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(An)elastic softening from static grain boundaries and possible effects on seismic wave propagation

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Abstract

It is argued that low-frequency wave propagation shows, in most cases, very little dependence on the atomistic properties of grain boundaries if the thickness of the grain boundary is atomistically thin while the grain size is in the mm region. Large effects do exist for specific textures (e.g. the brick wall texture). The essential ingredient for the assessment of an-elastic and non-linear elastic features of seismic wave propagation does not primarily depend on the structural properties of immobile, dry grain boundaries but on the way the grain boundary properties can be related to those of macroscopic mineral assemblies. Specific results for coated sphere textures are derived using Hashin-Shtrikman theory. An-elastic seismic features are more likely to be related to the mobility of boundaries and dislocations which can be attached to the grain boundaries, or bulk-related defect structures, rather than the intrinsic materials properties of the grain boundaries.

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References

  • Achenbach JD, Zhu H (1990) Effect of interfaces on micro and macromechanical behaviour of hexagonal–array fiber composites. J Appl Mech-ASME 57:956–963

    Article  Google Scholar 

  • Adams JM, Warner M (2005) Soft elasticity in smectic elastomers. Phys Rev 72:011703

    Google Scholar 

  • Andrews J, Deuss A, Woodhouse J (2006) Coupled normal-mode sensitivity to inner–core shear velocity and attenuation. Geophys J Int 167:204–212

    Article  Google Scholar 

  • Aubry S (1983) The twist map, the extended Frenkel-Kondorova model and the devils staircase. Phys D 7:240–258

    Article  Google Scholar 

  • Benveniste Y (1987) A new approach to the Mori-Tanaka theory in composite-materials. Mech Mater 6:147–157

    Article  Google Scholar 

  • Bowden FP, Taylor D (1950) Friction and Lubrication of Solids. Clarendon Press, Oxford

    Google Scholar 

  • Calleja M, Dove MT, Salje EKH (2003) Trapping of oxygen vacancies on twin walls of CaTiO3: a computer simulation study. J Phys Condens Matter 15:2301–2307

    Article  Google Scholar 

  • Carpick RW Agrait N, Ogletree DF, Salmeron M (1996) Variation of the interfacial shear strength and adhesion of a nanometer-sized contact. Langmuir 12:3334–3340

    Article  Google Scholar 

  • Chatterjee SN, Kibler JJ (1979) Modern developments in composite materials and structures In: Herakovich CT, (ed). ASME, p 269

  • Chrosch J, Salje EKH (1999) The temperature dependence of the domain wall width in LaAlO3. J Appl Phys 85:722–727

    Article  Google Scholar 

  • Conti S, Salje EKH (2001) Surface structure of ferroelastic domain walls: a continuum elasticity approach. J Phys Condens Matter 13:L847–L854

    Article  Google Scholar 

  • Darling TW, TenCate JA, Brown DW, Clausen B, Vogel SC (2004), Neutron diffraction study of the contribution of grain contacts to nonlinear stress-strain behavior. Geophys Res Lett 31:L16604

    Article  Google Scholar 

  • Faul UF, Jackson I (2004) Shear wave attenuation and dispersion in melt bearing olivine polycrystals: 2. Microstructural interpretation and seismological implications. J Geophys Res 109:B06202

    Article  Google Scholar 

  • Faul UF, Jackson I (2005) The seismological signature of temperature and grain size in the upper mantle. Earth Planet Sci Lett 234:119–134

    Article  Google Scholar 

  • Faul UF, Jackson I (2007) Diffusion creep of dry, melt-free olivine. J Geophys Res 112:B04204

    Article  Google Scholar 

  • Frost HJ, Ashby MF (1982) Deformation mechanism maps: The plasticity of metals and ceramics, Elsevier, New York

