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Volume 29 Issue 1
Jan 2018
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Journal of Earth Science  > 2018  >  29(1): 1-20.
Anne M. Hofmeister, Everett M. Criss. How Properties that Distinguish Solids from Fluids and Constraints of Spherical Geometry Suppress Lower Mantle Convection. Journal of Earth Science, 2018, 29(1): 1-20. doi: 10.1007/s12583-017-0819-4
Citation: Anne M. Hofmeister, Everett M. Criss. How Properties that Distinguish Solids from Fluids and Constraints of Spherical Geometry Suppress Lower Mantle Convection. Journal of Earth Science, 2018, 29(1): 1-20. doi: 10.1007/s12583-017-0819-4
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How Properties that Distinguish Solids from Fluids and Constraints of Spherical Geometry Suppress Lower Mantle Convection

doi: 10.1007/s12583-017-0819-4
  • 1.

    Department of Earth and Planetary Sciences, Washington University, St. Louis, MO 63130, USA

  • 2.

    Panasonic Avionics Corporation, Lake Forest, CA 92630, USA

More Information
  • Corresponding author: Anne M. Hofmeister, hofmeist@wustl.edu
  • Received Date: 11 Jun 2017
  • Accepted Date: 13 Nov 2017
  • Publish Date: 01 Feb 2018
    Abstract
  • The large magnitude of the dimensionless Rayleigh number (Ra ~108) for Earth's ~3 000 km thick mantle is considered evidence of whole mantle convection. However, the current formulation assumes behavior characteristic of gases and liquids and also assumes Cartesian geometry. Issues arising from neglecting physical properties unique to solids and ignoring the spherical shapes for planets include: (1) Planet radius must be incorporated into Ra, in addition to layer thickness, to conserve mass during radial displacements. (2) The vastly different rates for heat and mass diffusion in solids, which result from their decoupled transport mechanisms, promote stability. (3) Unlike liquids, substantial stress is needed to deform solids, which independently promotes stability. (4) High interior compression stabilizes the mantle in additional minor ways. Therefore, representing conditions for convection in solid, self-gravitating spheroids, requires modifying formulae developed for bottomheated fluids near ambient conditions under an invariant gravitational field. To derive stability criteria appropriate to solid spheres, we use dimensional analysis, and consider the effects of geometry, force competition, and microscopic behavior. We show that internal heating has been improperly accounted for in the Ra. We conclude that the lower mantle is stable for two independent reasons: heat diffusion far outpaces mass diffusion (creep) and yield strength of solids at high pressure exceeds the effective deviatoric stress. We discuss the role of partial melt in lubricating plate motion, and explain why the Ra is not applicable to the multi-component upper mantle. When conduction is insufficient to transport heat in the Earth, melt production and ascent are expected, not convection of solid rock.

