Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-24T16:14:30.837Z Has data issue: false hasContentIssue false

11 - Thermal Properties of Rocks and Minerals

Published online by Cambridge University Press:  19 November 2021

Nikolai Bagdassarov
Nikolai Bagdassarov
Affiliation:
Goethe-Universität Frankfurt Am Main
Get access

Summary

Conduction of thermal energy according to Fourier’s law is the principal mechanism of heat transport in rocks, which is due to movement of electrons (electron conduction) and by lattice atoms (phonon or lattice conduction). Heat capacity of minerals at low temperature is mostly due to lattice contributions. At high temperatures, electron heat capacity and thermal conductivity are significant. Pressure dependence of thermal conductivity is described by the Bridgman equation. Pressure derivative is scaled to the Bridgman parameter. For thermal conductivity of cubic crystals above Debye temperature, Slack’s formula is used. The Wiedemann–Franz law relates thermal conductivity (?) and electrical conductivity. Increased concentration of vacancies reduces thermal conductivity, but it increases with tilt angle of grain boundaries. To measure thermal conductivity, Forbes, Ångström, Kohlrausch, and flash diffusivity methods are used. Phase transition and melting/crystallization affect heat capacity and thermal conductivity. Geothermal energy is connected with the properties of fluid-saturated rocks. Focus Box 11.1: Phonons and Debye temperature. Focus Box 11.2: Grüneisen parameter.

Keywords

Fourier lawthermal diffusion and conductivityspecific and latent heat of minerals and rocksradiative heat transfer lawmodels of thermal conductivity of rocksthermal anisotropymethods of thermal conductivity measurementsphase transitions and heat transportgeothermal energy.
Type
Chapter
Information
Fundamentals of Rock Physics , pp. 455 - 504
Publisher: Cambridge University Press
Print publication year: 2021

