How to Measure the Thermal Expansion Coefficient at Low Temperatures

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


Thermal expansion measurements in the high temperature range have been thoroughly explored, and various experimental methods are available even as commercial instrumentation, measurements at cryogenic temperatures have been confined to the field of high-precision laboratory experiments, needing large experimental efforts and expenses, and often also suffering from intrinsic limitations. All techniques used for the measurements of thermal expansion can be divided into two categories, namely: absolute methods and relative methods. While in the former the linear changes of dimension of the sample are directly measured at various temperature, in the latter the coefficient of thermal expansion is determined through comparison with a reference materials of known thermal expansion. A lot of experimental set-ups are described in Sect.  2.1, while Sect.  2.2 some examples of measurements performed at very low temperatures are listed.


Beat Frequency Fuse Quartz Polarize Beam Splitter Capacitor Plate Guard Ring 
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.


  1. 1.
    Kanagaraj, S., Pattanayak, S.: Measurement of the thermal expansion of metal and FRPs. Cryogenics 43(7), 399–424 (2003)ADSCrossRefGoogle Scholar
  2. 2.
    Martelli, V., Bianchini, G., Natale, E., Scarpellini, D., Ventura, G.: A novel interferometric dilatometer in the 4–300 K temperature range: thermal expansion coefficient of SRM-731 borosilicate glass and stainless steel-304. Meas. Sci. Technol. 24(10), 105203 (2013)ADSCrossRefGoogle Scholar
  3. 3.
    Bijl, D., Pullan, H.: A new method for measuring the thermal expansion of solids at low temperatures; the thermal expansion of copper and aluminium and the Grüneisen rule. Physica 21(1), 285–298 (1954)ADSCrossRefGoogle Scholar
  4. 4.
    Sao, G., Tiwary, H.: Thermal expansion of poly (vinylidene fluoride) films. J. Appl. Phys. 53(4), 3040–3043 (1982)ADSCrossRefGoogle Scholar
  5. 5.
    Rao, K., Jeyasri, M.: Measurement of linear thermal expansion of solids by a capacitance method. Indian J. Pure Appl. Phys. 15, 437–440 (1977)Google Scholar
  6. 6.
    Tong, H., Hsuen, H., Saenger, K., Su, G.: Thickness-direction coefficient of thermal expansion measurement of thin polymer films. Rev. Sci. Instrum. 62(2), 422–430 (1991)ADSCrossRefGoogle Scholar
  7. 7.
    White, G.: Measurement of thermal expansion at low temperatures. Cryogenics 1(3), 151–158 (1961)ADSCrossRefGoogle Scholar
  8. 8.
    Pott, R., Schefzyk, R.: Apparatus for measuring the thermal expansion of solids between 1.5 and 380 K. J. Phys. E: Sci. Instrum. 16(5), 444 (1983)ADSCrossRefGoogle Scholar
  9. 9.
    Kroeger, F., Swenson, C.: Absolute linear thermal-expansion measurements on copper and aluminum from 5 to 320 K. J. Appl. Phys. 48(3), 853–864 (1977)ADSCrossRefGoogle Scholar
  10. 10.
    Subrahmanyam, H., Subramanyam, S.: Accurate measurement of thermal expansion of solids between 77 K and 350 K by 3-terminal capacitance method. Pramana 27(5), 647–660 (1986)ADSCrossRefGoogle Scholar
  11. 11.
    Neumeier, J., Bollinger, R., Timmins, G., Lane, C., Krogstad, R., Macaluso, J.: Capacitive-based dilatometer cell constructed of fused quartz for measuring the thermal expansion of solids. Rev. Sci. Instrum. 79(3), 033903–033908 (2008)ADSCrossRefGoogle Scholar
  12. 12.
    Rotter, M., Muller, H., Gratz, E., Doerr, M., Loewenhaupt, M.: A miniature capacitance dilatometer for thermal expansion and magnetostriction. Rev. Sci. Instrum. 69(7), 2742–2746 (1998)ADSCrossRefGoogle Scholar
  13. 13.
    Roth, P., Gmelin, E.: A capacitance displacement sensor with elastic diaphragm. Rev. Sci. Instrum. 63(3), 2051–2053 (1992)ADSCrossRefGoogle Scholar
  14. 14.
    Tokiwa, Y., Grüheit, S., Jeevan, H., Stingl, C., Gegenwart, P.: Low-temperature antiferromagnetic ordering in the heavy-fermion metal YbPd. J. Phys: Conf. Ser. 273, 012062 (IOP Publishing) (2011) Google Scholar
  15. 15.