     

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  • Agee, C. B., 1998. Phase Transformations and Seismic Structure in the Upper Mantle and Transition Zone. Reviews in Mineralogy, 37: 165-204 http://rimg.geoscienceworld.org/content/37/1/165.abstract
    Anderson, D. L., 1989. Theory of the Earth. Blackwell Scientific, Boston
    Armienti, P., Gasperini, D., 2010. Isotopic Evidence for Chaotic Imprint in Upper Mantle Heterogeneity. Geochemistry, Geophysics, Geosystems, 11(5): Q0AC02. https://doi.org/10.1029/2009gc002798
    Aurnou, J. M., Olson, P. L., 2001. Experiments on Rayleigh-Bénard Convection, Magnetoconvection and Rotating Magnetoconvection in Liquid Gallium. Journal of Fluid Mechanics, 430: 283-307. https://doi.org/10.1017/s0022112000002950
    Bercovici, D., 2015. Mantle Dynamics: An Introduction and Overview. In: Schubert, G., ed., Treatise on Geophysics, 7: 1-22 https://www.sciencedirect.com/science/article/pii/B9780444538024001251
    Birch, J. M., Wilshire, B., 1974. Transient and Steady State Creep Behaviour of Polycrystalline MgO. Journal of Materials Science, 9(6): 871-875. https://doi.org/10.1007/bf00570377
    Blagoveshchenskii, N., Novikov, A., Puchkov, A., et al., 2015. Self-Diffusion in Liquid Gallium and Hard Sphere Model. EPJ Web of Conferences, 83: 02018. https://doi.org/10.1051/epjconf/20158302018
    Bleazard, J. G., Sun, T. F., Teja, A. S., 1996. The Thermal Conductivity and Viscosity of Acetic Acid-Water Mixtures. International Journal of Thermophysics, 17(1): 111-125. https://doi.org/10.1007/bf01448214
    Boresi, A. P., Schmidt, R. J., 2003. Advanced Mechanics of Materials. John Wiley and Sons, Hoboken, NJ https://ci.nii.ac.jp/ncid/BA26967544
    Bridgeman, P., 1927. Dimensional Analysis. Yale University Press, New Haven
    Brillo, J., Pommrich, A. I., Meyer, A., 2011. Relation between Self-Diffusion and Viscosity in Dense Liquids: New Experimental Results from Electrostatic Levitation. Physical Review Letters, 107(16): 165902. https://doi.org/10.1103/physrevlett.107.165902
    Buckingham, E., 1914. On Physically Similar Systems; Illustrations of the Use of Dimensional Equations. Physical Review, 4(4): 345-376. https://doi.org/10.1103/physrev.4.345
    Bürgmann, R., Dresen, G., 2008. Rheology of the Lower Crust and Upper Mantle: Evidence from Rock Mechanics, Geodesy, and Field Observations. Annual Review of Earth and Planetary Sciences, 36(1): 531-567. https://doi.org/10.1146/annurev.earth.36.031207.124326
    Carslaw, H. S., Jaeger, J. C., 1959. Conduction of Heat in Solids, 2nd Edition. Oxford University Press, New York
    Chakraborty, S., 2010. Diffusion Coefficients in Olivine, Wadsleyite and Ringwoodite. Reviews in Mineralogy and Geochemistry, 72(1): 603-639. https://doi.org/10.2138/rmg.2010.72.13
    Chudinovskikh, L., Boehler, R., 2007. Eutectic Melting in the System Fe-S to 44 GPa. Earth and Planetary Science Letters, 257(1/2): 97-103. https://doi.org/10.1016/j.epsl.2007.02.024
    Costin, L. S., 1985. Damage Mechanics in the Post-Failure Regime. Mechanics of Materials, 4(2): 149-160. https://doi.org/10.1016/0167-6636(85)90013-4
    Coupland, J. N., McClements, D. J., 1997. Physical Properties of Liquid Edible Oils. Journal of the American Oil Chemists' Society, 74(12): 1559-1564. https://doi.org/10.1007/s11746-997-0077-1
