Skip to main content Accessibility help
×
Home

Elastic instabilities in dry, mesoporous minerals and their relevance to geological applications

  • E. K. H. Salje (a1), J. Koppensteiner (a2), W. Schranz (a2) and E. Fritsch (a3)

Abstract

The collapse of minerals and mineral assemblies under external stress is modelled using a master curve where the stress failure is related to the relative, effective elastic moduli which are in turn related to the porosity of the sample. While a universal description is known not to be possible, we argue that for most porous materials such as shales, silica, cement phases, hydroxyapatite, zircon and also carbonates in corals and agglomerates we can estimate the critical porosity ϕc at which small stresses will lead to the collapse of the sample. For several samples we find ϕc ~0.5 with an almost linear decay of the bulk moduli with porosity at ϕc <0.5. The second scenario involves the persistence of elasticity for porosities until almost 1 whereby the bulk modulus decreases following a power law κ ~ (1–ϕm, m>2, between ϕ = 0.5 and ϕ = 1.

Copyright

Corresponding author

References

Hide All
Aifantis, K.E. and Willis, J.R. (2005) The role of interfaces in enhancing the yield strength of composites and polycrystals. Journal of Mechanics and Physics of Solids, 53, 10471070.
Akao, M., Aoki, H. and Kato, K. (1981) Mechanical properties of sintered hydroxyapatite for prosthetic applications. Journal of Materials Science, 16, 809812.
Arita, I.H., Wilkinson, D.S., Mondragon, M.A. and Castaño, V.M. (1995) Chemistry and sintering behaviour of thin hydroxyapatite ceramics with controlled porosity. Biomaterials, 16, 403408.
Atkinson, A.J., Carpenter, M.A. and Salje, E.K.H. (1999) Hard mode infrared spectroscopy of plagioclase feldspars. European Journal of Mineralogy, 11, 721.
Barton, T.J., Bull, L.M., Klemperer, W.G., Loy, D.A., McEnaney, B., Misono, M., Monson, P.A., Pez, G., Scherer, G.W., Vartuli, J.C. and Yaghi, O.M. (1999) Tailored porous materials. Chemistry of Materials, 11, 26332656.
Bismayer, U. and Salje, E. (1981) Ferroelastic phases in Pb3(PO4)2–Pb3(AsO4)2 – X-ray and optical experiments. Acta Crystallographica A, 37, 145—153.
Bobko, C. and Ulm, F.J. (2007) The nano-mechanical morphology of shale. Mechanics of Materials, 40, 318337.
Boker, A., He, J., Emrick, T. and Russell, T.P. (2007) Self-assembly of nanoparticles at interfaces. Soft Matter, 3, 12311248.
Carpenter, M.A. and Salje, E.K.H. (1998) Elastic anomalies in minerals due to structural phase transitions. European Jounal of Mineralogy, 10, 693812.
Charrire, E., Terrazzoni, S. and Pittet, C. (2001) Mechanical characterization of brushite and hydroxyapatite cements. Biomaterials, 21, 29372945.
Constantinides, G. and Ulm, F-J. (2007) The nanogranular nature of C–S–H. Journal of Mechanics and Physics of Solids, 55, 6490.
Craciun, F., Galassi, C., Roncari, E., Filippi, A. and Guidarelli, G. (1998) Electro-elastic properties of porous piezoelectric ceramics obtained by tape casting. Ferroelectrics, 205, 4967.
DeWitt, G., van Dijk, H., Hattu, N. and Prijs, K. (1981) Preparation, microstructure and mechanical properties of dense polycrystalline hydroxyapatite. Journal of Material Sciences, 16, 15921958.
Dmitriev, V.P., Rochal, S.B. and Gufan, Y.M. (1988) Definition of a transcendental order parameter for reconstructive phase transitions. Physical Review Letters, 60, 19581961.
Dmitriev, V.P., Toledano, P., Torgashev, V.I. and Salje, E.K.H. (1998) Theory of reconstructive phase transitions between SiO2 polymorphs. Physical Review B, 58, 1191111921.
Eschricht, N., Hoinkins, E., Mädler, F. and Schubert-Bischoff, P. (2002) Reconstruction of the mesoporous silica glass Gelsil50. Surface Science and Catalysis, 144, 355–262.
