Advertisement

Heat Capacity

  • Guglielmo VenturaEmail author
  • Mauro Perfetti
Chapter
Part of the International Cryogenics Monograph Series book series (ICMS)

Abstract

Specific heat provides a link among the many solid state theories; vice versa these theories can also be used to estimate the specific heat of materials. From a practical point of view, the knowledge of the specific heat of technically important materials is often fundamental in the design of instruments and systems which have to work in the low temperature regime. Since cryogenics is presently used in research, aerospace, industry and energy production and storage, specific heat data for commonly used materials are mandatory. In this chapter theories about contributions to specific heat are reported: lattice specific heat (Sect. 1.2), electronic specific heat in normal (Sect. 1.3) and superconducting (Sect. 1.4) materials, contributions from transitions and defects (Sect. 1.5), magnetic specific heat (Sect. 1.6), contributions present in amorphous materials (Sect. 1.7).

Keywords

Magnetic Refrigeration Nuclear Magnetic Moment Phonon Contribution Linear Contribution Electronic Specific Heat 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Reed, R.P., Clark, A.F.: Materials at Low Temperatures. American Society for Metals, Metals Park, US (1983) Google Scholar
  2. 2.
    DiMarzio, E., Dowell, F.: Theoretical prediction of the specific heat of polymer glasses. J. Appl. Phys. 50(10), 6061–6066 (1979)ADSCrossRefGoogle Scholar
  3. 3.
    Sakiadis, B.C., Coates, J.: Prediction of specific heat of organic liquids. AlChE J. 2(1), 88–93 (1956)CrossRefGoogle Scholar
  4. 4.
    Turney, J.E.: Predicting Phonon Properties and Thermal Conductivity Using Anharmonic Lattice Dynamics Calculations. Carnegie Mellon University, Pittsburgh (2009)Google Scholar
  5. 5.
    Ashcroft, N.W., Mermin, N.D.: Solid State Physics. Holt, Rinehart and Winston, New York (1976)Google Scholar
  6. 6.
    Rosenberg, H.M. (ed.): The Solid State. Clarendon Press, Oxford (1984)Google Scholar
  7. 7.
    Cezairliyan, A., Ho, C.Y.O. (eds.): Specific Heat of Solids, ed. by C.Y.O. Ho and A. Cezairliyan. Hemisphere Publishing Corp., New York (1988) Google Scholar
  8. 8.
    Gopal, E.S.R. (ed.): Specific Heats at Low Temperatures. Plenum Press, New York (1966)Google Scholar
  9. 9.
    Barron, T.H.K., White, G.K. (eds.): Heat Capacity and Thermal Expansion at Low Temperatures. Plenum Press, New York (1999)Google Scholar
  10. 10.
    Kittel, C. (ed.): Introduction to Solid State Physics, 8th edn. Wiley, New York (2005)Google Scholar
  11. 11.
    Ibach, H., Lüth, H. (eds.): Solid-State Physics, an Introduction to Theory and Experiments. Springer, Berlin (1991)Google Scholar
  12. 12.
    Ziman, J. (ed.): Electrons and Phonons. Clarendon Press, Oxford (1972)Google Scholar
  13. 13.
    McClintock, P.V.E., Meredith, D.J., Wigmore, J.K. (eds.): Matter at Low Temperatures. Blackie, London (1984)Google Scholar
  14. 14.
    Ventura, G., Risegari, L.: The Art of Cryogenics: Low-Temperature Experimental Techniques. Elsevier, Amsterdam (2007)Google Scholar
  15. 15.
    Petit, A.T., Dulong, P.L.: Recherches sur quelques points importants de la Théorie de la Chaleur. Annales de Chimie et de Physique 10, 395–413 (1819)Google Scholar
  16. 16.
    Corruccini, R.J., Gniewek, J.J.: Specific Heats and Enthalpies of Technical Solids at Low Temperatures: A Compilation from the Literature. National Bureau of Standards, Washington, DC (1960)Google Scholar
  17. 17.