    Criss, E. M., Smith, R. J., Meyers, M. A., 2015. Failure Mechanisms in Cobalt Welded with a Silver-Copper Filler. Materials Science and Engineering: A, 645: 369-382. https://doi.org/10.1016/j.msea.2015.07.094
    Criss, R. E., Hofmeister, A. M., 2016. Conductive Cooling of Spherical Bodies with Emphasis on the Earth. Terra Nova, 28(2): 101-109. https://doi.org/10.13039/100000001
    Cussler, E. L., 2008. Diffusion: Mass Transport in Fluid Systems. Cambridge University Press, Cambridge
    Davies, G. F., 2011. Mantle Convection for Geologists. Cambridge University Press, Cambridge
    Davis, R. O., Selvadurai, A. P. S., 2005. Plasticity and Geomechanics. Cambridge University Press, Cambridge
    de Freitas Cabral, A. J., de Oliveira, P. C., Moreira, S. G. C., et al., 2011. Thermal Diffusivity of Palm Olein and Compounds Containing Β-Carotene. International Journal of Thermophysics, 32(9): 1966-1972. https://doi.org/10.1007/s10765-011-1059-y
    Diamante, L. M., Lan, T. Y., 2014. Absolute Viscosities of Vegetable Oils at Different Temperatures and Shear Rate Range of 64.5 to 4 835 s-1. Journal of Food Processing, 2014(3): 1-6. https://doi.org/10.1155/2014/234583
    Doglioni, C., Anderson, D. L., 2015. Top Driven Asymmetric Mantle Convection. In: Foulger, G. R., Lustrino, M., King, S. D., eds., The Interdisciplinary Earth: In Honor of Don L. Anderson. GSA Special Papers, 214: 51-64
    Doglioni, C., Panza, G., 2015. Polarized Plate Tectonics. Advances in Geophysics, 56: 1-167 doi: 10.1016/bs.agph.2014.12.001
    Domínguez-Rodríguez, A., Gómez-García, D., Zapata-Solvas, E., et al., 2007. Making Ceramics Ductile at Low Homologous Temperatures. Scripta Materialia, 56(2): 89-91. https://doi.org/10.1016/j.scriptamat.2006.09.024
    Doremus, R. H., 2002. Viscosity of Silica. Journal of Applied Physics, 92(12): 7619-7629. https://doi.org/10.1063/1.1515132
    Du, Z., Vinnik, L. P., Foulger, G. R., 2006. Evidence from P-to-S Mantle Converted Waves for a Flat "660-km" Discontinuity beneath Iceland. Earth and Planetary Science Letters, 241(1/2): 271-280. https://doi.org/10.1016/j.epsl.2005.09.066
    Dziewonski, A. M., Anderson, D. L., 1981. Preliminary Reference Earth Model. Physics of the Earth and Planetary Interiors, 25(4): 297-356. https://doi.org/10.1016/0031-9201(81)90046-7
    Elder, J., 1976. The Bowels of the Earth. Oxford University Press, Oxford. ISBN 0-19-854413-8
    Ertl, H., Dullien, F. A. L., 1973. Self-Diffusion and Viscosity of some Liquids as a Function of Temperature. AIChE Journal, 19(6): 1215-1223. https://doi.org/10.1002/aic.690190619
    Fegley, B. Jr., 2015. Practical Chemical Thermodynamics for Geoscientists. Academic Press/Elsevier, Waltham, Massachusetts http://www.sciencedirect.com/science/book/9780122511004
    Fichtner, A., Villase or, A., 2015. Crust and Upper Mantle of the Western Mediterranean—Constraints from Full-Waveform Inversion. Earth and Planetary Science Letters, 428: 52-62. https://doi.org/10.1016/j.epsl.2015.07.038
    Foulger, G. R., 2010. Plates vs Plumes: A Geological Controversy. Wiley-Blackwell, ISBN 978-1-4443-3679-5. 328 http://ci.nii.ac.jp/ncid/BB0376920X?l=en
    Foulger, G. R., Panza, G. F., Artemieva, I. M., et al., 2013. Caveats on Tomographic Images. Terra Nova, 25: 259-281 doi: 10.1111/ter.2013.25.issue-4
