Prediction of effective thermal conductivity of textured polycrystals taking into account intergranular gaps


Аuthors

1*, Bardushkin V. V.2**, Yakovlev V. B.3***

1. National Research University of Electronic Technology, Bld. 1, Shokin Square, Zelenograd, Moscow, Russia, 124498
2. Institute of Nanotechnology of Microelectronics of the Russian Academy of Sciences, Moscow, Russia
3. Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia

*e-mail: iglavr@mail.ru
**e-mail: bardushkin@mail.ru
***e-mail: yakvb@mail.ru

Abstract

In real polycrystals, the crystallites are separated fr om each other by an intergranular space which can be considered as one of components in a given material because the structure of location of atoms in them differs from structure of atoms in crystallites. As a result, the material characteristics of the intergranular and crystalline phases differ significantly. The present paper discusses the problem of calculating the effective thermal conductivity of a polycrystalline material taking into account intergranular gaps. Two methods have been proposed for predicting the effective thermal conductivity of polycrystalline textured materials taking into account intergranular gaps. The first method is based on polycrystal model with the non-uniform crystallites consisting of a uniform anisotropic core and a uniform isotropic shell. To calculate the effective thermal conductivity tensor, a generalized effective field approximation is used. In this method, the intercrystalline phase is modeled by crystallite shells. The second method uses a matrix composite model and a generalized singular approximation. In this method, the intercrystalline phase is taken as a matrix in which homogeneous anisotropic crystallites are immersed. In both models crystallites are considered as spherical, orientations of crystallographic axes of crystallites are considered distributed under some probabilistic law. Based on the proposed methods, model calculations were carried out for tin and graphite polycrystals. It was shown that: 1) both methods give close results if the thermal conductivities of the intergranular and crystalline phases have the same order; 2) in the case wh ere the thermal conductivity of the intergranular phase is several orders of magnitude smaller than that of the crystalline phase, the second method gives a very overestimated result.

References

  1. Gleiter H. Deformation of polycrystals. Proc. of 2nd RISO Symposium on Metallurgy and Materials Science. (Eds. N. Hansen, T. Leffers, H. Lithold). Roskild, RISO Nat. Lab., 1981. pp. 15–21.

  2. Gleiter H. Nanostructured materials: Basic concepts and microstructure. Acta Materialia, 2000, vol. 48, no. 1, pp. 1–29. https://doi.org/10.1016/S1359-6454(99)00285-2

  3. Yakovlev V.B., Roshchin V.M. Nanokompozity i nanokeramiki kak osnova funktsional'noj elektroniki [Nanocomposites and nanoceramics as the basis of functional electronics]. V «Nanotekhnologii v elektronike», pod red. Yu.А. Chaplygina (In «Nanotechnologies in electronics», ed. Yu.A. Chaplygin). Moscow, Tekhnosfera, 2005, pp. 323–360. In Russ.

  4. Progelhof R.C., Throne J.L., Ruetsch R.R. Methods for predicting the thermal conductivity of composite systems: A review. Polymer Engineering and Science, 1976, vol. 76, no. 9, pp. 615–625.

  5. Pietrak K., Wiśniewski T.S. A review of models for effective thermal conductivity of composite materials. Journal of Power Technologies, 2015, vol. 95, no. 1, pp. 14–24.

  6. Lavrov I.V. Metod prognozirovaniya effektivnoy provodimosti teksturirovannyh polikristallov s uchyotom mezhkristallitnyh promezhutkov [Method of prediction of effective conductivity of textured polycrystals taking into account intergranular gaps]. Izv. vuzov. Elektronika – Proceedings of universities. Electronics, 2020, vol. 25, no. 4, pp. 299–309. In Russ. DOI: 10.24151/1561-5405-2020-25-4-299-309

  7. Kolesnikov V.I., Bardushkin V.V., Lavrov I.V., Sychev A.P., Yakovlev V.B. A generalized effective-field approximation for an inhomogeneous medium with coated inclusions. Dokl. Phys., 2017, vol. 62, no. 9, pp. 415–419. DOI: 10.1134/S1028335817090087

  8. Shermergor T.D. Teoriya Uprugosti Mikroneodnorodnykh Sred [Micromechanics of inhomogeneous medium]. Moscow: Nauka, 1977. 399 p. In Russ.

  9. Kolesnikov V.I., Yakovlev V.B., Bardushkin V.V., Lavrov I.V., Sychev A.P., Yakovleva E.N. Association of evaluation methods of the effective permittivity of heterogeneous media on the basis of a generalized singular approximation. Doklady Physics, 2013, vol. 58, no. 9, pp. 379–383. DOI: 10.1134/S1028335813090012

  10. Lavrov I.V., Kochetygov A.A., Bardushkin V.V., Yakovlev V.B. Ob uchyote kontaktnogo termosoprotivleniya mezhdu vklyucheniyami i matritsey pri prognozirovanii effektivnoy teploprovodnosti kompositov [On accounting for thermal resistance between inclusions and matrix in effective thermal conductivity prediction of composites]. Teplovye protsessy v tehnike – Thermal processes in engineering, 2020, vol. 12, no. 2, pp. 78–86. In Russ. DOI: 10.34759/tpt-2020-12-1-78-86

  11. Giordano S., Palla P.L. Dielectric behavior of anisotropic inhomogeneities: interior and exterior point Eshelby tensors. J. Phys. A: Math. Theor., 2008, vol. 41, 415205 (24 pp).

  12. Landau L.D., Lifshitz E.M. Electrodynamics of Continuous Media. Butterworth-Heinemann, 1984. 460 p. Osborn J.A. Demagnetizing factors of the general ellipsoid. Phys. Rev., 1945, vol. 67, pp. 351–357.

  13. Gel’fand I.M., Minlos R.A., Shapiro Z.Ya. Representations of the Rotation and Lorentz Groups and Their Applications. Oxford, Pergamon, 1963. 384 p.

  14. Maxwell Garnett J.C. Colours in metal glasses and in metallic films. Phil. Trans. R. Soc. London, 1904, vol. 203, pp. 385–420.

  15. Levy O., Stroud D. Maxwell Garnett theory for mixtures of anisotropic inclusions: Application to conducting polymers. Phys. Rev. B, 1997, vol. 56, no. 13, pp. 8035–8046. DOI: https://doi.org/10.1103/PhysRevB.56.8035

  16. Bruggeman D.A.G. Berechnung verschiedener physikalischer Konstanten von heterogenen Substanzen. I. Dielektrizitätskonstanten und Leitfähigkeiten der Mischkörper aus isotropen Substanzen. Ann. Physik, 1935, vol. 24. pp. 636–664.

  17. Bohren C.F., Huffman D.R. Absorption and Scattering of Light by Small Particles. Weinheim: Wiley-VCH Publ., 1998. 544 p.

  18. Berezin I.S., Zhidkov N.P. Metody Vychisleniy [Methods of calculaions]. Vol. 2. Moscow: GIFML Publ., 1962, 640 p. In Russ.

  19. Grigor’ev I.S., Meilikhov E.Z. (eds.) Fizicheskie Velichiny: Spravochnik [Physical quantities: A handbook]. Moscow: Energoatomizdat, 1991. 1232 p. In Russ.

mai.ru — informational site of MAI

Copyright © 2009-2024 by MAI