The spin diffusion coefficient of3He in3He-4He solutions

The transport properties of³He in³He-⁴He solutions with molar concentrations of 5, 9, 14, and 24% have been studied for 0.9 KT2.5 K. The spin diffusion coefficientD _s and the longitudinal relaxation timeT ₁ were measured by the spin-echo method for temperatures both above and below the solution lambda temperatureT . The spin-echo method measures the diffusion coefficient for magnetizationD _s, which differs from the usual diffusion coefficient for particlesD belowT .D _s depends on the³He-³He scattering cross section _FF and the³He-roton/phonon cross section _FB, whileD depends only on _FB. The distinction betweenD _s andD is elaborated in terms of a simple mutual-friction model for diffusion. The two scattering mechanisms are clearly evident in the behavior ofD _s as a function of concentrationx and temperature. The contribution due to the³He-³He scattering is inversely proportional tox, indicating that the³He can be treated in first approximation as a classical gas (the Pomeranchuk model). The predictions of various theoretical models are compared with the results, where possible, but most of the previous theoretical work is not applicable to the concentration range and temperatures of these measurements.Supported in part by the National Science Foundation and the U.S. Office of Naval Research.     

Diffusive motion of hydrogen in mordenite studied by quasi-elastic neutron scattering

Neutron time-of-flight experiments have been done with hydrogen adsorbed in Na-mordenite at temperatures between 35 and 130 K and densities betweenn = 43 andn = 13 H₂ molecules in the unit cell of the zeolite lattice. The quasi-elastically scattered neutrons give rise to a peak that is not broadened at half-height with respect to the experimental energy resolution of 90 μeV (46 ns). A Lorentzian broadening at the bottom of the quasi-elastic peak has been interpreted in terms of a diffusion model yielding a rotational diffusion constantD_r = 2 · 10^{11rad s−1} and a translational diffusion constantD_t = 2 · 10⁻³cm² s⁻¹ atT = 130K andn = 35 H₂ molecules/unit cell.     

Specific heats of solid hydrogen,solid deuterium,and solid mixtures of hydrogen and deuterium

Measurements have been made in the temperature range 0.5–5 K of the specific heats of pure solid H₂, pure solid D₂, and four solid mixtures of H₂ and D₂ with D₂ fractions between 15 and 95%, all of which systems had low concentrationc of molecules in the rotational stateJ=1. For the H₂,c=0.0023, and for the D₂,c=0.030. It was found that the observed specific heats could be described as the sum of three terms as follows. (1) A lattice specific heat. This was found to follow aT ³ function with _D =122 K for solid H₂ and _D=113.8 K for solid D₂. For the solid mixtures the lattice specifi heats have in first approximation values given by a weighted mean of the lattice specific heats of the pure components. (2) A Schottky term with a maximum at about 1.3 K for solid H₂ and 1.4 K for solid D₂, which can quantitatively be described in terms of electric quadrupole-quadrupole (EQQ) interactions in nearest-neighbor pairs and triples of molecules in the rotational stateJ=1. This term led to evaluation of , the EQQ interaction energy, giving /k=0.9 ± 0.1 K for solid H₂ and 0.93 ± 0.05 K for solid D₂. It was found, moreover, that in solid H₂ there was an appreciable enhancement with time of the number of clusters of molecules in the rotational stateJ=1 at the expense of the number of isolated singles of similar molecules, due to rotation diffusion. On the other hand no rotation diffusion was observed in solid D₂ or in the solid mixtures of H₂ and D₂, except possibly in those mixtures containing 85% H₂. (3) A second anomalous term occurring at temperatures below about 0.8 K and, by extrapolation, having its maximum below 0.5 K (the lowest temperature of our measurements). This anomaly was observed only in those samples containing D₂ and is, as yet, unexplained in detail. A further major conclusion from our results in the temperature range 0.5–5 K is that there was no evidence in the form of a sharp anomalous jump in the specific heat of any of the mixtures which could be interpreted as indicating the occurrence of isotopic phase separation. This absence of phase separation is noted, in spite of the fact that thermodynamically it is energetically favorable in the temperature range of observation.Work partially supported by a grant from the National Science Foundation and by contracts with the Office of Naval Research and DOD (Themis Program).     

