Skip to main content
Log in

Frictional Properties of a Low-Angle Normal Fault Under In Situ Conditions: Thermally-Activated Velocity Weakening

  • Published:
Pure and Applied Geophysics Aims and scope Submit manuscript

Abstract

The Zuccale fault is a regional, low-angle, normal fault, exposed on the Isle of Elba in central Italy that accommodated a total shear displacement of 6–8 km. The fault zone structure and fault rocks formed at <8 km crustal depth. The present-day fault structure is the final product of several deformation processes superposed during the fault history. In this study, we report results from a series of rotary shear experiments performed on 1-mm thick powdered gouges made from several fault rock types obtained from the Zuccale fault. The tests were done under conditions ranging from room temperature to in situ conditions (i.e., at temperatures up to 300 °C, applied normal stresses up to 150 MPa, and fluid-saturated.) The ratio of fluid pressure to normal stress was held constant at either λ = 0.4 or λ = 0.8 to simulate an overpressurized fault. The samples were sheared at a constant sliding velocity of 10 μm/s for at least 5 mm, after which a velocity-stepping sequence from 1 to 300 μm/s was started to determine the velocity dependence of friction. This can be represented by the rate-and-state parameter (a–b), which was determined by an inversion of the data to the rate-and-state equations. Friction of the various fault rocks varies between 0.3 and 0.8, similar to values obtained in previous studies, and decreases with increasing phyllosilicate content. Friction decreases mildly with temperature, whereas normal stress and fluid pressure do not affect friction values systematically. All samples exhibited velocity strengthening, conditionally stable behavior under room temperature conditions and (ab) increased with increasing sliding velocity. In contrast, velocity weakening, accompanied by stick–slips, was observed for the strongest samples at 300 °C and sliding velocities below 10 μm/s. An increase in fluid pressure under these conditions led to a further reduction in (a–b) for all samples, so that they exhibited unstable, stick–slip behavior at low sliding velocity. The results suggest that phyllosilicate-bearing fault rocks can deform by stable, aseismic creep at low, resolved shear stress and low shear rate conditions. An increase in fluid pressure or loading of stronger portions could lead to a runaway instability. The runaway instability might be limited in size because of (1) the fault heterogeneity, (2) the observed strengthening at higher sliding velocities, and (3) a co-seismic drop in pore-fluid pressure.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

References

  • Abers, G., Mutter, C., & Fang, J. (1997). Shallow dips of normal faults during rapid extension: Earthquakes in the Woodlark–D’Entrecasteaux rift system, Papua New Guinea. Journal of Geophysical Research, 102, B7, 15301–15317.

    Google Scholar 

  • Atkinson, B. K. (1982). Subcritical crack propagation in rocks: theory, experimental results and applications. Journal of Structural Geology, 4, 41–56.

    Google Scholar 

  • Barchi, M., Minelli, G., & Pialli, G. (1998). The CROP 03 Profile: A synthesis of results on deep structures of the Northern Appennines. Memorie della Societa Geologica Italiana, 52, 383–400.

  • Baumberger, T., Berthoud, P., & Caroli, C. (1999). Physical analysis of the state- and rate-dependent friction law. II. Dynamic friction. Physical Review B, 60(6), 3928–3939.

  • Beeler, N. M., Tullis, T. E., & Kronenberg, A. M. (2007). The instantaneous rate dependence in low temperature laboratory rock friction and rock deformation experiments. Journal of Geophysical Research, 112(B07310). doi:10.1029/2005JB003772.

  • Blanpied, M. L., Tullis, T. E., & Weeks, J. D. (1987). Frictional behavior of granite at low and high sliding velocities. Geophysical Research Letters, 14(5), 554-557.

  • Blanpied, M. L., Lockner, D. A., & Byerlee, J. D. (1995). Frictional slip of granite at hydrothermal conditions. Journal of Geophysical Research, 100(B7), 13045–13064.

    Google Scholar 

  • Blanpied, M. L., Tullis, T. E., & Weeks, J. D. (1998). Effects of slip, slip rate, and shear heating on the friction of granite. Journal of Geophysical Research, 103(B1), 489–511.

