Mass transport in cuprous oxide

The chemical diffusion coefficient of Cu₂O has been obtained for an oxygen partial pressure near 5 10^?4 atm as a function of the temperature in the range 700–900°C D? = 1 62 10^?4 exp(?5140 ± 600 cal mol ^?1)/RT cm²s^?1 This was easily achieved according to the electrochemical method used for the preparation of gaseous mixtures whose Po₂; is lower than 10^?5 atm The slight difference observed with the previously published results by Maluenda, and obtained for Po₂ values which increase with T between 10^?4 and 0.21 atm, may be due to an oxygen partial pressure effect already observed in the case of CoO. An ambipolar treatment of the chemical diffusion, in the case of p-type semiconductor M_aO_b, oxides, has allowed us to express the chemical diffusion coefficient as a function of the concentration of the prevailing defects and of their diffusion coefficient In the case where the prevailing defects are cationic vacancies α times ionized we have shown that the expression D? = (1 + α)D_vα can be generalized to the A₂O compounds This set of results has allowed us, according to the copper self diffusion data obtained recently by Peterson etal, to estimate the apparent enthalpy of formation of the catiomc vacancies ΔH_f 23 ± 0 8 kcal mol^?1.     

The coupled coherent and incoherent motion of excitons and its influence on the line shape of optical absorption

We treat the coupled coherent and incoherent motion of Frenkel excitons by a model calculation. The model contains the four parametersa (distance of neighbouring atoms),J (exchange interaction integral), γ_o (describing the strength of the local energy fluctuations) and γ₁ (a measure of the fluctuations of the exchange interaction integral, i.e. nonlocal fluctuations). Calculation of the optical absorption of systems with two differently oriented molecules/unit cells results in the Davydov-splitting given by Δ=8J and the linewidth given by Γ=γ_o+γ₁. From the equation of motion of the density matrix we derive a diffusion equation. The diffusion constant is given by \(D = \frac{{a^2 }}{\hbar }\left( {2\gamma _1 + \frac{{J^2 }}{{\gamma _1 + \Gamma }}} \right)\) . Comparison with experiment yields γ_o=70cm^?1, γ₁=0.1 cm^?1 at room temperature and Γ<1 cm^?1 at 4.2 °K. Using these numerical values and the criterium of Haken and Strobl we derive that at room temperature the exciton motion is incoherent and may be described by a hopping process whereas at low temperature it is coherent.     

Heterodiffusion of chromium and cobalt in liquid iron

The heterodiffusion has been studied by the method of stationary diffusion source. In that method the saturated radioactive vapour of the diffusing element comes into contact with the liquid in which diffusion is being studied. Two variants of that method were applied and the diffusion coefficients of chromium and cobalt in liquid iron were determined, i.e.D _{(Cr→Fe, 1860K)}= =4·9×10^?5cm²/s andD _{(Co→Fe, 1820K)}=5×10^?5cm²/s, respectively. The values of maximum concentration of chromium in Fe-samples after diffusion were of the order of 10^?1 to 10^?2 wt-%, those of cobalt of 10^?4 wt-%. This experimental method is rather simple and the results obtained are in good conformity with other measurements.     

Diffusion of hydrogen and deuterium on the (111) plane of tungsten

The diffusion of ¹H and ²H on the (111) plane of a W field emitter has been studied by the fluctuation method at various coverages. Both activated and unactivated diffusion is observed; the latter shows very little isotope effect, suggesting that coupling to the substrate is so strong that mass renormalization makes the effective masses of ¹H and ²H nearly identical. Values of D in the tunneling, i.e. temperature independent, regime are 10^?13?5 × 10^?14 cm²/s depending on coverage. For activated diffusion at high coverages, corresponding to population of the β₁ state E = 2.4?3.2 kcal/mol and D₀ = 2 × 10^?8 ?5 × 10^?7 cm²/s, depending on coverage. For lower coverages, corresponding to β₂ population, E = 7–9 kcal/mol, D₀ = 9 × 10^?6 ?2 × 10^?3 cm²/s, again depending on coverage. Similar values are obtained for ²H, with E and D₀ values slightly reduced. An exponentially decaying correlation signal for clean W was also seen and interpreted in terms of flip-flop of W atoms.     

Die Diffusionskoeffizienten und mittleren freien Weglängen der geladenen und neutralen Radon-Folgeprodukte in Luft

The knowledge of the diffusion coefficients of radioactive atoms and ions in air is very important in a number of investigations on and computations of the attachment of radon decay products to aerosol particles. In this work measurements of the diffusion coefficients of neutral and charged²¹²Pb atoms are reported. The values found areD ₀=(7.6±0.4)·10^?2cm²s^?1 for neutral atomsD=(5.0±0.3)·10^?2cm²s^?1 for charged atoms The used method of measurement allowed to determine these constants 1–5 seconds after the formation aged²¹²Pb atoms, so that a “cluster” formation was improbable. The mean free path for neutral (λ₀=(4.9±0.3)·10^?6cm) and charged (λ=(3.2±0.2)· 10^?6cm) lead 212 atoms in air were computed from the measured diffusion coefficients. All obtained results were compared with values, calculated from theory.     

