Abstract
The most important mechanisms of heat transfer in solids are transfer by the lattice waves and transfer by the conduction electrons, and consequently the materials to be studied are broadly divided into three groups: (i) non-metals, where transfer is only by lattice waves, (ii) metals, where transfer is mainly by the conduction electrons and lattice conduction, though present, is unimportant, and (iii) alloys and other badly conducting metallic solids, where the electronic conductivity is so small that both processes are important.
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References
Review Papers and Books
Sommerfeld, A., u. H. Bethe: Electron Theory of Metals. In Handbuch der Physik, Vol. 24/2. 1933.
Born, M., u. M. Goeppert-Mayer: Dynamical Theory of Crystal Lattices. In Handbuch der Physik, Vol. 24/2. 1933.
Mott, N. F., and H. Jones: Theory of the Properties of Metals and Alloys. Oxford: University Press 1936.
Wilson, A. H.: Theory of Metals, 2nd ed. Cambridge: University Press 1953.
Berman, R.: Adv. Physics 2, 103 (1953); thermal conductivity of dielectric solids at low temperatures.
Olsen, J. L., and H. M. Rosenberg: Adv. Physics 2, 28 (1953); thermal conductivity of metals at low temperatures.
Powell, R. L., and W. A. Blanpied: Thermal Conductivity of Metals and Alloys at Low Temperatures —A Review of the Literature. United States National Bureau of Standards, Circular No. 556 (1954).
Thermal Conductivity of Non-metals, Theory
Debye, P.: Equation of State and the Quantum Hypothesis with an Appendix on Thermal Conduction, in: Vorträge über die kinetische Theorie der Materie und Elektrizität. Berlin: Teubner 1914.
Peierls, R.: Ann. Phys., Lpz. 3, 1055 (1929); kinetic theory of thermal conduction in dielectric crystals.
Peierls, R.: Ann. Inst. Poincaré 5, 177 (1935); lattice periodicity and properties of solids
Casimir, H. B. G.: Physica, Haag 5, 495 (1938); thermal resistance at low temperatures due to external boundaries.
Landau, L., and G. Rumer: Phys. Z. Sowjet. 11, 18 (1937); scattering of transverse waves due to cubic anharmonicities.
Pomeranchuk, I.: J. Phys. USSR. 4, 259 (1941); insufficiency of three-phonon interactions, acting alone, to maintain equilibrium of low-frequency longitudinal waves at high temperatures.
Pomeranchuk, I.: J. Phys. USSR. 6, 237 (1942); thermal conduction at low temperatures, role of longitudinal waves, effects of boundary and imperfections.
Pomeranchuk, I.: J. Phys. USSR. 7, 197 (1943); effect of four-phonon interactions.
Froehlich, H., and W. Heitler: Proc. Roy. Soc. Lond., Ser. A 155, 640 (1936); thermal conductivity of paramagnetic crystals.
Pomeranchuk, I.: J. Phys. USSR. 4, 357 (1941); thermal conductivity of paramagnetic solids at low temperatures.
Akhieser, A., and I. Pomeranchuk: J. Phys. USSR. 8, 216 (1944); thermal conductivity of salts used for magnetic cooling.
Kittel, C.: Phys. Rev. 75, 972 (1949); thermal conductivity of glasses.
Klemens, P. G.: Proc. Roy. Soc. Lond., Ser. A 208, 108 (1951); thermal conductivity of dielectric solids at low temperatures.
Klemens, P. G.: Proc. Phys. Soc. Lond. A 68, 1113 (1955); scattering of low-frequency phonons by static imperfections.
Herpin, A.: Ann. Physique 7, 91 (1952); three-phonon interactions and thermal conduction.
Herring, C.: Phys. Rev. 95, 954 (1954); role of low-energy phonons in thermal conduction.
Leibfried, G., u. E. Schloemann: Nachr. Akad. Wiss. Göttingen IIa, No. 4, 71 (1954); thermal conductivity of dielectric solids by a variational technique.