    Chang, S.S.: Heat capacity and thermodynamic properties of polyvinylchloride. J. Res. Natl. Bur. Stand. 82, 9–17 (1977)CrossRefGoogle Scholar
  18. 18.
    Sirdeshmukh, D.B., Sirdeshmukh, L., Subhadra, K.: Atomistic Properties of Solids, vol. 147. Springer, Berlin (2011)Google Scholar
  19. 19.
    Rosen, M., Kalir, D., Klimker, H.: Single crystal elastic constants and magnetoelasticity of holmium from 4.2 to 300 K. J. Phys. Chem. Solids 35(9), 1333–1338 (1974)ADSCrossRefGoogle Scholar
  20. 20.
    Klein, M., Goldman, V., Horton, G.: Thermodynamic properties of solid Ar, Kr and Xe based upon a short range central force and the improved self-consistent phonon scheme. J. Phys. Chem. Solids 31(11), 2441–2452 (1970)ADSCrossRefGoogle Scholar
  21. 21.
    Finegold, L., Phillips, N.E.: Low-temperature heat capacities of solid argon and krypton. Phys. Rev. 177(3), 1383 (1969)ADSCrossRefGoogle Scholar
  22. 22.
    Anderson, O.L.: A simplified method for calculating the Debye temperature from elastic constants. J. Phys. Chem. Solids 24(7), 909–917 (1963)ADSCrossRefGoogle Scholar
  23. 23.
    Somasundari, C., Pillai, N.N.: Debye temperature calculation from various experimental methods for—grown from aqueous solution. IOSR J. Appl. Phys. (IOSR-JAP) 3(5), 1–7 (2013). http:\\www.iosrjournals.org
  24. 24.
    Phillips, N.E.: Low-temperature heat capacity of metals. Crit. Rev. Solid State Mater. Sci. 2(4), 467–553 (1971)CrossRefGoogle Scholar
  25. 25.
    Lounasmaa, O.: Specific heat of holmium metal between 0.38 and 4.2 K. Phys. Rev. 128(3), 1136 (1962)ADSCrossRefGoogle Scholar
  26. 26.
    Lounasmaa, O.: Specific heat of lutetium metal between 0.38 and 4 K. Phys. Rev. 133(1A), A219 (1964)ADSCrossRefGoogle Scholar
  27. 27.
    Lounasmaa, O.: Specific heat of gadolinium and ytterbium metals between 0.4 and 4 K. Phys. Rev. 129(6), 2460 (1963)ADSCrossRefGoogle Scholar
  28. 28.
    Lounasmaa, O.: Specific heat of samarium metal between 0.4 and 4 K. Phys. Rev. 126(4), 1352 (1962)ADSCrossRefGoogle Scholar
  29. 29.
    Lounasmaa, O.: Specific heat of thulium metal between 0.38 and 3.9 K. Phys. Rev. 134(6A), A1620 (1964)ADSCrossRefGoogle Scholar
  30. 30.
    Lounasmaa, O.: Specific heat of praseodymium and neodymium metals between 0.4 and 4 K. Phys. Rev. 133(1A), A211 (1964)ADSCrossRefGoogle Scholar
  31. 31.
    Lounasmaa, O.: Specific heat of cerium and europium metals between 0.4 and 4 K. Phys. Rev. 133(2A), A502 (1964)ADSCrossRefGoogle Scholar
  32. 32.
    Lounasmaa, O., Guenther, R.: Specific heat of dysprosium metal between 0.4 and 4 K. Phys. Rev. 126(4), 1357 (1962)ADSCrossRefGoogle Scholar
  33. 33.
    Lounasmaa, O., Roach, P.R.: Specific heat of terbium metal between 0.37 and 4.2 K. Phys. Rev. 128(2), 622 (1962)ADSCrossRefGoogle Scholar
  34. 34.
    Dreyfus, B., Goodman, B., Lacaze, A., Trolliet, G.: The specific heat of rare earth metals between 0.5 and 4 K. Compt. Rend. 253, 1764–1766 (1961) Google Scholar
  35. 35.