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Literature

Abdulagatova, Z., Abdulagatov, I. M. & Emirov, V. N. (2009). Effect of temperature and pressure on the thermal conductivity of sandstone. International Journal of Rock Mechanics & Mining Sciences 46, 1055–1071.Google Scholar
Abramson, E. H., Brown, M., Slutsky, L. J. & Zaug, J. (1997). The elastic constants of San Carlos olivine to 17 GPa. Journal of Geophysical Research 102(B6), 12 253–12 263.CrossRefGoogle Scholar
Agne, M. T., Hanus, R. & Snyder, G. J. (2018). Minimum thermal conductivity in the context of diffusion-mediated thermal transport. Energy & Environmental Science 11, 609–616.CrossRefGoogle Scholar
Aramberri, H., Rurali, R. & Íñiguez, J. (2017). Thermal conductivity changes across a structural phase transition: The case of high-pressure silica. Physics Review B 96, 195201. doi: 10.1103/PhysRevB.96.195201.CrossRefGoogle Scholar
Arnórrson, S., Thórhallsson, S. & Stefánsson, A. (2015). Utilization of geothermal resources. In: Sigurdsson, H. (Ed.) The Encyclopedia of Volcanoes. Elsevier, Amsterdam, pp.1235–1252.CrossRefGoogle Scholar
Askari, R., Taheri, S. & Hejazi, S. H. (2015). Thermal conductivity of granular porous media: A pore scale modeling approach. AIP Advances 5, 097106 (1–16). doi.org/10.1063/1.4930258.CrossRefGoogle Scholar
Beck, A. E., Darbha, D.M. & Schloessin, H. H. (1978). Lattice conductivities of single-crystal and polycrystalline materials at mantle pressures and temperatures. Physics of the Earth and Planetary Interiors 17, 35–53.CrossRefGoogle Scholar
Bina, C. R. & Helffrich, G. (1994). Phase transition Clapeyron slopes and transition zone seismic discontinuity topography. Journal of Geophysical Research 99(B8), 15 853–15 860.Google Scholar
Cahill, D. G., Watson, S. K. & Pohl, R. O. (1992). Lower limit to the thermal conductivity of disordered crystals. Physics Review B 46(10), 6131–6139.CrossRefGoogle Scholar
Carslaw, H. S. & Jaeger, J. C. (1959). Conduction of Heat in Solids. Clarendon Press, Oxford.Google Scholar
Carson, J. K., Lovatt, S. J., Tanner, D. J. & Cleland, A. C. (2005). Thermal conductivity bounds for isotropic, porous materials. International Journal of Heat and Mass Transfer 48, 2150–2158.Google Scholar
Cermak, V. & Rybach, L. (1982). Thermal properties. In: Hellwege, K.-H. (Ed.) Landolt-Börstein. Numerical Data and Functional Relationships in Science and Technology, New Series, Group V. Geophysics and Space Research, Band I, Teil a. Springer, Berlin, pp. 305–343.Google Scholar
Chai, M., Brown, J. M. & Slutsky, L. J. (1997). The elastic constants of a pyrope-grossular-almandine garnet to 20 GPa. Geophysical Research Letters 24, 523–526.Google Scholar
Chang, Y.-Y., Hsieh, W.-P., Tan, E. & Chen, J. (2017). Hydration-reduced lattice thermal conductivity of olivine in Earth’s upper mantle. PNAS 114(16), 4078–4081. www.pnas.org/cgi/doi/10.1073/pnas.1616216114.Google Scholar
Che, J., Çağın, T., Deng, W. & Goddard, W. A. III (2000). Thermal conductivity of diamond and related materials from molecular dynamics simulations. Journal of Chemical Physics 113(16), 6888–6900.CrossRefGoogle Scholar
Chen, W. & Decker, D. L. (1992). Pressure dependence of the thermal conductivity of pyrophyllite to 40 kbar. Journal of Applied Physics 71, 2624–2627.CrossRefGoogle Scholar
Chopelas, A. (1990). Thermal expansion, heat capacity, and entropy of MgO at mantle pressures. Physics and Chemistry of Minerals 17, 142–148.Google Scholar
Chu, T. K. & Ho, C. Y. (1982). Electrical resistivity of chromium, cobalt, iron, and nickel. CINDAS Report 60, Office of Standard Reference Data, National Bureau of Standards, US Department of Commerce, Washington, DC.Google Scholar
