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.     

The influence of surface kinetics in modelling chemical vapour deposition processes in porous preforms

The isothermal chemical vapour infiltration (ICVI) process is a well known technique for the production of composites and the surface modification of porous preforms. Mathematical modelling of the process can provide a better understanding of the influence of individual process parameters on the deposition characteristics such as final porosity or deposition profiles in the pore network. The influence of different rate expressions for several binary compounds on the ICVI process is discussed. Experimental work is used to validate the importance of correct kinetic expressions in a continuous ICVI model for cylindrical pores. The predicted infiltration characteristics are compared with experimental results. The final densification and Thiele modulus, i.e. a number which is a measure for the diffusion limitations in a pore, are used for the evaluation of the presented model, and conditions are given for an optimal densification of a porous preform by the ICVI process for several binary compounds. The deposition profiles as predicted by the model calculations are in agreement with the experimentally determined deposition profiles of TiN and TiC in small tubes. Moreover, it can be concluded that the shape of the deposition profiles is determined by the heterogeneous reaction kinetics. There is only a qualitative agreement between the predicted densification and measured densification for the synthesis of TiN and TiB₂ in sintered porous alumina. This mismatch can be explained in terms of a complexity of the pore network and differences in reaction kinetics. Model calculations reveal that there is a scattering for the predicted residual porosity as a function of the Thiele modulus for TiN. Moreover, this Thiele modulus can not fully account for the changes in densification at different temperatures. Given these uncertainties it is likely that a residual porosity of less than one percent can be obtained if the Thiele modulus is smaller than 1 × 10^–4. However, a CVI process with such a small Thiele modulus will not be practical, because of the concomitant long process times. Therefore, more precise conditions for the individual process parameters, i.e. concentration, reactor pressure, and temperature are deduced from the model calculations.Nomenclature a, b, c reaction order constants - C _i(x, t) concentration of species i at axial position x and time t (mole m^–3) - C _i ^o bulk concentration of species i (mole m^–3) - C _i ^* (x, t) dimensionless concentration of species i at axial position x and time t - D _e(x, t) effective diffusion coefficient at axial position x and time t (m²s^–1) - D _ij(x, t) binary diffusion coefficient (m²s^–1) - D _K(x, t) Knudsen diffusion coefficient at position x and time t (m²s^–1) - F correction factor for effective diffusion coefficient - k growth rate constant (ms^–1(m³mole^–1)^a+b-1) - K _i adsorption-desorption equilibrium constant (m³mole^–1) - L length of a pore (m) - M _i molecular weight of species i (g mole^–1) - M _ij harmonic mean of the molecular weights of species i andj (g mole^–1) - M _s molecular weight of deposit (g mole^–1) - m _t measured mass increase (g) - n _i stoichiometric number - P reactor pressure (Pa) - R(C _i) growth rate (mole(m^–2s^–1)) - r(x, t) pore radius at position x and time t (m) - r ^o initial pore radius (m) - r ^* dimensionless pore radius - S geometrical surface area (m²) - s ^t fraction of free titanium sites at the surface of TiN - s ⁿ fraction of free nitrogen sites at the surface of TiN - T temperature (K) - t time (s) - t _p process time (s) - U K _HCl/(K _{H 2} C _{H 2})^1/2 (m³ mole^–1) - V volume of alumina substrate (m³) - W K _TiCl3(m³ mole^–1) - X volume of infiltrated deposit relative to initial pore volume - x axial distance (m) - x ^* dimensionless axial distance - z number of time steps - dummy variable for integration - porosity of sintered porous alumina substrate - ratio of the volume over the surface area perpendicular to the flux (m) - density deposit (kg m^–3) - _ij a characteristic length (Å) - tortuosity factor of substrate - Thiele modulus - _D collision integral     

