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.     

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.     

Non diffusive mobility of solid hydrogen films

We have used a hole-burning technique to study the mobility of thin solid films of H₂ and D₂ for temperatures between 1.6 K and 5 K. Even at low temperatures where transport through the vapor is negligible, the solid films remain mobile. The transport is thermally activated with an activation energy of 19 K for H₂ and 38 K for D₂. The time dependence of the regrowth shows that surface transport is not due to simple diffusion.     

Solid hydrogen and deuterium. I. Ground-state energy calculated by a lowest order constrained-variation method

The ground-state energy of solid hydrogen and deuterium is calculated by means of a modified variational lowest order constrained-variation (LOCV) method. Both fcc and hcp H₂ and D₂ are considered, and the calculations are done for five different two-body potentials. For solid H₂ we obtain theoretical results for the ground-state binding energy per particle from –74.9 K at an equilibrium particle density of 0.700 ^–3 or a molar volume of 22.3 cm³/mole to –91.3 K at a particle density of 0.725 ^–3 or a molar volume of 21.5 cm³/mole, where =2.958 Å. The corresponding experimental result is –92.3 K at a particle density of 0.688 ^–3 or a molar volume of 22.7 cm³/mole. For solid D₂ we obtain theoretical results for the ground-state binding energy per particle from –125.7 K at an equilibrium particle density of 0.830 ^–3 or a molar volume of 18.8 cm³/mole to –140.1 K at a particle density of 0.843 ^–3 or a molar volume of 18.5 cm³/mole. The corresponding experimental result is –137.9 K at a particle density of 0.797 ^–3 or a molar volume of 19.6 cm³/mole.     

Low-temperature quadrupole and crystalline field effects in the specific heat of solid D2

Measurements have been made of the specific heat of solid D ₂ with concentrations of para-D ₂ between approximately0.9 and6%. The measurements are an extension of previously reported results to 150 mK and to various para-D ₂ concentrations. An anomalous specific heat is observed below 0.6 K which cannot be accounted for by the nearest-neighbor electric quadruple-quadrupole (EQQ) interactions betweenJ=1 molecules. This anomaly is explained in terms of next- and next-next-nearest-neighbor interactions between pairs and nearest-neighbor interactions between triple configurations ofJ=1 molecules. In addition, estimates are presented of the crystalline field splitting parameter (/k) in solid deuterium with lowJ=1 concentration.This work was partially supported by a grant from the National Science Foundation and by a contract with the Office of Naval Research.     

First and Second Order Phase Transitions and Magnetic Hysteresis in a Superconducting Plate

The self-consistent solutions of the nonlinear Ginzburg–Landau equations, which describe the behavior of a superconducting plate of thickness 2D in a magnetic field H parallel to its surface (provided that there are no vortices inside the plate), are studied. We distinguish two classes of superconductors according to the behavior of their magnetization M(H) in an increasing field. The magnetization can vanish either by a first order phase transition (class-I superconductors), or by a second order (class-II). The boundary S _I–II, which separates two regions (I and II) on the plane of variables (D,), is found. The boundary (D,) of the region, where the hysteresis in a decreasing field is possible (for superconductors of both classes), is also calculated. The metastable d-states, which are responsible for the hysteresis in class-II superconductors, are described. The region of parameters (D,) for class-I superconductors is found, where the supercooled normal metal (before passing to a superconducting Meissner state) goes over into a metastable precursor state (p-). In the limit 1/2 and D( is the London penetration depth) the self-consistent p-solution coincides with the analytic solution, found from the degenerate Bogomolnyi equations. The critical fields H ₁, H ₂, H _p, H _r for class-I and class-II superconducting plates are also found.     