Clauser, C. (2011). Thermal storage and transport properties of rocks, I: Heat capacity and latent heat, and II: Thermal conductivity and diffusivity. In: Gupta, H. K. (Ed.) Encyclopedia of Solid Earth Geophysics. Encyclopedia of Earth Sciences Series. Springer, Dordrecht.Google Scholar
Cosenza, P., Guérin, R. & Tabbagh, A. (2003). Relationship between thermal conductivity and water content of soils using numerical modelling. European Journal of Soil Science 54, 581–587.Google Scholar
Crocombette, J.-P. & Gelebart, L. (2009). Multiscale modeling of the thermal conductivity of polycrystalline silicon carbide. Journal of Applied Physics 106(083520), 1–7.CrossRefGoogle Scholar
Dachs, E. & Geiger, C. A. (2008). Low-temperature heat capacity of synthetic Fe- and Mg-cordierite: Thermodynamic properties and phase relations in the system FeO-Al2O3-SiO2-(H2O). European Journal of Mineralogy 20, 47–62.Google Scholar
Dalton, D. A., Hsieh, W.-P., Hohensee, G. T., Cahill, D. G. & Goncharov, A. F. (2013). Effect of mass disorder on the lattice thermal conductivity of MgO periclase under pressure. Nature Scientific Reports 3, 2400. doi: 10.1038/srep02400.Google Scholar
Dao, L. Q., Delage, P., Tang, A. M., et al. (2014). Anisotropic thermal conductivity of natural Boom Clay. Applied Clay Science 101, 282–287.Google Scholar
Darbha, D. M. & Schloessin, H. H. (1976). Anisotropic lattice thermal conductivity of α-quartz as a function of pressure and temperature. In: Klemens, P. G. & Chu, T. K. (Eds.) Thermal Conductivity, Vol. 14. Springer, New York, pp. 183–190. https://doi.org/10.1007/978-1-4899-3751-3.Google Scholar
Dickson, M. H. & Fanelli, M. (2003). Geothermal Energy: Utilization and Technology. Renewable Energy Series. UNESCO, New York, p. 206.Google Scholar
Genter, A., Guillou-Frottier, L., Feybesse, J.-L., et al. (2003). Typology of potential hot fractured rock resources in Europe. Geothermics 32, 701–710.CrossRefGoogle Scholar
Ghaderi, N., Zhang, D.-B., Zhang, H., et al. (2017). Lattice thermal conductivity of MgSiO3 perovskite from first principles. Nature Scientific Reports 7, 5417. doi:10.1038/s41598-017-05523-6.CrossRefGoogle ScholarPubMed
Gibert, B. & Mainprice, D. (2009). Effect of crystal preferred orientations on the thermal diffusivity of quartz polycrystalline aggregates at high temperature. Tectonophysics 465, 150–163.Google Scholar
Goldstein, B., Hiriart, G., Tester, J., et al. (2013). Geothermal energy, nature, use, and expectations. In: Kaltschmitt, M., Themelis, N. J., Bronicki, L. Y., Söder, L. & Vega, L. A. (Eds.) Renewable Energy Systems. Springer, New York, pp. 4190–4201. doi: 10.1007/978-1-4614-5820-3_309.Google Scholar
Guéguen, Y. & Palciauskas, V. (1994). Introduction to the Physics of Rocks. Princeton University Press, Princeton, 294pp.Google Scholar
Gupta, H. & Roy, S. (2007). Exploration techniques. Chapter 5 in: Geothermal Energy, an Alternative Resource for the 21st Century, Elsevier, Amsterdam, pp. 61–119. https://doi.org/10.1016/B978-044452875-9/50005-8.Google Scholar
Haigis, V., Salanne, M. & Jahn, S. (2012). Thermal conductivity of MgO, MgSiO3 perovskite and post-perovskite in the Earth’s deep mantle. Earth and Planetary Science Letters 355 –356, 102–108.CrossRefGoogle Scholar
Hardee, H. C. (1983). Heat transfer measurements of the 1983 Kilauea lava flow. Science 222, 47–48.CrossRefGoogle ScholarPubMed
Häring, M. O. (2007). Geothermische Stromproduktion aus Enhanced Geothermal Systems (EGS) Stand der Technik, – Geothermal Explorers Ltd, CH-4133 Pratteln. www.geo-ex.ch/assets/uploads/publikationen/egs061207.pdf.Google Scholar
Hartlieb, P., Toifl, M., Kuchar, F., Meisels, R. & Antretter, T. (2016). Thermo-physical properties of selected hard rocks and their relation to microwave-assisted comminution. Minerals Engineering 91, 34–41.CrossRefGoogle Scholar