    Peruzzi, A., Gottardi, E., Pavese, F., Peroni, I., Ventura, G.: Investigation of the titanium superconducting transition as a temperature reference point below 0.65 K. Metrologia 37(3), 229 (2000)ADSCrossRefGoogle Scholar
  36. 36.
    Van der Hoeven Jr, B., Keesom, P.: Specific heat of mercury and thallium between 0.35 and 4.2 K. Phys. Rev. 135(3A), A631 (1964)CrossRefGoogle Scholar
  37. 37.
    Tilley, D.R., Tilley, J.: Superfluidity and Superconductivity. CRC Press, Boca Raton (1990)Google Scholar
  38. 38.
    Biondi, M.A., Forrester, A.T., Garfunkel, M.P., Satterthwaite, C.B.: Experimental evidence for an energy gap in superconductors. Rev. Mod. Phys. 30(4), 1109–1136 (1958)ADSCrossRefGoogle Scholar
  39. 39.
    Phillips, N.E., Lambert, M.H., Gardner, W.R.: Lattice heat capacity of superconducting mercury and lead. Rev. Mod. Phys. 36(1), 131–134 (1964)ADSCrossRefGoogle Scholar
  40. 40.
    Tinkham, M. (ed.): Introduction to Superconductivity. McGraw-Hill, New York (1975)Google Scholar
  41. 41.
    Rose-Innes, A.C., Rhoderick, E.H. (eds.): Introduction to Superconductivity. Pergamon Press, London (1977)Google Scholar
  42. 42.
    Phillips, N.E.: Heat capacity of aluminium between 0.1 and 4.0 K. Phys. Rev. 114(3), 676–685 (1959)ADSCrossRefGoogle Scholar
  43. 43.
    Pobell, F.: Matter and methods at low temperatures. Springer, Berlin (2007)Google Scholar
  44. 44.
    Zemansky, M.W. (ed.): Heat and Thermodynamics. McGraw-Hill, New York (1968)Google Scholar
  45. 45.
    Rosenberg, H.M.: The thermal conductivity of metals at low temperatures. Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Sci. 245, 441–497 (1955) Google Scholar
  46. 46.
    Smith, J.L., Haire, R.G.: Superconductivity of americium. Science 200(4341), 535–537 (1978)ADSCrossRefGoogle Scholar
  47. 47.
    Myers, H.P. (ed.): Introductory Solid State Physics, 2nd edn. CRC Press, Boca Raton (1997) Google Scholar
  48. 48.
    Debessai, M., Matsuoka, T., Hamlin, J., Schilling, J., Shimizu, K.: Pressure-induced superconducting state of europium metal at low temperatures. Phys. Rev. Lett. 102(19), 197002 (2009)ADSCrossRefGoogle Scholar
  49. 49.
    Dunn, K., Bundy, F.: Pressure-induced superconductivity in strontium and barium. Phys. Rev. B 25(1), 194 (1982)ADSCrossRefGoogle Scholar
  50. 50.
    Wittig, J., Probst, C., Schmidt, F., Gschneidner Jr, K.: Superconductivity in a new high-pressure phase of scandium. Phys. Rev. Lett. 42(7), 469 (1979)ADSCrossRefGoogle Scholar
  51. 51.
    König, R., Schindler, A., Herrmannsdörfer, T.: Superconductivity of compacted platinum powder at very low temperatures. Phys. Rev. Lett. 82(22), 4528 (1999)CrossRefGoogle Scholar
  52. 52.
    Shimizu, K., Kimura, T., Furomoto, S., Takeda, K., Kontani, K., Onuki, Y., Amaya, K.: Superconductivity in the non-magnetic state of iron under pressure. Nature 412(6844), 316–318 (2001)ADSCrossRefGoogle Scholar
  53. 53.
    Eremets, M.I., Struzhkin, V.V., Mao, H.-K., Hemley, R.J.: Superconductivity in boron. Science 293(5528), 272–274 (2001)ADSCrossRefGoogle Scholar
  54. 54.
