Far-infrared absorption in solid hydrogen and deuterium in the ordered state as a function of density

We present an experimental study of the infrared absorption spectra of solid enriched ortho-hydrogen and para-deuterium in the ordered state for pressures up to 6 kbar. From our observations we can conclude that the structure of the ordered state remains the Pa3 space group for all pressures studied. We find that the low-frequency optical phonon remains sharp at increased density and we have determined the mode Grüneisen constants as H ₂=1.95±0.03 and D ₂=1.87±0.03. The high-frequency optical phonon remains broad, and develops a double-peaked structure with increasing density, which is explained by anharmonicity and two-phonon decay. Comparison is made to theoretical expressions and numerical results for the absorption due to various microscopic processes involving phonons and combinations of librons and phonons. The integrated absorption intensity is also obtained, and compared with calculations based upon the quadrupole-induced dipole mechanism.Financially supported in part by the Stichting FOM, Utrecht.     

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.     

Rotational molecular motion in solid H2 and D2 under pressure

The rotational state of a H₂ or D₂ molecule in solid hydrogen or deuterium is calculated over the range of densities for which the molecular phases are expected to be stable. For para-H₂ and ortho-D₂ we predict sudden transitions as the pressure is increased from states where the molecules are rotating freely to states where they are librating about equilibrium orientations. These transitions are predicted to occur in the region of several hundred megabars of pressure. Although in principle observable, these first-order transitions are expected to lead to only small changes in the equation-of-state curves. These transitions from rotating to librating molecular motion are expected to be accompanied by changes in the crystal structures from hcp to fcc.Supported by NSF Grant No. 22553.     

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.     

Orientational ordering in solid D2 from NMR studies. II. The cubic ordered phase

An NMR study in the cubic phase of D₂ which exhibits long-range orientational order is reported. The spin systems in both para D₂ (with angular momentum J=1 and spinI=1) and in ortho D₂ (with J=0 andI=2) were investigated. The integrated intensity ratio of theI=1 andI=2 components in the solid echo, the NMR line shapes obtained by Fourier transforming the solid echoes, and the longitudinal relaxation times for theI=1 andI=2 systems are presented. Samples with D₂ concentrationX between 0.69 and 0.62 were studied over the temperature range 0.12<T<4 K. Measurements were carried out before and after repeated thermal cycling through the ordering transition to study the effect of this cycling on the temperature dependence of the relaxation times. The complex behavior of these relaxation times was found to be similar to that in cubic H₂ at a comparable concentration, and the interpretation of this behavior is discussed. Over most of the temperature range, the relaxation time of theI=2 spins is larger than that of theI=1 spins and is believed to be determined by cross-relaxation with the latter, whose intrinsic spin-lattice relaxation is observed. However, at low enough temperatures, the relaxation time for theI=2 spins is found to be shorter than that for theI=1 spins, and this observation cannot be understood on the basis of predictions. Furthermore, theI=2 relaxation time in this temperature region is found to depend on the position within the NMR line. Another observation not yet understood is that the ratio of the integrated intensitiesS(I=1)/S(I=2) in the solid echo is smaller than the theoretically predicted one by about 20%. The NMR line shapes for theI=1 spins in the ordered phase obtained from pulse measurements are compared with those from continuous-wave methods and to those from H₂.     

Analysis of C2H4 in C2H6 and C2H5D with VUV absorption spectroscopy and a method to remove C2H4 from C2H6 and C2H5D

The photoabsorption cross section of C2H4 was measured in the spectral region 107-183 nm and those of C2H6 and C2H5D were accurately determined in the spectral region 107-162 nm using radiation from a synchrotron as source of VUV light. Typically, C2H4 present as a minor impurity in samples of C2H6 and C2H5D distorted the absorption cross section in curves of C2H6 and C2H5D in the onset region. We completely eliminated C2H4 from C2H6 and C2H5D using adsorption on activated Pd/charcoal at 195 K. By this means, we detected no C2H4 in samples of C2H6 and C2H5D according to their absorption spectra. The detection limit of C2H4 in C2H6 and C2H5D is less than 0.03 ppm with VUV absorption spectroscopy.     

Production of H atoms in solid H2 by RF discharge

Hydrogen atoms have been produced by RF discharge at the surface of an H₂ crystal and studied by ESR techniques. The mean concentration at 4.2 K was estimated to be 10¹⁵ atoms per cm³ for about 14 h of source pulsing. This atom concentration was shown to be stable for long times. The results suggest that diffusion of atoms into the interior of the solid takes place very rapidly.     

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.     

The red-shift of surface plasmon absorption of 2D nanogold arrangement from disordered to ordered

In this article, the changing of surface plasmon resonance (SPR) absorption of 2D arrangement of Au (3 nm) nanoparticles coated with 1-dodecanethiol (C12H25SH), obtained at different desolvation extents, had been investigated. It has been found that an obvious red-shifted happened when these arrays changed from loose, disordered to close-packed and ordered. Both transmission electron microscopy pictures and variation of SPR absorption of these arrays showed that the formation of long range two-dimension (2D) arrangement of nanoparticles coated with C12H25SH might be involved in two stages: At the first stage the particles can move freely and random patterns from loose to close package was driven by the Brownian Movement of solvated particles and as a result the voids were eliminated. The red shift of SPR absorption with the coverage (d lamda/d theta) is relative low. At the second stage, where the particles cannot move freely because of lack of solvent and a long-range two-dimension crystal was formed, the SPR shift to a longer wavelength with a larger d lamda/d theta. It is mainly attributed to the strong increase of the orientation and dipolar moment of the absorbed C12H25SH molecule on nanoparticles.     