    Google Scholar 

  • Boncio, P., Brozzetti, F., & Lavecchia, G. (2000). Architecture and seismotectonics of a regional low-angle normal fault zone in central Italy. Tectonics, 19(6), 1038–1055.

  • Bos, B., & Spiers, C. J. (2001). Experimental investigation into the microstructural and mechanical evolution of phyllosilicate-bearing fault rock under conditions favouring pressure solution. Journal of Structural Geology, 23(8), 1187–2002.

    Google Scholar 

  • Bos, B., & Spiers, C. J. (2002). Frictional-viscous flow of phyllosilicate-bearing fault rock: microphysical model and implications for crustal strength profiles. Journal of Geophysical Research, 107(B2), doi:10.1029/2001JB000301.

  • Boulton, C., Carpenter, B. M., Toy, V., & Marone, C. (2012). Physical properties of surface outcrop cataclastic fault rocks, Alpine Fault, New Zealand. Geochemistry Geophysics Geosystems, 13(1), 1-13. doi:10.1029/2011GC003872.

  • Byerlee, J. (1978). Friction of rocks. Pure and Applied Geophysics, 116, 615–627.

  • Carpenter, B M, Marone, C., & Saffer, D. M. (2009). Frictional behavior of materials in the 3D SAFOD volume. Geophysical Research Letters, 36(L05302), doi:10.1029/2008GL036660.

  • Carpenter, B. M., Marone, C., & Saffer, D. M. (2011). Weakness of the San Andreas Fault revealed by samples from the active fault zone. Nature Geoscience, 4(4), 251–254. Nature Publishing Group. doi:10.1038/ngeo1089.

  • Chester, F. M., Evans, J. P., & Biegel, R. L. (1993). Internal structure and weakening mechanisms of the San Andreas Fault. Journal of Geophysical Research, 98(B1), 771–786.

    Google Scholar 

  • Chester, F. M. (1994). Effects of temperature on friction: Constitutive equations and experiments with quartz gouge. Journal of Geophysical Research, 99(B4), 7247–7261.

    Google Scholar 

  • Chiaraluce, L., Chiarabba, C., Collettini, C., Piccinini, D., & Cocco, M. (2007). Architecture and mechanics of an active low-angle normal fault: Alto Tiberina Fault, northern Apennines, Italy. Journal of Geophysical Research, 112(B10). doi:10.1029/2007JB005015.

  • Chiodini, G., Frondini, F., Cardellini, C., Parello, F. and Peruzzi, L. (2000). Rate of diffuse carbon dioxide Earth degassing estimated from carbon balance of regional aquifers: The case of central Apennine, Italy. Journal of Geophysical Research, 105, 8423–8434.

    Google Scholar 

  • Chiodini, G., Cardellini, C., Amato, A., Boschi, E., Caliro, S., Frondini, F., & Ventura, G. (2004). Carbon dioxide Earth degassing and seismogenesis in central and southern Italy. Geophysical Research Letters, 31(7), L07615. doi:10.1029/2004GL019480.

  • Collettini, C & Sibson, R. H. (2001). Normal faults normal friction? Geology, 29, 927–930.

  • Collettini, C., & Holdsworth, R. E. (2004). Fault zone weakening and character of slip along low-angle normal faults: insights from the Zuccale Fault, Isle of Elba, Italy. Journal of Geological Society of London, 161(6), 1039–1051. doi:10.1144/0016-764903-179.

    Google Scholar 

  • Collettini, C., De Paola, N, Holdsworth, R.E. & Barchi, M.R (2006). The development and behaviour of low-angle normal faults during Cenozoic asymmetric extension in the Northern Apennines, Italy. Journal of Structural Geology, 28, 333–352. doi:10.1016/j.jsg.2005.10.003.

  • Collettini, C., Viti, C., Smith, S. A. F., & Holdsworth, R. E. (2009a). The development of interconnected talc networks and weakening of continental low-angle normal faults. Geology, 37, 567–570. doi:10.1130/G25645A.1.

  • Collettini, C., Niemeijer, A., Viti, C., & Marone, C. (2009b). Fault zone fabric and fault weakness. Nature, 462(7275), 907–910. Macmillan Publishers Limited. doi:10.1038/nature08585.

  • Collettini, C. (2011). The mechanical paradox of low-angle normal faults: Current understanding and open questions. Tectonophysics, 510(3-4), 253–268. doi:10.1016/j.tecto.2011.07.015.