Dissolution kinetics of iron in liquid zinc

In hot dip galvanizing, steel strip is coated by immersion in a bath of molten zinc. The principal reactions that occur at the steel/liquid zinc interface are (1) dissolution of iron and (2) nucleation and growth of intermetallic compounds. In order to improve the management of industrial galvanizing baths, it is essential to evaluate the flux of dissolved iron that diffuses into the bath from the sheet. For this purpose, a rotating disk device has been developed to study the dissolution and diffusion of iron in pure liquid zinc at the temperature usually employed in galvanizing baths (465°C). Since the dissolution reaction is controlled by diffusion under these conditions, the diffusion coefficient of iron in liquid zinc has been measured and found to be: D _Fe ^Zn(L) = (9.8 ± 0.1) × 10^–10 m²·s^–1     

Grain growth in nanocrystalline NbAl3 prepared by mechanical alloying

Grain growth and its kinetics were studied on an intermetallic compound, NbAl₃ powder prepared by mechanical alloying of elemental Nb and Al powders for 1.8 Ms in an argon atmosphere at ambient temperature. The initial and grown grain sizes were measured from the X-ray line broadening of as-alloyed and annealed powders. Isochronal annealing of mechanically alloyed powders from 573 to 1373 K indicated that substantial grain growth occurs only in a temperature range of 1048 to 1173 K and ceases at 1273 K regardless of anneal time. Accordingly isothermal annealing of 1.8 to 18 ks was carried out at 1048, 1073 and 1098 K to obtain the grain growth kinetic that is described by In (dD/dt) = In(r_o/3) –2.0 In D where D is the measured grain size and r _o a constant. This r _o depends on temperature according to r _o=r_o exp (– Q/kT) where Q is the activation energy for grain growth, k the Boltzmann constant and T the absolute temperature. Arrhenius plots of r _o against the reciprocal of temperature yield a straight line, from whose slope the activation energy for grain growth is deduced to be 162±2 kJ mol^–1. Of significance is the fact that the ultimate grain size at 1273 K is approximately 70 nm, which will not grow by further annealing even at 1373 K.On leave from Ibaraki University, Japan.     

Surface and grain-boundary energies as well as surface mass transport in polycrystalline CeO2

The multiphase equilibration technique for the determination of the equilibrium angles that develop at the interphase boundaries of a solid–liquid–vapor system, has been used to calculate the surface and interfacial energies in polycrystalline CeO₂ and CeO₂/Cu system in argon atmosphere at the temperature range 1473–1773 K. Linear temperature functions were obtained by extrapolation, for the surface energy γ_sv (J/m²) = 2.465–0.563 × 10⁻³ T and the grain-boundary energy γ_ss (J/m²) = 1.687–0.391 × 10⁻³ T of the ceramic, as well as for the interfacial energy γ_sl (J/m²) = 2.623–1.389 × 10⁻³(T −1356 K) of the CeO₂/Cu system. Grain-boundary grooving studied on polished surfaces of CeO₂ annealed in argon atmosphere at the same temperature range has shown that surface diffusion was the dominant mechanism for the mass transport. The surface diffusion coefficient can be expressed according to the equation D_s (m²/s) = 3.82 × 10⁻⁴ exp(−308,250/RT).     

The surface diffusion coefficients of MgO and Al2O3

From the measurement of neck size and neck curvature during the sintering of two spheres the surface diffusion coefficients of MgO and Al₂O₃ were determined. The spheres of both materials were machined from single crystals. The following values of surface diffusion coefficients were found: for MgO,D _{s s} = 3.7 × 10^–4 exp (407.8 kJ mol^–1/RT m³ sec^–1; for Al₂O₃,D _{s s} = 1.5 × 10^–2 exp (518.7 kJ mol^–1/RT) m³ sec^–1.     