Surface Diffusion of Solid Hydrogen

A number of experiments have shown that hydrogen molecules can migrate on films of solid hydrogen. This was thought to be a diffusive process but recent experimental findings have led others to a different conclusion, so a question remains about the process by which the hydrogen molecules migrate over their own solid surface. We report new measurements using a hole-burning technique which confirm these recent experiments but we interpret them differently. We have developed a model for the recovery of the hydrogen which accounts for these results and shows that the H₂ does move diffusively. The diffusion is thermally activated and we have determined the diffusion constant, D ₀=4.03×10^–4±2.5×10^–5 m²s^–1, and the activation energy, E=43±7 K, for hydrogen.     

Vacancy Assisted Motion of Charges in Quantum Crystals

From comparison of results of measurements of diffusion coefficients D(T) of the positively and negatively charged complexes (charges), created under irradiation in perfect crystals, grown from pure helium or hydrogen at small pressures, with diffusion coefficients of the isotopic impurities or the self-diffusion coefficients known from NMR studies one can conclude that motion of the more mobile charges through these crystals (of positive charges in HCP ⁴ He, ³ He and D ₂ samples and of negative charges in BCC ⁴ He and ³ He and also in HCP crystals, grown from pure p–H ₂ ) is vacancy assisted. Thus strong departures of the temperature dependencies of diffusion coefficients of the positive charges D ₊(T) in HCP ⁴ He samples and of the negative charges D _–(T) in p–H ₂ samples from the simple Arrhenius type of behavior D= D ₀ exp[–G/T] at low temperatures can be attributed to the change of the mechanism of diffusion of thermal vacancies: from classical thermally activated hopping of the localized vacancies near T _melt to the band motion of delocalized vacancions at T< T _melt/2. To explain the nature of the maxima on the D ₊(T) curves observed in perfect ⁴ He crystals, it may be assumed that the flow conditions of the vacancion gas around a positive charge (a probe particle with an effective radius of a few lattice constants) can change significantly with lowering the temperature: from a hydrodynamic flow of the viscous gas round the probe at the transition temperatures to a kinetic flow of the rarefied vacancion gas at low temperatures. In this case the bandwidth of the vacancions in studied ⁴ He samples is near Q _V 10^–4 K.     

3He diffusion in liquid isotopic mixtures

Spin echo techniques have been used to study the diffusion of³He in liquid isotopic mixtures with molar concentrations in the range fromX ₃=0.137toX ₃=0.850 over a temperature range from 3.0 to 0.4 K. AboveT the diffusive behavior is very similar to that of pure³He, although there is an increased scattering associated with⁴He. BelowT the diffusion coefficient increases with decreasing temperature and shows a dependence on the³He number density much like that of a classical gas. The excitations of⁴He have little influence on the³He diffusion coefficient, even at temperatures well above 1 K.The Rhodes Trust and the National Research Council of Canada supported one of us (R.B.H.) during the course of this research.     

Search for low temperature liquid H2 in 2-D films

Thermodynamic, scattering, and nmr measurements on films of H₂, HD, D₂, and mixtures of these molecules adsorbed on MgO and graphite have found phase diagrams for individual monolayers with solid-liquid-vapor triple points ranging from 7.2K (for the 2nd layer of H₂ on MgO) to 5.74K (for a monolayer of H₂ on top of a solid layer of D₂ on graphite). We review the experimental evidence for the proposed phase diagrams.     

