Thermal Properties

  • Harald Ibach
  • Hans Lüth
Part of the Advanced Texts in Physics book series (ADTP)


In Sect. 4.2 we saw how the 3 rN equations of motion of a periodic solid can be largely decoupled by means of the plane-wave ansatz and the assumption of harmonic forces. With (4.7) we arrived at a system of equations that, for a given wave vector q, couples the wave amplitudes of the atoms within a unit cell. It can be shown mathematically that within the harmonic approximation the equations of motion, even for a nonperiodic solid, can be completely decoupled by means of a linear coordinate transformation to so-called normal coordinates. We thereby obtain a total of 3 rN independent forms of motion of the crystal, each with a harmonic time dependence and a specific frequency which, in the case of a periodic solid, is given by the dispersion relation ω(q). Any one of these “normal modes” can gain or lose energy independently of the others.


Specific Heat Capacity Harmonic Approximation Anharmonic Oscillator Thermal Current Radiation Shield 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. IV.1
    W. Buckel: Supraleitung, 2nd. edn. ( Physik Verlag, Weinheim 1977 )Google Scholar
  2. IV.2
    K. Gloos, R. Smeibidel, C. Kennedy, A. Singsaas, R. Sekowski, R.M. Muelle, F. Pobell: J. Low Temp. Phys. 73, 101 (1988)ADSCrossRefGoogle Scholar
  3. IV.3
    E.Gmelin: Thermochimica Acta 29, 1 (1979)CrossRefGoogle Scholar
  4. IV.4
    W.D. Seward, V. Narayanamurti: Phys. Rev. 148, 463 (1966)ADSCrossRefGoogle Scholar
  5. 5.1
    G. Dolling, R.A. Cowley: Proc. R. Soc. London 88, 463 (1966)CrossRefGoogle Scholar
  6. 5.2
    American Institute of Physics Handbook,3rd edn. (McGraw-Hill, New York 1972) pp. 4–115Google Scholar
  7. 5.3
    Wei Chen, D.L., Mills: Phys. Rev. B 36, 6269 (1987)CrossRefGoogle Scholar
  8. 5.4
    H. Ibach: Phys. Status Solidi 31, 625 (1969)CrossRefGoogle Scholar
  9. 5.5
    R.W. Powell, C.Y. Ho, P.E. Liley: NSRDS-N 1358 (1966)Google Scholar
  10. 5.6
    R. Berman, P.G. Klemens, F.E. Simon, T.M. Fry: Nature 166, 865 (1950)ADSCrossRefGoogle Scholar

Further Reading

  1. Rosenberg, H.M.: Low Temperature Solid-State Physics ( Clarendon, Oxford 1963 )Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Harald Ibach
    • 1
    • 2
  • Hans Lüth
    • 1
    • 2
  1. 1.Institut für Schichten und GrenzflächenForschungszentrum Jülich GmbHJülichGermany
  2. 2.Rheinisch-Westfälische Technische HochschuleAachenGermany

Personalised recommendations