Rotational motion under pressure in the solid molecular hydrogen isotopes

Rotational states as functions of pressure for H₂, D₂, T₂ HD, and HT molecules are calculated in the corresponding molecular solids. Sudden transitions from spherically symmetric rotational states occur in para-H₂, para-T₂, ortho-D₂, and in HD and HT as the pressure increases. Only the predicted T₂ transition pressure of about 24 kbar lies within current experimentally accessible ranges. All other transitions occur in the region 150–300 kbar.Supported in part by NSF Grant No. GH-35581, National Aeronautics and Space Administration Grant No. NGR 06-002-159, and United States Energy Research and Development Administration.     

A Monte Carlo study of the rotation-libration transition in solid H2 under pressure

The pressure-induced transition in solid para-H₂ from free rotation of molecules to libration around the threefold axes of the fcc structure is calculated using an anisotropic potential including quadrupole-quadrupole and repulsive valence interactions. The rotational part of the Hamiltonian is assumed to be operating on a Jastrow-type wave function, including two variational parameters. Two forms of pair correlation functions are examined, while the variational integrals are evaluated by a Monte Carlo procedure. The results are: (a) no significant correlation effects are detected; (b) the transition density corresponds to R/R ₀ = 0.676, where R ₀ is the nearest neighbor separation at zero pressure; the transition is first order as obtained also in mean field calculations; (c) the order parameter at the transition is 0.09, as opposed to 0.17 in mean field; (d) the transition density is not very sensitive to variations in the interaction strength.     

Further Monte Carlo studies of the rotation-libration transition in solid H2 under pressure

The pressure-induced transition in solid para-H₂ from free rotation of molecules to libration around the three-fold axes of the fcc structure is calculated using a completely anisotropic interaction potential of the form % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaeOvamaaBa% aaleaacaqGPbGaaeOAaaqabaGccqGH9aqpdaaeqaqaaiaaboeaaSqa% aiaab2gaaeqaniabggHiLdGcdaWgaaWcbaGaaeyBaaqabaGccaGGOa% GaaeOCamaaBaaaleaacaqGPbGaaeOAaaqabaGccaGGPaGaaeywamaa% BaaaleaacaqGYaGaaeyBaaqabaGccaGGOaGaeuyQdC1aaSbaaSqaai% aabMgaaeqaaOGaaiykaiaabMfadaWgaaWcbaGaaeOmaiaab2cacaqG% TbaabeaakiaacIcacqqHPoWvdaWgaaWcbaGaaeOAaaqabaGccaGGPa% aaaa!5132!\[{\text{V}}_{{\text{ij}}} = \sum\nolimits_{\text{m}} {\text{C}} _{\text{m}} ({\text{r}}_{{\text{ij}}} ){\text{Y}}_{{\text{2m}}} (\Omega _{\text{i}} ){\text{Y}}_{{\text{2 - m}}} (\Omega _{\text{j}} )\] including quadrupole-quadrupole and repulsive valence interactions. The rotational part of the Hamiltonian is assumed to be operating on a Jastrow-type wave function, including two variational parameters. The variational integrals are evaluated by a Monte Carlo procedure. The orientational order parameter in the low-density region increases very gradually with increasing density, until a sharp jump (indicating first-order) is observed at the transition density corresponding to R/R ₀ = 0.5775, where R ₀ is the nearest neighbor distance at zero pressure. This is 60% higher than the density obtained in previous work.     

The phonon absorption line shape of solid molecular H2 and D2 as a function of density

A theoretical study is presented of the lattice dynamics of the cubic phases of solid hydrogen and deuterium as a function of density. The calculations are performed in the self-consistent phonon approximation and include cubic three-phonon processes and higher anharmonic corrections. The anisotropic part of the intermolecular potential is neglected and libronic effects are not included. The line shape of the one-phonon far-infrared absorption process is studied in detail and is found to display a complex and interesting behavior as a function of pressure. The experimental absorption line is well accounted for by the one-phonon line shapes calculated here and phonon-libron and multi-phonon absorption, which has been treated elsewhere. Phonon dispersion curves and elastic constants are also presented.Partial financial support provided by the Dutch Foundation for Fundamental Research of Matter (FOM).     

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

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.Work supported by grants from the National Science Foundation and from the Army Research Office, Durham.     