Thermal Conductivity of Non-metals, Experimental
Eucken, A.: Ann. Phys., Lpz. 34, 185 (1911). — Verh. dtsch. phys. Ges. 13, 829 (1911). — Z. Physik 12, 1005 (1911); thermal conductivity of various crystals below room temperature.
Eucken, A., u. G. Kuhn: Z. phys. Chem. 134, 193 (1928); thermal conductivity of mixed crystals.
Eucken, A., u. E. Schroeder: Ann. Phys., Lpz. 36, 609 (1939); thermal conductivity of solidified benzene, hydrogen bromide and nitrous oxide.
Haas, W. J. de, and T. Biermasz: Physica, Haag 2, 673 (1935); low temperature thermal conductivity of quartz.
Haas, W. J. de, and T. Biermasz: Physica, Haag 4, 752 (1937); low temperature thermal conductivity of quartz, potassium chloride and potassium bromide.
Haas, W. J. de, and T. Biermasz: Physica, Haag 5, 47, 320, 619 (1938); boundary resistance observed for quartz, diamond, potassium chloride.
Kurti, N., B. V. Rollin and F. Simon: Physica, Haag 3, 266 (1936); thermal conductivity of single crystals of potassium chrome alum and iron ammonium alum below 0.2° K.
Dijk, H. van, and W. H. Keesom: Physica, Haag 7, 970 (1940); thermal conductivity or iron ammonium alum (compressed).
Gerritsen, A. N., and P. van der Star: Physica, Haag 9, 503 (1942); thermal conductivity of solid methane.
Bijl, D.: Physica, Haag 14, 684 (1949); thermal conductivity of potassium chrome alum and some glasses.
Hudson, R. P.: Thesis, Oxford (1949); thermal conductivity of iron ammonium alum (compressed) below 0.2° K.
Wilkinson K. R., and J. Wilks: J. Sci. Instrum. 26, 19 (1949); thermal conductivity of glass and some technical alloys.
Garrett, C. B. G.: Phil. Mag. 41, 621 (1950); thermal conductivity of potassium chrome alum below 0.3° K.
Berman, R.: Phys. Rev. 76, 315 (1949); thermal conductivity of quartz glass at low temperature.
Berman, R.: Proc. Roy. Soc. Lond., Ser. A 208, 90 (1951); thermal conductivity of glass, quartz, neutron-irradiated quartz and synthetic sapphire.
Berman, R., F. E. Simon, P. G. Klemens and T. M. Fry: Nature, Lond. 166, 277 (1950); thermal conductivity of neutron-irradiated quartz.
Berman, R.: Proc. Phys. Soc. Lond. A 65, 1029 (1952); thermal conductivity of polycrystalline alumina, beryllia and graphite.
Wilkinson, K. R., and J. Wilks: Proc. Phys. Soc. Lond., A 64, 89 (1951); thermal conductivity of solid helium.
Berman, R., F. E. Simon and J. Wilks: Nature, Lond. 168, 277 (1951); Umklappresistance in various dielectric solids.
Webb, F. J., K. R. Wilkinson and J. Wilks: Proc. Roy. Soc. Lond., Ser. A 214, 546 (1953); thermal conductivity of solid helium.
Webb, F. J., and J. Wilks: Phil. Mag. 44, 664 (1953); thermal conductivity of solid helium.
Berman, R., F. E. Simon and J. M. Ziman: Proç. Roy. Soc. Lond., Ser. A 220, 171 (1953); thermal conductivity and size effect of diamond.
Devyatkova, D., and L. S. Stilbans: Zh. Tekh. Fiz. 22, 968 (1952); influence of F-centres on thermal conductivity of potassium chloride.
Smith, A. W.: Phys. Rev. 95, 1095 (1954); thermal conductivity of graphite.
Estermann, T., and J. E. Zimmerman: Technical Report 6, O.N.R. Carnegie Institute of Technology, USA. (1951).
Rosenberg, H. M.: Proc. Phys. Soc. Lond. A 67, 837 (1954); thermal conductivity of silicon and germanium.
Berman, R.: To be published; thermal conductivity of some alkali halides.
Berman, R., E. L. Foster and J. M. Ziman: Proc. Roy. Soc. Lond.. Ser. A 231, 130 (1955); thermal conductivity and size effect of artificial sapphires.
