Abstract
Knowledge of heat transport properties as a function of mineral- and rock-composition and temperature is of major relevance to understand and model heat transfer in the Earth’s interior. A systematic study on 13 natural and 4 synthetic garnets was carried out in an attempt to obtain a better systematic understanding of the processes that affect the heat transport in minerals, especially the effect of chemical substitution in solid solution series. It is found that substitution significantly lowers the thermal diffusivity from end-member values for both synthetic and natural garnets with a minimum of thermal diffusivity at an intermediate composition. The thermal diffusivity as a function of the degree of substitution can be described by the approach of Padture and Klemens (J Am Ceram Soc 80 (4):1018–1020, 1997). With increasing temperature the thermal diffusivity decreases due to phonon-phonon-scattering effects. A quantitative analysis of the high-temperature behaviour was carried out by using the model of Roufosse and Klemens (J Geophys Res 79 (5):703–705, 1974), which takes a lower limit of thermal diffusivity at elevated temperatures into account. The model allows for an extrapolation of the deduced room temperature thermal diffusivities to higher temperatures. Furthermore, the model was modified to determine the high temperature limit of the thermal diffusivity for all investigated natural garnets D min to be 0.64 ± 0.03 mm2/s.
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References
Anderson DL (1989). Theory of the Earth. Blackwell, Oxford
Anderson OL (1999) Mantle convection: a thermal balancing act. Science 283(5408):1652–1653
Blumm J, Lemarchand S (2002) Influence of test conditions on the accuracy of laser flash measurements. High Temp High Press 34:523–528
Bohlen SR, Dollase WA, Wall VJ (1986) Calibration and applications of spinel equilibria in the system FeO-Al2O3-SiO2 (thermobarometer). J Petrol 27(5):1143–1156
Branlund JM, Hofmeister AM (2007) Thermal diffusivity of quartz to 1, 000°C: effects of impurities and the α-β phase transition. Phys Chem Miner 34:581–595. doi:10.1007/s00269-007-0173-7
Bräuer H, Dusza L, Schulz B (1992) New laser flash equipment LFA 427. Interceram 41:489–492
Bruls RJ, Hintzen HT, Metselaar R (2005) A new estimation method for the intrinsic thermal conductivity of nonmetallic compounds: A case study for MgSiN2, AlN and b-Si3N4 ceramics. J Eur Ceram Soc 25:767–779
Chai M, Brown JM, Slutsky LJ (1996) Thermal diffusivity of mantle minerals. Phys Chem Miner 23(7):470–475
Debye P (1914) Vorträge über die kinetische Theorie der Materie und der Elektrizität. B. G. Teubner, Berlin
Eucken A (1911) Uber die Temperaturabhängigkeit der Wärmeleitfähigkeit fester Nichtmetalle. Ann Phys Leipzig IV(34):185–221
Gaumé R, Viana B, Vivien D, Roger J-P, Fournier D (2003) A simple model for the prediction of thermal conductivity in pure and doped insulating crystals. Appl Phys Lett 83(7):1355–1357
Geiger CA, Armbruster T (1997) Mn3Al2Si3O12 spessartine and Ca3Al2Si3O12 grossular garnet; structural dynamic and thermodynamic properties. Am Miner 82(7–8):740–747
Gibert B, Seipold U, Tommasi A, Mainprice D (2003) Thermal diffusivity of upper mantle rocks: Influence of temperature, pressure, and the deformation fabric. J Geophys Res 108(B8):2359. doi:10.1029/2002JB002108
Gibert B, Schilling FR, Gratz K, Tommasi A (2005) Thermal diffusivity of olivine single crystals and a dunite at high temperature: Evidence for heat transfer by radiation in the upper mantle. Phys Earth Planet Inter 151(1–2):129–141
Giesting PA, Hofmeister AM (2002) Thermal conductivity of disordered garnets from infrared spectroscopy. Phys Rev B 65:144305