Slow Diffusion of Molecular Hydrogen in Zeolite 13X

High-resolution quasi-elastic neutron scattering measurements have been performed on molecular hydrogen in zeolite 13X. Previous NMR measurements suggested that the freezing temperature is suppressed from 14 K down to 8 K. In contrast, previous intermediate resolution quasi-elastic neutron scattering studies suggested freezing occurred between 25 and 35 K. Unfortunately, the limited instrumental resolution available in the previous quasi-elastic neutron scattering study was not sufficient to show this point definitively. We report new quasi-elastic neutron scattering measurements with very high resolution that show no evidence of mobile hydrogen below 25 K, which is well above the bulk liquid-solid transition temperature for hydrogen. A quasi-elastic component appears between 25 and 30 K indicating the presence of mobile H₂. However, the width and momentum dependence of the quasi-elastic scattering are much different than would be expected for the diffusive motion of liquid hydrogen in this temperature range. Instead, we find that a slow diffusive component representing jumps between well-defined sites appears first at low temperatures. As the temperature is raised, a faster liquid like diffusive component appears.     

Grain growth in copper and alpha-brasses

The wires of 99.999% copper and alpha-brasses containing 12, 20, 30 and 35 at % Zn have been annealed in vacuum for 30 to 240 min at 873, 923, 973 and 1023 K. The grain-growth data obtained are well encompassed by the relationD ², —D ₀ ² , =Kt exp(-H/kT), whereD is the instantaneous mean grain diameter at the time,t, of isothermal anneal andD ₀ refers to the initial mean grain diameter. In alpha-brasses the activation energy for grain-boundary self-diffusion,H, and the pre-exponential factor,K, depends on the zinc concentration,c, asH = (H ₀ — 1.1c) eV andK =K ₀ exp(-10.7c) cm² sec^–1. The values ofH ₀ andK ₀, referred to the base metal are respectively 0.87 eV and 3.0 × 10^–4 cm² sec^–1, which are in good agreement with those (0.85 eV and 3.6 × 10^–4 cm² sec^–1) found for copper.     

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.     

Thermodynamic functions of ScVO<Subscript>4</Subscript> at temperatures from 0 to 350 K

The heat capacity of ScVO₄ has been determined by adiabatic calorimetry at temperatures from 14.52 to 347.13 K, and smoothed heat capacity data have been used to evaluate its thermodynamic functions (entropy, enthalpy increment, and reduced Gibbs energy). At 298.15 K, the thermodynamic functions of scandium orthovanadate are C _p ⁰(298.15 K) = 110.5 ± 0.1 J/(mol K), S ⁰(298.15 K) = 110.9 ± 0.1 J/(mol K), H ⁰(298.15 K) − H ⁰(0) = 18.53 ± 0.01 kJ/mol, and Φ⁰(298.15 K) = −[G ⁰(298.15 K)/298.15] = 48.75 ± 0.12 J/(mol K). The calculated Gibbs energy of formation of scandium orthovanadate from its constituent elements is Δ_f G ⁰(ScVO₄, 298.15 K) = −1644.0 ± 2.2 kJ/mol.     

Oxygen self-diffusion in a potassium strontium silicate glass using proton activation analysis

Oxygen self-diffusion coefficients were measured in a 20K₂O-20SrO-60SiO₂ (wt%) glass above and below the glass transition temperature using the single spectrum proton activation analysis of oxygen-18 using the nuclear reaction ¹⁸O(p, )¹⁵N. The -particle spectrum recorded during proton irradiation is used to determine the ¹⁸O concentration profile. The self-diffusion coefficients, D, determined for the three diffusion times of about 22 h, 3 1/2 and 7 1/2 days were in good agreement within experimental error, except for the two lowest temperatures of the short-time run possibly because of the shallow depths of diffusion and surface exchange. In the temperature range 600 to 1000 K, D values with the relations, above the glass transition temperature D=7.6×10¹⁴ exp(–119 kcal/RT) cm²sec^–1, and below the glass transition temperature D=1×10^–12 exp(–10 kcal/RT) cm²sec^–1, were obtained.     