Simson, C. v.: Naturwiss. 38, 559 (1951); thermal conductivity of ammonium chloride.
Uhlir, A.: J. Chem. Phys. 20, 463 (1953); thermal conductivity of fluid argon and nitrogen.
Prosad, S.: Brit. J. Appl. Phys. 3, 58 (1952); thermal conductivity of liquid oxygen.
Grenier, C.: Phys. Rev. 83, 598 (1951); thermal conductivity of liquid helium I.
Bowers, R.: Proc. Phys. Soc. Lond., A 65, 511 (1952); thermal conductivity of liquid helium I.
Fairbank, H. A., and J. Wilks: Phys. Rev. 95, 277 (1954); Proc. Roy. Soc. Lond., Ser. A 231, 545 (1955); thermal conductivity of liquid helium below 1° K.
Thermal Conductivity of Metals, Theory
Bloch, F.: Z. Physik 52, 555 (1928); interaction between electrons and lattice, electronic conduction in metals.
Wilson, A. H.: Proc. Camb. Phil. Soc. 33, 371 (1937); first order approximation to solution of transport equation for electrical and thermal conduction.
Makinson, R. E. B.: Proc. Camb. Phil. Soc. 34, 474 (1938); numerical evaluation of electronic thermal conductivity, treatment of lattice component, influence of anisotropy of phonon distribution on the electronic component.
Kohler, M.: Z. Physik 124, 772 (1948); 125, 679 (1949); solution of transport equation by variational method and application to electronic conduction properties.
Kroll, W.: Sci. Papers Inst. Phys. Chem. Res. Tokyo 34, 194 (1938); solution of transport equation by successive approximations.
Sondheimer, E. H.: Proc. Roy. Soc. Lond., Ser. A 203, 75 (1950); solution of transport equation to third order by the variational method.
Sondheimer, E. H.: Proc. Phys. Soc. Lond., Ser. A 65, 561, 562 (1952); modification of theory for small number of conduction electrons.
Toda, M.: J. Phys. Soc. Japan 8, 339 (1953); diffusion on the Fermi surface and conductivity.
Blatt, F. J.: J. Phys. Soc. Japan 9, 444 (1954); diffusion on the Fermi surface, evaluation of thermal conductivity by numerical solution.
Makinson, R. E. B.: Proc. Phys. Soc. Lond., Ser. A 67, 290 (1954); comment on stationarity in Sondheimer’s variational treatment.
Klemens, P. G.: Proc. Phys. Soc. Lond., Ser. A 67, 194 (1954); Austral. J. Phys. 7, 64 (1954); numerical solution of transport equation for pure metals at low temperatures.
Klemens, P. G.: Proc. Phys. Soc. Lond., Ser. A 67, 194 (1954); Austral. J. Phys. 7, 70 (1954); modification of electronic band structure of monovalent metals to account for low temperature conduction properties.
Ziman, J. M.: Proc. Roy. Soc. Lond., Ser. A 226, 436 (1954); modification of electron-phonon interaction parameter to account for conduction properties.
Klemens, P. G.: Austral. J. Phys. 7, 57 (1954); lattice component of thermal conductivity and electron-phonon interaction.
Rezanov, A. J., and V. J. Cherepanov: Proc. Acad. Sci. USSR. 93, 641 (1953); low temperature thermal conductivity of ferromagnetic metals.
Sondheimer, E. H., and A. H. Wilson: Proc. Roy. Soc. Lond., Ser. A 190, 435 (1947); magneto-resistance effects in metals assuming relaxation times.
Kohler, M.: Naturwiss. 36, 186 (1949); similarity rule for thermal resistance in magnetic fields.
Kohler, M.: Ann. Phys., Lpz. 5, 181 (1949); thermal conduction in strong magnetic fields, extrapolation for the lattice component.
Kohler, M.: Ann. Phys., Lpz. 6, 18 (1949); magneto-resistance effects, first order variational treatment.
Akhieser, A, and I. Pomeranchuk: J. Phys. USSR. 9, 93 (1945); thermal conductivity of bismuth.