    Struzhkin, V.V., Hemley, R.J., Mao, H.-K., Timofeev, Y.A.: Superconductivity at 10–17 K in compressed sulphur. Nature 390(6658), 382–384 (1997)ADSCrossRefGoogle Scholar
  55. 55.
    Shimizu, K., Suhara, K., Ikumo, M., Eremets, M., Amaya, K.: Superconductivity in oxygen. Nature 393(6687), 767–769 (1998)ADSCrossRefGoogle Scholar
  56. 56.
    Gschneidner, K.A., Bünzli, J.-C., Pecharsky, V.K.: Handbook on the physics and chemistry of rare earths, vol. 34. (Access Online via Elsevier, Amsterdam, 2004)Google Scholar
  57. 57.
    Buzea, C., Robbie, K.: Assembling the puzzle of superconducting elements: a review. Supercond. Sci. Technol. 18(1), R1 (2005)ADSCrossRefGoogle Scholar
  58. 58.
    Duan, D., Meng, X., Tian, F., Chen, C., Wang, L., Ma, Y., Cui, T., Liu, B., He, Z., Zou, G.: The crystal structure and superconducting properties of monatomic bromine. J. Phys.: Condens. Matter 22(1), 015702 (2010)ADSGoogle Scholar
  59. 59.
    Corak, W.S., Goodman, B.B., Satterthwaite, C.B., Wexler, A.: Atomic heats of normal and superconducting vanadium. Phys. Rev. 102(3), 656–661 (1956)ADSCrossRefGoogle Scholar
  60. 60.
    Schoenberg, D. (ed.): Superconductivity. Cambridge University Press, Cambridge (1952)Google Scholar
  61. 61.
    Ekin, J. (ed.): Experimental Techniques for Low Temperature Measurements. Oxford University Press, Oxford (2006)Google Scholar
  62. 62.
    Ehrenfest, P., Klein, M.J., Casimir, H.: Collected Scientific Papers. North-Holland, Amsterdam (1959)Google Scholar
  63. 63.
    Stokka, S., Fossheim, K., Ziolkiewicz, S.: Specific heat at a first-order phase transition: SbSI. Phys. Rev. B 24(5), 2807 (1981)ADSCrossRefGoogle Scholar
  64. 64.
    Leupold, H., Boorse, H.: Superconducting and normal specific heats of a single crystal of niobium. Phys. Rev. 134(5A), A1322 (1964)ADSCrossRefGoogle Scholar
  65. 65.
    Robinson, W., Friedberg, S.: Specific heats of NiCl2·6H2O and CoCl2·6H2O between 1.4 and 20 K. Phys. Rev. 117(2), 402 (1960)ADSCrossRefGoogle Scholar
  66. 66.
    Granato, A.: Thermal properties of mobile defects. Phys. Rev. 111(3), 740–746 (1958)ADSCrossRefGoogle Scholar
  67. 67.
    Martin, D.L.: The specific heat of copper from 20 to 300 K. Can. J. Phys. 38(1), 17–24 (1960). doi: 10.1139/p60-003 ADSCrossRefGoogle Scholar
  68. 68.
    Collings, E., Jelinek, F., Ho, J., Mathur, M., Timmerhaus, K., Reed, R., Clark, A.: Advances in Cryogenic Engineering, vol. 22, pp. 159. Plenum Press, New York (1977)Google Scholar
  69. 69.
    Gopal, E.: Magnetic contribution to specific heats. In: Specific Heats at Low Temperatures, pp. 84–111. Springer, New York (1966) Google Scholar
  70. 70.
    Kahn, O.: Molecular Magnetism. VCH, Weinheim (1993)Google Scholar
  71. 71.
    Schweiger, A., Jeschke, G.: Principles of Pulse Electron Paramagnetic Resonance Spectroscopy. Oxford University Press, Oxford (2001)Google Scholar
  72. 72.