Ultrasound propagation near the martensitic order-disorder transition in solid H2 and D2

The behavior of the longitudinal and transverse sound velocities and the qualitative change of acoustic attenuation are reported for solid H ₂ and D ₂ at constant volume upon repeated thermal cycling through the martensitic transition between the orientationally disordered and the ordered (cubic) phases. The observed relative velocity changes across the transition in D ₂ are only about 10^–3 –10^–2 , whereas the acoustic attenuation is strongly dependent upon the history of thermal cycling. In general the attenuation increases dramatically as the crystal is cooled for the first time through the transition and is thermally cycled. The behavior in solid H ₂ is quite different: In the ordered phase the sound attenuation is so great that the velocity cannot be measured, but upon warming the solid back into the disordered phase, the sound signal returns practically to its original intensity, even after several cyclings. It is shown that the observations are consistent with a soft-mode model for the martensitic transformation and that the effect of the order-disorder transition on the sound velocity is likely to be small.Work supported by a contract with the Office of Naval Research and a grant from the U.S. Army Research Office (Durham), and performed under the auspices of the United States Atomic Energy Commission.     

Far-infrared absorption by phonons and librons in solid H2 and D2 in the ordered state

We present an experimental study of the infrared absorption spectra of solid, enriched ortho-hydrogen and para-deuterium in the ordered state for concentrations x of J = 1 molecules between 0.65 and 0.98 and temperatures from 0.9 to 11K. Comparison is made to theoretical expressions and numerical results for the absorption due to various microscopic processes, involving phonons and combinations oflibrons and phonons, which couple to the dipole moment induced by the electric quadrupole (EQ) fields of J = 1 molecules. The concentration dependence of the sharp, low-frequency optical phonon has also been studied. The integrated intensity of this feature is found to be quadratic in x and the frequency is well described by (x) = a + bx ²,which is the expected behavior for shifts arising from pairwise EQQ interactions. For constant x, the temperature dependence of the intensity of this phonon scales with the square of the long-range orientational order parameter. Our measurements of this quantity are compared to NMR determinations of the temperature dependence of the Pake splitting in the ordered state.Supported financially by the Stichting FOM.     

Quantum diffusion in solid H2

A study of quantum diffusion in solid H₂ is reported based on the measurement of the pressure versus time at constant volume. Solid samples with ortho-H₂ concentrations between 0.01 and 0.025 were investigated over the temperature range 0.4–4 K. The characteristic time constant for ortho pair formation or breaking up and the resulting pressure changes are presented and compared with other experiments and with theory. The pressure change calculated from a simple statistical model is in good agreement with the experiment and this leads to the conclusion that both in-plane and out-of-plane pairs appear to form (or break up) at the same rate, at least in our concentration range. The experiments also suggest that the concentration dependence of is in qualitative agreement with theory, which, however, makes no predictions on the temperature dependence. Comparison with other experiments also suggests that might be a function of strains in the sample.Supported by a grant from the National Science Foundation.Duke Medical School, Duke University     

The libron spectra and conversion as a function of ortho-para concentration in solid H2 and D2

A study of the Raman scattering spectra of orientationally ordered ortho-H₂ and para -D₂ as a function of J = 0 impurities is presented. Libron peak frequencies over the concentration region 0.75 <c ₁< 0.98 are determined and show a linear concentration dependence that can be represented by the relation (1)[1 – K(1 – c₁)]. A least squares fit of our data gives values of K = 1.27 ± 0.05, 1.28 ± 0.05, and 0.96 ± 0.05 in D₂ where = E _g, T _g ⁽¹⁾ , and T _g ⁽²⁾ , respectively, and K 1.32 ± 0.05 and 0.97 ± 0.05 for the E _g and T _g ⁽²⁾ modes in H₂. Results are compared to the values calculated by Diehl et al. using the coherent potential approximation for the J = 0 impurity problem. Extrapolated values for (1) were obtained that are slightly higher than those given by Hardy, Silvera, and McTague, resulting in an increased value for the effective interaction parameter _eff. Conversion rates for H₂ and D₂ are determined, resulting in k _H2 = 0.0193 ± 0.0007h^–1 and k _D2 = 0.00063 ± 0.0001 h^–1.Supported by the Stichting voor Fundamenteel Onderzoek der Materie (FOM).     

Density dependence of the Raman-active optical phonon in the hcp phase of solid H2 and D2

Raman scattering from the transverse optical phonon in the hcp phase of solid H₂ and D₂ has been observed as a function of the density of the solid. Frequencies have been measured, with an accuracy of 0.3 cm^–1, in crystals under pressures up to 5000 bar at the melting line. A linear dependence of ln _TO on ln V is found (_TO is the phonon frequency and V the molar volume) with mode Grüneisen constants of _TO = 2.07 ± 0.03 for H₂ and _TO = 1.95 ± 0.03 for D₂. The ratio of the phonon frequencies of H₂ and D₂ at the same molar volume varies between 1.38 and 1.41 over the whole density range, in contrast to the harmonic ratio of 2 obtained from the mass ratio of 2 between H₂ and D₂. The results are compared with calculations of the phonon frequencies. A fit is provided so that phonon frequencies can be used as a pressure or density calibration scale.Supported financially by the Stichting FOM.     

