Velocity of sound in solid hexagonal close-packed H2 and D2

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 Gruneisen 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.