    Sanchez, J., Griveau, J.-C., Javorsky, P., Colineau, E., Eloirdi, R., Boulet, P., Rebizant, J., Wastin, F., Shick, A., Caciuffo, R.: Magnetic and electronic properties of NpCo2: evidence for long-range magnetic order. Phys. Rev. B 87(13), 134410 (2013)ADSCrossRefGoogle Scholar
  73. 73.
    De Jongh, L., Miedema, A.: Experiments on simple magnetic model systems. Adv. Phys. 50(8), 947–1170 (2001)ADSCrossRefGoogle Scholar
  74. 74.
    Van Kranendonk, J., Van Vleck, J.H.: Spin waves. Rev. Mod. Phys. 30(1), 1–23 (1958)ADSCrossRefzbMATHMathSciNetGoogle Scholar
  75. 75.
    Hemingway, B.S., Robie, R.A.: Heat capacity and thermodynamic functions for gehlenite and staurolite: with comments on the Schoitky anomaly in the heat capacity of staurolite. Am. Mineral. 69, 307–318 (1984)Google Scholar
  76. 76.
    Berman, R. (ed.): Thermal Conduction in Solids. Clarendon Press, Oxford (1976)Google Scholar
  77. 77.
    Hagmann, C., Richards, P.: Adiabatic demagnetization refrigerators for small laboratory experiments and space astronomy. Cryogenics 35(5), 303–309 (1995)ADSCrossRefGoogle Scholar
  78. 78.
    Ho, J.C., Phillips, N.E.: Tungsten-Platinum alloy for heater wire in calorimetry below 0.1 K. Rev. Sci. Instrum. 36(9), 1382 (1965)ADSCrossRefGoogle Scholar
  79. 79.
    Pobell, F. (ed.) Matter and Methods at Low Temperature, 2nd edn. Springer, Berlin (1991)Google Scholar
  80. 80.
    Friedberg, S., Raquet, C.: The heat capacity of Cu(NO3)2·2.5H2O at low temperatures. J. Appl. Phys. 39(2), 1132–1134 (1968)ADSCrossRefGoogle Scholar
  81. 81.
    Friedberg, S., Cohen, A., Schelleng, J.: The specific heat of FeCl2·4H20 between 1.1 and 20 K. In: DTIC Document (1961)Google Scholar
  82. 82.
    Lounasmaa, O., Sundström, L.J.: Specific heat of gadolinium, terbium, dysprosium, holmium, and thulium metals between 3 and 25 K. Phys. Rev. 150(2), 399 (1966)Google Scholar
  83. 83.
    Lounasmaa, O., Sundström, L.J.: Specific heat of lanthanum, praseodymium, neodymium, and samarium metals between 3 and 25 K. Phys. Rev. 158(3), 591 (1967)Google Scholar
  84. 84.
    Colineau, E., Javorský, P., Boulet, P., Wastin, F., Griveau, J., Rebizant, J., Sanchez, J., Stewart, G.: Magnetic and electronic properties of the antiferromagnet NpCoGa5. Phys. Rev. B 69(18), 184411 (2004)Google Scholar
  85. 85.
    Sanchez, J., Aoki, D., Eloirdi, R., Gaczyński, P., Griveau, J., Colineau, E., Caciuffo, R.: Magnetic and electronic properties of NpFeGa5. J. Phys. Condens. Matter 23(29), 295601 (2011)Google Scholar
  86. 86.
    srdata.nist.govGoogle Scholar
  87. 87.
    Bromiley, P.A.: Development of an Adiabatic Demagnetisation Refrigerator for Use in Space. University of London, London (2000)Google Scholar
  88. 88.
    Wikus, P., Burghart, G., Figueroa-Feliciano, E.: Optimum Operating Regimes of Common Paramagnetic Refrigerants. Cryogenics 51(9), 555–558 (2011)Google Scholar
  89. 89.