Diffusion coefficients of tetrazolium blue in homogeneous and micellar solutions

Diffusion coefficients of the electron acceptor dye tetrazolium blue were measured by the Taylor dispersion method, with an accuracy better than 4%, in two solvents: (i) a homogeneous one-aqueous phosphate buffer, 0.1 M, pH=7.0 (medium I); and (ii) a heterogeneous one-nonionic micelles of Triton X-100, 2.0 mM (where M stands for mol·dm^–3), in the same aqueous phosphate buffer (medium II). The values obtained were D ₁₂ ^I =3.64×10^–10m²·s^–1 and D ₁₂ ^II =3.01×10^–10m²·s^–1·D ₁₂ ^II has the meaning of a macroscopird or average diffusion coefficient, in which the partition coefficient of tetrazolium blue between micelles and water, as well as the diffusion coefficients of this dye and of the micelles in the aqueous phase, are involved.     

The anisotropic diffusion of water in Kevlar-epoxy composites

The diffusion of water into unidirectional Kevlar fibre reinforced epoxy resins was studied as a function of fibre orientation and, for unidirectional (0°) composites, as a function of volume fraction (V_f). As the angle increased from 0 to 90°, the diffusivity increased dramatically; i.e. as more and more fibre-ends were exposed to the shorter diffusion path, the diffusivity increased. The equilibrium weight gain of water (M) in the composites increased with theV _f of the fibre. M of Kevlar fibre was calculated to be 4.9%. At a constantV _f, specimens of the same thickness and width but different lengths were used to determineD ₂₂, the diffusion coefficient of the composite along the fibre, andD ₂₂, the diffusion coefficient transverse to the fibre. The initial data for the percentage weight gain against the square root of time were non-linear, which was attributed to the anisotropy of the diffusion process. The anisotropy arises from the much higher value ofD ₁₁ as compared toD ₂₂. AsV _f increased from 0.37 to 0.59,D ₁₁ increased from about 0.83 to about 4.2 × 10^–12m² sec^–1, whereasD ₂₂ decreased from 0.21 to 0.033 × 10^–12 m2 sec^–1. Thus, the ratioD ₁₁/D ₂₂ increased from 3 to over 100 as U increased. The experimental sorption data could be fitted satisfactorily with these diffusion coefficients.     

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.     

The Second Order Recombination and Spin-Exchange Relaxation of Atomic Deuterium at Low Temperatures in a Low Magnetic Field

We measured the 2nd order recombination rates and spin-exchange relaxation of atomic deuterium (D) in a ⁴ He coated sample cell, using the hyperfine resonance of (F = 1/2, m_F = –1/2) – (F = 3/2, m_F = –1/2) transition in a low magnetic field (3.9 mT) at temperatures between 0.6 K and 1.2 K. At lower temperatures below 0.9 K, the density decay of D atoms was dominated by D-D recombination on the liquid He surface. We found that the surface recombination cross length was 1_DD = (5.5 ± 1.3) × 10 ^–9 cm and the adsorption energy of D on ⁴ He surface was _a = 3.97 ± 0.07 K. Compared with prior measurements at high magnetic fields by other groups, 1_DD at low field was orders of magnitude smaller than what was expected when the scaling of 1/B² dependence of the direct recombination mechanism was used, and in addition, _a was significantly larger. This was attributed to the onset of the resonant recombination mechanism for the D-D surface recombination at high fields. Above 0.9 K, D-D volume recombination and recombination of D with hydrogen impurity became dominant processes of the density decay of D. The transverse relaxation times were measured and we determined the D-D spin-exchange relaxation rates, G_DD = (1.4 ± 0.6) × 10 ^–10 cm ³ sec ^–1 . It was smaller than theoretical calculations.     

Concentration dependence ofD,T 1, andT 2 for dilute solutions of3He in solid4He

Measurements of the spin diffusion coefficientD and NMR relaxation timesT ₁ andT ₂ are reported for dilute solutions of³He in solid⁴He at two molar volumes, 20.95 and 20.7 cm³. The weakly interacting impuriton model, for whichD ^–1 is proportional to impurity concentration, is observed only at fractional impurity concentrationx ₃ below 3 × 10^–4. Forx ₃ around 10^–3,T ₁ andT ₂ are controlled by the formation and breakup of³He₂ molecules.     