    Foulger, G. R., Pritchard, M. J., Julian, B. R., et al., 2001. Seismic Tomography Shows that Upwelling beneath Iceland is Confined to the Upper Mantle. Geophysical Journal International, 146(2): 504-530. https://doi.org/10.1046/j.0956-540x.2001.01470.x
    French, S. W., Romanowicz, B., 2015. Broad Plumes Rooted at the Base of the Earth's Mantle beneath Major Hotspots. Nature, 525(7567): 95-99. https://doi.org/10.1038/nature14876
    Frenkel, J., 1926. Zur Theorie Der Elastizit tsgrenze Und Der Festigkeit Kristallinischer K rper. Zeitschrift für Physik, 37(7/8): 572-609. https://doi.org/10.1007/bf01397292
    Gando, A., Gando, Y., Ichimura, K., et al., 2011. Partial Radiogenic Heat Model for Earth Revealed by Geoneutrino Measurements. Nature Geoscience, 4(9): 647-651. https://doi.org/10.1038/ngeo1205
    Gao, S. S., Liu, K. H., 2014. Imaging Mantle Discontinuities Using Multiply-Reflected P-to-S Conversions. Earth and Planetary Science Letters, 402: 99-106. https://doi.org/10.13039/501100004342
    Gasparik, T., 2000. Evidence for the Transition Zone Origin of some [Mg, Fe]O Inclusions in Diamonds. Earth and Planetary Science Letters, 183(1/2): 1-5. https://doi.org/10.1016/s0012-821x(00)00254-5
    Glazier, J. A., Segawa, T., Naert, A., et al., 1999. Evidence against 'Ultrahard' Thermal Turbulence at very High Rayleigh Numbers. Nature, 398(6725): 307-310. https://doi.org/10.1038/18626
    Goes, S., Agrusta, R., van Hunen, J., et al., 2017. Subduction-Transition Zone Interaction: A Review. Geosphere, 13(3): 644-664. https://doi.org/10.1130/ges01476.1
    Hamilton, W. B., 2002. The Closed Upper-Mantle Circulation of Plate Tectonics. In: Stein S., Freymueller, J. T., eds., Plate Boundary Zones: Geodynamics Series. American Geophysical Union, Washington, D. C. . 359-410
    Hamilton, W. B., 2011. Plate Tectonics Began in Neoproterozoic Time, and Plumes from Deep Mantle have never Operated. Lithos, 123(1/2/3/4): 1-20. https://doi.org/10.1016/j.lithos.2010.12.007
    Hamilton, W. B., 2015. Terrestrial Planets Fractionated Synchronously with Accretion, but Earth Progressed through Subsequent Internally Dynamic Stages whereas Venus and Mars have been Inert for more than 4 Billion Years. GSA Special Papers, 514: 123-156 http://mines.academia.edu/WarrenHamilton
    Hamza, V. M., 2013. Global Heat Flow without Invoking "Kelvin Paradox". Frontiers in Geosciences, 1: 11-20 https://www.researchgate.net/publication/259853177_Global_Heat_Flow_without_Invoking_Kelvin_Paradox
    He, X. M., Fowler, A., Toner, M., 2006. Water Activity and Mobility in Solutions of Glycerol and Small Molecular Weight Sugars: Implication for Cryo-and Lyopreservation. Journal of Applied Physics, 100(7): 074702. https://doi.org/10.1063/1.2336304
    Heap, M. J., Baud, P., Meredith, P. G., et al., 2011. Brittle Creep in Basalt and Its Application to Time-Dependent Volcano Deformation. Earth and Planetary Science Letters, 307(1/2): 71-82. https://doi.org/10.1016/j.epsl.2011.04.035
    Heep, M. J., 2009. Creep: Time‐Dependent Brittle Deformation in Rocks: [Dissertation]. University College London, London
    Henderson, G., 1982. Inorganic Geochemistry. Permagon Press, New York. ISBN 0-08-020448-1
    Hetényi, G., 2014. To Conserve or not to Conserve (Mass in Numerical Models). Terra Nova, 26(5): 372-376. https://doi.org/10.1111/ter.12109