  • Green AE, Zerna W (1954) Theoretical Elasticity. Clarendon Press, Oxford

    Google Scholar 

  • Grabovsky Y, Kohn RV (1995a) Microstructures minimizing the energy of a 2-phase elastic compositein 2 space dimensions.1.the confocal ellipse construction. J Mech Phys Solids 43:933–947

    Article  Google Scholar 

  • Grabovsky Y, Kohn RV (1995b) Microstructures minimizing the energy of a 2-phase elastic compositein 2 space dimensions.2. the vigdergauz microstructure. J Mech Phys Solids 43:949–972

    Article  Google Scholar 

  • Hashin Z (1962) The elastic moduli of heterogeneous materials. J Appl Mech 29:143–150

    Google Scholar 

  • Hashin Z (1965) Viscoelastic behaviour of heterogenous matter. J Appl Mech 32:630–636

    Google Scholar 

  • Hashin Z (1985) Large isotropic elastic deformation of composites and porous media. Int J Solids struct 21:711–720

    Article  Google Scholar 

  • Hashin Z (1991) Composite materials with viscoelastic interphase: creep and relaxation. Mech Mater 11:135–148

    Article  Google Scholar 

  • Hashin Z (1992) Extremum principles for elastic heterogeneous media with imperfect interfaces and their application to bounding of effective moduli. J Mech Phys Solids 40:767–781

    Article  Google Scholar 

  • Hashin Z (2002) Thin interface/imperfect interface in elasticity with application to coated fiber composites. J Mech Phys Solids 50:2509–2537

    Article  Google Scholar 

  • Harrison RJ, Redfern SAT, Salje EKH (2004) Dynamical excitation and anelastic relaxation of ferroelastic domain walls in LaAlO3. Phys Rev B 69:144101

    Article  Google Scholar 

  • Hertz H (1881) Ueber die Beruehrung fester elastische Koerper. J Reine Angewandte Mathematik 92:156–171

    Google Scholar 

  • Hiraga T, Anderson I M, Zimmerman ME, Mei S, Kohlstedt DL (2002) Structure and chemistry of grain boundaries in deformed, olivine + basalt and partially molten lherzolite aggregates: evidence of melt-free grain boundaries. Contrib Mineral Petrol 144:163–175

    Article  Google Scholar 

  • Houchmanzadeh B, Lajzerovicz J, Salje EKH (1992) Relaxations near surfaces and interfaces for first, second and third neighbour interactions: theory and applications for polytypism. J Phys Condens Matter 4:9779–9794

    Article  Google Scholar 

  • Israelachvili JN (1992) Adhesion forces between surfaces in liquids and condensable vapors. Surf Sci Reports 14:109–159

    Article  Google Scholar 

  • Jackson I, Paterson MS (1987) Shear modulus and internal friction of calcite rocks at seismic frequencies: pressure, frequency and grain size dependence. Phys Earth Planet Interiors 45:349–367

    Article  Google Scholar 

  • Jackson I, Fitz Gerald J, Kokkonen H (2000) High-temperature voscoelastic relaxation in iron and its implications for the shear modulus and attenuation of the earth’s inner core. J Geophys Res 105:23605–23634

    Article  Google Scholar 

  • Jackson I, Faul UF, FitzGerald JD, Morris SJS (2006) Contrasting viscoelastic behaviour of melt-free and melt-bearing olivine: implications for the nature of grain-boundary sliding. Mater Sci Eng A 442:170–174

    Article  Google Scholar 

  • Ji SC, Wang ZC (1999) Elastic properties of forsterite-enstatite composites up to 3.0 GPa. J Geodyna 28:147–174

    Article  Google Scholar 

  • Johnson KL (1987) Contact Mechanics. Cambridge University Press, Cambridge

    Google Scholar 

  • Johnson KL, Kendall K, Roberts AD (1971) Surface energy and contact of solids. Pro R Soc Lond A 324:301–313