Isochoric Heat Capacity Measurements for 0.5 H2O+0.5 D2O Mixture in the Critical Region

The isochoric heat capacity C _V of an equimolar H₂O+D₂O mixture was measured in the temperature range from 391 to 655 K, at near-critical liquid and vapor densities between 274.05 and 385.36 kgm^–3. A high-temperature, high-pressure, nearly constant-volume adiabatic calorimeter was used. The measurements were performed in the one- and two-phase regions including the coexistence curve. The uncertainty of the heat-capacity measurement is estimated to be ±2%. The liquid and vapor one- and two-phase isochoric heat capacities, temperatures, and densities at saturation were extracted from the experimental data for each measured isochore. The critical temperature and the critical density for the equimolar H₂O+D₂O mixture were obtained from isochoric heat capacity measurements using the method of quasi-static thermograms. The measurements were compared with a crossover equation of state for H₂O+D₂O mixtures. The near-critical isochoric heat capacity behavior for the 0.5 H₂O+0.5 D₂O mixture was studied using the principle of isomorphism of critical phenomena. The experimental isochoric heat capacity data for the 0.5 H₂O+0.5 D₂O mixture exhibit a weak singularity, like that of both pure components. The reliability of the experimental method was confirmed with measurements on pure light water, for which the isochoric heat capacity was measured on the critical isochore (321.96 kgm^–3) in both the one- and two-phase regions. The result for the phase-transition temperature (the critical temperature, T _{C, this work}=647.104±0.003 K) agreed, within experimental uncertainty, with the critical temperature (T _{C, IAPWS}=647.096 K) adopted by IAPWS.     

Equation of State of He-H2 and He-D2 Dense Fluid Mixtures at High Pressures and Temperatures

The fluid variational theory is used to calculate the Hugoniot equation of state (EOS) of He, D₂, He + H₂, and He + D₂ fluid mixtures with different He:H₂ and He:D₂ compositions at high pressures and temperatures. He, H₂, and D₂ are the lightest elements. Therefore, the quantum effect is included via a first-order quantum correction in the framework of the Wigner-Kirkwood expansion. An examination of the reliability of the above computations is performed by comparing experiments and calculations, in which the calculation procedure used for He and D₂ is adopted also for He + D₂ and He + H₂, since no experimental data for the mixtures are available to conduct these comparisons. Good agreement in both comparisons is found. This result may be seen as an indirect verification of the calculation procedures used here, at least, in the pressure and temperature domains covered by the experimental data for He and D₂ used for comparisons, which is nearly up to 40 GPa and 10⁵ K. Also, the equation of state of He + H₂ fluid mixtures with different compositions is predicted over a wide range of temperatures and pressures.     

Cationic conduction and diffusion and the compensation law

It is shown that measurements of ionic conductivity or diffusion made in the region intermediate between the intrinsic and extrinsic ranges closely obey the compensation law logD ₀ =a + bH _d, whereD ₀ is the pre-exponential term in the equation for the diffusion coefficient, H _d is the experimentally determined activation enthalpy, anda andb are constants. It is further shown that such measurements can allow determination of defect formation energies. A procedure for analysing results in the intermediate region is proposed and tested for ion conduction by Li⁺ in LiF. Data for oxides are presented to show semi-quantitative agreement with the procedure.     

Hydrogen permeation through mild steel in temperature range 20–500°C measured by hydrogen collection method

Abstract

Hydrogen permeation through steel plate maintained at various constant temperatures between 20 and 500°C was investigated using the hydrogen collection method. Fused salts were employed at elevated temperatures. Hydrogen entry was induced by step changes in cathodic charging current density. Emanating flux transients obtained at the hydrogen exit face corresponded closely to a model for permeation determined exclusively by bulk hydrogen diffusion through steel, induced by stepped changes in hydrogen concentration at the steel entry face subsurface, and zero hydogen at the exit face subsurface. An Arrhenius plot of log (D) v. 1/T, using diffusion coefficients D derived from permeation transients was approximately linear in the range 20–310°C. The values derived for activation energy E _a of 17 kJ mol ^-1 and for the pre-exponential factor D ₀ of 2·6 × 10^-3 cm2 s^-1, according to D = D ₀ exp (-E _a/RT) were similar to literature values. Between 310 and 500°C, stable permeation conditions were difficult to obtain, but flux measurements were repeatable and unaffected by moisture in air.     