  • Collettini, C., Niemeijer, A., Viti, C., Smith, S. a. F., & Marone, C. (2011). Fault structure, frictional properties and mixed-mode fault slip behavior. Earth and Planetary Science Letters, 311(3-4), 316–327. Elsevier B.V. doi:10.1016/j.epsl.2011.09.020.

  • Den Hartog, S. A. M., Peach, C. J., De Winter, D. A. M., Spiers, C. J., & Shimamoto, T. (2012a). Frictional properties of megathrust fault gouges at low sliding velocities: New data on effects of normal stress and temperature. Journal of Structural Geology, 38, 156–171. doi:10.1016/j.jsg.2011.12.001.

  • Den Hartog, S. A. M., Niemeijer, A. R., & Spiers, C. J. (2012b). New constraints on megathrust slip stability under subduction zone P–T conditions. Earth and Planetary Science Letters, 353–354, 240–252. doi:10.1016/j.epsl.2012.08.022.

  • Den Hartog, S. A. M., Niemeijer, A. R., & Spiers, C. J. (2013). Friction on subduction megathrust faults: Beyond the illite–muscovite transition. Earth and Planetary Science Letters, 373, 8–19. doi:10.1016/j.epsl.2013.04.036.

  • Dieterich, J. H. (1978). Time-dependent friction and the mechanics of stick-slip. Pure and Applied Geophysics, 116, 790–806.

    Google Scholar 

  • Elter, P., Giglia, G., Tongiorgi, M., & Trevisan, L. (1975). Tensional and compressional areas in recent (Tortonian to Present) evolution of the Northern Apennines. Bolletino di Geofisica Teorica ed Applicata, 17.

  • Escartín, J., Andreani, M., Hirth, G., & Evans, B. (2008). Relationships between the microstructural evolution and the rheology of talc at elevated pressures and temperatures. Earth and Planetary Science Letters, 268(3–4), 463–475. doi:10.1016/j.epsl.2008.02.004.

  • Faulkner, D. R., Lewis, A. C., & Rutter, E. H. (2003). On the internal structure and mechanics of large strike-slip fault zones: field observations of the Carboneras fault in southeastern Spain. Tectonophysics, 367(3-4), 235–251.

    Google Scholar 

  • Faulkner, D. R., Mitchell, T. M., Behnsen, J., Hirose, T., & Shimamoto, T. (2011). Stuck in the mud? Earthquake nucleation and propagation through accretionary forearcs. Geophys. Res. Lett., 38(18), L18303. doi:10.1029/2011gl048552.

  • Giger, S. B., Cox, S. F., & Tenthorey, E. (2008). Slip localization and fault weakening as a consequence of fault gouge strengthening – Insights from laboratory experiments. Earth and Planetary Science Letters, 276(1-2), 73–84.

    Google Scholar 

  • Gratier, J-P., D. Dysthe, F. Renard (2013). The role of pressure solution creep in the ductility of the Earth’s upper crust. Advances in Geophysics, 54. doi: 10.1016/B978-0-12-380940-7.00002-0.

  • He, C., Yao, W., Wang, Z., & Zhou, Y. (2007). Strength and stability of frictional sliding of gabbro gouge at elevated temperatures. Tectonophysics, 427(1-4), 217–229. doi:10.1016/j.tecto.2006.05.023.

    Google Scholar 

  • Holness, M. (1997). Fluid flow paths and mechanisms of fluid infiltration in carbonates during contact metamorphism: the Beinn an Dubhaich aureole, Skye. Journal of Metamorphic Geology, 59–70.

  • Hreinsdottir, S., & Bennett, R. a. (2009). Active aseismic creep on the Alto Tiberina low-angle normal fault, Italy. Geology, 37(8), 683–686. doi:10.1130/G30194A.1.

  • Ikari, M. J., Saffer, D. M., & Marone, C. (2009). Frictional and hydrologic properties of clay-rich fault gouge. Journal of Geophysical Research, 114(B5), B05409. doi:10.1029/2008JB006089.

  • Ikari, M. J., Marone, C., & Saffer, D. M. (2010). On the relation between fault strength and frictional stability. Geology, 39(1), 83–86. doi:10.1130/g31416.1.