Hellwege, K.-H. (1988). Einführung in die Festkörperphysik. Springer-Verlag, Berlin, 644pp.Google Scholar
Höfer, M. & Schilling, F. R. (2002). Heat transfer in quartz, orthoclase, and sanidine at elevated temperature. Physics and Chemistry of Minerals 29, 571–584. doi: 10.1007/s00269-002-0277-z.Google Scholar
Hofmeister, A. M. (1999). Mantle values of thermal conductivity and the geotherm from phonon lifetimes. Science 283(5408), 1699–1706. doi: 10.1126/science.283.5408.1699.CrossRefGoogle ScholarPubMed
Hofmeister, A. M. (2007). Pressure dependence of thermal transport properties. PNAS 104(22), 9192–9197.CrossRefGoogle ScholarPubMed
Hofmeister, A. M. (2014). Thermal diffusivity and thermal conductivity of single-crystal MgO and Al2O3 and related compounds as a function of temperature. Physics and Chemistry of Minerals 41, 361–371. doi 10.1007/s00269-014-0655-3.CrossRefGoogle Scholar
Hofmeister, A. M. (2019). Measurements, Mechanisms, and Models of Heat Transport. Elsevier, Amsterdam, 427pp.Google Scholar
Hogan, C. L. & Sawyer, R. B. (1952). The thermal conductivity of metals at high temperature. Journal of Applied Physics 23(2), 177–180.Google Scholar
Holzapfel, W. B. (2005). Effects of intrinsic anharmonicity in the Mie–Grüneisen equation of state and higher order corrections. High Pressure Research 25(3), 187–203.CrossRefGoogle Scholar
Horai, K.-i. & Susaki, J.-i. (1989). The effect of pressure on the thermal conductivity of silicate rocks up to 12 kbar. Physics of the Earth and Planetary Interiors 55, 292–305.CrossRefGoogle Scholar
Hsieh, W.-P., Deschamps, F., Okushi, T. & Lin, J.-F. (2018). Effects of iron on the lattice thermal conductivity of Earth’s deep mantle and implications for mantle dynamics. PNAS 115(16), 4099–4104. www.pnas.org/cgi/doi/10.1073/pnas.1718557115.CrossRefGoogle ScholarPubMed
Huddlestone-Holmes, C. & Hayward, J. (2011). The potential of geothermal energy. CSIRO, March 2011. www.researchgate.net/publication/228591316_The_potential_of_geothermal_energy.Google Scholar
Hugh-Jones, D. (1997). Thermal expansion of MgSiO3 and FeSiO3 ortho- and clinopyroxenes. American Mineralogist 82, 689–696.Google Scholar
IPCC (2012). Special Report on Renewable Energy Sources and Climate Change Mitigation. (Eds. Edenhofer, O., Pichs-Madruga, R., Youba Sokona, Y. et al.) Intergovernmental Panel on Climate Change. Cambridge University Press, Cambridge and New York.Google Scholar
Jain, S. C. & Goel, T. C. (1968). Thermal conductivity of metals at high temperatures by the Jain and Krishnan method I. Nickel. Journal of Physics D: Applied Physics 1, 573–580.Google Scholar
Jaupart, C. & Mareschal, J.-C. (2011). Heat Generation and Transport in the Earth. Cambridge University Press, Cambridge, 464pp.Google Scholar
Kanamori, H., Fujii, N. & Mizutani, H. (1968). Thermal diffusivity measurement of rock-forming minerals from 390° to 1,100°K. Journal of Geophysical Research 73, 595–605.CrossRefGoogle Scholar
Katsura, T., Yamada, H., Nishikawa, O., et al. (2004). Olivine-wadsleyite transition in the system (Mg,Fe)2SiO4. Journal of Geophysical Research 109, B02209. doi:10.1029/2003JB002438.Google Scholar
Kojitani, H. & Akaogi, M. (1997). Melting enthalpies of mantle peridotite: calorimetric determinations in the system CaO-MgO-Al2O3-SiO2 and application to magma generation. Earth and Planetary Science Letters 153, 209–222.Google Scholar
Krupka, K. M. (1985). Low-temperature_heat-capacities and derived thermodynamic properties of anthophyllite, diopside, enstatite, bronzite, and wollastonite. American Mineralogist 70, 249–260.Google Scholar