Orientational ordering in solid D2 from NMR studies. I. The hcp phase

Using a coherent pulsed NMR spectrometer operating at 5.9 MHz, measurements have been made of the free induction decay and of the solid echo in hcp solid D₂. From these data, and using Fourier transform techniques, the NMR line shapes and longitudinal relaxation times have been found for both o-D₂ (angular momentumJ=0 and spinI=2) and p-D₂ (withJ=1 andI=1) separately. The concentration and temperature extended over the ranges 0.05X(J=1)0.56 and 0.04<T<3 K, respectively. For both o-D₂ and p-D₂, the second moment of the NMR line shape rises smoothly as the temperature decreases, while the relaxation times pass through a minimum. No evidence of a thermal hysteresis could be found in the line shape or relaxation times. The orientational ordering increases continuously as the temperature decreases and the results lead to the conclusion that there is no evidence for a well-defined transition into a phase that has the characteristics of a glassy state, at least above 0.05 K. Calculations of the rms order parameter for p-D₂ as a function ofX andT are presented and the results compared with those for solid H₂. Above 0.5 K, the agreement is very good, while below 0.3 K, (H₂)>(D₂). The orientational polarization of theJ=0 molecules in D₂ by the surroundingJ=1 molecules is measured from the ratio of the lineshape second moments and is found to be in order-of-magnitude agreement with the predictions by A. B. Harris in the high-temperature limit. An analysis and correlation of the various measured relaxation times via energy diffusion models is presented. From the spin-lattice relaxation times of theJ=1 molecules, the orientational fluctuation rates are estimated for various concentrations as a function ofT and compared with the results from H₂. Good agreement is found. Some unusual features in the intensity ratio of theI=1 andI=2 signals that is different from the expected one are described. In an Appendix, corrections made to the observed line shapes to compensate for the instrumental limitations of the pulse spectrometer are outlined.     

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).     

Solid hydrogen and deuterium. II. Pressure and compressibility calculated by a lowest-order constrained-variation method

The pressure and the compressibility of solid H₂ and D₂ are obtained from ground-state energies calculated by means of a modified variational lowest-order constrained-variation (LOCV) method. Both fcc and hcp structures are considered, but results are given for the fcc structure only. The pressure and the compressibility are calculated or estimated from the dependence of the ground-state energy on density or molar volume, generally in a density region of 0.65^–3 to 1.3^–3, corresponding to a molar volume of 12–24 cm³/mole, where = 2.958 å, and the calculations are done for five different two-body potentials. Theoretical results for the pressure are 340–460 atm for solid H₂ at a particle density of 0.82^–3 or a molar volume of 19 cm³/mole, and 370–490 atm for solid ⁴He at a particle density of 0.92^–3 or a molar volume of 17 cm³/mole. The corresponding experimental results are 650 and 700 atm, respectively. Theoretical results for the compressibility are 210 × 10^–6 to 260 × 10^–6 atm^–1 for solid H₂ at a particle density of 0.82^–3 or a molar volume of 19 cm³/mole, and 150 × 10^–6 to 180 × 10^–6 atm^–1 for solid D₂ at a particle density of 0.92^–3 or a molar volume of 17 cm³/mole. The corresponding experimental results are 180 × 10^–6 and 140 × 10^–6 atm^–1, respectively. The agreement with experimental results is better for higher densities.     

Nearly isochoric finite torsion of a compressible isotropic elastic circular cylinder

Summary Finite torsion of a circular bar of isotropic compressible hyperelastic material is considered. A procedure suggested by Truesdell is used to obtain solutions for a particular strain energy function although the method used is not restricted to this particular form. The procedure is applicable if the volume strain is small. Results for finite twist with the length prevented from changing and with the length allowed to change so that the resultant longitudinal force is zero are presented.

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Fast-isochore endliche Torsion eines kompressiblen, isotropen, elastischen Kreiszylinders

Zusammenfassung Betrachtet wird die endliche Verdrehung eines Stabes mit Kreisquerschnitt aus einem isotropen, kompressiblen, hyperelastischen Werkstoff. Eine von Truesdell vorgeschlagene Vorgangsweise wird zur Bestimmung der Lösungen, für eine spezielle Verzerrungsenergiefunktion, verwendet, obwohl die verwendete Methode nicht auf diese spezielle Form beschränkt ist. Diese Vorgangsweise ist anwendbar, sofern die Volumsverzerrung klein ist. Ergebnisse für die endliche Verdrehung werden angegeben, wobei entweder die Längenänderung unterbunden ist oder die Länge sich ändern kann, so daß die resultierende Längskraft verschwindet.