    Hill, R., 1950. The Mathematical Theory of Plasticity. Oxford University Press, Oxford
    Hiraga, T., Miyazaki, T., Tasaka, M., et al., 2010. Mantle Superplasticity and Its Self-Made Demise. Nature, 468(7327): 1091-1094. https://doi.org/10.1038/nature09685
    Hirth, G., 2002. Laboratory Constraints on the Rheology of the Upper Mantle. Reviews in Mineralogy and Geochemistry, 51(1): 97-120. https://doi.org/10.2138/gsrmg.51.1.97
    Hofmeister, A. M., 2010. Scale Aspects of Heat Transport in the Diamond Anvil Cell, in Spectroscopic Modeling, and in Earth's Mantle: Implications for Secular Cooling. Physics of the Earth and Planetary Interiors, 180(3/4): 138-147. https://doi.org/10.1016/j.pepi.2009.12.006
    Hofmeister, A. M., Branlund, J. M., 2016. Thermal Conductivity of the Earth. In: Schubert, G., ed., Treatise in Geophysics, 2nd Edition. V. 2 Mineral Physics (Price, G. D., ed. ). Elsevier, The Netherlands. 584-608
    Hofmeister, A. M., Criss, R. E., 2005. Earth's Heat Flux Revised and Linked to Chemistry. Tectonophysics, 395(3/4): 159-177. https://doi.org/10.1016/j.tecto.2004.09.006
    Hofmeister, A. M., Criss, R. E., 2012. A Thermodynamic and Mechanical Model for Formation of the Solar System via 3-Dimensional Collapse of the Dusty Pre-Solar Nebula. Planetary and Space Science, 62(1): 111-131. https://doi.org/10.13039/100000104
    Hofmeister, A. M., Criss, R. E., 2013. How Irreversible Heat Transport Processes Drive Earth's Interdependent Thermal, Structural, and Chemical Evolution. Gondwana Research, 24(2): 490-500. https://doi.org/10.1016/j.gr.2013.02.009
    Hofmeister, A. M., Criss, R. E., 2015. Evaluation of the Heat, Entropy, and Rotational Changes Produced by Gravitational Segregation during Core Formation. Journal of Earth Science, 26(1): 124-133. https://doi.org/10.1007/s12583-015-0509-z http://en.earth-science.net/WebPage/Article.aspx?id=1068
    Hofmeister, A. M., Sehlke, A., Avard, G., et al., 2016. Transport Properties of Glassy and Molten Lavas as a Function of Temperature and Composition. Journal of Volcanology and Geothermal Research, 327: 330-348. https://doi.org/10.13039/100000001
    Hofmeister, A. M., Whittington, A. G., 2012. Effects of Hydration, Annealing, and Melting on Heat Transport Properties of Fused Quartz and Fused Silica from Laser-Flash Analysis. Journal of Non-Crystalline Solids, 358(8): 1072-1082. https://doi.org/10.1016/j.jnoncrysol.2012.02.012
    Huang, L. H., Liu, L. S., 2009. Simultaneous Determination of Thermal Conductivity and Thermal Diffusivity of Food and Agricultural Materials Using a Transient Plane-Source Method. Journal of Food Engineering, 95(1): 179-185. https://doi.org/10.1016/j.jfoodeng.2009.04.024
    Jin, Z. M., Zhang, J. F., Green, H. W. II, et al., 2001. Eclogite Rheology: Implications for Subducted Lithosphere. Geology, 29(8): 667-670. https://doi.org/10.1130/0091-7613(2001)029<0667:erifsl>2.0.co;2 doi: 10.1130/0091-7613(2001)029<0667:erifsl>2.0.co;2
    Kajihara, K., Kamioka, H., Hirano, M., et al., 2005. Interstitial Oxygen Molecules in Amorphous SiO2. Ⅲ. Measurements of Dissolution Kinetics, Diffusion Coefficient, and Solubility by Infrared Photoluminescence. Journal of Applied Physics, 98(1): 013529. https://doi.org/10.1063/1.1943506
