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Thermal diffusivity of natural and synthetic garnet solid solution series

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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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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Correspondence to Hauke Marquardt.

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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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Keywords

  • Thermal diffusivity
  • Thermal transport properties
  • Garnets
  • YAG
  • YbAG
  • Solid solution series
  • Substitution