    Kuriyama, T., Hakamada, R., Nakagome, H., Tokai, Y., Sahashi, M., Li, R., Yoshida, O., Matsumoto, K., Hashimoto, T.: High efficient two-stage GM refrigerator with magnetic material in the liquid helium temperature region. In: Proceedings of the 1989 Cryogenic Engineering Conference. Advances in Cryogenic Engineering, vol. 35B, pp. 1261–1269 (1990)Google Scholar
  90. 90.
    Sahashi, M., Tokai, Y., Kuriyama, T., Nakagome, H., Li, R., Ogawa, M., Hashimoto, T.: New magnetic material R3T system with extremely large heat capacities used as heat regenerators. Adv. Cryog. Eng. 35(Part B) (1990)Google Scholar
  91. 91.
    Ackermann, R.A.: Cryogenic Regenerative Heat Exchangers. Springer, Berlin (1997)Google Scholar
  92. 92.
    Satoh, T., Onishi, A., Umehara, I., Adachi, Y., Sato, K., Minehara, E.: A Gifford-McMahon cycle cryocooler below 2 K. In: Cryocoolers 11, pp. 381–386. Springer, New York (2002)Google Scholar
  93. 93.
    Gschneidner, K.A., Jr., Pecharsky, A.O., Pecharsky, V.K.: Low temperature cryocooler regenerator materials. In: Ross, R., Jr. (ed.) Cryocoolers 12, pp. 457–465. Springer, New York (2002)Google Scholar
  94. 94.
    Hill, R., Cosier, J., Hukin, D.: The specific heat of erbium from 0.4 to 23 K. J. Phys. F Met. Phys. 14(5), 1267 (1984)Google Scholar
  95. 95.
    Parkinson, D., Roberts, L.: The atomic heat of cerium between 1.5 and 20 K. Proc. Phys. Soc. Sect. B 70(5), 471 (1957)Google Scholar
  96. 96.
    Lounasmaa, O.: Specific heat of europium and ytterbium metals between 3 and 25 K. Phys. Rev. 143(2), 399 (1966)Google Scholar
  97. 97.
    Gatteschi, D., Sessoli, R., Villain, J.: Molecular Nanomagnets. Oxford University Press, Oxford (2006)Google Scholar
  98. 98.
    Boulon, M.-E., Cucinotta, G., Luzon, J., Degl’innocenti, C., Perfetti, M., Bernot, K., Calvez, G., Caneschi, A., Sessoli, R.: Magnetic anisotropy and spin-parity effect along the series of lanthanide complexes with DOTA. Angewandte Chemie (International ed. in English) 52(1), 350–354 (2013). doi: 10.1002/anie.201205938
  99. 99.
    Kirchmayr, H.R., Poldy, C.A., Groessinger, R., Haferl, R., Hilscher, G., Steiner, W., Wiesinger, G.: Magnetic properties of intermetallic compounds of rare earth metals. In: Handb. Phys. Chem. Rare Earths 2, 55–230 (1979)Google Scholar
  100. 100.
    Konings, R., van Miltenburg, J., Van Genderen, A.: Heat capacity and entropy of monoclinic Gd2O3. J. Chem. Thermodyn. 37(11), 1219–1225 (2005)Google Scholar
  101. 101.
    Jin, T., Li, C., Tang, K., Chen, L., Xu, B., Chen, G.: Hydrogenation-induced variation in crystal structure and heat capacity of magnetic regenerative material Er3 Ni. Cryogenics 51(5), 214–217 (2011)Google Scholar
  102. 102.
    Alekseev, P., Znamenskiĭ, N., Lazukov, V., Keĭlin, V., Kovalev, I., Kruglov, S., Nefedova, E., Sadikov, I.: Microscopic nature of the extremely high specific heat of rare earth intermetallic compounds at low temperatures and the possibility of its application in technical superconductivity. Crystallogr. Rep. 51(1), S79–S84 (2006)Google Scholar
  103. 103.
    Zeller, R., Pohl, R.: Thermal conductivity and specific heat of noncrystalline solids. Phys. Rev. B 4(6), 2029 (1971)Google Scholar
  104. 104.
