1932
0
  1. Home
  2. A-Z Publications
  3. Annual Review of Earth and Planetary Sciences
  4. Volume 45, 2017
  5. Article

Annual Review of Earth and Planetary Sciences

Volume 45, 2017

Interface Kinetics, Grain-Scale Deformation, and Polymorphism

Abstract

Deviatoric stress generated within subducting slabs by the olivine–spinel transformation has been modeled by assuming the phases to be simply connected rather than comprising a mixture in which one phase is embedded within another. Here, we use a simplified model to explain how transformation strain is incorporated into a continuum model, and we then use the simplified model to explain quantitatively the origin of the unreasonably large deviatoric stresses predicted by existing slab models. We review experiments on the transformation of single-crystal samples and argue that they are consistent with the occurrence, at the grain scale, of deviatoric stresses comparable with those predicted (erroneously) to exist at the slab scale by those slab models. Using a simple example, we show that although large deviatoric stresses can exist at the grain scale, their average over a sample containing many grains can be hydrostatic. This leads us to the problem of modeling the microscale structure. We outline the thermodynamics needed for such nonhydrostatic systems, and we illustrate their use and implications with examples.

Keyword(s): coherent and incoherent interfaces, mixed-phase region, olivine–spinel
Loading

Article metrics loading...

/content/journals/10.1146/annurev-earth-040610-133511
2017-08-30
2024-04-20
Loading full text...

Full text loading...

/deliver/fulltext/earth/45/1/annurev-earth-040610-133511.html?itemId=/content/journals/10.1146/annurev-earth-040610-133511&mimeType=html&fmt=ahah

