Solid Parahydrogen Research Articles

Density dependence of the single-particle kinetic energy of solid hydrogen

We have measured the inelastic neutron scattering from solid parahydrogen at molar volumes from 23.2 to 17.0 ${\mathrm{cm}}^{3}$. We observe peaks in the differential cross section ${d}^{2}$\ensuremath{\sigma}/d\ensuremath{\Omega} dE corresponding to internal molecular transitions from ground to excited rotational and vibrational states. From the widths of these peaks we determine the center-of-mass translational energy per molecule using an underlying Gaussian momentum distribution for the initial center-of-mass translational wave function. For volumes of 23.2, 21.3, 19.5, 18.2, and 17.0 ${\mathrm{cm}}^{3}$/mole we find kinetic energies per particle of 77\ifmmode\pm\else\textpm\fi{}3, 101\ifmmode\pm\else\textpm\fi{}8, 122\ifmmode\pm\else\textpm\fi{}14, 131\ifmmode\pm\else\textpm\fi{}14, and 146\ifmmode\pm\else\textpm\fi{}11 K, respectively.

Theory of Vibrational Overtones and Rotational Excitations in Solid Parahydrogen –Frequency Analysis of the Infrared Spectra–

Infrared absorption spectra of S v (0), Q v (0)+ S 0 (0) and S v (0)+ S 0 (0) ( v =1, 2,…) in solid parahydrogen are calculated on the basis of the induction mechanism of dipole moment. Effects of the propagation of rotational excitation on the spectral shape through the electric quadrupole-quadrupole interaction are studied in detail, in agreement with the recent experiments. The difference of the excitation energy in the solid phase from that in a free molecule, which increases systematically for higher overtones, is discussed. The dispersion and overlap interactions can be shown to cause such difference.

Pressure dependence of tunneling of isotopic impurities in solid parahydrogen

Pulsed NMR measurements have been performed at low temperatures on solid hydrogen mixtures containing 1.1%HD and 0.5% ortho-H 2 impurities for pressures between 0.1 and 136 bar. The pressure dependence of the transverse spin relaxation time T 2 is analyzed in terms of a model in which the HD particles move through the parahydrogen lattice by quantum tunneling. The Grüneisen constant for the tunneling frequency τ −1 c, Γ τ c =∂ln τ c ∂ lnV , is found to be −31±3, using the theory of Kubo and Tomita to estimate τ c from T 2.

Quantum diffusion of vacancies and impurities in solid hydrogen.

The proton nuclear transverse relaxation ${T}_{2}$ of HD impurities and ortho-${\mathrm{H}}_{2}$ impurities in solid parahydrogen is observed to be essentially temperature independent below 8 K, passes through a minimum near 9.2 K on warming, and then increases exponentially on approaching the melting point. The low-temperature values of ${T}_{2}$ are pressure dependent and a factor of 5.4 larger than the rigid lattice values. This ``line narrowing'' is attributed to quantum tunneling of the HD impurities at low temperatures. The minimum in ${T}_{2}$ is attributed to the breakup of coherent tunneling due to scattering by phonons and vacancies.

Intensities of multipole-induced zero-phonon transitions in solid parahydrogen.

Theoretical expressions are given for the intensities of zero-phonon single and double transitions in solid parahydrogen arising from the isotropic ${2}^{\mathrm{l}}$ multipole induction mechanism. Comparisons between theory and experiment for l=2 and 4 [corresponding to ${S}_{v\mathcal{'}}$(0) and ${S}_{v\mathcal{'}}$(0)+${Q}_{v\mathcal{'}\mathcal{'}}$(0) and ${U}_{v\mathcal{'}}$(0) and ${U}_{v\mathcal{'}}$(0)+${Q}_{v\mathcal{'}\mathcal{'}}$(0) transitions, respectively] have been given previously, and the results are in reasonably good agreement. A direct comparison is not possible for the recently observed l=6 [${W}_{v\mathcal{'}}$(0) and ${W}_{v\mathcal{'}}$(0)+${Q}_{v\mathcal{'}\mathcal{'}}$(0)] transitions because of the unavailability of ab initio values of the vibration-rotational matrix elements of the 64-pole moment function, or for the as yet unobserved l=8[${Y}_{v\mathcal{'}}$(0) and ${Y}_{v\mathcal{'}}$(0)+${Q}_{v\mathcal{'}\mathcal{'}}$(0)] transitions. Modifications of the intensities of the ${W}_{v\mathcal{'}}$(0) transitions due to the mixing of rotational levels by the quadrupole-quadrupole interaction have been calculated, and they contribute less than 1%. These corrections are smaller than those due to phonon renormalization and thus will not appreciably affect the magnitudes of the 64-pole moment matrix elements deduced from the experimental intensities.

Inelastic neutron scattering from liquid and solid hydrogen at high momentum transfer.