    Zaitlin, M.P., Anderson, A.: Phonon thermal transport in noncrystalline materials. Phys. Rev. B 12(10), 4475 (1975)Google Scholar
  105. 105.
    Anderson, P.W., Halperin, B., Varma, C.M.: Anomalous low-temperature thermal properties of glasses and spin glasses. Phil. Mag. 25(1), 1–9 (1972)Google Scholar
  106. 106.
    Phillips, W.: Tunneling states in amorphous solids. J. Low Temp. Phys. 7(3–4), 351–360 (1972)Google Scholar
  107. 107.
    Hunklinger, S.: Ultrasonics Symposium Proceedings. In: IEEE, New York, pp. 443 (1974)Google Scholar
  108. 108.
    Hunklinger, S.: Tunneling in amorphous solids. Cryogenics 28(4), 224–229 (1988)Google Scholar
  109. 109.
    Lasjaunias, J., Ravex, A., Vandorpe, M., Hunklinger, S.: The density of low energy states in vitreous silica: specific heat and thermal conductivity down to 25 mK. Solid State Commun. 17(9), 1045–1049 (1975)Google Scholar
  110. 110.
    Black, J.L.: Relationship between the time-dependent specific heat and the ultrasonic properties of glasses at low temperatures. Phys. Rev. B 17(6), 2740–2761 (1978)Google Scholar
  111. 111.
    Meissner, M., Abens, S., Strelow, P.: Hahn-Meitner Institute Report, Berlin (2000)Google Scholar
  112. 112.
    Jug†, G.: Theory of the thermal magnetocapacitance of multicomponent silicate glasses at low temperature. Phil. Mag. 84(33), 3599–3615 (2004)Google Scholar
  113. 113.
    Hartwig, G.: Polymer Properties at Room and Cryogenic Temperatures. Springer, Berlin (1994)Google Scholar
  114. 114.
    Engeln, I., Meissner, M., Hartwig, G., Evans, D.: Non-metallic Materials and Composites at Low Temperatures, vol. 2. Plenum, New York (1982)Google Scholar
  115. 115.
    Baur, H.: Über die Wärmekapazität des kristallinen Polyäthylens. Colloid Polym. Sci. 241(1), 1057–1070 (1970)Google Scholar
  116. 116.
    Baur, H.: Bemerkungen zur Wärmeleitfähigkeit und Visko-Elastizität von Polymer-Festkörpern. Kolloid-Zeitschrift und Zeitschrift für Polymere 247(1–2), 753–762 (1971)Google Scholar
  117. 117.
    Baur, H.: Einfluß der Valenzwinkelsteifigkeit auf die thermischen Schwankungen und den Debye-Waller-Faktor von Polymer-Kristallen. Kolloid-Zeitschrift und Zeitschrift für Polymere 250(4), 289–297 (1972)Google Scholar
  118. 118.
    Barucci, M., Di Renzone, S., Olivieri, E., Risegari, L., Ventura, G.: Very-low temperature specific heat of Torlon. Cryogenics 46(11), 767–770 (2006)Google Scholar
  119. 119.
    Touloukian, Y., Powell, R., Ho, C., Klernens, P.: Thermal conductivity, Thermophysical Properties of Matter. IFI/Plenum, New York (1970)Google Scholar
  120. 120.
    Johnson, V.J.: A compendium of the properties of materials at low temperature (phase I). Part II. Properties of solids. In: DTIC Document (1960)Google Scholar
  121. 121.
    White, G.K., Meeson, P.: Experimental techniques in low-temperature physics. In: Monographs on the Physics and Chemistry of Materials, vol. 59 (2002)Google Scholar
  122. 122.
    Marquardt, E., Le, J., Radebaugh, R.: 11th international cryocooler conference Keystone, Co. Cryogenic Material Properties Database, National Institute of Standards and Technology, Boulder, 20–22 June 2000Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.INFNRomeItaly
  2. 2.Dipartimento di ChimicaUniversità di FirenzeSesto FiorentinoItaly

Personalised recommendations