    Kavner, A., Duffy, T. S., 2001. Strength and Elasticity of Ringwoodite at Upper Mantle Pressures. Geophysical Research Letters, 28(14): 2691-2694. https://doi.org/10.1029/2000gl012671
    Kestin, J., Knierim, K., Mason, E. A., et al., 1984. Equilibrium and Transport Properties of the Noble Gases and Their Mixtures at Low Density. Journal of Physical and Chemical Reference Data, 13(1): 229-303. https://doi.org/10.1063/1.555703
    Kohlstedt, D. L., Hansen, L. N., 2015. Constituative Behavior, Rheological Behavior, and Viscosity of Rocks. In: Schubert, G., ed., Treatise in Geophysics, 2nd Edition, Vol. 2. Elsevier, The Netherlands. 389-427
    Koschmieder, E. L., Pallas, S. G., 1974. Heat Transfer through a Shallow, Horizontal Convecting Fluid Layer. International Journal of Heat and Mass Transfer, 17(9): 991-1002. https://doi.org/10.1016/0017-9310(74)90181-1
    Langdon, T. G., 1982. Fracture Processes in Superplastic Flow. Metal Science, 16(4): 175-183. https://doi.org/10.1179/030634582790427208
    Lodders, K., 2000. An Oxygen Isotope Mixing Model for the Accretion and Composition of Rocky Planets. Space Science Review, 92: 341-354 doi: 10.1023/A:1005220003004
    Luca, J., Mrawira, D., 2005. New Measurement of Thermal Properties of Superpave Asphalt Concrete. Journal of Materials in Civil Engineering, 17(1): 72-79. https://doi.org/10.1061/(asce)0899-1561(2005)17:1(72)
    Meyer, R. E., 1961. Self-Diffusion of Liquid Mercury. The Journal of Physical Chemistry, 65(3): 567-568. https://doi.org/10.1021/j100821a507
    Meyers, M. A., Chawla, K. K., 2009. Mechanical Behavior of Materials. Cambridge University Press, Cambridge
    Mitchell, B. S., 2004. An Introduction to Materials Engineering and Science for Chemical and Materials Engineers. John Wiley and Sons, Inc., Hoboken
    Moghadam, R. H., Trepmann, C. A., St ckhert, B., et al., 2010. Rheology of Synthetic Omphacite Aggregates at High Pressure and High Temperature. Journal of Petrology, 51(4): 921-945. https://doi.org/10.1093/petrology/egq006
    Mukherjee, A. K., Bird, J. E., Dorn, J. E., 1969. Experimental Correlation for High-Temperature Creep. Transactions of the American Society of Metals, 62: 155-179
    Nabelek, P. I., Hofmeister, A. M., Whittington, A. G., 2012. The Influence of Temperature-Dependent Thermal Diffusivity on the Conductive Cooling Rates of Plutons and Temperature-Time Paths in Contact Aureoles. Earth and Planetary Science Letters, 317/318: 157-164 https://www.sciencedirect.com/science/article/pii/S0012821X11006649
    Nguyen, L. T., Balasubramaniam, V. M., Sastry, S. K., 2012. Determination of In-Situ Thermal Conductivity, Thermal Diffusivity, Volumetric Specific Heat and Isobaric Specific Heat of Selected Foods under Pressure. International Journal of Food Properties, 15(1): 169-187. https://doi.org/10.1080/10942911003754726
    Nishi, T., Shibata, H., Waseda, Y., et al., 2003. Thermal Conductivities of Molten Iron, Cobalt, and Nickel by Laser Flash Method. Metallurgical and Materials Transactions A, 34(12): 2801-2807. https://doi.org/10.1007/s11661-003-0181-2
    Nishihara, Y., Tinker, D., Kawazoe, T., et al., 2008. Plastic Deformation of Wadsleyite and Olivine at High-Pressure and High-Temperature Using a Rotational Drickamer Apparatus (RDA). Physics of the Earth and Planetary Interiors, 170(3/4): 156-169. https://doi.org/10.1016/j.pepi.2008.03.003