Literature Cited

  1. Ashby MF. 1972. Boundary defects and atomistic aspects of boundary sliding and diffusional creep. Surf. Sci. 31:498–542 [Google Scholar]
  2. Bhattacharya K. 2003. Microstructure of Martensite New York: Oxford Univ. Press
  3. Bloor MIG, Wilson MJW. 2006. An approximate analytic solution method for the biharmonic problem. Proc. R. Soc. A 462:1107–21 [Google Scholar]
  4. Bos C, Sommer F, Mittemeijer EJ. 2005. An atomistic analysis of the interface mobility in a massive transformation. Acta Mater. 53:5333–41 [Google Scholar]
  5. Christian JW. 1965. The Theory of Transformations in Metals and Alloys Amsterdam: Pergamon, 1st ed..
  6. Devaux J-P, Fleitout L, Schubert G, Anderson C. 2000. Stresses in a subducting slab in the presence of a metastable olivine wedge. J. Geophys. Res. 105:B613365–73 [Google Scholar]
  7. Devaux J-P, Schubert G, Anderson C. 1997. Formation of a metastable olivine wedge in a descending slab. J. Geophys. Res. 102:B1124627–37 [Google Scholar]
  8. Diedrich T, Sharp TG, Leinenweber K, Holloway JR. 2009. The effect of small amounts of H2O on olivine to ringwoodite transformation growth rates and implications for subduction of metastable olivine. Chem. Geol. 262:87–99 [Google Scholar]
  9. Dolino G. 1990. The α-inc-β transitions of quartz: a century of research on displacive phase transitions. Phase Transit. 21:59–72 [Google Scholar]
  10. Du Frane WL, Sharp TG, Mosenfelder JL, Leinenweber K. 2013. Ringwoodite growth rates from olivine with ∼75 ppmw H2O: Metastable olivine must be nearly anhydrous to exist in the mantle transition zone. Phys. Earth Planet. Inter. 219:1–10 [Google Scholar]
  11. Eshelby JD. 1961. Elastic inclusions and inhomogeneities. Progress in Solid Mechanics 2 ed. IN Sneddon, R Hill 89–140 Amsterdam: North-Holland [Google Scholar]
  12. Frohlich C. 2006. Deep Earthquakes Cambridge, UK: Cambridge Univ. Press
  13. Fung YC. 1965. Foundations of Solid Mechanics Englewood Cliffs, NJ: Prentice-Hall
  14. Gibbs JW. 1928. On the equilibrium of heterogeneous substances. Collected Works of J. Willard Gibbs 1 WR Longley, RG Van Name New York: Longmans, Green and Co. [Google Scholar]
  15. Green HW. 1986. Phase transformation under stress and volume transfer creep. Mineral and Rock Deformation: Laboratory Studies: The Paterson Volume BE Hobbs, HC Heard 201–13 Geophys. Monogr. Ser. 36 Washington, DC: AGU [Google Scholar]
  16. Green HW, Young TE, Walker D, Scholz CH. 1992. The effect of non-hydrostatic stress on the α–β and α–γ phase transformations. High-Pressure Research: Application to Earth and Planetary Sciences Y Syono, MH Manghnani 229–35 Tokyo: Terra Sci./Am. Geophys. Union [Google Scholar]
  17. Grinfeld M. 1981. On heterogenous equilibrium of nonlinear elastic phases and chemical potential tensors. Lett. Appl. Eng. Sci. 19:1031–39 [Google Scholar]
  18. Guest A, Schubert G, Gable CW. 2003. Stress field in the subducting lithosphere and comparison with deep earthquakes in Tonga. J. Geophys. Res. 108:B62288 [Google Scholar]
  19. Guest A, Schubert G, Gable CW. 2004. Stresses along the metastable wedge of olivine in a subducting slab: possible explanation for the Tonga double seismic layer. Phys. Earth Planet. Inter. 141:253–67 [Google Scholar]
  20. Gulida LS, Lifshitz IM. 1952. On the development of local melting nuclei. Dokl. Akad. Nauk SSSR 87:523–26 [Google Scholar]
  21. Heaney PJ, Veblen DR. 1991. Observations of the α–β phase transition in quartz: a review of imaging and diffraction studies and some new results. Am. Mineral. 76:1018–32 [Google Scholar]
  22. Heidug W, Lehner FK. 1985. Thermodynamics of coherent phase transformations in nonhydrostatically stressed solids. Pure Appl. Geophys. 123:91–98 [Google Scholar]
  23. Higo Y, Inoue T, Irifune T, Funakoshi K-I, Li B. 2008. Elastic wave velocities of (Mg0.91Fe0.91) 2SiO4 ringwoodite under P–T conditions of the mantle transition region. Phys. Earth Planet. Inter. 166:167–74 [Google Scholar]