    Google Scholar 

  • Ikari, M. J., & Saffer, D. M. (2011). Comparison of frictional strength and velocity dependence between fault zones in the Nankai accretionary complex. Geochemistry, Geophysics, Geosystems, 12(4). doi:10.1029/2010GC003442.

  • Israelachvili, J. N. (1986). Measurement of the viscosity of liquids in very thin films. Journal of Colloid and Interface Science, 110(1), 263–271. doi:10.1016/0021-9797(86)90376-0.

    Google Scholar 

  • Imber, J., Holdsworth, R. E., Smith, S. a. F., Jefferies, S. P., & Collettini, C. (2008). Frictional-viscous flow, seismicity and the geology of weak faults: a review and future directions. Geological Society, London, Special Publications, 299(1), 151–173. doi:10.1144/SP299.10.

  • Jefferies, S. P., Holdsworth, R. E., Wibberley, C. A. J., Shimamoto, T., Spiers, C. J., Niemeijer, A. R., & Lloyd, G. E. (2006). The nature and importance of phyllonite development in crustal-scale fault cores: an example from the Median Tectonic Line, Japan. Journal of Structural Geology, 1–16.

  • Jolivet, L., Faccenna, C., Goffé, B., Mattei, M., Rossetti, F., Brunet, C., Storti, F., et al. (1998). Midcrustal shear zones in postorogenic extension: Example from the northern Tyrrhenian Sea. Journal of Geophysical Research, 103(97).

  • Kilgore, B. D., Blanpied, M. L., & Dieterich, J. H. (1993). Velocity dependent friction of granite over a wide range of conditions. Geophysical Research Letters, 20(10), 903–906.

    Google Scholar 

  • Liteanu, E., Niemeijer, a., Spiers, C. J., Peach, C. J., & De Bresser, J. H. P. (2012). The effect of CO 2 on creep of wet calcite aggregates. Journal of Geophysical Research, 117(B3), B03211. doi:10.1029/2011JB008789.

  • Marone, C., Raleigh, B., & Scholz, C. H. (1990). Frictional Behavior and Constitutive Modeling of Simulated Fault Gouge. Journal of Geophysical Research, 95(B5), 7007–7025.

    Google Scholar 

  • Marone, C. (1998). Laboratory-derived friction laws and their application to seismic faulting. Annual Reviews Earth and Planetary Science Letters, 26, 643–696.

    Google Scholar 

  • Moore, D. E., & Lockner, D. A. (2004). Crystallographic controls on the frictional behavior of dry and water-saturated sheet structure minerals. Journal of Geophysical Research, 109(B03401). doi:10.1029/2003JB002582.

  • Moore, D. E., & Lockner, D. A. (2007). Comparative deformation behavior of minerals in serpentinized ultramafic rock: application to the slab-mantle interface in subduction zones. International Geology Review, 49(5), 401–415.

  • Moore, D. E., & Lockner, D. a. (2008). Talc friction in the temperature range 25 o –400 o : relevance for fault-zone weakening. Tectonophysics, 449(1-4), 120–132. doi:10.1016/j.tecto.2007.11.039.

  • Moore, D. E., & Lockner, D. a. (2011). Frictional strengths of talc-serpentine and talc-quartz mixtures. Journal of Geophysical Research, 116(B1), 1–17. doi:10.1029/2010JB007881.

    Google Scholar 

  • Nakatani, M. (2001). Conceptual and physical clarification of rate and state friction: Frictional sliding as a thermally activated rheology. Journal of Geophysical Research, 106(B7), 13347–13380.

    Google Scholar 

  • Niemeijer, A.R. & Spiers, C. J. (2006). Velocity dependence of strength and healing behaviour in simulated phyllosilicate-bearing fault gouge. Journal of Geophysical Research, 427(1-4), 231–253. doi:10.1016/j.tecto.2006.03.048.

  • Niemeijer, A. R. & Spiers, C. J. (2005). Influence of phyllosilicates on fault strength in the brittle-ductile transition: Insights from rock analogue experiments. In D. Bruhn & L. Burlini (Eds.), High-Strain Zones: Structure and Physical Properties (Vol. 245, pp. 303–327). Nice: Geological Society of London. doi:10.1144/GSL.SP.2005.245.01.15.