Thermal Conductivity of Metals, Experimental
Meissner, W.: Ann. Phys., Lpz. 47, 1001 (1915). — Z. Physik 2, 373 (1915); thermal conductivity of Li, Au and Pt down to liquid hydrogen temperatures.
Bidwell, C. C.: Phys. Rev. 27, 819 (1926); 28, 584 (1926); thermal conductivity of lithium and sodium.
Grüneisen, E., u. E. Goens: Z. Physik 44, 615 (1927); thermal conductivity down to liquid hydrogen temperatures of a wide range of metals. of high purity.
Grüneisen, E., u. H. Reddemann: Ann. Phys., Lpz. 20, 843 (1934); thermal conductivity of alloys, role of lattice conduction.
Berman, R., and D. K. C. MacDonald: Proc. Roy. Soc. Lond., Ser. A 209, 368 (1951); low temperature thermal conductivity of sodium.
Berman, R., and D. K. C. MacDonald: Proc. Roy. Soc. Lond., Ser. A 211, 122 (1952); low temperature thermal conductivity of copper.
Mendelssohn, K., and H. M. Rosenberg: Proc. Phys. Soc. Lond., Ser. A 65, 385 (1952); low temperature thermal conductivity of Cu, Ag, Au, Mg, Zn, Cd, Al and In.
Mendelssohn, K., and H. M. Rosenberg: Proc. Phys. Soc. Lond., Ser. A 65, 388 (1952); low temperature thermal conductivity of Ti, Mn, Fe, Ni, Zr, Cb, Mo, Rh, Pd, Ta, W, Ir, Pt, U and Pb.
Rosenberg, H. M.: Phil. Trans. Roy. Soc. Lond., Ser. A 247, 441 (1955); low temperature thermal conductivity of Cu, Ag, Au, Be, Mg, Zn, Cd, Al, Ga, In,Tl, Ti, Zr, Sn, Pb, V, Cb, Ta, Sb, Mo, W, Mn, Fe, Co, Ni, Rh, Pd, Ir, Pt, Ce, La and U.
White, G. K.: Proc. Phys. Soc. Lond. Ser. A 66, 559 (1953); low temperature thermal conductivity of gold.
White, G. K.: Proc. Phys. Soc. Lond., Ser. A 66, 844 (1953); low temperature thermal conductivity of silver.
White, G. K.: Austral. J. Phys. 6, 397 (1953); low temperature thermal conductivity of copper.
MacDonald, D. K. C., G. K. White and S. B. Woods: Proc. Roy. Soc. Lond., to be published; thermal conductivity of K, Rb and Cs at low temperatures.
Hulm, J. K.: Proc. Roy. Soc. Lond., Ser. A 204, 98 (1950); thermal conductivity of superconductors (Sn, Hg, In and Ta and dilute alloys) at liquid helium temperatures in normal and superconducting state.
Hulm, J. K.: Proc. Phys. Soc. Lond., Ser. A 65, 227 (1952); discussion of discrepancy between theory and experiments of ideal thermal resistivity.
Nobel, J. de: Physica, Haag 17, 551 (1951); low temperature thermal conductivity of Al, Fe, Ni, various steels and monel.
Andrews, F. A., R. T. Webber and D. A. Spohr: Phys. Rev. 84, 994 (1951); low temperature thermal conductivity of aluminium.
Kemp, W. R. G., A. K. Sreedhar and G. K. White: Proc. Phys. Soc. Lond., Ser. A 66, 1077 (1953); low temperature thermal conductivity of magnesium.
Rosenberg, H. M.: Phil. Mag. 45, 73 (1954); thermal and electrical conductivity of magnesium.
Spohr, D. A., and R. T. Webber: Phys. Rev. 95, 602 (1954) and private communication; thermal and electrical conductivity of magnesium.
Rosenberg, H. M.: Phil. Mag. 45, 767 (1954); anisotropy of thermal resistivity of gallium single crystals.
Kemp, W. R. G., P. G. Klemens, A. K. Sreedhar and G. K. White: Phil. Mag. 46, 811 (1955); low temperature thermal conductivity of palladium.