    Paterson, M. S., 1958. Experimental Deformation and Faulting in Wombeyan Marble. Geological Society of America Bulletin, 69(4): 465-475. https://doi.org/10.1130/0016-7606(1958)69[465:edafiw]2.0.co;2
    Paterson, M. S., Weaver, C. W., 1970. Deformation of Polycrystalline MgO under Pressure. Journal of the American Ceramic Society, 53(8): 463-471. https://doi.org/10.1111/j.1151-2916.1970.tb12678.x
    Pearson, D. S., Ver Strate, G., Von Meerwall, E., et al., 1987. Viscosity and Self-Diffusion Coefficient of Linear Polyethylene. Macromolecules, 20(5): 1133-1141. https://doi.org/10.1021/ma00171a044
    Prewitt, C. T., Downs, R. T., 1998. High-Pressure Crystal Chemistry. Reviews in Mineralogy, 37: 284-342 http://rimg.geoscienceworld.org/content/37/1/283.short
    Rayleigh, L., 1916. On Convection Currents in a Horizontal Layer of Fluid, when the Higher Temperature is on the under Side. Philosophical Magazine Series 6, 32(192): 529-546. https://doi.org/10.1080/14786441608635602
    Rees, B. A., Okal, E. A., 1987. The Depth of the Deepest Historical Earthquakes. Pure and Applied Geophysics, 125(5): 699-715. https://doi.org/10.1007/bf00878029
    Reif, F., 1965. Fundamentals of Statistical and Thermal Physics. McGraw-Hill Book Company, St. Louis. 651 http://katalog.ub.uni-heidelberg.de/titel/67214658
    Romine, W. L., Whittington, A. G., 2015. A Simple Model for the Viscosity of Rhyolites as a Function of Temperature, Pressure and Water Content. Geochimica et Cosmochimica Acta, 170: 281-300. https://doi.org/10.1016/j.gca.2015.08.009
    Romine, W. L., Whittington, A. G., Nabelek, P. I., et al., 2012. Thermal Diffusivity of Rhyolitic Glasses and Melts: Effects of Temperature, Crystals and Dissolved Water. Bulletin of Volcanology, 74(10): 2273-2287. https://doi.org/10.1007/s00445-012-0661-6
    Schriempf, J. T., 1972. A Laser Flash Technique for Determining Thermal Diffusivity of Liquid Metals at Elevated Temperatures. Review of Scientific Instruments, 43(5): 781-786. https://doi.org/10.1063/1.1685757
    Schriempf, J. T., 1973. Thermal Diffusivity of Liquid Gallium. Solid State Communications, 13(6): 651-653. https://doi.org/10.1016/0038-1098(73)90451-1
    Schubert, G., Turcotte, D. L., Olson, P., 2001. Mantle Convection in the Earth and Planets. Cambridge University Press, Cambridge
    Sehlke, A., Whittington, A., Robert, B., et al., 2014. Pahoehoe to 'a'a Transition of Hawaiian Lavas: An Experimental Study. Bulletin of Volcanology, 76(11): 876-896. https://doi.org/10.1007/s00445-014-0876-9
    Shimada, M., Cho, A., Yukutake, H., 1983. Fracture Strength of Dry Silicate Rocks at High Confining Pressures and Activity of Acoustic Emission. Tectonophysics, 96(1/2): 159-172. https://doi.org/10.1016/0040-1951(83)90248-2
    Siggia, E. D., 1994. High Rayleigh Number Convection. Annual Review of Fluid Mechanics, 26(1): 137-168. https://doi.org/10.1146/annurev.fl.26.010194.001033
    Smith, E. M., Shirey, S. B., Nestola, F., et al., 2016. Large Gem Diamonds from Metallic Liquid in Earth's Deep Mantle. Science, 354(6318): 1403-1405. https://doi.org/10.13039/100000001
    Soutas-Little, R., 2011. History of Continuum Mechanics. In: Meridio, J., Saccomandi, G., eds., Continuum Mechanics. Eolss Publishers, Singapore. 80-93