Analytical technique for the determination of solidification rates during the inward freezing of cylinders

An analytical/experimental approach which permits the determination of solidification rates during the inward solidification of cylinders is proposed. The technique is based on a previous analytical solution that treats the generalized problem of solidification of slabs. This solution is modified by a geometric correlation to compensate for the cylindrical geometry. A number of experiments have been carried out with a special experimental set-up, designed to simulate the inward solidification of cylinders in a water-cooled mould. A series of comparisons of experimental results, numerical predictions and calculations furnished by the proposed technique were made, showing good agreement for any case examined.Nomenclature a _s Thermal diffusivity of solid metal = k _s/c _s d _s (m² sec^–1) - A _i Internal surface area of the mould (m²) - b _s Heat diffusivity of solid metal = (k _s c _s d _s ^1/2(J m^–2 sec^–1/2 K^–1) - c _s Specific heat of solid metal (J kg^–1 K^–1) - d _s Density of solid metal (kg m^–3) - h Newtonian heat transfer coefficien (W m^–2 K^–1) - H Latent heat of fusion (J kg^–1) - k _s Thermal conductivity of solid metal (W m^–1 K^–1) - q Heat flux (W m^–2) - r Radial position (m) - r _o Radius of cylinder (m) - r _f Radius of solid/liquid interface (m) - S Thickness of solidified metal (m) - S _o Thickness of metal side adjunct (m) - t Solidification time (sec) - T Temperature (K) - T _i Surface temperature (K) - T _f Freezing temperature of metal (K) - T _o Temperature of the coolant (K) - T _s Temperature at any point in the solidified metal (K) - V ₁ Volume of remaining liquid metal during the solidification (m³) - V _s Volume of solidified metal (m³) - V _T Total volume of metal in the mould (m³) - x Distance from metal/mould interface (m) - Dimensionless solidification constant.     

Dissipation in the superfluid helium film

We have measured the rate of energy dissipation in superfluid helium film flow in an attempt to test a recent theory due to Harris-Lowe, which predicts that for superfluid stream velocitiesv _sthat just exceed the critical velocityv _c0, the rate of dissipation is given by an equation of the form Q=C(v_s–v_c0)^3/2. Our experiments at 1.33 K show that the exponent, predicted to be 3/2, is 1.491±0.021.The research for this paper was supported by the Defence Research Board of Canada, Grant number 9550-57.     

Oxygen self-diffusion in rutile under hydrothermal conditions

Oxygen self-diffusion coefficients have been determined for synthetic and natural rutile single crystals under hydrothermal conditions at 100 MPa total pressure and in the temperature range 873–1373 K. The diffusion coefficients are lower than the results from dry gas exchange studies would predict. Between 973 and 1373 K the results can be characterized by two linear Arrhenius relationships. D=1.14×10^–11 exp(–168.8 kJ mol^–1/RT) m^–2s^–1 for the natural rutile, and D=2.41×10^–12 exp(–172.5 kJ mol^–1/RT) m²s^–1 for the synthetic crystal. The results have been interpreted in terms of a defect model involving the dissolution of water in rutile as substitutional hydroxyl defects on oxygen lattice sites, with a solution enthalpy in the range 81–106 kJmol^–1.     

