Abstract
Sound velocity measurements are reported on samples of hexagonal close-packed H2 and D2, believed to be single crystals. In the first part of the experiments, both the longitudinal and transverse velocities (v 1 and v t ) of crystals grown at a given melting pressureP M were measured at 4.2 K. For each mode, the velocities plotted vs.P M were found to lie between approximately parallel lines that represented the maximum and minimum observable velocities under the given experimental conditions set by the acoustic cell dimensions. From these extreme velocities v 1max, v 1min, v tmax, and v tmin an estimation of the elastic constants was made. Knowledge of these constants in turn permitted the calculation of the velocity surface, the bulk modulus, and the Debye temperature. In spite of the uncertainties in the analysis of the present data, a meaningful comparison could be made with results from other experiments. For both and D 2 , the elastic constants are on the average ∼20% below those derived from neutron scattering data. The transverse velocities, both for H 2 and D 2 , are consistent with those of Bezuglyi and Minyafaev for polycrystalline samples, but the longitudinal velocities are about 10% smaller than those of these authors. The bulk modulus and the Debye temperature from our experiments are compared with those from equation-of-state and calorimetric experiments. In the second part of this research, we have investigated the temperature dependence of the sound velocities at constant volume for both H 2 and D 2 with low concentrationsX of molecules with rotational angular momentumJ=1. From the measurements in H 2 , we are able to calculate the temperature change in the bulk modulus, which is then compared with that calculated from calorimetric data assuming the validity of the Grüneisen equation of state. Good agreement is obtained. In solid D 2 , were were able to deduce the temperature dependence of the adiabatic and isothermal modulusc 33 and make a rough estimation for that ofc 13 . In the third part we present measurements of v 1 and v t at 42 K and at constant volume as a function ofX in solid H 2 . It is found that as the orthopara conversion proceeds,v 1 increases andv t decreases. From these measurements the bulk modulus change withX is calculated. Comparison with the bulk modulus change calculated from static pressure measurements, assuming electric quadrupole-quadrupole interaction between the (J=1) molecules, shows very good agreement. The calculated dependence of the Debye temperature onX, as obtained from a combination of sound velocity and static measurements, is smaller than that reported from recent neutron scattering results. A short section is then devoted to absorption measurements in solid H 2 , which gave only qualitative results. Finally, in Section 4, we present measurements of the sound velocity in liquid D 2 at saturated vapor pressure as a function of temperature and for both liquid H 2 and D 2 along the melting curve.
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References
N. R. Werthamer,Am. J. Phys. 37, 763 (1969).
See, for instance, G. Ahlers,Phys. Rev. A2, 1505 (1970), and references therein.
R. H. Crepeau, O. Heybey, D. M. Lee, and S. A. Strauss,Phys. Rev. A3, 1162 (1971); R. H. Crepeau and D. M. Lee,Phys. Rev. A6, 516 (1972).
R. Wanner and J. P. Franck,Phys. Rev. Letters 24, 365 (1970).
D. S. Greywall and J. A. Munarin,Phys. Rev. Letters 24, 1282 (1970); D. S. Greywall,Phys. Rev. A3, 2106 (1971).
R. Wanner, thesis, University of Alberta, 1970, unpublished.
R. D. Etters, J. C. Raich, and P. Chand,J. Low Temp. Phys. 5, 711 (1971); C. Ebner and C. C. Sung,Solid State Commun. 11, 489 (1972), and references therein.
M. L. Klein and T. R. Koehler,Phys. Letters 33A, 253 (1970);J. Phys. C 3, 102 (1970); K. N. Klump, O. Schnepp, and L. H. Nosanow,Phys. Rev. B1, 2496 (1970).
H. D. Megaw,Phil. Mag. 28, 129 (1933).
J. W. Stewart,Phys. Rev. 97, 578 (1955).
B. G. Udovidchenko and V. G. Manzhelii,J. Low Temp. Phys. 3, 429 (1970).
G. Ahlers,J. Chem. Phys. 41, 86 (1964).
R. J. Roberts and J. G. Daunt,J. Low Temp. Phys. 6, 97 (1972).
J. F. Jarvis, D. Ramm, and H. Meyer,Phys. Rev. 178, 1461 (1969), and unpublished data above 4 K.
R. W. Hill and O. V. Lounasmaa,Phil. Mag. 4, 785 (1959).
D. Ramm, H. Meyer, and R. L. Mills,Phys. Rev. B1, 2763 (1970).
P. A. Bezuglyi and R. Kh. Minyafaev,Fiz. Tverd. Tela 9, 624 (1967) [English transl.,Soviet Phys.—Solid State 9, 480 (1967)].