    Schafer, D., Thomas, G., Wudl, F.: High-resolution thermal-expansion measurements of tetrathiafulvalenetetracyanoquinodimethane (TTF-TCNQ). Phys. Rev. B 12(12), 5532 (1975)ADSCrossRefGoogle Scholar
  16. 16.
    McCammon, R., Work, R.: Measurement of the dielectric properties and thermal expansion of polymers from ambient to liquid helium temperatures. Rev. Sci. Instrum. 36(8), 1169–1173 (1965)ADSCrossRefGoogle Scholar
  17. 17.
    Kanagaraj, S., Pattanayak, S.: Simultaneous measurements of thermal expansion and thermal conductivity of FRPs by employing a hybrid measuring head on a GM refrigerator. Cryogenics 43(8), 451–458 (2003)ADSCrossRefGoogle Scholar
  18. 18.
    García-Moreno, O., Fernández, A., Khainakov, S., Torrecillas, R.: Negative thermal expansion of lithium aluminosilicate ceramics at cryogenic temperatures. Scripta Mater. 63(2), 170–173 (2010)CrossRefGoogle Scholar
  19. 19.
    Keesom, W.H., Andronikashvili, E., Lifshits, E.M.: Helium. Elsevier, Amsterdam (1942)Google Scholar
  20. 20.
    Maxwell, J.C.: Lehrbuch der Electricität und des Magnetismus, vol. 1. J. Springer, Berlin (1883)Google Scholar
  21. 21.
    Hartshorn, L.: Radio-Frequency Measurements by Bridge and Resonance Methods, vol. 10. Chapman and Hall, London (1940)Google Scholar
  22. 22.
    Jones, R.: Some developments and applications of the optical lever. J. Sci. Instrum. 38(2), 37 (1961)ADSCrossRefGoogle Scholar
  23. 23.
    James, J., Spittle, J., Brown, S., Evans, R.: A review of measurement techniques for the thermal expansion coefficient of metals and alloys at elevated temperatures. Meas. Sci. Technol. 12(3), R1 (2001)ADSCrossRefGoogle Scholar
  24. 24.
    Bennett, S.: An absolute interferometric dilatometer. J. Phys. E: Sci. Instrum. 10(5), 525 (1977)ADSCrossRefGoogle Scholar
  25. 25.
    Imai, H., Bates, W.: Measurement of the linear thermal expansion coefficient of thin specimens. J. Phys. E: Sci. Instrum. 14(7), 883 (1981)ADSCrossRefGoogle Scholar
  26. 26.
    Schödel, R.: Ultra-high accuracy thermal expansion measurements with PTB’s precision interferometer. Meas. Sci. Technol. 19(8), 084003 (2008)ADSCrossRefGoogle Scholar
  27. 27.
    Cordero, J., Heinrich, T., Schuldt, T., Gohlke, M., Lucarelli, S., Weise, D., Johann, U., Braxmaier, C.: Interferometry based high-precision dilatometry for dimensional characterization of highly stable materials. Meas. Sci. Technol. 20(9), 095301 (2009)ADSCrossRefGoogle Scholar
  28. 28.
    Okaji, M., Imai, H.: A practical measurement system for the accurate determination of linear thermal expansion coefficients. J. Phys. E: Sci. Instrum. 17(8), 669 (1984)ADSCrossRefGoogle Scholar
  29. 29.
    Uchil, J., Mohanchandra, K., Ganesh Kumara, K., Mahesh, K., P Murali, T.: Thermal expansion in various phases of nitinol using TMA. Phys. B: Condens. Matter 270(3), 289–297 (1999)Google Scholar
  30. 30.
    Vijay, A.: Temperature dependence of elastic constants and volume expansion for cubic and non-cubic minerals. Phys. B 349(1), 62–70 (2004)ADSCrossRefGoogle Scholar
  31. 31.
    Singh, K., Gupta, B.: A simple approach to analyse the thermal expansion in minerals under the effect of high temperature. Phys. B 334(3), 266–271 (2003)ADSGoogle Scholar
  32. 32.
    Birch, K.: An automatic absolute interferometric dilatometer. J. Phys. E: Sci. Instrum. 20(11), 1387 (1987)ADSCrossRefGoogle Scholar
  33. 33.
    Okaji, M., Inai, H.: A high-temperature dilatometer using optical heterodyne interferometry. J. Phys. E: Sci. Instrum. 20, 887–891 (1987)ADSCrossRefGoogle Scholar
  34. 34.
    Bianchini, G., Barucci, M., Del Rosso, T., Pasca, E., Ventura, G.: Interferometric dilatometer for thermal expansion coefficient determination in the 4–300 K range. Meas. Sci. Technol. 17(4), 689 (2006)ADSCrossRefGoogle Scholar
  35. 35.