Viscosity and diffusivity of a binary liquid mixture of critical composition: Study of the system 2-butoxyethanol/water

Results of measurements of the temperature dependence of the shear viscosity and the mutual diffusion coefficient of a 2-butoxyethanol/water mixture of critical composition are reported. The shear viscosities are measured with a capillary viscometer, and the diffusion coefficients by dynamic light scattering. The viscosity data are used to determine the regular (background) and the singular (critical) part of the viscosity and to analyze the crossover regime.Q ₀ has a value ofQ _o = (1.54 ± 0.60) × 10⁶ cm^–1, which is small for a binary mixture of components of small molar mass. The viscosity is dominated by singular contributions in a narrow temperature range (T _c – T) 1.2 K. The singular contributions can be neglected for temperatures (T_c–T) 11 K. The function =_b expz H, given in the literature, represents the viscosity data in the temperature range 3 mK (T _c – T) 25 K using the asymptotic form of the functionH for (q _d/q _c) 0 (q _d,q _c, parameter of the theory). This limit corresponds to the case in which the background diffusion coefficient Lib can be neglected. The reduced diffusion coefficient D^* calculated from the light-scattering data as a function of the scaling variable x(=q) is represented by the approximation of the dynamic scaling function proposed in the literature.     

Freezing of molecular hydrogen and its isotopes in porous vycor glass

We have made a detailed ultrasonic study of freezing and melting of molecular H₂, HD and D₂ in the pores of Vycor glass. The behavior was similar to that seen in previous measurements with argon and helium. The hydrogen liquids under cooled about 2.5 K below their bulk triple points before freezing began and there was substantial hysteresis between freezing and melting. The velocity and attenuation began to increase suddenly at the onset of freezing. The velocity continued to increase to the lowest temperatures (2 K) and the attenuation had a broad peak at about two thirds of the freezing temperature. We attribute these effects to stress relaxation via thermally activated vacancy motion in the solid hydrogen, an interpretation confirmed by looking at the frequency dependence of the velocity and attenuation. The magnitude of the velocity and attenuation changes increased in going from H₂ to HD to D₂, as expected based on their increasing densities and elastic constants. However, there were no qualitative differences between the boson (H₂ and D₂) and fermion (HD) cases nor, for that matter, between hydrogen and argon. We believe that essentially all the hydrogen was frozen a few tenths of a kelvin belowT _F, at the point where the melting/freezing hysteresis began. If even a few per cent of the hydrogen had remained liquid and become superfluid at some lower temperature, it would have been seen as a further increase in the velocity and a critical attenuation peak. The sensitivity of our ultrasonic measurements allowed us to make accurate measurements of the freezing and melting temperatures of the different liquids in Vycor. We found that the fractional undercooling, (T _B -T _F )/T _B , increased as the molecular mass decreased which may indicate the importance of quantum effects on the liquid-solid interfacial energy _ls .     

Thermodynamic properties of NaZr2(PO4)3

The heat capacity of crystalline NaZr₂(PO₄)₃ was measured between 7 and 340 K by adiabatic calorimetry. The results were used to calculate the thermodynamic functionsC _p ⁰ ,H ⁰(T) -H ⁰(0),S ⁰(T), andG ⁰(T) -H ⁰(0) in the range 0-340 K. The absolute entropy was found to be S⁰NaZr₂(PO₄)₃, cr, 298.15 K) = 327.1 ±1.0 J/(mol K), and the standard entropy of formation Δ_fS⁰(NaZr₂(PO₄)₃, cr, 298.15 K) = -1101±1 J/(mol K). Solution calorimetry was used to determine the standard enthalpy of formation, Δ_f H ⁰(NaZr₂(PO₄)₃, cr, 298.15 K) = -5236 ±5 kJ/mol. By combining the data obtained by the two techniques, the standard Gibbs energy of formation was determined to be Δ_fG⁰(NaZr₂(PO₄)₃, cr, 298.15 K) = -4908 ±5 kJ/mol.     

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.