Solid and liquid para-hydrogen and a solid mixture of ortho- and para-hydrogen have been studied by inelastic neutron scattering at momentum transfers from 5 to 30 A${\r{}}^{\mathrm{\ensuremath{-}}1}$. The observed scattering function can be interpreted in terms of scattering from independent hydrogen molecules using the impulse approximation when internal excitations of the molecules are included. Scattering peaks are observed at the recoil energy, shifted by the energy of the internal rotational transitions, and broadened by the translational motion of the molecules. The peaks can be fitted by Gaussian functions, showing that, to within the accuracy of the measurement, the translational momentum distribution of the hydrogen molecules in the condensed phases has a Gaussian form. The kinetic energy of the para-hydrogen molecules at 1 bar is 76\ifmmode\pm\else\textpm\fi{}9 K in the solid at 10 K and 63\ifmmode\pm\else\textpm\fi{}6 K in the liquid at 17 K. The kinetic energy for the ortho component in the solid ortho-para mixture is estimated to be the same as for the para solid within the experimental error, although extraction of quantitative information is more difficult because of the complicated spectra.

Scattering-model calculation of the impurity-induced dephasing relaxation rates of the Raman-active J=2 rotons in solid parahydrogen.

The dephasing relaxation of the J=2 Raman-active \ensuremath{\Vert}k\ensuremath{\Vert}\ensuremath{\approxeq}0 rotons in solid p-${\mathrm{H}}_{2}$ induced by o-${\mathrm{H}}_{2}$ impurities is described as elastic scattering of the rotons by these point defects into k\ensuremath{\ne}0 rotons with equal energy. The specific rotational properties of the impurities and the intermolecular interactions between the impurity and the host molecules are not involved in the model calculation: It is argued that the defect can be represented by an empty site in the crystal, leaving the other intermolecular interactions unaltered. The total scattering rate is obtained from a detailed Brillouin zone integration of the golden-rule-type scattering probabilities. The results for the \ensuremath{\Vert}M\ensuremath{\Vert}=0 and 1 Raman-active J=2 rotons are very close to the experimental values determined from the linear increase of the dephasing relaxation rates, ${T}_{2}^{\mathrm{\ensuremath{-}}1}$, as a function of o-${\mathrm{H}}_{2}$ concentration. However, the calculated results for the \ensuremath{\Vert}M\ensuremath{\Vert}=2 transition are too small by more than an order of magnitude. The origin of this discrepancy is discussed and possible refinements of the calculation are suggested.

Double transitions in the Raman spectrum of the fundamental band of solid parahydrogen.

In this paper we report the observation of double Raman transitions of the type ${Q}_{1}$(0)+${S}_{0}$(0) in the fundamental band of solid parahydrogen. Although this band is a forbidden one, its intensity is of the order of 20% of the corresponding allowed ${S}_{1}$(0) band. The reason for this unusual behavior is discussed in some detail and is attributed to the strong mixing of the final states in the two manifolds involved.

Calculation of Raman Linewidths Due to Roton in Solid Parahydrogen with Orthohydrogen Impurities

Raman linewidths of rotons are calculated in solid parahydrogen with low concentration of orthohydrogen molecules. The electric quadrupole-quadrupole interaction between molecules is considered in the scattering of a roton by an orthohydrogen impuruty, where the phonon contribution to linewidths is neglected. Our results are in good agreement with the recent experiment.

Quantum Diffusion of HD Impurities in Solid Hydrogen

The NMR linewidth of HD impurities in solid para hydrogen has been measured to be less than the rigid lattice value. Motion due to quantum diffusion, similar to the exchange of atoms in dense hcp 3He, of the HD molecules is believed to be the cause of the narrowing of the linewidth. This motion is severely restricted for ortho-H2 because of their quadrupole-quadrupole interactions with ortho neighbors. Pulsed NMR experiments designed to measure the motional effects on NMR spin echos are discussed. Pressure and temperature effects on the HD motion are also examined.

High Energy Neutron Spectroscopy of Compressed Solid Para-Hydrogen

The deep inelastic neutron scattering study of solid hydrogen at 12 K at a molar volume of 23.0 cm3 by Langel et al. has been extended to 19.5 K para-hydrogen samples compressed to molar volumes of 21.2, 19.5, and 18.3 cm3, respectively. In each case, inelastic scattering peaks were observed at energy transfers a) shifted due to the molecular translational recoil energy plus internal rotational excitation and b) broadened due to the translational motion of the initial single-particle ground state. The data are analyzed directly to yield the average kinetic energy <KE> of the ground state center-of-mass translational motion as a function of molar volume in this quantum solid. Over a 20% decrease in molar volume, <KE> values increase from 76±9 to 141±9 K. These are compared to indirect measurements.

Observation of fourth vibrational overtone of hydrogen.

We report the first observation of the fourth vibrational overtone ($\ensuremath{\Delta}v=5$) transition of molecular hydrogen in solid parahydrogen at 19 062 ${\mathrm{cm}}^{\ensuremath{-}1}$. We also report the first measurements of an almost complete set of the third vibrational overtone ($\ensuremath{\Delta}v=4$) transitions.

Calculation of rotational T2 relaxation in solid parahydrogen and orthodeuterium.