    Ventura, G., Bianchini, G., Gottardi, E., Peroni, I., Peruzzi, A.: Thermal expansion and thermal conductivity of Torlon at low temperatures. Cryogenics 39(5), 481–484 (1999)ADSCrossRefGoogle Scholar
  36. 36.
    Barucci, M., Bianchini, G., Del Rosso, T., Gottardi, E., Peroni, I., Ventura, G.: Thermal expansion and thermal conductivity of glass-fibre reinforced nylon at low temperature. Cryogenics 40(7), 465–467 (2000)ADSCrossRefGoogle Scholar
  37. 37.
    Greco, V., Molesini, G., Quercioli, F.: Accurate polarization interferometer. Rev. Sci. Instrum. 66(7), 3729–3734 (1995)ADSCrossRefGoogle Scholar
  38. 38.
    Raine, K., Downs, M.: Beam-splitter coatings for producing phase quadrature interferometer outputs. J. Mod. Opt. 25(7), 549–558 (1978)Google Scholar
  39. 39.
    Okaji, M., Yamada, N., Nara, K., Kato, H.: Laser interferometric dilatometer at low temperatures: application to fused silica SRM 739. Cryogenics 35(12), 887–891 (1995)ADSCrossRefGoogle Scholar
  40. 40.
    Okaji, M., Birch, K.: Intercomparison of Interferometric Dilatometers at NRLM and NPL. Metrologia 28(1), 27 (1991)ADSCrossRefGoogle Scholar
  41. 41.
    Okaji, M., Yamada, N., Kato, H., Nara, K.: Measurements of linear thermal expansion coefficients of copper SRM 736 and some commercially available coppers in the temperature range 20–300 K by means of an absolute interferometric dilatometer. Cryogenics 37(5), 251–254 (1997)ADSCrossRefGoogle Scholar
  42. 42.
    Barucci, M., Gottardi, E., Olivieri, E., Pasca, E., Risegari, L., Ventura, G.: Low-temperature thermal properties of polypropylene. Cryogenics 42(9), 551–555 (2002)ADSCrossRefGoogle Scholar
  43. 43.
    Gottardi, E., Bianchini, G., Peroni, I., Peruzzi, A., Ventura, G.: Thermal conductivity of polyetheretherketone at low temperatures. In: Proceedings of Tempmeco, Berlin (2001)Google Scholar
  44. 44.
    Corporation, Z.: Laurel Brook Road, Middlefield, Connecticut 06455–0448 Google Scholar
  45. 45.
    GmbH, E.O.: Zur Giesserei 19–27, 76227 Karlsruhe, GermanyGoogle Scholar
  46. 46.
    Elschukom, E., GmbH, Gewerbestrasse 87, D-98669 VeilsdorfGoogle Scholar
  47. 47.
    Hahn, T.A.: Thermal expansion of copper from 20 to 800 K—standard reference material 736. J. Appl. Phys. 41(13), 5096–5101 (1970)ADSCrossRefGoogle Scholar
  48. 48.
    Karlmann, P.B., Dudik, M.J., Halverson, P.G., Levin, M., Marcin, M., Peters, R.D., Shaklan, S., van Buren, D.: JLP Technical Report. California Institute of Technology, (1992)Google Scholar
  49. 49.
    Yamada, N., Okaji, M.: Development of a low-temperature laser interferometric dilatometer using a cryogenic refrigerator. High Temp. High Pressures 32(2), 199–206 (2000)CrossRefGoogle Scholar
  50. 50.
    Ackerman, D., Anderson, A.: Dilatometry at low temperatures. Rev. Sci. Instrum. 53(11), 1657–1660 (1982)ADSCrossRefGoogle Scholar
  51. 51.
    Bassan, M., Buonomo, B., Cavallari, G., Coccia, E., D’Antonio, S., Fafone, V., Foggetta, L., Ligi, C., Marini, A., Mazzitelli, G.: Measurement of the thermal expansion coefficient of AN Al-Mg alloy at ultra-low temperatures. Int. J. Mod. Phys. B 27(22), 1350119–1350131 (2013) Google Scholar
  52. 52.
    Barucci, M., Bassan, M., Buonomo, B., Cavallari, G., Coccia, E., D’Antonio, S., Fafone, V., Ligi, C., Lolli, L., Marini, A.: Experimental study of high energy electron interactions in a superconducting aluminum alloy resonant bar. Phys. Lett. A 373(21), 1801–1806 (2009)ADSCrossRefGoogle Scholar
  53. 53.
    Barucci, M., Ligi, C., Lolli, L., Marini, A., Martelli, V., Risegari, L., Ventura, G.: Very low temperature specific heat of Al 5056. Phys. B 405(6), 1452–1454 (2010)ADSCrossRefGoogle 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