Describing non-Fickian water-vapour sorption in wood

Moisture transport and sorption in wood may not be accurately described by Fick's law of diffusion. The problem of making a model of non-Fickian behaviour (NFB) for wood is discussed. Some measurements in which NFB in wood is clearly seen are also reviewed. Four criteria, which must be satisfied by a model describing sorption in wood cell walls, are presented: (1) the model should not only describe the response to step changes in vapour pressure; (2) it should be able to predict sorption with more than one time scale; (3) the sorption rate should not depend on the thickness of the cell wall; (4) small rapid changes in vapour pressure should give slower fractional weight change than large rapid changes. A review of models of NFB in synthetic polymers indicates that there is presently no model of NFB which fulfills the above criteria. More measurements of the sorption behaviour of the cell wall are needed to construct such a model for wood. This model can then probably be used, together with a Fickian diffusion model, to model the sorption behaviour of whole wood.Nomenclature c concentration in a material kg m^–3 - D _c diffusivity with c as potential m² s^–1 - D _p diffusivity with p as potential kg/(m s Pa) - F flux kgm^–2–1 - p partial vapour pressure Pa - t time s - x distance m     

Aerobic composting of tobacco industry solid waste—simulation of the process

Solid waste accumulated during the processing of tobacco for cigarette manufacture mostly contains tobacco particles and flavoring agents. Its main characteristics are a high content of nicotine (2,000 mg per kg of total solids), which is a toxic compound, and high value of total organic carbon of the aqueous extract (12,620.0 mg l^–1). Because of this fact tobacco waste cannot be disposed of with urban waste.The aim of this work was to stabilize tobacco solid waste by aerobic composting. The experiments were carried out in closed thermally insulated column reactors (1.0 l and 25 l) under adiabatic conditions and at an airflow rate of 0.9 l min^–1 kg^–1 of volatile solids for 16 days. During the process, temperature changes in the reactor, CO₂ production and the numbers of mesophilic and thermophilic organisms in the mixed microbial culture were closely monitored. Nicotine concentration in the samples was analyzed at the start and at the end of process. It was estimated that at the end of composting the volume and mass of total solids in the tobacco waste were reduced by about 50% and those of nicotine by 80%. A simple empirical model was used to simulate the biodegradation rate of the organic fraction of the solid waste. It was found that the selected model describes aerobic composting fairly well, although only two kinetic parameters (k₀ and n) were estimated.List of symbols c_pS specific heat capacity of the substrate, kJ kg^–1 K^–1 - c_pz specific heat capacity of air, kJ kg^–1 K^–1 - F_Ku and F_Ki molar airflow at the reactor inlet and outlet, mol h^–1 - H_r reaction enthalpy, kJ kg^–1 of dry substrate - k specific rate, Eqs. (5) and (9), h^–1 - k_o constant in Eq. (9), day^–1 - m_o initial mass of the substrate, kg - m_S mass of dry substrate, kg - n order of the reaction in Eq. (5) - n_K molar amount of oxygen, mol - Q_v airflow volume, m³ h^–1 - r_K oxygen depletion rate, mol kg^–1 h^–1 - r_S degradation rate, kg kg^–1 h^–1 - _z air density, kg m^–3 - SD mean square deviation - t time, h - T temperature in reactor, °C - T_o temperature of substrate at the beginning of reaction, °C - T_K temperature of compost at the end of reaction, °C - T_u temperature of air at the reactor inlet - space time, day - w_S mass fraction of compost, m_sm_o^–1, kg kg^–1     

Oxygen self-diffusion in single and polycrystalline magnesio-ferrites

Self-diffusion coefficients of oxygen ion in polycrystalline and single-crystal magnesioferrites have been measured by a gas-solid isotopic exchange technique using¹⁸O as a tracer at temperature in the range 975 to 1465° C. A new method was considered for the oxygen volume diffusion in polycrystalline magnesio-ferrite, and its reliability is discussed. The volume diffusion coefficients of polycrystalline magnesio-ferrite (MgO/Fe₂O₃=0.95 in mole ratio) can be expressed asD=1.51×10^–1exp (–78 600/RT) cm² sec^–1 (1135 to 1465° C) andD=1.2×10^–7exp (–38 000/RT) cm²sec^–1 (975 to 1135° C). The volume diffusion coefficients of the polycrystal in the high temperature range were very close to those of single crystal ferrite of the same composition as the polycrystal. The activation energy of grain-boundary diffusion in this polycrystal was expected to be greater than that of the volume diffusion. A possible interpretation of this unusual behaviour is given in terms of an increased enrichment of Fe²⁺ ion along the grain boundary with temperature elevation, by which oxygen vacancies increase.     