Giesting PA, Hofmeister AM, Wopenka B, Gwanmesia GD, Jolliff BL (2004) Thermal conductivity and thermodynamics of majoritic garnets; implications for the transition zone. Earth Planet Sci Lett 218(1–2):45–56
Grigull U, Sandner H (1979) Wärmeleitung. Springer, Berlin
Höfer M, Schilling FR (2002) Heat transfer in quartz, orthoclase, and sanidine at elevated temperatures. Phys Chem Miner 29:571–584
Hofmeister AM (1999) Mantle values of thermal conductivity and the geotherm from phonon lifetimes. Science 283(5408):1699–1706
Hofmeister AM (2005) Dependence of diffusive radiative transfer on grainsize, temperature, and fe-content: Implications for mantle processes. J Geodyn 40:51–72
Hofmeister AM (2006) Thermal diffusivity of garnets at high temperature. Phys Chem Miner 33(1):45–62
Hofmeister AM (2007) Pressure dependence of thermal transport properties. Proc Natl Acad Sci 104(22):9192–9197
Hofmeister AM, Chopelas A (1991) Vibrational spectroscopy of end-member silicate garnets. Phys Chem Miner 17(6):503–526
Hofmeister AM, Pertermann M, Branlund JM, Whittington AG (2006) Geophysical implications of reduction in thermal conductivity due to hydration. Geophys Res Lett 33(11):L11310. doi:10.1029/2006GL026036
Hofmeister AM, Pertermann M, Branlund JM (2007). Thermal conductivity of the Earth. In: Schubert G (ed) Treatise in Geophysics, vol 2 Mineral physics (Price GD, ed) Elsevier, The Netherlands, pp 543–578
Horai KI, Simmons G (1969) Thermal conductivity of rock-forming minerals. Earth Planet Sci Lett 6(5):359–368
Kanamori H, Fujii N, Mizutani H (1968) Thermal diffusivity measurement of rock-forming minerals from 300 to 1, 100°K. J Geoph Res 73(2):595–605
Klimm D, Ganschow S, Pajaczkowska A, Lipinska L (2007) On the solubility of Nd3+ in Y3Al5O12. J Alloys Comp 436:204–208
Krupke W, Shinn M, Marion J, Caird J, Stokowski S (1986) Spectroscopic, optical, and thermomechanical properties of neodymiumand chromium-doped gadolinium scandium gallium garnet. J Opt Soc Am B 3(1):102–114
Kuwano Y, Suda K, Ishizawa N, Yamada T (2004) Crystal growth and properties of (Lu, Y)3Al5O12. J Cryst Growth 260(1–2):159–165
Lee HL, Hasselmann DPH (1985) Comparison of data for thermal diffusivity obtained by laser-flash method using thermocouple and photodetector. J Am Ceram Soc 68(1):C12–C13
Marquardt H, Schilling FR, Gratz K (2005) Thermal diffusivity of garnets as a function of temperature. Ber Dtsch Mineral Ges, Beih Eur J Miner 17(1):87
Nye JF (1985) Physical properties of crystals. Clarendon Press, Oxford
Osako M, Eiji I (1997). Simultaneous thermal diffusivity and thermal conductivity measurements of mantle materials up to 10 GPa. Tech Rep ISEI A(67):1–6
Osako M, Ito E, Yoneda A (2004) Simultaneous measurements of thermal conductivity and thermal diffusivity for garnet and olivine under high pressure. Phys Earth Planet Inter 143(1–2):311–320
Padture NP, Klemens PG (1997) Low thermal conductivity in garnets. J Am Ceram Soc 80(4):1018–1020
Parker WJ, Jenkins RJ, Butler CP, Abbott GL (1961) Flash method of determining thermal diffusivity, heat capacity, and thermal conductivity. J Appl Phys 32(9):1679–1684
Patel FD, Honea EC, Speth J, Payne SA, Hutcheson R, Equall R (2001) Laser demonstration of Yb3Al5O12 (YbAG) and materials properties of highly doped Yb: YAG. IEEE J Quantum Electronic 37(1):135–144
Peierls R (1929) Zur kinetischen Theorie der Wärmeleitung in Kristallen. Ann Phys 395 (5(3)):1055–1101
Pertermann M, Hofmeister AM (2006) Thermal diffusivity of olivine group minerals at high temperatures. Am Miner 91:1747–1760
Ray L, Förster H-J, Schilling FR, Förster A (2006). Thermal diffusivity of felsic to mafic granulites at elevated temperatures. Earth Planet Sci Lett. doi:10.1016/j.epsl.2006.09.010
Robie, RA, Hemingway BS, Fisher JR (1979) Thermodynamic properties of minerals and related substances at 298.15 K and 1 bar (105 pascals) pressure and at higher temperatures. US Geol Surv Bull
