The Frequency Distribution of Ice by Neutron Scattering

  • Henry Prask
  • Henri Boutin
  • Sidney Yip
Part of the Developments in Applied Spectroscopy book series (DAIS, volume 6)


The frequency distribution of phonons in a solid known to be proportional to the one-phonon neutron incoherent-scattering cross section when the crystal is monatomic and cubic. In the present work, it is shown that, for molecular crystals, an “effective” frequency distribution, which is simply related to the true frequency distribution, can be derived directly from a measurement of the energy and angle differential neutron cross section if translation-rotation couplings can be ignored. This approach is applied to ice, for which the differential neutron cross section at 150°K has been measured from 20 to 1000 cm-1 with the use of a beryllium-filter-time-of-flight spectrometer. The number of degrees of freedom of rotational and translational motions is assumed equal from which an effective rotational mass of 1,3 amu is obtained. The “true” frequency distribution determined from the neutron data with this value of effective mass is used to calculate absolute values of thermodynamic quantities as a function of temperature (20 to 270°K), in reasonably good agreement with directly measured values. The application of this approach to liquid water and H2O in crystal hydrates is currently being investigated.


Frequency Distribution Thermodynamic Quantity Neutron Spectrum Crystal Hydrate Neutron Data 
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. 1.
    P.A. Egelstaff, Thermal Neutron Scattering, Academic Press, Inc., New York (1965).Google Scholar
  2. 2.
    M. Tasumi and T. Schimanouchi, J. Chem. Phys. 43:1245 (1965);CrossRefGoogle Scholar
  3. T. Kitagowa and T. Miyazawa, Rept. Progr. Polymer Phys. (Japan) 8:53 (1965).Google Scholar
  4. 3.
    G. Placzek and L. van Hove, Phys. Rev. 93:1207 (1954).CrossRefGoogle Scholar
  5. 4.
    H. Hahn, in: Inelastic Scattering of Neutrons, Intern, At. Energy Agency, Vienna, 1965, Vol. II, p. 279.Google Scholar
  6. 5.
    P. A. Egelstaff, ed.. Thermal Neutron Scattering, Chap. 9, Academic Press, Inc., New York (1965).Google Scholar
  7. 6.
    A. Sjolander, Arkiv. Fysik. 14:315 (1958).Google Scholar
  8. S. Yip, to be published.Google Scholar
  9. 8.
    N. Ockman, Advan. Phys. 7:199 (1958).CrossRefGoogle Scholar
  10. 9.
    J.E. Bertie and E. Whalley, J. Chem. Phys. 46:1271 (1967).CrossRefGoogle Scholar
  11. 10.
    K.E. Larsson and U. Dahlborg, in: Inelastic Scattering of Neutrons, I.A.E.A., Vienna, Vol. I (1963), p. 317.Google Scholar
  12. 11.
    G.J. Safford, Cryobiology (1966), in press.Google Scholar
  13. E. Forslind, Proc. Swed. Cement Concrete Res. Inst., Stockholm, No. 21 (1954).Google Scholar
  14. 13.
    E. Whalley and J.E. Bertie, J. Chem. Phys. 46:1264 (1967).CrossRefGoogle Scholar
  15. 14.
    W. Bagdade, Mid-America Symposium on Spectroscopy, Chicago, May 1967.Google Scholar
  16. 15.
    A. A. Maradudin, E. W. Montroll, and G.H. Weiss, Solid State Physics, Suppl. 3 (1963).Google Scholar
  17. 16.
    W.F. Giaque and J.W. Stout, J. Am. Chem. Soc. 58:1144 (1936).CrossRefGoogle Scholar
  18. 17.
    F. Simon, Hand, d, Physik 10:363 (1929).Google Scholar
  19. L. Slaggie, private communication.Google Scholar
  20. 19.
    A. J. Leadbetter, Proc. Roy. Soc. (London), Ser. A 287:403 (1965).CrossRefGoogle Scholar

Copyright information

© Chicago Section of the Society for Applied Spectroscopy 1968

Authors and Affiliations

  • Henry Prask
    • 1
  • Henri Boutin
    • 1
  • Sidney Yip
    • 2
  1. 1.Picatinny ArsenalDoverUSA
  2. 2.Massachusetts Institute of TechnologyCambridgeUSA

Personalised recommendations