Mass and spin diffusion near the λ line in dilute3He-4He mixtures

We examine the possibility of using NMR and other measurements on very weak solutions of ³ He in liquid ⁴ He to investigate the superfluid phase transition. It is found that even for these very weak solutions the mass (D _m) and spin (D _s) diffusion coefficients associated with the ³ He behave in radically different ways:D _m is predicted to diverge asT approaches T from above as (T–T) ^–1/3 , while the behavior ofD _s depends on the type of experiment, and for the ordinary spin-echo type has no particular singularity.Based on a D.Phil. thesis submitted to the University of Sussex by M. A. Eggington.     

Bismuth deformation potentials calculated from SdH periods under static strain and from magnetoacoustic attenuation

We describe the non-parabolicity of the electron dispersion in bismuth by the Lax model, which replaces the energy Eby E(1+E/E_G), E_G being the L-point energy gap. It is assumed that the effect of small strains can be accounted for solely by small changes of the electron and hole Fermi energies, dE_F = D_jke_jk,where D_jk and e_jk denote deformation potentials and strains. With this assumption we show that the deformation potentials come out the same whether the dispersion relation is non-parabolic or parabolic. This finding we use in a re-evaluation of the deformation potentials obtained from SdH-measurements under static strain. We further make a mass data correction of deformation potentials obtained from magnetoacoustic attenuation. The two sets of values so obtained are in excellent agreement. This allows us to improve the accuracy, and we recommend to use the following values (unit eV): for electrons: D₁₁ = 2.74 ± 0.50, D₂₂ = –7.38 ± 0.56, D₃₃ = 2.17 ±0.25, D₂₃ = –1.85 ± 0.44and for holes: D₁₁ = –1.06 ± 0.27, D₃₃ = –1.06 ± 0.09     

A Spectrophotometric Study of the Interaction of Np(VI) with Orthosilicic Acid and Polymeric Silicic Acids in Aqueous Solutions

The interaction of NpO ₂ ²⁺ ions with orthosilicic acid Si(OH)₄ and polymeric silicic acids (PSAs) in aqueous solutions was studied spectrophotometrically. The interaction at pH ≤ 4.5 is described by the equation NpO ₂ ²⁺ + Si(OH)₄ = NpO₂OSi(OH) ₃ ⁺ + H⁺ with the equilibrium constant log K = − 2.88±0.12 at the ionic strength I = 0.1–0.2 (log K ⁰ = −2.61±0.12 recalculated to I = 0); the stability constant of the complex NpO₂OSi(OH) ₃ ⁺ (I = 0) is log β⁰ = 7.20± 0.12. At pH > 5, a second complex of NpO ₂ ²⁺ with PSAs of the presumed composition NpO₂(≡ SiO)₂(≡SiOH) _{m − 2}, where (≡SiOH)_m denotes a PSA molecule with surface Si-OH groups, is formed. The absorption spectra of the complexes NpO₂OSi(OH) ₃ ⁺ and NpO₂(≡ SiO)₂(≡SiOH) _{m − 2} were obtained. In contrast to the hydroxo complexes, they have pronounced maxima at 560 – 600 nm with the molar extinction coefficients of about 25–30 l mol⁻¹ cm⁻¹, which is several times higher compared to the Np(VI) aqua ion.__________Translated from Radiokhimiya, Vol. 47, No. 4, 2005, pp. 322–327.Original Russian Text Copyright © 2005 by Yusov, Shilov, Fedoseev, Astafurova, Delegard.