2005) Particle size and energetics of gouge from earthquake rupture zones. Nature 434:749–752CrossRefGoogle Scholar
  50. Yamazaki D, Inoue T, Okamoto M, Irifune T (2005) Grain growth kinetics of ringwoodite and its implication for rheology of the subduction slab. Earth Planet Sci Lett 236:871–881CrossRefGoogle Scholar
  51. Yeheskel O, Chaim R, Shen Z, Nygren M (2004) Elastic moduli of grain boundaries in nanocrystalline MgO ceramics. J Mater Res 20(3):719–725CrossRefGoogle Scholar
  52. Zha C-S, Duffy TS, Downs RT, Mao H-K et al (1996) Sound velocity and elasticity of single-crystal forsterite to 16 GPa. J Geophys Res 101(B8):17535–17545CrossRefGoogle Scholar
  53. Zha C-S, Duffy TS, Downs RT, Mao H-K et al (1998a) Brillouin scattering and X-ray diffraction of San Carlos olivine: direct pressure determination to 32 GPa. Earth Planet Sci Lett 159:25–33CrossRefGoogle Scholar
  54. Zha C-S, Duffy TS, Downs RT, Mao H-K (1998b) Single-crystal elasticity of the alpha and beta of Mg2SiO4 polymorphs at high pressure. In: Manghnani MH, Yagi T et al (eds) Properties of earth and planetary materials at high pressure and temperature. American Geophysical Union, Washington DC, pp 9–16Google Scholar
  55. Zhao Z, Hearne GR, Maaza M, Laher-Lacour F et al (2001) Compressibility of nanostructured alumina phases determined from synchrotron X-ray diffraction studies at high pressure. J Appl Phys 90(7):3280–3285CrossRefGoogle Scholar
  56. Zhao S-J, Albe K, Hahn H (2006) Grain size dependence of the bulk modulus of nanocrystalline nickel. Scripta Mater 55:473–476CrossRefGoogle Scholar
  57. Zhao Y, Zhang Y, Clausen B, Shen TD et al (2007) Thermomechanics of nanocrystalline nickel under high pressure-temperature conditions. Nano Lett 72:426–432CrossRefGoogle Scholar
  58. Zhou Y, Erb U, Aust KT, Palumbo G (2003) The effects of triple junctions and grain boundaries on hardness and Young’s modulus in nanostructured Ni-P. Scripta Mater 48:825–830CrossRefGoogle Scholar
  59. Zhou Y, Erb U, Aust KT (2007) The role of interface volume fractions in the nanocrystalline to amorphous transition in fully dense materials. Phil Mag 87(36):5749–5761CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Department of Mechanical and Materials Engineering, The Center for the Study of Matter at Extreme ConditionsFlorida International UniversityMiamiUSA

Personalised recommendations