The shifts, the relative intensities, and the linewidths of the rotational Raman spectrum of solid parahydrogen (p-${\mathrm{H}}_{2}$) and orthodeuterium (o-${\mathrm{D}}_{2}$) are calculated by combining the memory-function formalism and a second-order perturbation treatment of the electric-quadrupole--quadrupole interaction. Lattice vibrations are neglected in the present theory. The linewidth is shown to represent the phenomenological ${T}_{2}$-dephasing relaxation time, an upper bound of which can be set at \ensuremath{\approxeq}600 ps for p-${\mathrm{H}}_{2}$ and \ensuremath{\approxeq}100 ps for o-${\mathrm{D}}_{2}$. It is shown that at low pressure, the present theory compares favorably with the spontaneous Raman measurements on this solid.

Single particle scattering and momentum distributions in solid hydrogen

The incoherent inelastic neutron scattering function of solid para-hydrogen was recorded. It was shown that at momentum transfers above 5Å −1 the data can be interpreted as recoil spectra from single particle scattering at hydrogen molecules. The evaluation of the momentum distribution and kinetic energy of the scattering particles from such data is discussed.

Roton-phonon mixing in solid hydrogen and deuterium.

Solid parahydrogen and orthodeuterium have been studied under high pressure in a diamond anvil cell at low temperature. The frequency of the k\ensuremath{\rightarrow}=0 ${E}_{2g}$ transverse-optical phonon increases rapidly with density. In the vicinity of the roton modes it hybridizes with the ${E}_{2g}$ roton resulting in a level anticrossing. The interaction Hamiltonian is analyzed for an (effective) linear coupling between the roton and phonon. Of the two most important contributions to the coupling, the crystal-field interaction B(R) is found to be significantly stronger than the mechanism arising from the electric quadrupole-quadrupole interaction \ensuremath{\Gamma}(R). This enables us to make the first determination of B(R) in the solids at two densities. The resulting experimental potential is significantly smaller than the theoretical pair potential. These measurements provide an important experimental test for theoretical anisotropic potentials.

Orientational ordering in solid parahydrogen and orthodeuterium

The low-temperature pressure-induced orientational ordering transition in solid parahydrogen (p-H2) and orthodeuterium (o-D2) is investigated using a model consisting of quantum rotors on a rigid fcc lattice. A correlated variational wave function of the Jastrow type is used to describe the zero-point orientational fluctuations which inhibit ordering into a Pa3 structure. Using the bare electrostatic quadrupole–quadrupole interaction, the predicted ordering pressure for o-D2 is about half the experimental value; realistic intermolecular potentials, with anisotropic exchange repulsion, yield even lower estimates. Hence, at high pressure the hydrogen molecule appears more isotropic (spherical) than indicated by the model potentials used here. Possible explanations for this are discussed, a likely candidate being the assumption of a rigid lattice and hence the neglect of translation-rotation coupling.

An improved experimental equation of state of solid hydrogen and deuterium

We have analyzed a large set of data in the literature as well as new data of our own to provide an improved equation of state of solid para-hydrogen and ortho-deuterium, with pressures ranging from 0 to 25 kbar (at the melting line). Results, including pressure, bulk modulus, and thermal expansion, are tabulated for a dense set of molar volumes as a function of temperature.

Observation ofΔν=4Vibrational Overtone Transitions in Solid hcp Parahydrogen

The first observations of the third vibrational overtone of molecular hydrogen are reported. This overtone, long sought in high-pressure gaseous hydrogen studies, is important in the interpretation of some of the observed features in the spectra of outer giant planets. The observations carried out in hcp solid parahydrogen should provide the much needed incentive for increased theoretical understanding of the simplest of the molecular solids.

Infrared spectrum of hydrogen in the condensed phase with high-sensitivity spectrometers: Experiments with a 0.04-cm −1 Fourier transform spectrometer in the range 1.5–12 μm

The infrared spectrum of solid and liquid hydrogen was recorded using a Fourier spectrometer. The pure rotational U transitions, U 0(0) in solid para hydrogen and U 0(1) in solid normal hydrogen, with the accompanying phonon branches were observed for the first time. In addition, the rotational double transitions S 0(0) + S 0(1) and S 0(1) + S 0(1) were identified. The identifications of these transitions are based on positions calculated by making use of gas phase molecular constants. In the liquid the double transitions are preserved but the single transitions U 0(0) and U 0(1) are entirely absent. The region of Q 1←0( J) reveals structure which has not been reported before. Its interpretation is presented.

Effect of density on the induced near-infrared spectra of solid parahydrogen and normal hydrogen at 4.2 K and 2 K up to 12 kbar

The induced near-infrared absorption spectra of solid parahydrogen and solid normal hydrogen up to 12 kbar at 4.2 and 2 K have been measured. A blue frequency shift and a strong increase in intensity which depend upon the nature of the transition are observed. The continuing presence of aS1(0) line in the spectrum of parahydrogen shows that its crystalline structure remains hexagonal-close-packed in the compressed solid up to 12 kbar.