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Notation F deformation gradient tensor - B=FF ^T left Cauchy-Green tensor - I identity matrix - I ₁=trB first invariant ofB - I ₂=1/2[(trB)²–trB ²] second invariant ofB - I ₃=detB third invariant ofB - W strain energy per unit volume of unstrained stateB ₀ - gradient operator for stateB - u small displacement from stateB - H=u small displacement gradient based on stateB - T true stress tensor based on stateB - f body force vector - T additional stress - =T+T true stress for final configuration - elastic constant equivalent to shear modulus for small deformation - elastic constant equivalent to Poisson's ratio for small deformation - r, ,z cylindrical polar coordinates - _r , , _z , _z physical components of stress tensor for cylindrical polar coordinates With 3 Figures     

Synthesis,crystal structure,and proton conductivity of KFe(H<Subscript>2</Subscript>P<Subscript>2</Subscript>O<Subscript>7</Subscript>)<Subscript>2</Subscript>

KFe H₂P₂O7)₂ is synthesized at 443 K in molten polyphosphoric acids containing K and Fe ions, and its crystal structure is determined: triclinic unit cell with a = 4.9974(6) Å, b = 7.4766(9) Å, c = 7.8185(9) Å, = 82.29(2)°, = 83.37(2)° , = 74.13(2)° ; Z = 1, sp. gr. P . The structure is made up of infinite ribbons formed by corner-shared PO₄ tetrahedra and FeO₆ octahedra, with the K atoms in between. Neighboring ribbons are linked by hydrogen bonds. The proton conductivity of potassium iron(III) dihydrogen diphosphate is rather low.Translated from Neorganicheskie Materialy, Vol. 41, No. 1, 2005, pp. 74–77. Original Russian Text Copyright © 2005 by Chudinova, Murashova, Ilyukhin, Tarnopolskii, Yaroslavtsev.     

Density dependence of the elastic constants of hcp hydrogen and deuterium

The elastic constants of hcp H₂ and D₂ are calculated for densities up to 10 cm³/mole (20 kbar at T = 4.2 K). An Isotropic pair potential is utilized in the computations and cubic anharmonic corrections are incorporated into the lattice dynamics. The results are compared with sound velocity, specific heat, and Brillouin and neutron scattering measurements.     

Surface structure and surface-spin induced magnetic properties and spin-glass transition in nanometer Co-granules of FCC crystal structure

Separated Co-granules, of an average diameter as small as D = 2.0 nm, of FCC crystal structure have been synthesized by co-reducing Co²⁺ cations dispersed in a liquid. They exhibit an enhancedsaturation magnetization _s by as much as 34% with a more than an order of enhanced magnitude for the effective anisotropy constant K _eff over the bulk values at 4.2 K. An irreversibility in the ZFC-FC (zero field cooled-field cooled) thermomagnetograms occurs at temperatures T T _B, where T _B is their blocking temperature. The ZFC thermomagnetogram peaks at T _B according to their K _eff and volume V. T _B = 152 K has been found for D = 10 nm granules in an applied magnetic field of H = 1 kA/m. The sample, which is superparamagnetic(coercivity H _c = 0) in nature at T T _B, develops H _c at T < T _B with a unique dependence on temperature, H _c(T) = H _c(0)[1 – T/T _B]^1/2, with H _c(0) = 40.0 kA/m. The results are discussed with a two-phase modelstructure of granules. In this model, the grain-surface atoms have amodified magnetic structure of the core atoms. An inter-couplingbetween the magnetic spins in the two regions occurs in aferromagnetic or antiferromagnetic manner according to theirinterface that mediates their exchange interactions through it. Thestudies of , K _eff, or H _c as a function of temperature (4.2 to 380 K) and/or size D (2 to 20 nm) demonstrate their strong correlation with the dynamics of the surface spins (DSS). An enhanced surfaceanisotropy with large total interface-energy in small granulesgoverns the DSS. An average value of the surface anisotropy constantK _s = 2.28 mJ/m² is determined by a linear plot of K _eff with D ^–1 at D 2.9 nm. Larger granules follow a modified K _eff – D ^–1 plot with an order of smaller K _s-value. The surface spins form a surface-spin-glass, which undergoes a magnetic transition to a spin-frozen state at a critical temperature T _F = 71 K. The T _F evolves following the well-known de Almeida-Thouless line, T _F H ^2/3, at H 42 kA/m.     