Elmer, T.H. (1992) ASM Engineered Materials Handbook 4: Ceramics and Glasses. Materials Park, Ohio, US.
Fritsch, A., Dormieux, L., Hellmich, C. and Sanahuja, J. (2007) Micromechanics of crystal interfaces in polycrystalline solid phases of porous media: fundamentals and application to strength of hydroxyapatite biomaterials. Journal of Material Science, 42, 88248837.
Fritsch, A., Dormieux, L. and Hellmich, C. (2009) Mechanical behavior of hydroxyapatite biomaterials: An experimentally validated micromechanical model for elasticity and strength. Journal of Biomedical Materials Research A, 88, 149161.
Gatta, G.D. (2008) Does porous mean soft? On the elastic behaviour and structural evolution of zeolites underpressure. Zeitschrift fur Kristallographie, 223, 160170.
Gibson, L.J. and Ashby, M.F. (1997) Cellular solids: Structure and and properties, second ed. Cambridge Univ. Press, Cambridge, UK.
Gilmore, R.S. and Katz, J.L. (1982) Elastic properties of apatites. Journal of Material Sciences, 17, 11311141.
Gross, J., Schlief, T. and Fricke, J. (1993) Ultrasonic evaluation of elastic properties of silica aerogels. Materials Science and Engineering A, 168, 235238.
Harrison, R.J., Redfern, S.A.T. and Salje, E.K.H. (2004) Dynamical excitation and anelastic relaxation of ferroelastic domain walls in LaAlO3 . Physical Review B, 69, 144101.
Herrmann, A., Schwarzer, N. and Richter, F. (2006) Determination of Young's modulus and yield stress of porous low-k materials by nanoindentation. Surface Coatings Technology, 201, 43054310.
Hill, R (1972) On constitutive macro-variables for heterogeneous solids at finite strain. Proceedings of the Royal Society A, 326, 131147.
Hornby, B.E., Schwartz, L.M. and Hudson, J.A. (1994) Anisotropic effective-medium modeling of the elastic properties of shales. Geophysics, 59, 15701583.
Jakobson, M., Hudson, J.A., Minshull, T.A. and Singh, S.C. (2000) Elastic properties of hydrate-bearing sediments using effective medium theory. Journal of Geophysical Research, 105, 561577.
Kityk, A.V., Schranz, W., Sondergeld, P. and Salje, E.K.H. (2000) Low-frequency superelasticity and nonlinear elastic behavior of SrTiO3 crystals. Physical Review B, 61, 946956.
Knackstedt, M.A., Arns, C.H., Senden, T.J. and Gross, K. (2006) Structure and properties of clinical coralline implants measured via 3D imaging and analysis. Biomaterials, 27, 27762786.
Koppensteiner, J., Schranz, W. and Puica, M.R. (2008) Confinement effects on glass forming liquids probed by dynamic mechanical analysis. Physical Review B, 78, 054203.
Lee, W.T., Salje, E.K.H. and Dove, M.T. (1999) Effect of surface relaxations on the equilibrium growth morphology of crystals: platelet formation. Journal of Physics, Condensed Matter, 11, 73857410.
Lee, W.T., Dove, M.T. and Salje, E.K.H. (2000) Surface relaxations in hydroxyapatite. Journal of Physics: Condensed Matter, 12, 98299841.
Levitz, P., Ehert, G., Sinha, S.K. and Drake, J.M. (1991) Porous Vycor glass – the microstructure as probed by electron-microscopy, dielectric energy-transfer, small-angle scattering and molecular absorption. Journal of Chemical Physics, 95, 61516161.
Liu, D-M. (1998) Preparation and characterisation of porous hydroxyapatite biocheramic via a slip-casting route. Ceramics International, 24, 441446.
Ma, H-S., Prévost, J-H., Jullien, R. and Scherer, G.W. (2002) Elasticity of DLCA model gels with loops. International Journal of Solids and Structures, 39, 46064614.
Michel, J.C., Lopez-Pamies, O., Castaneda, P.P. and Triantafyllidis, N. (2007) Microscopic and macroscopic instabilities in finitely strained porous elastomers. Journal of Mechanics and Physics of Solids, 55, 900938.