  • Niemeijer, A. R., & Spiers, C. J. (2007). A microphysical model for strong velocity weakening in phyllosilicate-bearing fault gouges. Journal of Geophysical Research, 112(B10405). doi:10.1029/2007JB005008.

  • Niemeijer, A. R., Spiers, C. J., & Peach, C. J. (2008). Frictional behaviour of simulated quartz fault gouges under hydrothermal conditions: Results from ultra-high strain rotary shear experiments. Tectonophysics, 460(1-4), 288–303.

    Google Scholar 

  • Niemeijer, A., Marone, C., & Elsworth, D. (2010a). Frictional strength and strain weakening in simulated fault gouge: Competition between geometrical weakening and chemical strengthening. Journal of Geophysical Research, 115(B10), B10207. doi:10.1029/2009jb000838.

  • Niemeijer, A., Marone, C., & Elsworth, D. (2010b). Fabric induced weakness of tectonic faults. Geophys. Res. Lett., 37(3), L03304. AGU. doi:10.1029/2009gl041689.

  • Piccinini, D., Piana Agostinetti, N., Roselli, P., Seht, M. I., & Braun, T. (2009). Analysis of small magnitude seismic sequences along the Northern Apennines (Italy). Tectonophysics, 476(1–2), 136–144. doi:10.1016/j.tecto.2009.04.005.

  • Noda, H., & Lapusta, N. (2013). Stable creeping fault segments can become destructive as a result of dynamic weakening. Nature. doi:10.1038/nature11703.

  • Numelin, T., Marone, C., & Kirby, E. (2007). Frictional properties of natural fault gouge from a low-angle normal fault, Panamint Valley, California. Tectonics, 26(2), TC2004. AGU. doi:10.1029/2005tc001916.

  • Reinen, L. A., Weeks, J. D., & Tullis, T. E. (1994). The frictional behavior of lizardite and antigorite serpentinites: Experiments, constitutive models and implications for natural faults. Pure and Applied Geophysics, 143, 317–358.

  • Reinen, L. a., & Weeks, J. D. (1993). Determination of rock friction constitutive parameters using an iterative least squares inversion method. Journal of Geophysical Research, 98(B9), 15937. doi:10.1029/93JB00780.

  • Renard, F., & Ortoleva, P. (1997). Water films at grain–grain contacts: Debye-Hückel, osmotic model of stress, salinity, and mineralogy dependence. Geochimica et Cosmochimica Acta, 61(10), 1963–1970.

  • Rigo, A., Lyon-Caen, H., Armijo, R., Deschamps, A., Hatzfeld, D., Makropoulos, K., Papadimitriou, P., et al. (1996). A microseismic study in the western part of the Gulf of Corinth (Greece): Implications for large‐scale normal faulting mechanisms. Geophysical Journal International, 663–688.

  • Ruina, A., (1983). Slip instability and state variable friction laws. Journal of Geophysical Research, 88 (B12), 10,310–359,370.

    Google Scholar 

  • Saffer, D. M., & Marone, C. (2003). Comparison of smectite- and illite-rich gouge frictional properties: application to the updip limit of the seismogenic zone along subduction megathrusts. Earth and Planetary Science Letters, 215(1-2), 219–235.

    Google Scholar 

  • Sammis, C. G., & Steacy, S. J. (1994). The Micromechanics of Friction in a Granular Layer. Pure and Applied Geophysics, 142(3/4), 778–794.

  • Scuderi, M. M., Niemeijer, A. R., Collettini, C., & Marone, C. (2013). Frictional properties and slip stability of active faults within carbonate–evaporite sequences: The role of dolomite and anhydrite. Earth and Planetary Science Letters, 1–13. doi:10.1016/j.epsl.2013.03.024.

  • Scruggs, V. J., & Tullis, T. E. (1998). Correlation between velocity dependence of friction and strain localization in large displacement experiments on feldspar, muscovite and biotite gouge. Tectonophysics, 295, 15–40.

    Google Scholar 

  • Sibson, R. H. (1977). Fault rocks and fault mechanisms. Journal of the Geological Society of London, 133(3), 191–213. doi:10.1144/gsjgs.133.3.0191.