Nicol, J., and T. P. Tseng: Phys. Rev. 92, 1062 (1953); thermal conductivity of copper between 0.25 and 4.2° K.
Reddemann, H.: Ann. Phys., Lpz. 20, 441 (1934); thermal conductivity of a Bi single crystal in magnetic fields.
Grüneisen, E., and H. Adenstedt: Ann. Phys., Lpz. 29, 597 (1937); 31, 714 (1938); effect of transverse magnetic fields on thermal conductivity of some pure metals at liquid hydrogen temperatures.
Grüneisen, E., and H. D. Erfling: Ann. Phys., Lpz. 38, 399 (1940); electrical and thermal resistance of Be single crystals in transverse magnetic fields.
Rausch, K.: Ann. Phys., Lpz. 1, 190 (1947); thermal conductivity of Sb single crystal in magnetic fields.
Grüneisen, E., K. Rausch and K. Weiss: Ann. Phys., Lpz. 7, 1 (1950); electrical and thermal resistance of Bi single crystals in magnetic fields.
Haas, W. J. de, A. N. Gerritsen and W. H. Capel: Physica, Haag 3, 1143 (1936); thermal resistance of Bi single crystals in magnetic fields.
Haas, W. J. de, and J. de Nobel: Physica, Haag 5, 449 (1938); electrical and thermal resistance of W single crystal in magnetic fields.
Nobel, J. de: Physica, Haag 15, 532 (1949); thermal and electrical resistance of W single crystal in high magnetic fields.
Shalyt, S.: J. Phys. USSR. 8, 315 (1944); thermal conductivity of bismuth and effect of magnetic fields down to liquid helium temperatures.
Mendelssohn, K., and H. M. Rosenberg: Proc. Phys. Soc. Lond., Ser. A 64, 1057 (1951); thermal conductivity of cadmium in magnetic fields at liquid helium temperatures.
Mendelssohn, K., and H. M. Rosenberg: Proc. Roy. Soc. Lond., Ser. A 218, 190 (1953); thermal conductivity of various metals in magnetic fields at liquid helium temperatures, in particular Zn, Cd, Sn, Pb and Ga.
Karweil, J., u. K. Schäfer: Ann. Phys., Lpz. 36, 567 (1939); thermal conductivity of various alloys between 3 and 30° K.
Allen, J. F., and E. Mendoza: Proc. Camb. Phil. Soc. 44, 280 (1948); thermal conductivity of copper and German silver at liquid helium temperatures.
Hulm, J. K.: Proc. Phys. Soc. Lond., Ser. A 64, 207 (1951); thermal conductivity and lattice component of alloy Cu 90 – Ni 10.
Berman, R.: Phil. Mag. 42, 642 (1951); low temperature thermal conductivity and lattice component of German silver, stainless steel and Cu 60 –Ni 40.
Estermann, I., and J. E. Zimmerman: J. Appl. Phys. 23, 578 (1952); low temperature thermal conductivity and lattice component of monel, inconel, stainless steel and Cu 90 – Ni 10 and effect of cold work.
Kemp, W. R. G., P. G. Klemens, A. K. Sreedhar and G.K. White: Proc. Phys. Soc. Lond., Ser. A 67, 728 (1954); lattice component of thermal conductivity of Ag-Pd alloys.
Kemp, W. R. G., P. G. Klemens, A. K. Sreedhar and G. K. White: Proc. Roy. Soc. Lond., Ser. A 233, 41 (1956); thermal and electrical conductivities of Ag-Pd and Ag-Cd alloys.
White, G. K., and S.B. Woods: Phil. Mag. 45, 1343 (1954); lattice component of thermal conductivity of a dilute copper alloy.
White, G. K., and S.B. Woods: Canad. J. Phys. 33, 58 (1955); low temperature thermal conductivity and lattice component of copper alloys, Bi, Ge and Be.
Thermal Conductivity of Superconductors
Gorter, C. J., u. H. B. G. Casimir: Phys. Z. 35, 963 (1934). — Z. techn. Phys. 15, 539 (1934); two-fluid model of superconductivity.