Thermal conductivity of solid NaF under high pressure

The thermal conductivity () of solid NaF has been measured over the temperature (T) range 100–350 K and at pressures (P) up to 2.5 GPa, using the transient hot-wire method. Results for (T,P) could be described to a good approximation by the Leibfried-Schlömann formula. It was found that the isochoric temperature derivative of the thermal resistivity W (= ^–1) increased systematically with the mass ratio for the B1-type phases of the sodium and potassium halides.     

Thermal conductivity and quantum diffusion in solid H2

The thermal conductivity of solid H₂ and the NMR absorption signal of isolated o-H₂ were measured simultaneously along isotherms 0.07<T<1.5 K as a function of time after a rapid cooldown from 2 K. The o-H₂ concentration ranged from 3.4% to 0.4%, and the pressure was 90 atm. During the measurements, clustering of o-H₂ particles occurred as seen from the changes both of the NMR signal amplitude and of with time t. The difference ^–1 = ^–1 ()– ^–1(0) between the thermal resistivity ^–1 (t=0) just after cool down and in equilibrium, ^–1 (), was found to change sign near 0.23 K, and this result is discussed with respect to previous experiments. The equilibrium resistivity attributed to the o-H₂ impurities, , is derived and is compared with previous determinations and with predictions. An analysis of the equilibration process for ^–1 and for the NMR signal amplitude is presented. It shows that the characteristic times are of comparable but not equal magnitude. Comparison of the derived from NMR data atP=90 and 0 atm favors resonant ortho-para conversion over quantum tunneling as the leading mechanism for quantum diffusion.     

Thermal conductivity and heat capacity of solid nabr under pressure

Using the transient hot-wire method, measurements were made for solid NaBr of both the thermal conductivity and the heat capacity per unit volume. The measurements were performed in the temperature range 100 to 400 K and at pressures up to 2 GPa. An adiabatic compression technique allowed the determination of the thermal expansivity as a function of pressure at room temperature. The heat capacity did not vary with pressure. Analysis of the thermal conductivity data showed that it can be described adequately by the Leibfried-Schlömann formula. For temperatures up to 400 K only acoustic modes needed to be taken into account. A small contribution of optic modes to the heat transport might be apparent at the highest temperatures.     

Thermal conductivity and heat capacity of solid AgCl under pressure

Using the transient hot-wire method, measurements were made for solid AgCl of both the thermal conductivity, , and the heat capacity per unit volume, c _p, where is the mass density. Measurements were made in the temperature range 100 to 400 K, and at pressures up to 2 GPa. c _p(P, T) could be adequately described if the acoustic modes were represented by a Debye model and the optic modes by an Einstein model. Analysis of (T) showed that only the acoustic modes needed to be taken into account up to 300 K, but that the optic modes were increasingly effective in carrying heat at higher temperatures. (P) was adequately described by the Lawson formula, but not by the Leibfried-Schlömann formula, to which it is formally equivalent. Agreement with experiment could be achieved by two different modifications of the Leibfried-Schlömann formula, although neither has a firm theoretical basis.     

Numerical and experimental investigation of solid particle motion in a fluid cell under microgravity

This research aims at understanding the mechanisms and parameters that affect particle motion induced by g-jitter. Simultaneous experimental (parabolic flights) and numerical work was conducted to study the motion of a spherical particle in a microgravity environment subjected to vibrations in either horizontal or vertical direction. The data from both vertically and horizontally vibrated experiments clearly show that the investigated particle properties, size and density, affect the amplitude of the particle motion. In all experiments the amplitude of the particle motion increased with the density and diameter of the particle in the cell frame of reference. It was also observed that the particles moved at the frequency equal to that of applied vibration. These results are consistent with the preliminary numerical simulation predictions. Numerical simulations also showed that increasing the viscosity of the surrounding fluid would reduce the amplitude of the particle motion.     

Vacancy motion in solid helium

A model calculation of the vacancy tunneling frequency in bcc ³ He, hcp ³ He, and hcp ⁴ He is presented. Only the Debye temperature (and its volume dependence) and vacancy activation energies (from NMR data) are used; comparison with experiment is made. The relative tunneling rates in the three systems along with NMR and specific heat data provide evidence for the nature of vacancy motion in each of these systems.This work submitted in partial fulfillment of the requirements for Ph.D. degree, University of Massachusetts (1975).     

Charge motion in solid argon

The measurement of currents induced in solid argon by a radioactive source is described. The results show evidence of negative and positive charge motion. In one sample small bubbles were observed at the interface between solid and anode at a threshold field. The movement of these bubbles shows the possibility of mass transport through solid argon.