2D nanoparticle arrays by partial dissolution of ordered pore films

A low cost and simple route was presented to fabricate large-scale ordered nanoparticle arrays by partial dissolution of ordered pore films (or monolayer inverse opal) in a solution. By this method, we have fabricated Fe₂O₃ and In₂O₃ hexagonal close-packed nanoparticle arrays. This method is also applicable for synthesis of other material nanoparticle arrays. The particle size in the arrays can be controlled by the dissolution time, which is, additionally, beneficial to study size dependent optical, magnetic, electrochemical, thermodynamic, catalytic properties of nanoparticls.     

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).     

The temperature dependence of the dielectric constant in solid H2, D2,4He,and Ne

The dielectric constant ε of solid hexagonal close-packed H₂ (X?0), H₂(X?0.7), D₂(X=0.33), and He ⁴ at constant volume and of H₂(X=0.75) and Ne at saturated vapor pressure is studied as a function of temperature between 1.17 and 10 K. HereX is the fraction of molecules with angular rotational momentumJ=1, the fraction 1?X havingJ=0. These are the first reported measurements on van der Waals solids at constant volume. The experiments were carried out using a thick-walled capacitance cell, the measurement frequency being 14 MHz. The observed changes of ε withT are expressed in terms of the effective polarizability α_CM defined by the Clausius-Mosotti relation. A reduced polarizability α*=α_CM (T)/α_CM (T=1.17 K) is presented as a function of temperature. The initial purpose of the measurements was to observe the effect of rotational ordering of the(J=1) molecules in H ₂ , to be detected by a change in polarizability, as suggested by A. B. Harris. With increasing temperature it was found that α_CM decreased of the order of 0.1% for H ₂ and D ₂ . Also, differences were found between H₂(X=0) and H₂(X=0.75), which are briefly discussed. For He ₄ , α_CM decreased by about 3×10 ^?5 between 1.17 K and the melting point, 3.8 K. An analysis of the results showed that the temperature variation of α_CM could not be caused by the effect of lattice vibrations. Also, a simple calculation shows that the rearrangement of molecular positions in H ₂ and D ₂ at constant volume would have to be quite substantial to account for the observed temperature change in α_CM, which change is therefore not understood. The dielectric constant of Ne was measured at saturated vapor pressure and corrections were made to obtain the change of α_CM at constant volume. Rather different results were obtained for Ne than for the other solids: α_CM rose sharply with temperature, and this behavior also is not understood. Measurements of the diectric constant of H₂(X=0) and H₂(X=0.73) near the melting curve showed that the polarizability α_CM is the same within 0.1% in both the liquid and the solid phases. In the solid and liquid phases the density differences between H₂(X=0) and H₂(X=0.75) and also the differences in the respective melting pressures are in good agreement with the previous published work.     

SnO2纳米棒的固相反应制备与表征

利用室温固相反应方法,合成了SnO2纳米颗粒前驱物.在NaCl、KCl等熔盐介质中,在600～785℃对前驱物进行焙烧,前驱物纳米颗粒自组装生长形成SnO2纳米棒.利用TEM、XRD和XPS对SnO2纳米棒形貌、成分进行了表征和分析,SnO2纳米棒直径为20～80 nm,长度从几百纳米到几个微米.研究了SnO2纳米颗粒前驱体熔盐介质中的生长,探讨了SnO2纳米颗粒在熔盐介质中的固相转变生长机理.     

NMR studies of a D2 single crystal in the ordered phase

We report the first experimental study of the NMR lineshape anisotropy in the orientationally ordered cubic phase of a D₂ single crystal. The para-D₂ concentration covered the range 0.72<X<0.82. The observed line shapes were obtained by means of Fourier transform techniques from the solid echoes recorded with a pulsed NMR spectrometer operating at 5.9 MHz. Theoretical line shapes and their second moments forp-D₂ (with angular momentumJ=1 and spinI=1) and foro-D₂ (withJ=0, I=2) were calculated as a function of the applied field direction from the theory by A. B. Harris. Good agreement was obtained for all directions, provided that, just as for solid H₂, a Gaussian function for the distribution of molecular axial alignment was assumed with an rms spreading angle of 6 deg forX=0.77. No change in the anisotropy of the second moment in the disordered phase was detected between the initial (hcp) crystal and after repeated thermal cyclings through the martensitic transition. This result implies no change in the orientation of the plane for the sliding nets during repeated passages through the transition. Furthermore, we report measurements of the longitudinal relaxation time for bothp-D₂ ando-H₂ versusT over the temperature range 0.5<T<3.5 K. The complex behavior reported previously for both H₂ and D₂ was confirmed. Measurements of the relaxation times as a function of the applied field direction in the ordered phase at 1.2 K showed no anisotropy within experimental error, and this result is discussed in the light of predictions by Hardy and Berlinsky. Finally, the polarization of theJ=0 molecules is studied as a function of the concentrationX of theJ=1 molecules and their state of orientational order over a wide range ofX andT in the ordered and disordered states. The results are compared with predictions of A. B. Harris and with previous data on polycrystalline samples.     

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.