  • Smith, S. A. F., Holdsworth, R. E., Collettini, C., & Imber, J. (2007). Using footwall structures to constrain the evolution of low-angle normal faults. Journal of the Geological Society, 164(6), 1187–1191. doi:10.1144/0016-76492007-009.

  • Smith, S. A. F., Collettini, C., & Holdsworth, R. E. (2008). Recognizing the seismic cycle along ancient faults: CO 2 -induced fluidization of breccias in the footwall of a sealing low-angle normal fault. Journal of Structural Geology, 30(8), 1034–1046. doi:10.1016/j.jsg.2008.04.010.

  • Smith, S. A. F., & Faulkner, D. R. (2010). Laboratory measurements of the frictional properties of a natural low-angle normal fault: The Zuccale fault, Elba Island, Italy. Journal of Geophysical Research. doi:10.1029/2008JB006274.

  • Tembe, S., Lockner, D. A., & Wong, T.-F. (2010). Effect of clay content and mineralogy on frictional sliding behavior of simulated gouges: Binary and ternary mixtures of quartz, illite, and montmorillonite. Journal of Geophysical Research, 115(B3), B03416. doi:10.1029/2009JB006383.

  • Tesei, T., Collettini, C., Carpenter, B. M., Viti, C., & Marone, C. (2012). Frictional strength and healing behavior of phyllosilicate-rich faults. Journal of Geophysical Research, 117(B9), B09402. doi:10.1029/2012JB009204.

  • Trippetta, F., Collettini, C., Barchi, M. R., Lupattelli, a., & Mirabella, F. (2013). A multidisciplinary study of a natural example of a CO 2 geological reservoir in central Italy. International Journal of Greenhouse Gas Control, 12, 72–83. doi:10.1016/j.ijggc.2012.11.010.

  • Van Diggelen, E. W. E., De Bresser, J. H. P., Peach, C. J., & Spiers, C. J. (2010). High shear strain behaviour of synthetic muscovite fault gouges under hydrothermal conditions. Journal of Structural Geology, 32(11), 1685–1700. doi:10.1016/j.jsg.2009.08.020.

    Google Scholar 

  • Verberne, B.A.V., He, C., & Spiers, C. J. (2010). Frictional Properties of Sedimentary Rocks and Natural Fault Gouge from the Longmen Shan Fault Zone, Sichuan, China. Bulletin of the Seismological Society of America, 100(5B), 2767–2790. doi:10.1785/0120090287.

  • Verberne, B. A., de Bresser, J. H. P., Niemeijer, A. R., Spiers, C. J., de Winter, D. A. M., Plümper, O. (2013). Nanocrystalline slip zones in calcite fault gouge show intense crystallographic preferred orientation: Crystal plasticity at sub- seismic slip rates at 18 – 150° C, 18–21. doi:10.1130/G34279.1.

  • Viti, C., & Collettini, C. (2009). Growth and deformation mechanisms of talc along a natural fault: a micro/nanostructural investigation, 529–542. doi:10.1007/s00410-009-0395-4.

  • Zhang, X., Spiers, C. J., & Peach, C. J. (2010). Compaction creep of wet granular calcite by pressure solution at 28°C to 150°C. Journal of Geophysical Research, 115(B9), B09217. doi:10.1029/2008jb005853.

Download references

Acknowledgments

We wish to thank Eimert de Graaff, Gert Kastelein, Thony van de Gon-Netscher, and Peter van Krieken for technical support, and an anonymous reviewer for his/her comments that helped to improve this paper. A. Niemeijer is/was supported by the Dutch Foundation for Scientific Research (NWO) through a VENI grant (nr. 863.09.013) and a VIDI grant (nr. 854.12.011), and by the ERC starting grant SEISMIC (nr. 335915). C. Collettini is supported by the ERC Starting Grant GLASS (Grant 259256).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to André R. Niemeijer.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Niemeijer, A.R., Collettini, C. Frictional Properties of a Low-Angle Normal Fault Under In Situ Conditions: Thermally-Activated Velocity Weakening. Pure Appl. Geophys. 171, 2641–2664 (2014). https://doi.org/10.1007/s00024-013-0759-6

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00024-013-0759-6

Keywords

Navigation