P. A. Bezuglyi and R. Kh. Minyafaev,Fiz. Tverd. Tela 9, 3622 (1967) [English transl.,Soviet Phys.—Solid State 9, 2854 (1968)].
P. A. Bezuglyi, R. O. Plakhotin, and L. M. Tarasenko,Fiz. Tverd. Tela 13, 309 (1971) [English trans].,Soviet Phys.—Solid State 13, 250 (1971)].
Solid D2, M. Nielsen and H. Bjerrum Møller,Phys. Rev. B3, 4383 (1971); solid D2 and H2, M. Nielsen, private communication and to be published.
L. Meyer, inAdvances in Chemical Physics, I. Prigogine and S. A. Rice, eds. (Interscience Publishers, New York, 1969), Vol. 16, p. 353ff.
T. Nakamura,Progr. Theoret. Phys. (Kyoto)14, 135 (1955).
R. Wanner, H. Meyer, and R. L. Mills, to be published.
J. H. Vignos and H. A. Fairbank,Phys. Rev. 147, 185 (1966).
R. Wanner and H. Meyer,Phys. Letters 41A, 189 (1972); Proc. Intern. Low Temperature Physics, LT 13, Boulder, Colorado, 1973, to be published.
M. Nielsen, private communication; see also M. Nielsen in Ref. 20.
J. P. Franck and R. Wanner,Phys. Rev. Letters 25, 345 (1970).
M. J. P. Musgrave,Proc. Roy Soc. (London)A226, 329, 356 (1954).
Landolt-Börnstein, inNew Series, Vol. III/1, Elastic, Piezoelectric and Related Constants of Crystals, R. F. S. Hearmon and K. H. Hellwege, ed. (Springer Verlag, New York, 1966).
R. L. Mills and A. F. Schuch,Phys. Rev. Letters 15, 722 (1965); A. F. Schuch and R. L. Mills,Phys. Rev. Letters 16, 616 (1966);
O. Bostanjoglo and R. Kleinschmidt,J. Chem. Phys. 46, 2004 (1967);
K. F. Mucker, P. M. Harris, D. White, and R. A. Erickson,J. Chem. Phys. 49, 1922 (1968).
B. A. Younglove,J. Chem. Phys. 48, 4181 (1968); see also R. F. Dwyer, G. A. Cook, O. E. Berwaldt, and H. E. Nevins,J. Chem. Phys. 43, 801 (1965).
B. Wallace and H. Meyer, Proc. International Low Temperature Conference, LT 13, Boulder, Colorado, 1972, to be published.
E. Bartholomé, Z. Physik. Chem.B33, 387 (1936).
J. F. Nye,Physical Properties of Crystals (The Clarendon Press, Oxford, 1964).
W. B. Daniels, inLattice Dynamics, R. F. Wallis, ed. (Pergamon Press, London, 1965).
H. Stein, H. Stiller, and R. Stockmeyer,J. Chem. Phys. 57, 1726 (1972).
A. B. Bhatia,Ultrasonic Absorption (Oxford University Press, London, 1967), p. 40 and ff.
C. A. Swenson,J. Phys. Chem. Solids 29, 1337 (1968).
H. Miyagi and T. Nakamura,Progr. Theoret. Phys. (Kyoto),37, 641 (1967).
H. Miyagi, thesis, Osaka University, 1970, unpublished.
A. J. Berlinsky, A. B. Harris, and H. Meyer,Effects of Librational Anharmonicity in the Solid Hydrogens (submitted for publication), and references therein.
R. W. Hill and B. Schneidmesser,Z. Phys. Chem. 16, 257 (1958); R. G. Bohn and C. F. Mate,Phys. Rev. B2, 2121 (1971).
A. Van Itterbeek, W. van Dael, and A. Cops,Physica 27, 111 (1961);29, 965 (1963).
B. A. Younglove,J. Acoust. Soc. Am. 38, 433 (1965).
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Work supported by grants from the National Science Foundation and from the Army Research Office, Durham.
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Wanner, R., Meyer, H. Velocity of sound in solid hexagonal close-packed H2 and D2 . J Low Temp Phys 11, 715–744 (1973). https://doi.org/10.1007/BF00654454
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DOI: https://doi.org/10.1007/BF00654454