Solid Hydrogen pp 197-223 | Cite as

Clusters of J = 1 Impurities in J = 0 Solids

  • Jan Van Kranendonk


For a random distribution of NX impurities over the N sites of a close-packed lattice, the average size of clusters of impurities connected by nn separations is finite for X ≲ 20%, as discussed in section 3.4. At sufficiently low concentrations X, it is therefore appropriate to analyze the properties of these solids in terms of clusters containing small numbers of J = 1 molecules, such as singles, nn pairs, triples with at least two nn separations, etc.1, 2 The distribution of the impurities over the lattice may be random, as realized after quick freezing of a liquid sample, or may correspond to the true equilibrium distribution, attained after a time long compared to the diffusion time constant. Valuable information on various cluster properties has been obtained from measurements of the specific heat of solid H2, D2, and their mixtures for J = 1 concentrations in the range 0.1–1%.2–4 The finer details of the effective interaction between the J = 1 impurities have been revealed by the Raman,5 NMR,6,7 and microwave (MW)8 spectroscopy of pairs of J = 1 molecules.


Partition Function Induce Dipole Moment Solid Hydrogen Rigid Lattice Pair Frame 


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  1. 1.
    T. Nakamura, On the quenching of molecular rotation of ortho-hydrogen in solid state, Progr. Thwor. Phys. (Kyoto) 44, 135–150 (1955).ADSCrossRefGoogle Scholar
  2. 2.
    R. J. Roberts and J. G. Daunt, Specific heats of solid hydrogen, solid deuterium, and solid mixtures of hydrogen and deuterium, J. Low Temp. Phys. 6, 97–129 (1972).ADSCrossRefGoogle Scholar
  3. 3.
    R. J. Roberts and J. G. Daunt, Anomalous specific heat of solid deuterium below 0.6 K, J. Low Temp. Phys. 16, 405–408 (1974).ADSCrossRefGoogle Scholar
  4. 4.
    R. J. Roberts, E. Rojas, and J. G. Daunt, Low-temperature quadrupole and crystalline field effects in the specific heat of solid D2, J. Low Temp. Phys. 24, 265–273 (1976).ADSCrossRefGoogle Scholar
  5. 5.
    I. F. Silvera, W. N. Hardy, and J. P. McTague, Direct observation of isolated J = 1 pairs in solid deuterium and hydrogen by Raman scattering, Phys. Rev. B4, 2724–2733 (1971).ADSGoogle Scholar
  6. 6.
    A. Brooks Harris, L. I. Amstutz, H. Meyer, and S. M. Myers, Observation of pair interaction between orthomolecules in solid H2, Phys. Rev. 175, 603–609 (1968).ADSCrossRefGoogle Scholar
  7. 7.
    R. Schweizer, S. Washburn, and H. Meyer, NMR studies of single crystals of H2:11. The spectrum of isolated ortho-H2 pairs, J. Low Temp. Phys. 37, 309–341 (1979).ADSCrossRefGoogle Scholar
  8. 8.
    W. N. Hardy, A. J. Berlinsky, and A. B. Harris, Microwave absorption by ortho-H2 pairs in solid hydrogen, Can. J. Phys. 55, 1150–1179 (1977).ADSCrossRefGoogle Scholar
  9. 9.
    A. Brooks Harris, Interactions between molecules in solid hydrogen, Phys. Rev. Bl, 1881–1902 (1970).ADSGoogle Scholar
  10. 10.
    H. Miyagi, Energy levels of triangular clusters of ortho-hydrogen molecules due to quadrupole interaction in crystals, Progr. Theor. Phys. (Kyoto) 40, 1448–1449 (1968).ADSCrossRefGoogle Scholar
  11. 11.
    H. Meyer, Comments on two recent papers on solid H2, Phys. Rev. 187, 1173–1174 (1969).ADSCrossRefGoogle Scholar
  12. 12.
    J. F. Jarvis, H. Meyer, and D. Ramm, Measurement of (∂pP/∂T)v and related properties in solidified gases. IE Solid H2. Phys. Rev. 178, 1461–1471 (1969).ADSCrossRefGoogle Scholar
  13. 13.
    I. F. Silvera, The solid molecular hydrogens in the condensed phase: Fundamentals and static properties, Rer. Mod. Phys. 52, 393–452 (1980).ADSCrossRefGoogle Scholar
  14. 14.
    A. B. Harris, A. J. Berlinsky, and W. N. Hardy, Interactions between ortho-H2 molecules in nearly pure para-H2, Can. J. Phys. 55, 1180–1210 (1977).ADSCrossRefGoogle Scholar
  15. 15.
    B. W. Statt, W. N. Hardy, and R. Jochemsen, Observation of new lines in the microwave spectrum of ortho-H2 pairs in solid hydrogen, Can. J. Phys. 58, 1326–1340 (1980).ADSGoogle Scholar
  16. 16.
    S. Luryi and J. Van Kranendonk, Renormalized interactions in solid hydrogen and analysis of the ortho-pair level structure. Can.J. Phys. 57, 307–326 (1979).ADSCrossRefGoogle Scholar
  17. 17.
    B. W. Statt and W. N. Hardy, Line broadening mechanisms of the ortho-H2 pair spectrum, Can. J. Phys. 58, 1341–1355 (1980).ADSGoogle Scholar
  18. 18.
    S. Washburn, R. Schweizer, and H. Meyer, NMR studies on single crystals of H2: III. Dynamic effects, J. Low Temp. Phys. 40, 187–205 (1980).ADSCrossRefGoogle Scholar
  19. 19.
    V. V. Goldman, Short-range correlations in quantum crystals and motional renormalization of anisotropic interactions in solid hydrogen as a function of density, Phys. Rev. B20, 4478–4481 (1979).ADSGoogle Scholar

Copyright information

© Plenum Press, New York 1983

Authors and Affiliations

  • Jan Van Kranendonk
    • 1
  1. 1.University of TorontoTorontoCanada

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