  24. Hill R. 1963. Elastic properties of reinforced solids: some theoretical principles. J. Mech. Phys. Solids 11:357–72 [Google Scholar]
  25. James RD. 1986. Displacive phase transformations in solids. J. Mech. Phys. Solids 34:359–94 [Google Scholar]
  26. James RD, Hane KF. 2000. Martensitic transformations and shape-memory materials. Acta Mater. 48:197–222 [Google Scholar]
  27. Karato S-I. 2008. Deformation of Earth Materials. Cambridge, UK: Cambridge Univ. Press
  28. Kerschhofer L, Dupas C, Liu M, Sharp TG, Durham WB, Rubie DC. 1998. Polymorphic transformations between olivine, wadsleyite and ringwoodite: mechanisms of intracrystalline nucleation and the role of elastic strain. Mineral. Mag. 62:617–38 [Google Scholar]
  29. Kirby SH, Stein S, Okal EA, Rubie DC. 1996. Metastable phase transformations and deep earthquakes in subducting oceanic lithosphere. Rev. Geophys. 34:261–306 [Google Scholar]
  30. Kohlstedt DL, Keppler H, Rubie DC. 1996. Solubility of water in the α, β and γ phases of (Mg,Fe)2SiO4. Contrib. Mineral. Petrol. 123:345–57 [Google Scholar]
  31. Kolmogorov AN. 1937. On the statistical theory of the crystallization of metals. Bull. Acad. Sci. USSR 1: 355–59 Transl. G Lindquist (from Russian), 1992, Selected Works of A.N. Kolmogorov, Vol. 2: Probability Theory and Mathematical Statistics AN Shiryayev 188–92 Dordrecht, Neth.: Springer [Google Scholar]
  32. Kubo T, Kaneshima S, Torii Y, Yoshioka S. 2009. Seismological and experimental constraints on metastable phase transformations and rheology of the Mariana slab. Earth Planet. Sci. Lett. 287:12–23 [Google Scholar]
  33. Kubo T, Ohtani E, Kato T, Shinmei T, Fujino K. 1998a. Effects of water on the α–β transformation kinetics in San Carlos olivine. Science 281:85–87 [Google Scholar]
  34. Kubo T, Ohtani E, Kato T, Shinmei T, Fujino K. 1998b. Experimental investigation of the α–β transformation of San Carlos olivine single crystal. Phys. Chem. Minerals 26:1–6 [Google Scholar]
  35. Le Chatelier H. 1890. Sur la polarisation rotatoire du quartz. Bull. Soc. Fr. Minéral. 13:119–22 [Google Scholar]
  36. Lee JK, Johnson WC. 1978. Re-examination of the elastic strain energy of an incoherent ellipsoidal particle. Acta Metall. 26:541–45 [Google Scholar]
  37. Lee JKW, Tromp J. 1995. Self-induced fracture generation in zircon. J. Geophys. Res. 100:17753–70 [Google Scholar]
  38. Lee KM, Lee HC, Lee JK. 2010. Influence of coherency strain and applied stress upon diffusional ferrite nucleation in austenite: micromechanics approach. Philos. Mag. 90:437–59 [Google Scholar]
  39. Lifshitz IM, Gulida LS. 1952. On the theory of local melting. Dokl. Akad. Nauk. SSSR 87:377–80 [Google Scholar]
  40. Mallard E, Le Chatelier H. 1890. Sur la variation qu'éprouvent, avec la température, les biréfringences du quartz, de la barytine et du disthéne. Bull. Soc. Fr. Minéral. 13:123–29 [Google Scholar]
  41. Mishin Y, Asta M, Li Ju. 2010. Atomistic modeling of interfaces and their impact on microstructure and properties. Acta Mater. 58:1117–51 [Google Scholar]
  42. Morris SJS. 2014. Kinematics and thermodynamics of a growing rim of high-pressure phase. Phys. Earth Planet. Inter. 228:127–43 [Google Scholar]
  43. Morris SJS. 2017. On polymorphic change via an incoherent intermediate state. Phys. Earth Planet. Inter. In press
  44. Mosenfelder JL, Connolly JAD, Rubie DC, Liu M. 2000. Strength of (Mg, Fe)2SiO4 wadsleyite determined by relaxation of transformation stress. Phys. Earth Planet. Inter. 120:63–78 [Google Scholar]
  45. Mosenfelder JL, Marton FC, Ross CR, Kerschhofer L, Rubie DC. 2001. Experimental constraints on the depth of olivine metastability in subducting lithosphere. Phys. Earth Planet. Inter. 127:165–80 [Google Scholar]
  46. Nabarro FRN. 1940. The strains produced by precipitation in alloys. Proc. R. Soc. A 175:519–38 [Google Scholar]