Krupka, K. M., Hemingway, B. S., Robie, R. A. & Kerrick, D. M. (1985). High-temperature heat capacities and derived thermodynamic properties of anthophyllite, diopside, enstatite, dolomite, bronzite, talc, tremolite, and wollastonite. American Mineralogist 70, 261–271.Google Scholar
Lanchbury, M. D. & Saunders, N. H. (1976). Critical behaviour in the transport properties of pure iron. Journal of Phys. F: Metal Physics 6, 1967–1977.CrossRefGoogle Scholar
Lange, R. A., Cashman, K. V. & Navrotsky, A. (1994). Direct measurements of latent heat during crystallization and melting of a ugandite and an olivine basalt. Contributions to Mineralogy and Petrology 118, 169–181.CrossRefGoogle Scholar
Lebedev, S., Chevrot, S. & van der Hilst, R. D. (2002). Seismic evidence for olivine phase changes at the 410- and 660-kilometer discontinuities. Science 296, 1300–1302.CrossRefGoogle ScholarPubMed
Lobanov, S. S., Holtgrewe, N., Lin, J. F. & Goncharov, A. F. (2017). Radiative conductivity and abundance of post-perovskite in the lowermost mantle. Earth and Planetary Science Letters 479, 43–49. https://doi.org/10.1016/j.epsl.2017.09.016.CrossRefGoogle Scholar
McGuire, C. (2018). Thermal conductivity measurements across a pressure-induced phase transition: Application to heat flow in Earth’s interior. UCLA Electronic Theses and Dissertations, CLA Electronic Theses and Dissertations, University of California, Los Angeles. https://escholarship.org/uc/item/7sb1w8k3.Google Scholar
McWilliams, R. S., Konôpková, Z. & Goncharov, A. F. (2015). A flash heating method for measuring thermal conductivity at high pressure and temperature: Application to Pt. Physics of the Earth and Planetary Interiors 247, 17–26.CrossRefGoogle Scholar
Miao, S. Q., Li, H. P. & Chen, G. (2014). Temperature dependence of thermal diffusivity, specific heat capacity, and thermal conductivity for several types of rocks. Journal of Thermal Analysis and Calorimetry 115, 1057–1063. doi: 10.1007/s10973-013-3427-2.CrossRefGoogle Scholar
Mingo, N. (2003). Calculation of Si nanowire thermal conductivity using complete phonon dispersion relations. Physics Review B 68, 113308.CrossRefGoogle Scholar
Nan, C.-W., Birringer, R., Clarke, D. R. & Gleiter, H. (1997). Effective thermal conductivity of particulate composites with interfacial thermal resistance. Journal of Applied Physics 81, 6692–6699. https://doi.org/10.1063/1.365209.Google Scholar
Ordonez-Miranda, J. & Alvarado-Gil, J. J. (2012). Effect of the pore shape on the thermal conductivity of porous media. Journal of Materials Science 47, 6733–6740. doi: 10.1007/s10853-012-6616-7.CrossRefGoogle Scholar
Osako, M., Ito, E. & Yoneda, A. (2004). Simultaneous measurements of thermal conductivity and thermal diffusivity for garnet and olivine under high pressure. Physics of the Earth and Planetary Interiors 143–144, 311–320.CrossRefGoogle Scholar
Osako, M., Yoneda, A. & Ito, E. (2010). Thermal conductivity, thermal diffusivity, and heat capacity, of serpentine (antigorite) under high pressure. Physics of the Earth and Planetary Interiors 183, 229–233.CrossRefGoogle Scholar
Ramakrishnan, D., Bharti, R., Singh, K. D. & Nithya, M. (2013). Thermal inertia mapping and its application in mineral exploration: Results from Mamandur polymetal prospect, India. Geophysical Journal International 195(1), 357–368. doi: 10.1093/gji/ggt237.CrossRefGoogle Scholar
Rao, K. R., Chaplot, S. L., Choudhury, N., et al. (1988). Lattice dynamics and inelastic neutron scattering from forsterite, Mg2SiO4: Phonon dispersion relation, density of states and specific heat. Physics and Chemistry of Minerals 16, 83–97. https://doi.org/10.1007/BF00201334.CrossRefGoogle Scholar
Robertson, E. C. (1988). Thermal properties of rocks. United States Department of the interior, Geological Survey, Open-File Report 88–441, Reston, Virginia, 107pp. https://doi.org/10.3133/ofr88441.CrossRefGoogle Scholar