Heisenberg, W.: Z. Naturforsch. 3a, 65 (1948); two-fluid model, including application to thermal conductivity of superconductors.
Klemens, P. G.: Proc. Phys. Soc. Lond., Ser. A 66, 576 (1953); electronic thermal conduction in superconductors and two-fluid circulation.
Cornish, F. H. J., and J.L. Olsen: Helv. Phys. Acta 26, 369 (1953); calculation of thermal conductivity of intermediate state, assuming loose coupling between electron and lattice temperatures.
Bremmer, H., and W. J. de Haas: Physica, Haag 3, 672 (1936); thermal conductivity of Pb and Cu.
Haas, W. J. de, and H. Bremmer: Physica, Haag 3, 687 (1936); thermal conductivity of mercury.
Bremmer, H., and W. J. de Haas: Physica, Haag 3, 692 (1936); thermal conductivity of some superconducting alloys.
Haas, W. J. de, and A. Rademakers: Physica, Haag 7, 992 (1940); thermal conductivity of lead in superconducting and normal states.
Rademakers, A.: Physica, Haag 15, 849 (1949); thermal conductivity of Pb and Sn in superconducting and normal states.
Mendelssohn, K., and R. B. Pontius: Phil. Mag. 24, 777 (1937); change of thermal conductivity of lead on going from normal to superconducting state.
Mendelssohn, K., and J. L. Olsen: Proc. Phys. Soc. Lond., Ser. A 63, 2 and 1182 (1950); Phys. Rev. 80, 859 (1950); thermal conductivity of lead and lead-bismuth alloys and intermediate state anomalies.
Olsen, J. L.: Proc. Phys. Soc. Lond., Ser. A 65, 518 (1952); thermal conductivity of lead-bismuth alloys and discussion in terms of enhanced lattice conduction.
Olsen, J. L., and C. A. Renton: Phil. Mag. 43, 946 (1952); thermal conductivity of lead below 1° K.
Mendelssohn, K., and C. A. Renton: Phil. Mag. 44, 776 (1953); thermal conductivity of Sn, In, Tl, Ta, Cb and Al below 1° K.
Mendelssohn K.: Physica, Haag 19, 775 (1953); review of Oxford work on thermal conductivity of superconductors; discussion.
Renton, C. A.: Phil. Mag. 46, 47 (1955); effect of magnetic fields and frozen-in flux on the thermal conductivity of superconductors.
Goodman, B. B.: Proc. Phys. Soc. Lond., Ser. A 66, 217 (1953); thermal conductivity of tin below 1° K.
Shoenberg, D.: Physica, Haag 19, 788 (1953); review of Cambridge work on the thermal conductivity of superconductors and size effect below 1° K.
Heer, C.V., and J. G. Daunt: Phys. Rev. 76, 854 (1949); thermal conductivity of Sn and Ta below 1° K.
Webber, R. T., and D. A. Spohr: Phys. Rev. 84, 384 (1951); thermal conductivity of lead in the intermediate state.
Webber, R. T., and D. A. Spohr: Phys. Rev. 91, 414 (1953); thermal conductivity of mercury in the intermediate state.
Detwiler, D. P., and H. A. Fairbank: Phys. Rev. 86, 574 (1952); 88, 1049 (1952); thermal conductivity of tin and indium in the intermediate state.
Hulm, J. K.: Phys. Rev. 90, 1116 (1953); thermal conductivity of mercury in the intermediate state.
Sladek, W. J.: Phys. Rev. 91, 1280 (1953); 97, 902 (1955); thermal conductivity of indium-thallium alloys, study of lattice conduction and of intermediate state.
Laredo, S. J., and A. B. Pippard: Proc. Camb. Phil. Soc. 51, 368 (1955); extra resi stivity in the intermediate state due to scattering of phonons.
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Klemens, P.G. (1956). Thermal Conductivity of Solids at Low Temperatures. In: Flügge, S. (eds) Low Temperature Physics I / Kältephysik I. Encyclopedia of Physics / Handbuch der Physik, vol 3 / 14. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-39773-2_4
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