Physics and Chemistry of Minerals

, Volume 32, Issue 8–9, pp 646–654 | Cite as

Pressure sensitivity of olivine slip systems: first-principle calculations of generalised stacking faults

  • J. Durinck
  • A. Legris
  • P. Cordier
Original Paper


We have used a first-principle approach based on the calculation of generalised stacking faults (GSF) to study the influence of pressure on the mechanical properties of forsterite. Six cases corresponding to [100] glide over (010), (021) and (001), and [001] glide over (100), (010) and (110) have been considered. The relaxed energy barriers associated with plastic shear have been calculated by constraining the Si atoms to move perpendicular to the fault plane and allowing Mg and O atoms to move in every direction. These conditions, which preserve dilations as a relaxation process, introduce Si–O tetrahedral tilting as an additional relaxation mechanism. Relaxed GSF show little plastic anisotropy of [100] glide over different planes and confirms that [001] glide is intrinsically easier than [100] glide. The GSF are affected by the application of a 10 GPa confining pressure with a different response for each slip system that cannot be explained by sole elastic effect. In particular, [100](010) is found to harden significantly under pressure compared to [001](010). Our results give the first theoretical framework to understand the pressure-induced change of dominant slip systems observed by Couvy et al. (in Eur J Mineral 16(6):877–889, 2004) and P. Raterron et al. (in GRL, submitted). It appears necessary to account for the influence of pressure on the mechanical properties of silicates in the context of the deep Earth.


Forsterite Pressure Plastic deformation Slip systems First-principle 



This work was supported by CNRS-INSU under the DyETI program. Computational resources have been provided by IDRIS (project # 031685) and CRI-USTL supported by the Fonds Européens de Développement Régional. Detailed reviews from S. Hier-Majumder and an anonymous reviewer are gratefully acknowledged.