Migliori, A. and Maynard, J.D. (2005) Implementation of a modern resonant ultrasound spectroscopy system for the measurement of the elastic moduli of small solid specimens. Review of Scientific Instruments, 76, 121301.
Milton, G.W. (2002) The Theory of Composites. Cambridge University Press, Cambridge, UK.
Miyoshi, H., Yamada, K., Kohmura, K., Fujii, N., Matsuo, H., Tanaka, H., Oku, Y., Seino, Y., Hata, N. and Kikkawa, T. (2005) Theoretical investigation of dielectric constant and elastic modulus of three-dimensional isotropic porous silica films with cubic and disordered pore arrangements. Japanese Journal of Applied Physics, 44, 59825986.
Muralidharan, V. and Hui, C-Y. (2004) Stability of nanoporous materials. Macromolecular Rapid Communications, 25, 14871490.
Murray, C., Flannery, C. and Streiter, I. (2002) Comparison of techniques to characterise the density, porosity and elastic modulus of porous low-k SiO2 xerogel films. Microelectronic Engineering, 60, 133141.
Nogues, J-L.R. and Moreshead, W. (1990) Porous gel silica, a matrix for optically-active components. Journal of Non-Crystalline Solids, 121, 136142.
Nur, A., Mavko, G., Dvorkin, J. and Galmudi, D. (1998) Critical porosity: A key to relating physical properties to porosity in rocks. The Leading Edge, 357362.
Pekala, R.W., Hrubesh, L.W., Tillotson, T.M., Alviso, C.T., Poco, J.F. and Lemay, J.D. (1991) A comparison of mechanical properties and scaling law relationships for silica aerogels and their organic counterparts. Materials Research Society Symposium Proceedings, 207, 197200.
Pertsev, N.A. and Salje, E.K.H. (2000) Thermodynamics of pseudoproper and improper ferroelastic inclusions and polycrystals: effect of elastic clamping on phase transitions. Physical Review B, 61, 902908.
Puchegger, S., Brandhuber, D., Hsing, N. and Peterlik, H. (2006) Changing poisson's ratio of mesoporous silica monoliths with high temperature treatment. Journal of Non-Crystalline Solids, 352, 52515256.
Puchegger, S., Dose, F., Loidl, D., Kromp, K., Janssen, R., Brandhuber, D., Hsing, N. and Peterlik, H. (2007) The dependence of the elastic moduli of reaction bonded alumina on porosity. Journal of the European Ceramic Society, 27, 3539.
Roberts, A.P. and Garboczi, E.J. (2000) Elastic properties of model porous ceramics. American Ceramic Society, 83, 30413048.
Roberts, A.P. and Garboczi, E.J. (2002) Computation of the linear elastic properties of random porous materials with a wide variety of microstructure. Proceedings of the Royal Society of London A, 458, 10331054.
Salje, E.K.H. (1992) Application of Landau theory for the analysis of phase-transitions in minerals. Physics Reports, 215, 4999.
Salje, E.K.H. (1993) Phase Transitions in Ferroelastic and Co-Elastic Crystals. Cambridge University Press, Cambridge, UK.
Salje, E.K.H. (2006) Elastic softening of zircon by radiation damage. Applied Physics Letters, 89, 131902.
Salje, E.K.H. (2007) An empirical scaling model for averaging elastic properties including interfacial effects. American Mineralogist, 92, 429432.
Salje, E.K.H. (2008 a) A pre-martensitic elastic anomaly in nanomaterials: elasticity of surface and interface layers. Journal of Physics: Condensed Matter, 20, 485003.
Salje, E.K.H. (2008 b) (An)elastic softening from static grain boundaries and possible effects on seismic wave propagation. Physics and Chemistry of Minerals, 35, 321330.
Salje, E. and Wruck, B. (1991) Order parameter saturation at low-temperatures – numerical results for displacive and o/d systems. Ferroelectrics, 124, 185188.
Salje, E.K.H. and Zhang, H.L. (2009) Domain boundary pinning and elastic softening in KMnF3 and KMn1-xCaxF3 . Journal of Physics, Condensed Matter, 21, 035901.