    Article  Google Scholar 

  • Khalil-Allafi J, Schmahl WW, Reinecke T (2005) Order parameter evolution and Landau free energy coefficients for the B2<->R-phase transition in a NiTi shape memory alloy. Smart Mater Struct 14:S192–S196

    Article  Google Scholar 

  • Kityk AV, Schranz W, Sondergeld P, Havlik D, Salje EKH (2000) Low-frequency superelasticity and nonlinear elastic behavior of SrTiO3 crystals. Phy Rev B 61:946–956

    Article  Google Scholar 

  • De Kloe R, Drury MR, van Roermund HLM (2000) Evidence for stable grain boundary melt films in experimentally deformed olivine-orthopyroxene rocks. Phys Chem Miner 27:480–494

    Article  Google Scholar 

  • Krylov SY, Jinesh KB, Valk H., Dienwiebel M, Frenken JWM (2005) Thermally induced suppression of friction at the atomic scale. Phys Rev E 71:R65101

    Article  Google Scholar 

  • Lee WT, Dove MT, Salje EKH (2003) Domain wall structure and domain wall strain. J Appl Phys 93:9890–9897

    Article  Google Scholar 

  • Lee WT, Salje EKH, Goncalves-Ferreira L, Dove MT (2006) Intrinsic activation energy for twin-wall motion in the ferroelastic perovskite CaTiO3. Phys Rev 73 (21):214110

    Google Scholar 

  • Mal AK, Bose SK (1975) Dynamic elastic-moduli of a suspension of imperfectly bonded spheres. Pro Camb Philol Soc 76:587–600

    Google Scholar 

  • Medyanik SN, Liu WK, Sung IH, Carpick RW (2006) Predictions and observations of multiple slip modes in atomic-scale friction. Phy Rev Lett 97:136106

    Article  Google Scholar 

  • Milton GW (2002) The theory of composites. Cambridge University Press, Cambridge

    Google Scholar 

  • Novak J, Salje EKH (1998a) Surface structure of domain walls. J Phys Condens Matt 10:L359–L366

    Article  Google Scholar 

  • Novak J, Salje EKH (1998b) Simulated mesoscopic structures of a domain wall in ferroelastic lattices. Eur Phys J B4:279–284

    Google Scholar 

  • Page KL, PoffenTh, McLain SE, Darling TW, TenCate JA (2004) Local atomic structure of Fountainbleau sandstone : avidence for an amorphous phase? Geophys Res Lett 31:L24606

    Article  Google Scholar 

  • Pertsev NA, Salje EKH (2000) Thermodynamics of pseudo-proper and improper ferroelastic inclusions and polycrystals: effect of clamping on phase transitions. Phy Rev B 61:902–908

    Article  Google Scholar 

  • Romanowicz B, Durek J (2000) Seismological constraintson attenuation in the earth: a review in Earth’s deep interior: mineral physics and tomography from the atomic to the global scale, vol 117,p 161–177. AGU Geophysical monograph

  • Roters L, Lubeck S, Usadel KD (2005) Creep motion in a random-field Ising model. Phys Rev E 63:026113

    Article  Google Scholar 

  • Rios S, Salje EKH, Zhang M, Ewing RC (2000) Amorphisation in zircon: evidence for direct impact damage. J Phys Condens Matter 12:2401–2412

    Article  Google Scholar 

  • Rios S, Salje EKH, Redfern SAT (2001) Nanoquartz vs. macroquartz: a study of the alpha-beta transition. Eur Phys J B 20:75–83

    Article  Google Scholar 

  • Saburi T, Yoshida M, Nenno S (1984) Deformation-behaviour of shape memory Ti-Ni alloy crystals. Scri Metallurgica 18:363–366

    Article  Google Scholar 

  • Salje EKH (1993) Phase transitions in ferroelastic and co-elastic crystals. Cambridge University Press, Cambridge

    Google Scholar 

  • Salje E, Devarajan V, Bismayer U, Guimaraes DMC (1983) Phase-transitions in Pb3(P1-x As x PO4)2 - Influence of the central peak and flip mode on the Raman scattering of hard modes. J Phys C Solid Stat Phys 16:5233–5243