Robie RA, Bin Z, Hemingway BS, Barton MD (1987) Heat capacity and thermodynamic properties of andradite garnet, Ca2Fe3Si3O12 between 10 to 1000 K and revised values for Δf Gm (298.15 K) of hedenbergite and wollastonite. Geochim Cosmochim Acta 51:2219–2224
Roufosse MC, Klemens PG (1973) Thermal conductivity of complex dielectric crystals. Phys Rev B 7(12):5379–5386
Roufosse MC, Klemens PG (1974) Lattice thermal conductivity of minerals at high temperatures. J Geophys Res 79(5):703–705
Sato Y, Taira T (2006) The studies of thermal conductivity in GdVO4, YVO4 and Y3Al5O12 measured by quasi-one-dimensional flash method. Opt express 14(22):10528–10536
Schilling FR (1999) A transient technique to measure thermal diffusivity at elevated temperatures. Eur J Miner 11(6):1115–1124
Seipold U (1998) Temperature dependence of thermal transport properties of crystalline rocks; a general law. In Heat flow and the structure of the lithosphere; IV, vol 291; 1–4. Elsevier, Amsterdam, pp 161–171
Shankland TJ, Nitsan U (1979) Optical absorption and radiative heat transfer in olivine at high temperature. J Geophys Res 84(B4):1603–1610
Slack GA, Oliver DW (1971) Thermal conductivity of garnets and phonon scattering by rare-earth ions. Phys Rev B 4(2):592–609
Sowe M, Schilling FR (2004) Diploma thesis
Sumino Y, Anderson OL (1982) Elastic constants of minerals. In: Carmichael RS (ed) Handbook of physical properties of rocks, vol 3. CRC Press, Boca Raton, pp 39–138
Wang Z, Ji S (2001) Elasticity of six polycrystalline silicate garnets at pressure up to 3.0 GPa. Am Miner 86(10):1209–1218
Weidenfeller B, Höfer M, Schilling FR (2004) Thermal conductivity, thermal diffusivity, and specific heat capacity of particle filled polypropylene. Compos Part A 35:423–429
Wu P, Pelton AD (1992) Coupled thermodynamic-phase diagram assessment of the rare earth oxide-aluminium oxide binary systems. J Alloys Comp 179:259–287
Yanagawa TKB, Nakada M, Yuen DA (2005) Influence of lattice thermal conductivity on thermal convection with strongly temperature dependent viscosity. Earth Planets Space 57(1):15–28
Yang P, Deng P, Yin Z (2002) Concentration quenching in Yb:YAG. J Lumin 97:51–54
Zharikov EV, Kitaeva VF, Osiko VV, Rustamov IR, Sobolev NN (1984) Elastic, photoelastic, and thermo-physical properties of gadolinium-scandium-gallium-garnet. Sov Phys Solid State 26:922–923
Zoth G, Haenel R (1988). Thermal conductivity. In: Haenel R, Rybach L, Stegena L (eds) Handbook of terrestrial heat-flow density determination. Kluwer, Dordrecht, pp 449–466
Acknowledgments
Many thanks to the institute for crystal growth in Berlin (IKZ) for producing and providing the synthetic garnets. We would also like to thank Netzsch GmbH for test measurements with the LFA 427. We would like to thank A. M. Hofmeister and two anonymous reviewers for their critical comments and helpful suggestions that helped to improve this manuscript. Many thanks to the entire Sect. 4.1 at the GeoForschungsZentrum Potsdam for support, especially Kristin Gratz for discussions and technical assistance, Andreas Ebert for continuous support, Matthias Gottschalk, Sandro Jahn, Sergio Speziale, Hans Josef Reichmann, and Katharina Hartmann for stimulating discussions, Gerhard Berger for microprobe sample preparation, Dieter Rhede for microprobe analysis and Andreas Hahn for X-ray diffraction measurements.
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Marquardt, H., Ganschow, S. & Schilling, F.R. Thermal diffusivity of natural and synthetic garnet solid solution series. Phys Chem Minerals 36, 107–118 (2009). https://doi.org/10.1007/s00269-008-0261-3
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DOI: https://doi.org/10.1007/s00269-008-0261-3