  47. Núñez-Valdez M, Wu Z, Yu YG, Wentzcovitch RM. 2013. Thermal elasticity of (Fex,Mg1–x) 2SiO4 olivine and wadsleyite. Geophys. Res. Lett. 40:290–94 [Google Scholar]
  48. Olson GB, Cohen M. 1979. Interphase-boundary dislocations and the concept of coherency. Acta Metall. 27:1907–18 [Google Scholar]
  49. Paterson MS. 1973. Nonhydrostatic thermodynamics and its geologic applications. Rev. Geophys. Space Phys. 11:355–89 [Google Scholar]
  50. Peslier AH, Bizimis M. 2015. Water in Hawaiian peridotite minerals: a case for a dry metasomatized oceanic mantle lithosphere. Geochem. Geophys. Geosyst. 16:1211–32 [Google Scholar]
  51. Pippard AB. 1957. Elements of Classical Thermodynamics Cambridge, UK: Cambridge Univ. Press
  52. Ringwood AE. 1972. Phase transitions and mantle dynamics. Earth Planet. Sci. Lett. 14:233–41 [Google Scholar]
  53. Ringwood AE, Major A. 1970. The system Mg2SiO4–Fe2SiO4 at high pressures and temperatures. Phys. Earth Planet. Inter. 3:89–108 [Google Scholar]
  54. Roitburd AL, Temkin DE. 1986. Plastic deformation and thermodynamic hysteresis in phase transformations in solids. Sov. Phys. Solid State 28:432–36 [Google Scholar]
  55. Rubie DC. 1993. Mechanisms and kinetics of reconstructive phase transformations in the Earth's mantle. Experiments at High Pressure and Applications to the Earth's Mantle RW Luth 247–303 Edmonton, Can.: Miner. Assoc. Can. [Google Scholar]
  56. Rubie DC, Karato S, Yan H, O'Neill HStC. 1993. Low differential stress and controlled chemical environment in multianvil high-pressure experiments. Phys. Chem. Minerals 20:315–22 [Google Scholar]
  57. Rubie DC, Ross CR. 1994. Kinetics of the olivine–spinel transformation in subducting lithosphere: experimental constraints and implications for deep slab processes. Phys. Earth Planet. Inter. 86:223–41 [Google Scholar]
  58. Rubie DC, Tsuchida Y, Tagi T, Utsumi W, Kiegawa T. et al. 1990. An in situ X-ray diffraction study of the kinetics of the Ni2SiO4 olivine–spinel transformation. J. Geophys. Res. 95:B1015829–44 [Google Scholar]
  59. Schubnel A, Brunet F, Hilairet N, Gasc J, Wang Y, Green HW. 2013. Deep–focus earthquake analogues recorded at high pressure and temperature in the laboratory. Science 341:1377–80 [Google Scholar]
  60. Sokolnikoff IS. 1956. Mathematical Theory of Elasticity New York: McGraw–Hill
  61. Sung C-M, Burns RG. 1976. Kinetics of high-pressure phase transformations: implications to the evolution of the olivine-spinel transition in the downgoing lithosphere and its consequences on the dynamics of the mantle. Tectonophysics 31:1–32 [Google Scholar]
  62. Truesdell C, Toupin RA. 1960. The classical field theories. Handbuch der Physik Vol. III/1 Principles of Classical Mechanics and Field Theory S. Flügge 226–858 Berlin: Springer [Google Scholar]
  63. Truskinovskiy LM. 1984a. The chemical potential tensor. Geochem. Int. 21:22–36 [Google Scholar]
  64. Truskinovskiy LM. 1984b. The equilibrium between a spherical nucleus and the matrix in a solid-state transformation. Geochem. Int. 21:14–18 [Google Scholar]
  65. Turnbull D. 1956. Phase changes. Solid State Phys. 3:226–306 [Google Scholar]
  66. Vaughan PJ, Green HW, Coe RS. 1982. Is the olivine–spinel transformation martensitic?. Nature 298:357–58 [Google Scholar]
  67. Vaughan PJ, Green HW, Coe RS. 1984. Anisotropic growth in the olivine–spinel transformation of Mg2SiO4 under non-hydrostatic stress. Tectonophysics 108:299–322 [Google Scholar]
/content/journals/10.1146/annurev-earth-040610-133511
Loading
Interface Kinetics, Grain-Scale Deformation, and Polymorphism
Annual Review of Earth and Planetary Sciences 45, 245 (2017); https://doi.org/10.1146/annurev-earth-040610-133511
/content/journals/10.1146/annurev-earth-040610-133511
/content/journals/10.1146/annurev-earth-040610-133511
Loading

Data & Media loading...

  • Article Type: Review Article

Most Cited Most Cited RSS feed

This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error