Schroeder, J. (1963). Apparatus for determining the thermal conductivity of solids in the temperature range from 20 to 200C. Review of Scientific Instruments 34(6), 615–621. https://doi.org/10.1063/1.1718523.Google Scholar
Seipold, U., Mueller, H.-J. & Tuisku, P. (1998). Principle differences in the pressure dependence of thermal and elastic properties of crystalline rocks. Physics and Chemistry of the Earth 23(3), 357–360.Google Scholar
Sekerka, R. (2015). Thermal Physics. Elsevier, Amsterdam, 600pp.Google Scholar
Silber, R. E., Secco, R. A. & Yong, W. (2017). Constant electrical resistivity of Ni along the melting boundary up to 9 GPa,. Journal of Geophysical Research: Solid Earth 122, 5064–5081. doi:10.1002/2017JB014259.CrossRefGoogle Scholar
Silva, M., Specht, E., Schmidt, J. & Al-Karawi, J. (2009). Influence of the origin of limestone on its decomposition temperature and on the specific heat capacity and conductivity of lime. High Temperatures-High Pressures 38(4), 361–378.Google Scholar
Slack, G. A. (1979). The thermal conductivity of nonmetallic crystals. In: Ehrenreich, H., Seitz, F. & Turnbull, D. (Eds.) Solid State Physics: Advances in Research and Applications, Vol. 34. Academic Press, New York, pp. 1–71.Google Scholar
Smyth, J. R., Jacobsen, S. D. & Hazen, R. M. (2000). Comparative crystal chemistry of orthosilicate minerals. Reviews in Mineralogy and Geochemistry 41(1), 187–209. doi: 10.2138/rmg.2000.41.7.Google Scholar
Somerton, W. H. (1992). Heat capacities of rocks. Chapter II in: Somerton, W.H. (Ed.) Developments in Petroleum Science 37, Elsevier, Amsterdam, pp. 8–21. https://doi.org/10.1016/S0376-7361(09)70022-6.Google Scholar
Sugawara, A. (1968). The precise determination of thermal conductivity of pure fused quartz. Journal of Applied Physics 39, 5994–5997. https://doi.org/10.1063/1.1656103Google Scholar
Sweet, J. N. (1978). Pressure effects on thermal conductivity and expansion of geologic materials. Report SAND78-1991 Sandia Labs, Albuquerque.Google Scholar
Taylor, R. E. & Maglic, K. D. (2003). Thermal diffusivity by the laser flash technique. In: Kaufmann, E. N. (Ed.) Characterization of Materials, Vol. I. John Wiley & Sons, New Jersey.Google Scholar
van der Tempel, L. (2002). Thermal conductivity of a glass: II. The empirical model. Glass Physics and Chemistry 28(3), 147–152.CrossRefGoogle Scholar
Wang, C., Yoneda, A., Osako, M., et al. (2014). Measurement of thermal conductivity of omphacite, jadeite, and diopside up to 14GPa and 1000 K: Implication for the role of eclogite in subduction slab. Journal of Geophysical Research: Solid Earth, 119, 6277–6287. doi:10.1002/2014JB011208.Google Scholar
Wentzcovitch, R. M. & Angel, R. J. (2010). First principles study of thermodynamics and phase transition in low-pressure (P21/c) and high-pressure (C2/c) clinoenstatite MgSiO3. Journal of Geophysical Research 115, B02201. doi:10.1029/2009JB006329.Google Scholar
Zharkov, V. N. & Kalinin, V. A. (1971). Equations of State for Solids at High Pressures and Temperatures. Springer-Verlag, Boston. https://doi.org/10.1007/978-1-4757–1517-0.CrossRefGoogle Scholar
Yagi, T., Ohta, K., Kobayashi, K., et al. (2011). Thermal diffusivity measurement in a diamond anvil cell using a light pulse thermoreflectance technique. Measurement Science and Technology 22, 024011, 10pp. doi:10.1088/0957-0233/22/2/024011.CrossRefGoogle Scholar
Yoneda, A., Yonehara, M. & Osako, M. (2012). Anisotropic thermal properties of talc under high temperature and pressure. Physics of the Earth and Planetary Interiors 190–191, 10–14.Google Scholar

Save book to Kindle

To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×