  1. Alfe D, Kresse G, Gillan MJ (2000) Structure and dynamics of liquid iron under Earth’s core conditions. Phys Rev B 61:132–142CrossRefGoogle Scholar
  2. Bai Q, Mackwell SJ, Kohlstedt DL (1991) High-temperature creep of olivine single crystals. 1. Mechanical results for buffered samples. J Geophys Res 96(B2):2441–2463Google Scholar
  3. Bai Q, Kohlstedt DL (1992a) High-temperature creep of olivine single crystals. 2. Dislocation structures. Tectonophysics 206:1–29CrossRefGoogle Scholar
  4. Bai Q, Kohlstedt DL (1992b) High-temperature creep of olivine single crystals. 3. Mechanical results for unbuffered samples and creep mechanisms. Phil Mag A 66(6):1149–1181CrossRefGoogle Scholar
  5. Bai Q, Kohlstedt DL (1993) Effects of chemical environment on the solubility and incorporation mechanism for hydrogen in olivine. Phys Chem Mineral 19:460–471Google Scholar
  6. Barron TH, Klein ML (1965) Second-order elastic constants of a solid under stress. Proc Phys Soc 85:523–532CrossRefGoogle Scholar
  7. Blacic JD, Christie JM (1973) Dislocation substructure in experimentally deformed olivine. Contrib Mineral Petrol 42:141–146CrossRefGoogle Scholar
  8. Chopra PN, Paterson MS (1981) The experimental deformation of dunite. Tectonophysics 78:453–473CrossRefGoogle Scholar
  9. Chopra PN, Paterson MS (1984) The role of water in the deformation of dunite. J Geophys Res 89(B9):7861–7876Google Scholar
  10. Cordier P, Rubie DC (2001) Plastic deformation of minerals under extreme pressure using a multi-anvil apparatus. Mater Sci Eng A Struct Mater 309:38–43CrossRefGoogle Scholar
  11. Cordier P, Barbe F, Durinck J, Tommasi A, Walker AM (2005) Plastic deformation of minerals at high pressure: multiscale numerical modelling. In: Miletich R (ed) Mineral behaviour at extreme conditions. EMU Notes in Mineralogy, vol 7, BudapestGoogle Scholar
  12. Couvy H et al (2004) Shear deformation experiments of forsterite at 11 GPa–1400°C in the multianvil apparatus. Eur J Mineral 16(6):877–889CrossRefGoogle Scholar
  13. Darot M, Gueguen Y (1981) High-temperature creep of forsterite single crystals. J Geophys Res 86(B7):6219–6234CrossRefGoogle Scholar
  14. Darot M (1980) Déformation expérimentale de l’olivine et de la forsterite. Doctorat d’Etat es Sciences Thesis, Université de Nantes, Nantes, p 80Google Scholar
  15. Domain C, Besson R, Legris A (2004) Atomic-scale ab initio study of the Zr-H system: II. Interaction of H with plane defects and mechanical properties. Acta Materialia 52:1495–1502CrossRefGoogle Scholar
  16. Durham WB, Goetze C, Blake B (1977) Plastic flow of oriented single crystals of olivine. 2. Observations and interpretations of the dislocation structures. J Geophys Res 82(36):5755–5770Google Scholar
  17. Durham WB, Goetze C (1977) Plastic flow of oriented single crystals of olivine. 1. Mechanical data. J Geophys Res 82(36):5737–5753Google Scholar
  18. Durinck J, Legris A, Cordier P (2005) Influence of crystal chemistry on ideal shear strength of forsterite: first principles calculations. Am Mineral (in press)Google Scholar
  19. Gaboriaud R-J, Darot M, Gueguen Y, Woirgard J (1981) Dislocations in olivine indented at low temperatures. Phys Chem Mineral 7:100–104CrossRefGoogle Scholar
  20. Gaboriaud R-J (1986) Dislocations in olivine single crystals indented between 25 and 1100°C. Bull Mineral 109:185–191Google Scholar
  21. Hartford J, von Sydow B, Wahnström G, Lundqvist BI (1998) Peierls barrier and stresses for edge dislocations in Pd and Al calculated from first principles. Phys Rev B 58(5):2487–2496CrossRefGoogle Scholar
  22. Hirth G, Kohlstedt DL (1995a) Experimental constraints on the dynamics of the partially molten upper mantle. Deformation in the diffusion creep regime. J Geophys Res 100:1981–2001CrossRefGoogle Scholar
  23. Hirth G, Kohlstedt DL (1995b) Experimental constraints on the dynamics of the partially molten upper mantle: 2. Deformation in the dislocation creep regime. J Geophys Res 100(15):441–449Google Scholar
  24. Karato S, Paterson MS, Fitz Gerald JD (1986) Rheology of synthetic olivine aggregates: influence of grain size and water. J Geophys Res 91:8151–8176CrossRefGoogle Scholar
  25. Karato S, Rubie DC (1997) Toward an experimental study of deep mantle rheology: a new multianvil sample assembly for deformation studies under high pressures and temperatures. J Geophys Res Solid Earth 102(B9):20111–20122CrossRefGoogle Scholar
  26. Kiefer B, Stixrude L, Hafner J, Kresse G (2001) Structure and elasticity of wadsleyite at high pressures. Am Mineral 86(11–12):1387–1395Google Scholar
  27. Kohlstedt DL, Goetze C (1974) Low-stress high-temperature creep in olivine single crystals. J Geophys Res 79(14):2045–2051CrossRefGoogle Scholar
  28. de Koning M, Antonelli A, Bazant MZ, Kaxiras E, Justo JF (1998) Finite-temperature molecular-dynamics study of unstable stacking fault free energies in silicon. Phys Rev B Condensed Matter 58(19):12555–12558Google Scholar
  29. Krenn CR, Roundy D, Morris JW Jr, Cohen ML (2001) The nonlinear elastic behavior and ideal shear strength of Al and Cu. Material Sci Eng A 317:44–48CrossRefGoogle Scholar
  30. Kresse G, Furthmüller J (1996a) Efficiency of ab initio total energy calculations for metals and semiconductors using a plane-wave basis set. Comput Mat Sci 6:15–50CrossRefGoogle Scholar
  31. Kresse G, Furthmüller J (1996b) Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys Rev B 54:11169CrossRefGoogle Scholar
  32. Kresse G, Hafner J (1993) Ab initio molecular dynamics for liquid metals. Phys Rev B 47:558CrossRefGoogle Scholar
  33. Kresse G, Hafner J (1994a) Ab initio molecular dynamics simulation of the liquid-metal amorphous-semiconductor transition in germanium. Phys Rev B 49:14251CrossRefGoogle Scholar
  34. Kresse G, Hafner J (1994b) Norm-conserving and ultrasoft pseudopotentials for first-row and transition elements. J Phys Condens Mat 6:8245CrossRefGoogle Scholar
  35. Kresse G, Joubert D (1999) From ultrasoft pseudopotentials to the projector augmented-wave method. Phys Rev B 59:1758–1775CrossRefGoogle Scholar
  36. Mackwell SJ, Kohlstedt DL, Paterson MS (1985) The role of water in the deformation of olivine single crystals. J Geophys Res 90(B13):11319–11333Google Scholar
  37. Mainprice D, Tommasi A, Couvy H, Cordier P, Frost D (2005) Pressure sensitivity of olivine slip systems and seismic anisotropy of Earth’s upper mantle. Nature 433:731–733CrossRefPubMedGoogle Scholar
  38. Medvedeva NI, Mryasov ON, Gornostyrev YN, Novikov DL, Freeman AJ (1996) First-principles total-energy calculations for planar shear and cleavage decohesion processes in B2-ordered NiAl and FeAl. Phys Rev B 54(19):13506–13514CrossRefGoogle Scholar
  39. Mei S, Kohlstedt DL (2000a) Influence of water on plastic deformation of olivine aggregates 1. Diffusion creep regime. J Geophys Res Solid Earth 105(B9):21457–21469CrossRefGoogle Scholar
  40. Mei S, Kohlstedt DL (2000b) Influence of water on plastic deformation of olivine aggregates 2. Dislocation creep regime. J Geophys Res Solid Earth 105(B9):21471–21481CrossRefGoogle Scholar
  41. Monkhorst HJ, Pack JD (1976) Special points for Brillouin-zone integrations. Phys Rev B 23:5048–5192Google Scholar
  42. Mryasov ON, Gornostyrev YN, Freeman AJ (1998) Generalized stacking-fault energetics and dislocation properties: compact versus spread unit-dislocation structures in TiAl and CuAu. Phys Rev B Condensed Matter 58(18):11927–11932Google Scholar
  43. Paxton AT, Gumbsch P, Methfessel M (1991) A quantum mechanical calculation of the theoretical strength of metals. Philos Mag Lett 63(5):267–274CrossRefGoogle Scholar
  44. Perdew JP, Burke K, Ernzerhof M (1996) Generalized gradient approximation made simple. Phys Rev Lett 18:3865–3868CrossRefGoogle Scholar
  45. Perdew JP, Wang Y (1992) Accurate and simple analytic representation of the electron-gas correlation energy. Phys Rev B 45:13244–13249CrossRefGoogle Scholar
  46. Phakey P, Dollinger G, Christie JM (1972) Transmission electron microscopy of experimentally deformed olivine crystals. Geophys Monogr Ser Flow Fract Rock 13:117–133Google Scholar
  47. Roundy D, Krenn CR, Cohen ML, Morris JW Jr (1999) Ideal shear strengths of fcc aluminum and copper. Phys Rev Lett 82(13):2713–2716CrossRefGoogle Scholar
  48. da Silva C, Stixrude L, Wentzcovitch RM (1997) Elastic constants and anisotropy of forsterite at high pressure. Geophys Res Lett 24(15):1963–1966CrossRefGoogle Scholar
  49. Sun Y, Kaxiras E (1997) Slip energy barrier in aluminum and implications for ductile-brittle behaviour. Philos Mag A 75(4):1117–1127CrossRefGoogle Scholar
  50. Söderlind P, Moriarty JA (1998) First-principles theory of Ta up to 10 Mbar pressure: Structural and mechanical properties. Phys Rev B 57(17):10340–10350CrossRefGoogle Scholar
  51. Vanderbilt D (1990) Soft self-consistent pseudopotentials in a generalized eigenvalue formalism. Phys Rev B 41:7892–7895CrossRefGoogle Scholar
  52. Vítek V (1974) Theory of the core structures of dislocations in body-centered-cubic metals. Cryst Lattice Defects 5:1–34Google Scholar
  53. Wang Y, Durham WB, Getting I, Weidner DJ (2003) The deformation-DIA: a new apparatus for high-temperature triaxial deformation to pressures up to 15 GPa. Rev Sci Instrum 74(6):3002–3011CrossRefGoogle Scholar
  54. Yamazaki D, Karato S (2001) High-pressure rotational deformation apparatus to 15 GPa. Rev Sci Instrum 72:4207–4211CrossRefGoogle Scholar
  55. Zha C-S, Duffy TS, Mao HK, HemPey R, Weidner D (1998) Single-crystal elasticity of the α and β Mg2SiO4 polymorphs at high pressure. In: Manghnani MH, Yagi T (eds) Properties of earth and planetary materials at high pressure and temperature geophysical monograph series. AGU, Washington, pp 9–16Google Scholar

Copyright information

© Springer-Verlag 2005

Authors and Affiliations

  1. 1.Laboratoire de Structure et Propriétés de l’Etat Solide - UMR CNRS 8008Université des Sciences et Technologies de Lille - Bat C6Villeneuve d’Ascq CedexFrance
  2. 2.Laboratoire de Métallurgie Physique et Génie des Matériaux, UMR CNRS 8517Université des Sciences et Technologies de LilleVilleneuve d’Ascq CedexFrance

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