Specific heat measurements of intercalation compounds M x TiS2 (M=3d transition metals) using ac calorimetry technique

Specific heats of 3d transition metal intercalates of 1T-CdI₂-type TiS₂, M _x TiS₂ (M=V, Cr, Mn, Fe, Co, and Ni; 0x1), have been measured in the temperature range 1.6–300 K using an ac calorimetry technique. The electronic specific heat coefficient (2–100 mJ/mole K²) and the Debye temperature _D (240–430 K) are found to depend on the guest 3d metals and their concentrations. All the intercalates show anomalous specific heat at low temperatures following an – lnT dependence ( and are constants), as found in dilute alloys.     

An apparatus for measuring the thermal conductivity and diffusivity of solid materials

An apparatus is described for measuring the thermal conductivity and diffusivity on small specimens of solid materials; also the results are shown which have been obtained for refractive high-alumina concrete by such measurements.Notation thermal conductivity at the mean temperature of specimens, W/m· °C - Q power of the central heater, W - F cross section area of a specimen, m² - t_1,2 temperature drop across the specimens, °C - ₁, ₂ difference in heights between the thermocouple beads, center-to-center, in the first and in the second specimen respectively, m - t temperature, °C - time coordinate, min - d₁= (d_1u+d_1l )/2 mean distance between specimen contact plane and nearest thermocouple beads, for the upper and lower specimen, m - d₂= (d_2u+d_2l )/2 mean distance between specimen contact plane and farthest thermocouple beads, for the upper and lower specimen, m - dt(d₁,)/d rate of temperature rise at section d₁ of the specimen at time, °C/h - t=t₁+t₂ sum of temperature drops in the specimens at time, °C - m heating rate, h^–1 - a thermal diffusivity of specimens, referred to their mean temperature, m²/h - =m/a, m^–1 b=¦(t_u–t_l)/t_u¦ heating nonuniformity factor Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 22, No. 6, pp. 1049–1054, June, 1972.     

Experimental determination of the equation of state of solid hydrogen and deuterium at high pressures

Isochores of solid hydrogen and deuterium have been measured for melting line pressures up to 2000 bar. These are corrected to correspond to para-H₂ and ortho-D₂. The 4.2 K isotherm of H₂ has been determined and compared to the extrapolated low-pressure isochore of Anderson and Swenson (AS). Deviations have led us to reanalyze the AS data. The 4.2 K isotherm and the isochores are used, with the aid of a Mie-Grüneisen analysis, to determine P-V-T data for these solids up to 25 kbar. An analysis is presented which enables a determination of P-V-T-C ₁ for all values of C ₁, the ortho-para concentration. Results, including the Debye temperature, Grüneisen constant, and bulk modulus, are presented both in tabulated and graphical form. We also present what we feel to be the best of the 4.2 K, zero-pressure molar volumes of disordered H₂ and D₂ as a function of C ₁. Our measurements show no indication of the premelting phase transition reported in recent Russian literature and a possible explanation is presented.Supported in part by the Stichting FOM.     

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.     