Salje, E., Palosz, B. and Wruck, B. (1987) In situ observation of the polytypoic phase-transition 2H-12R in PbI2 – investigation of the thermodynamic, structural and dielectric properties. Journal of Physics C: Solid State Physics, 20, 40774096.
Salje, E.K.H., Wruck, B. and Thomas, H. (1991) Order parameter saturation and low-temperature extension of Landau theory. Zeitschrift fr Physik B – Condensed Matter, 82, 399404.
Salje, E.K.H., Ridgwell, A., Guttler, B., Wruck, B., Dove, M.T. and Dolino, G. (1993 a) on the displacive character of the phase transition in quartz – a hard-mode spectroscopy study. Journal of Physics: Condensed Matter, 4, 571577.
Salje, E.K.H., Schmidt, C. and Bismayer, U. (19936) Structural phase-transition in titanite, CaTiSiO5 – a Raman-spectroscopic study. Physics and Chemistry of Minerals, 19, 502509.
Salje, E.K.H., Hayward, S.A. and Lee, W.T. (2005) Ferroelastic phase transitions: structure and microstructure. Acta Crystallographica, 61, 318.
Salje, E.K.H., Zhang, H., Planes, A. and Moya, X. (2008) Martensitic transformation B2-R in Ni-Ti-Fe: experimental determination of the Landau potential and quantum saturation of the order parameter. Journal of Physics, Condensed Matter, 20, 275216.
Scherer, G.W. (1998) Crystallization in pores. Cement and Concrete Research, 29, 13471358.
Scherer, G.W., Smith, D.M., Qiu, X. and Anderson, J.M. (1995) Compression of aerosols. Journal of Non-Crystalline Solids, 186, 316320.
Schranz, W., Trster, A., Kityk, A.V. and Salje, E.K.H. (2003) Ultralow-frequency elastic response in KMn1-xCaxF3 . Europhysics Letters, 62, 512518.
Sonmez, H., Tuncay, E. and Gokceoglu, C. (2004) Models to predict the uniaxial compressive strength and the modulus of elasticity for Ankara Agglomerate. International Journal of Rock Mechanics and Mining Sciences, 41, 717729.
Speer, D. and Salje, E. (1986) Phase transitions in langbeinites. 1 crystal chemistry and structures of K-double sulfates of the langbeinite type M2 ++K2(SO4)3, M++ = Mg, Ni, Co, Zn, Ca. Physics and Chemistry of Minerals, 13, 1724.
Takada, S., Hata, N., Seino, Y., Fujii, N. and Kikkawa, T. (2006) Dependences of Young's modulus of porous silica low dielectric constant films on skeletal structure and porosity. Journal of Applied Physics, 100, 123512.
Toledano, P., Fejer, M.M. and Auld, B.A. (1983) Non-linear elasticity in proper ferroelastics. Physical Review B, 27, 57175746.
Torquato, S., Gibiansky, L.V., Silva, M.J. and Gibson, L.J. (1998) Effective mechanical and transport properties of cellular solids. International Journal of Mechanical Sciences, 40, 7182.
Traore, D., Beauvais, A., Chabaux, F., Peiffert, C., Parisot, J.C., Ambrosi, J.P. and Colin, F.D. (2008) Chemical and physical transfers in an ultramatic rock weathering profile: Part 1. Supergene dissolution of Pt-bearing chromite. American Mineralogist, 93, 2230.
Ulm, F-J., Vandamme, M., Bobko, C., Ortega, J.A., Tai, K. and Ortiz, C. (2007) Statistical indentation techniques for hydrated nanocomposites: Concrete, bone, and shale. Journal of the American Ceramic Society, 90, 26772692.
Willis, J.R. (1977) Bounds and self-consistent estimates for the overall properties of anisotropic composites. Journal of Mechanics and Physical Solids, 25, 185202.
Woignier, T., Phalippou, J. and Vacher, R. (1989) Parameters affecting elastic properties in silica aerogels. Journal of Materials Research, 4, 688692.

Keywords

Elastic instabilities in dry, mesoporous minerals and their relevance to geological applications

  • E. K. H. Salje (a1), J. Koppensteiner (a2), W. Schranz (a2) and E. Fritsch (a3)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed