Physics and Chemistry of Minerals

, Volume 36, Issue 4, pp 233–239 | Cite as

Peierls dislocation modelling in perovskite (CaTiO3): comparison with tausonite (SrTiO3) and MgSiO3 perovskite

  • Denise Ferré
  • Philippe Carrez
  • Patrick Cordier
Original Paper


We present here a numerical modelling study of dislocations in perovskite CaTiO3. The dislocation core structures and properties are calculated through the Peierls–Nabarro model using the generalized stacking fault (GSF) results as a starting model. The GSF are determined from first-principles calculations using the VASP code. The dislocation properties such as collinear, planar core spreading and Peierls stresses are determined for the following slip systems: [100](010), [100](001), [010](100), [010](001), [001](100), [001](010), \( [001](\bar{1}10), \) \( [\bar{1}10](001) \) and \( [110](\bar{1}10). \) All dislocations exhibit lattice friction, but glide appears to be easier for \( [\bar{1}10](001), \) [100](010) and [010](100). \( [110](\bar{1}10), \) \( [\bar{1}10](001), \) \( [001](\bar{1}10), \) [001](010) and [001](100) exhibit collinear dissociation. Comparing Peierls stresses among tausonite (SrTiO3), perovskite (CaTiO3) and MgSiO3 perovskite demonstrates the strong influence of orthorhombic distortions on lattice friction. However, and despite some quantitative differences, CaTiO3 appears to be a satisfactory analogue material for MgSiO3 perovskite as far as dislocation glide is concerned.


CaTiO3 Perovskite Deformation mechanisms Dislocations Slip systems First-principle calculations PeierlsNabarro model 



Computational resources have been provided by IDRIS (project # 081685) and CRI-USTL supported by the Fonds Européens de Développement Régional and Région Nord—Pas de Calais.


  1. Beauchesne S, Poirier JP (1989) Creep of barium titanate perovskite: a contribution to a systematic approach to the viscosity of the mantle. Phys Earth Planet Inter 55:187–199. doi: 10.1016/0031-9201(89)90242-2 CrossRefGoogle Scholar
  2. Beauchesne S, Poirier JP (1990) In search of a systematics for the viscosity of perovskites: creep of potassium tantalate and niobate. Phys Earth Planet Inter 61:182–198. doi: 10.1016/0031-9201(90)90105-7 CrossRefGoogle Scholar
  3. Besson P, Poirier JP, Price GD (1996) Dislocations in CaTiO3 perovskite deformed at high temperature: a transmission electron microscopy study. Phys Chem Miner 23:337–344. doi: 10.1007/BF00199499 CrossRefGoogle Scholar
  4. Blöchl PE (1994) Projector augmented-wave method. Phys Rev B 50:17953–17979. doi: 10.1103/PhysRevB.50.17953 CrossRefGoogle Scholar
  5. Carrez P, Ferre D, Cordier P (2007) Peierls–Nabarro model for dislocations in MgSiO3 post-perovskite calculated at 120 GPa from first principles. Philos Mag 87:3229–3247. doi: 10.1080/14786430701268914 CrossRefGoogle Scholar
  6. Chen JH, Weidner DJ, Vaughan MT (2002) The strength of Mg0.9 Fe0.1 SiO3 perovskite at high pressure and temperature. Nature 419:824–826. doi: 10.1038/nature01130 CrossRefGoogle Scholar
  7. Christian JW, Vitek V (1970) Dislocations and stacking faults. Rep Prog Phys 33:307–411. doi: 10.1088/0034-4885/33/1/307 CrossRefGoogle Scholar
  8. Cordier P, Ungár T, Zsoldos L, Tichy G (2004) Dislocation creep in MgSiO3 Perovskite at conditions of the Earth’s uppermost lower mantle. Nature 428:837–840. doi: 10.1038/nature02472 CrossRefGoogle Scholar
  9. Doukhan N, Doukhan JC (1986) Dislocations in perovskites BaTiO3 and CaTiO3. Phys Chem Miner 13:403–410Google Scholar
  10. Ferré D, Carrez P, Cordier P (2007) First principles determination of dislocations properties of MgSiO3 perovskite at 30 GPa based on the Peierls–Nabarro model. Phys Earth Planet Inter 163:283–291. doi: 10.1016/j.pepi.2007.05.011 CrossRefGoogle Scholar
  11. Ferré D, Carrez P, Cordier P (2008a) Modeling dislocation cores in SrTiO3 using the Peierls–Nabarro model. Phys Rev B 77:014106. doi: 10.1103/PhysRevB.77.014106 CrossRefGoogle Scholar
  12. Ferré D, Carrez P, Cordier P (2008b) Dislocation modelling in calcium silicate perovskite based on the Peierls–Nabarro model. Am Mineral (in press). doi: 10.2138/am.2009.3003
  13. Frost HJ, Ashby MF (1982) Deformation-mechanism maps. Pergamon Press, OxfordGoogle Scholar
  14. Hirth JP, Lothe J (1982) Theory of dislocations. Wiley, New YorkGoogle Scholar
  15. Joos B, Ren Q, Duesbery MS (1994) Peierls–Nabarro model of dislocations in silicon with generalized stacking-fault restoring forces. Phys Rev B 50:5890–5898. doi: 10.1103/PhysRevB.50.5890 CrossRefGoogle Scholar
  16. Kresse G, Furthmüller J (1996a) Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys Rev B 54:11169–11186. doi: 10.1103/PhysRevB.54.11169 CrossRefGoogle Scholar
  17. Kresse G, Furthmüller J (1996b) Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set. Comput Mater Sci 6:15–50. doi: 10.1016/0927-0256(96)00008-0 CrossRefGoogle Scholar
  18. Kresse G, Hafner J (1993) Ab initio molecular dynamics for liquid metals. Phys Rev B 47:558. doi: 10.1103/PhysRevB.47.558 CrossRefGoogle Scholar
  19. Kresse G, Hafner J (1994) Ab initio molecular dynamics simulation of the liquid-metal amorphous-semiconductor transition in germanium. Phys Rev B 49:14251–14269. doi: 10.1103/PhysRevB.49.14251 CrossRefGoogle Scholar
  20. Kresse G, Joubert D (1999) From ultrasoft pseudopotentials to the projector augmented-wave method. Phys Rev B 59:1758–1775. doi: 10.1103/PhysRevB.59.1758 CrossRefGoogle Scholar
  21. Merkel S, Wenk HR, Badro J et al (2003) Deformation of (Mg0.9, Fe0.1)SiO3 Perovskite aggregates up to 32 GPa. Earth Planet Sci Lett 209:351–360. doi: 10.1016/S0012-821X(03)00098-0 CrossRefGoogle Scholar
  22. Mitchell RH (2002) Perovskites: modern and ancient. Almaz Press, Thunder BayGoogle Scholar
  23. Monkhorst HJ, Pack JD (1976) Special points for Brillouin-zone integrations. Phys Rev B 23:5048–5192Google Scholar
  24. Miyajima N, Yagi T, Ichihara M (2008) Dislocation microstructures of MgSiO3 perovskite at a high pressure and temperature condition. Phys Earth Planet Inter (in press). doi: 10.1016/j.pepi.2008.04.004
  25. Nabarro FRN (1947) Dislocations in a simple cubic lattice. Proc Phys Soc Lond 59:256–272. doi: 10.1088/0959-5309/59/2/309 CrossRefGoogle Scholar
  26. Nishigaki J, Kuroda K, Saka H (1991) Electron microscopy of dislocation structures in SrTiO3 deformed at high temperatures. Phys Status Solidi 128:319–336. doi: 10.1002/pssa.2211280207 CrossRefGoogle Scholar
  27. Peierls RE (1940) On the size of a dislocation. Proc Phys Soc Lond 52:34–37. doi: 10.1088/0959-5309/52/1/305 CrossRefGoogle Scholar
  28. Perdew JP, Wang Y (1992) Accurate and simple analytic representation of the electron-gas correlation energy. Phys Rev B 45:13244–13249. doi: 10.1103/PhysRevB.45.13244 CrossRefGoogle Scholar
  29. Poirier JP, Peyronneau J, Gesland JY, Brebec G (1983) Viscosity and conductivity of the lower mantle; an experimental study on a MgSiO3 perovskite analogue, KZnF3. Phys Earth Planet Inter 32:273–287. doi: 10.1016/0031-9201(83)90131-0 CrossRefGoogle Scholar
  30. Poirier JP, Beauchesne S, Guyot F (1989) Deformation mechanisms of crystals with perovskite structure. In: Navrotsky A, Weidner D (eds) Perovskite: a structure of great interest to geophysics and materials science. AGU, Washington DC, pp 119–123Google Scholar
  31. Schoeck G (2005) The Peierls model: progress and limitations. Mater Sci Eng A 400–401:7–17. doi: 10.1016/j.msea.2005.03.050 Google Scholar
  32. Vítek V (1968) Intrinsic stacking faults in body-centered cubic crystals. Philos Mag 18:773–786. doi: 10.1080/14786436808227500 CrossRefGoogle Scholar
  33. Wang Y, Liebermann RC (1993) Electron microscopy study of domain structure due to phase transitions in natural perovskite. Phys Chem Miner 20:147–158. doi: 10.1007/BF00200117 CrossRefGoogle Scholar
  34. Wang Y, Poirier JP, Liebermann RC (1989) Dislocation dissociation in CaGeO3 perovskite. Phys Chem Miner 16:630–633. doi: 10.1007/BF00223310 CrossRefGoogle Scholar
  35. Wang ZC, Dupas-Bruzek C, Karato S (1999) High temperature creep of an orthorhombic perovskite—YAlO3. Phys Earth Planet Inter 110:51–69. doi: 10.1016/S0031-9201(98)00130-7 CrossRefGoogle Scholar
  36. Wang ZC, Karato S, Fujino K (1993) High temperature creep of single crystal strontium titanate (SrTiO3)—a contribution to creep systematics in perovskites. Phys Earth Planet Inter 79:299–312. doi: 10.1016/0031-9201(93)90111-L CrossRefGoogle Scholar
  37. Wenk HR, Lonardelli I, Pehl J et al (2004) In situ observation of texture development in olivine, ringwoodite, magnesiowüstite and silicate perovskite. Earth Planet Sci Lett 226:507–519. doi: 10.1016/j.epsl.2004.07.033 CrossRefGoogle Scholar
  38. Wright K, Price GD, Poirier JP (1992) High-temperature creep of the perovskites CaTiO3 and NaNbO3. Phys Earth Planet Inter 74:9–22. doi: 10.1016/0031-9201(92)90064-3 CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  • Denise Ferré
    • 1
  • Philippe Carrez
    • 1
  • Patrick Cordier
    • 1
  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

Personalised recommendations