Attempts to increase the nuclear relaxation time of a3He gas at low temperatures

In an attempt to increase, at temperatures of a few kelvins, the relaxation time of a dilute³He gas enclosed in spherical Pyrex or pure silica bulbs 3 cm in diameter, we have studied the relaxing properties of various coatings, such as solid O₂ and solid N₂ and multiple coatings of H₂ on N₂, H₂ on O₂, and H₂ on H₂O. Contrary to naive expectations, thin films of solid oxygen proved to be very efficient coatings, although single molecules are paramagnetic. When multiple coatings are compared, they even provide the best undercoating to hydrogen films. The longest relaxation time we measured at 4.2 K was 8000 min, i.e., more than 5 days. We also found that Pyrex and pure silica, either bare or coated, give comparable results below 50 K. These experiments enabled us to measure the adsorption energy of³He on O₂, W(³He/O₂)=130±15 K, and of³He on N₂, W(³He/N₂)=200±50 K. In the absence of any theoretical calculation, these energies still need to be confirmed by other experimental techniques.Laboratory associated with the CNRS. U.A. 18.     

Studies of the dielectric constant in solid H2,4He,and Ne

Measurements of the static dielectric constant and of the resulting polarizability _CM defined by the Clausius-Mosotti relation are reported for several molecular solids under conditions of quasiconstant density. The range of measurements was between 0.4 and about 15 K, and pressures up to about 1 kbar were used. In solid H₂, the changes of as a function of ortho concentration are reported at 4.2 and 12 K, from which it is concluded that [(ortho)–(para)]/0.005, which is approximately 2 1/2 times larger than in the liquid phase. Furthermore the temperature change of _CM is studied for various densities at comparable ortho concentrationsX. Particular attention is paid to the orientational order-disorder transition in solid H₂ withX0.65, where _CM shows an abrupt change that appears to be a function ofX, density, and thermal history. In general _CM is lower in the ordered (cubic) phase than in the disordered (hexagonal) phase. The temperature change of _CM in almost pure para-H₂, measured between 4 and 0.4 K, is presented and is compared with other recently reported experiments. It is concluded that the mechanism that produces the change of _CM withT and at the order-disorder phase transition is not understood. In solid Ne, measurements of _CM are reported for one sample assumed to be at zero pressure and one where the density is quasiconstant. There is a strong temperature dependence in _CM for the former above 5 K (in agreement with previous findings), while for the latter _CM appears to be constant within the uncertainties introduced by strain-induced hysteresis effects. The sample of solid⁴He, investigated between its melting point at 4.3 and 0.8 K at constant density, shows a very weak temperature dependence of _CM, which is also consistent with previously reported measurements.Research supported by a grant of the U.S. Army Research Office (AROD) and from a contract with the Office of Naval Research. A preliminary account of this research was given inBull. Am. Phys. Soc. 20, 672 (1975).     

Diffusion separation of hydrogen from gas mixtures

Experiments are described and a model is evaluated for the process of production of superpure hydrogen from mixtures with ammonia and nitrogen by selective diffusion through thin metallic membranes.Notation j_H, j_C molar fluxes of hydrogen and ballast gas - k effective permeability coefficient (product of hydrogen solubility coefficient times diffusion coefficient, divided by membrane thickness) - l, L coordinate measured along supply channel and maximum value thereof (channel length) - M molecular weight of hydrogen - P working perimeter of diffusion cell - p, p pressure in supply and output channels - Q, Q_H mixture flow rate and hydrogen output for one cell or entire unit - S area of working section of supply channel - v velocity in output channel - x, x_o molar fraction of hydrogen in mixture and value thereof at inlet - z, Z dimensionless coordinate and length of apparatus - , dimensional and dimensionless hydraulic resistance coefficients - , _* dimensionless pressure in output channel and value thereof at outlet - dimensionless pressure (concentration) of hydrogen in supply channel - hydrogen density in output channel - relative output Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 47, No. 1, pp. 100–108, July, 1984.