    Article  Google Scholar 

  • Salje EKH (2007) An empirical scaling model for averaging elastic properties including interfacial effects. Am Mineral 92:429–432

    Article  Google Scholar 

  • Salje EKH (1992) Application of Landau theory for the analysis of phase-transitions in minerals. Phys Reports 215:49–99

    Article  Google Scholar 

  • Salje EKH, Chrosch J, Ewing RC (1999) Is ‘metamictization’ of zircon a phase transition. Am Mineral 84:1107–1116

    Google Scholar 

  • Salje EKH, Zhang M (2006) Hydrous species in ceramics for the encapsulation of nuclear waste: OH in zircon . J Phys Condens Matt 18:L277–281

    Article  Google Scholar 

  • Salje EKH, Zhang H, Schryvers D, Bartova B (2007) Quantitative Landau potentials for the martensitic transformation in Ni–Al. Appl Phys Lett 90:221903

    Article  Google Scholar 

  • Schmeling H (1985) Numerical models on the influence of partial melt on elastic, anelastic and electric properties of rocks. 1. elasticity and anelasticity. Phys Earth Planet Interior 41:34–57

    Article  Google Scholar 

  • Socoliuc A, Gnecco E, Maier S, Pfeiffer O, Baratoff A, Bennewitz R, Meyer E (2006) Atomic-scale control of friction by actuation of nanometer-sized contacts. Science 313:207–210

    Article  Google Scholar 

  • Tan H, Jackson I, Fitz Gerald JD (2001) High temperature voscoelasticity of fine-grained polycrystalline olivine. Phys Chem Mineral 28:641–664

    Article  Google Scholar 

  • Trachenko K (2007) Slow dynamics and stress relaxation in a liquid as an elastic medium. Phys Rev B 75:212201

    Article  Google Scholar 

  • Trachenko K, Dove MT, Salje EKH (2000) Modelling the percolation type transition in radiation damage. J Appl Phys 87:117702–117707

    Article  Google Scholar 

  • Trachenko K, Brazhkin VV, Tsiok OB, Dove MT, Salje EKH (2007) Pressure-induced structural transformation in radiation-amorphized zircon. Phys Rev Lett 98:135502

    Article  Google Scholar 

  • Trachenko K, Dove MT, Salje EKH (2003) Large swelling and percolation in irradiated zircon. J Phys Condens Matt 15:6457–6471

    Article  Google Scholar 

  • Watt JP (1988) Elastic properties of polycrystalline minerals–comparison of theory and experiment. Phys Chem Mineral 15:579–587

    Article  Google Scholar 

  • Wruck B,Salje EKH, Abraham T, Bismayer U (1994) On the thickness of ferroelastic twin boundaries in lead phosphate Pb3(PO4)2 – an X-ray diffraction study. Phase Transitions 48:135–148

    Article  Google Scholar 

  • Yoshino T, Nishihara Y, Karato S (2007) Complete wetting of olivine grain boundaries by a hydrous melt near the mantle transition zone. Earth Planet Sci Lett 256:466–472

    Article  Google Scholar 

  • Zhang M, Salje EKH, Capitani GC, Leroux H, Clark AM, Schluter J, Ewing RC (2000) Annealing of alpha-decay damage in zircon: a Raman spectroscopic study. J Phys Condens Matt 12:3131–3148

    Article  Google Scholar 

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  1. Department of Earth Sciences, University of Cambridge, Cambridge, UK

    Ekhard K. H. Salje

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Salje, E.K.H. (An)elastic softening from static grain boundaries and possible effects on seismic wave propagation. Phys Chem Minerals 35, 321–330 (2008). https://doi.org/10.1007/s00269-008-0225-7

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  • DOI: https://doi.org/10.1007/s00269-008-0225-7

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