    Stacey, F. D., Stacey, C. H. B., 1999. Gravitational Energy of Core Evolution: Implications for Thermal History and Geodynamo Power. Physics of the Earth and Planetary Interiors, 110(1/2): 83-93. https://doi.org/10.1016/s0031-9201(98)00141-1
    Stein, C. A., Stein, S. A., 1992. A Model for the Global Variation in Oceanic Depth and Heat Flow with Lithospheric Age. Nature, 359(6391): 123-129. https://doi.org/10.1038/359123a0
    Stengel, K. C., Oliver, D. S., Booker, J. R., 1982. Onset of Convection in a Variable-Viscosity Fluid. Journal of Fluid Mechanics, 120: 411-431. https://doi.org/10.1017/s0022112082002821
    Thern, A., Lüdemann, H. D., 1996. P, T Dependence of the Self Diffusion Coefficients and Densities in Liquid Silicone Oils. Zeitschrift für Naturforschung A, 51(3): 192-196. https://doi.org/10.1515/zna-1996-0310
    Timoshenko, S. P., Goodier, J. N., 1970. Theory of Elasticity. McGraw-Hill, New York
    Transtrum, M. K., Machta, B. B., Brown, K. S., et al., 2015. Perspective: Sloppiness and Emergent Theories in Physics, Biology, and beyond. The Journal of Chemical Physics, 143(1): 010901. https://doi.org/10.13039/100000001
    Tritton, D. J., 1977. Physical Fluid Dynamics. Van Nostrand Reinhold, New York
    Van Schmus, W. R., 1995. Natural Radioactivity of the Crust and Mantle. In: Ahrens, T. J., ed., Global Earth Physics. American Geophysical Union, Washington D. C. 283-291
    Wawersik, W. R., Brace, W. F., 1970. Post-Failure Behavior of a Granite and Diabase.Rock Mechanics and Rock Engineering, 3: 61-85 doi: 10.1007%2FBF01239627
    Weidner, D. J., Li, L., 2015. Methods for the Study of High P/T Deformation and Rheology. In: Schubert, G., ed., Treatise on Geophysics, 2: 339-358
    White, D. B., 1988. The Planforms and Onset of Convection with a Temperature-Dependent Viscosity. Journal of Fluid Mechanics, 191: 247-286. https://doi.org/10.1017/s0022112088001582
    Whittington, A. G., Hofmeister, A. M., Nabelek, P. I., 2009. Temperature-Dependent Thermal Diffusivity of Earth's Crust: Implications for Crustal Anatexis. Nature, 458: 319-321 doi: 10.1038/nature07818
    Xu, Z., Morris, R., Bencsik, M., et al., 2014. Detection of Virgin Olive Oil Adulteration Using Low Field Unilateral NMR. Sensors, 14(2): 2028-2035. https://doi.org/10.3390/s140202028
    Yá ez-Limón, J. M., Mayen-Mondragón, R., Martínez-Flores, O., et al., 2005. Thermal Diffusivity Studies in Edible Commercial Oils Using Thermal Lens Spectroscopy. Superficies y Vacio, 18: 31-37 http://www.redalyc.org/resumen.oa?id=94218106
    Zemansky, M. W., Dittman, R. H., 1981. Heat and Thermodynamics, 6th Edition. McGraw-Hill, New York
    Zener, C., 1938. Internal Friction in Solids Ⅱ. General Theory of Thermoelastic Internal Friction. Physical Review, 53(1): 90-99. https://doi.org/10.1103/physrev.53.90
    Zhang, Y., Ni, H., Chen, Y., 2010. Diffusion of H, C, and O Components in Silicate Melts. Reviews in Mineralogy and Geochemistry, 72(1): 171-225. https://doi.org/10.2138/rmg.2010.72.5
    Zhong, S. J., Yuen, D. A., Moresi, L. M, et al., 2015. Numerical Method for Mantle Convection. In: Schubert, G., ed., Treatise on Geophysics. Mantle Dynamics, 7: 197-222 https://www.sciencedirect.com/science/article/pii/S138410761630046X
    Zombeck, M. V., 2007. Handbook of Space Astronomy and Astrophysics. Cambridge University Press, Cambridge
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