Relativistic calculations of ground states of single-electron diatomic molecular ions

We have performed relativistic calculations of ground-state energies for a series of single-electron homonuclear dimers A ₂ ^(2Z?1)+ with nucleus charge Z = 1, 2, 10, 20, 30, 40, 50, 60, 70, 80, 90, 92, and 100 and internuclear distances R = 2/Z. The work involves the Born-Oppenheimer approximation and the single-electron two-center Dirac Hamiltonian, which describes the interaction between an electron and two immovable point charges. Analysis of the convergence process and comparison with data presented in other works for H ₂ ⁺ and Th ₂ ¹⁷⁹⁺ dimers shows that the relative error of the obtained results is on the order of 10^?11–10^?12. High-accuracy values of ground-state energies for some dimers other than Z = 1 and 90 have been obtained in this work for the first time.     

Diffusion of 55Fe in Fe2O3 single crystals

The diffusion of ⁵⁵Fe has been measured parallel to the c axis of Fe₂O₃ single crystals at temperatures in the range 708–1303°C and at an oxygen activity of unity. The tracer penetration profiles were determined using sectioning techniques. For temperatures above 900°C the tracer diffusion coefficient is given byD¹(Fe) = 1.6 × 10⁹ exp[?6.0 (eV)/kT] cm² s^?1 and below 900°C by 2.8 × 10^?9 exp[?1.8 (eV)kT]. The high-temperature behaviour is probably characteristic of pure Fe₂O₃, whereas diffusion at lower temperatures may be influenced by impurities. The most likely defects responsible for diffusion of Fe are iron interstitials and, for oxygen, oxygen vacancies, and the observed activation energies are discussed in terms of the properties of these defects. The diffusion data and defect models have been used to predict the rate of growth of Fe₂O₃ and indicate that outward Fe diffusion is the dominant transport process. Previously published data for Fe₂O₃ growth in a variety of experimental situations have been corrected to a single rate constant using a model for multilayer growth. The corrected data are all in good agreement but are approximately two orders of magnitude greater than predicted from diffusion data, which suggests that grain boundary diffusion controls the growth of Fe₂O₃ in practice.     

A monte-carlo/molecular dynamics study of the diffusional recombination kinetics of C(a) + O(a) → CO(g) on Pt(111)

The diffusion constants for C and O adsorbates on Pt(111) surfaces have been calculated with Monte-Carlo/Molecular Dynamics techniques. The diffusion constants are determined to be D_C(T)=(3.4 × 10^?3e^{$\text{?13156}\text{T}$})cm²s^?1 for carbon and D_O(T) = (1.5×10^?3 e^{$\text{?9089}\text{T}$}) cm² s^?1 for oxygen. Using a recently developed diffusion model for surface recombination kinetics an approximate upper bound to the recombination rate constant of C and O on Pt(111) to produce CO_(g) is found to be (9.4×10^?3 e^{$\text{?9089}\text{T}$}) cm² s^?1.     

Modelling the voltammetric study of intercalation in a host structure: application to lithium intercalation in RuO2

Intercalation process kinetics have been studied theoretically for the case of potential sweep voltammetry. The influence of the thickness (or the particle radius) of the “host” material and the potential sweep rate has been determined between the limits of thin film diffusion and semi-infinite diffusion for a reversible process. Experimental data have been obtained with the cell: RuO₂/LiClO₄-PEO/Li. The theoretical results have been used to calculate the diffusion coefficient of lithium in the “host” structure RuO₂ at 80°C, giving an approximate value of 1.6 × 10^?11 cm² s^?1     

Diffusion of sulfur in nickel oxide single crystals

The diffusion of sulfur in nickel oxide single crystals has been investigated over the temperature range from 1000 to 1250°C. The measured data were found to deviate markedly from the error function complement dependence for diffusion from a constant source. The deviation is attributed to the migration of sulfur by the “double mode simultaneous diffusion mechanism.” The faster mode diffusion is suggested to be via nickel vacancies, and the slower mode diffusion is suggested to be via oxygen vacancies. The diffusivities for faster mode are given by D_f = 2.94 exp[? 86.6 kcal/RT] cm² sec^?1 and, the slower mode, D_s = 1.08 × 10^?9 exp [?32.8 kcal/RT]cm²sec^?1.     

Proton and Li-7 NMR study on the effect of the OH− anion upon the Li+-ion conduction in the solid solution Li5NI2LiOH

From ¹H and ⁷LiNMR relaxation times T₁, T₂ and T_1ρ in Li₅NI₂ and the solid solution Li₅NI₂?0.77LiOH, the diffusive motion of the Li⁺ ion was studied to make clear the role of the OH^? ion in improving the Li⁺ ionic conduction. At temperatures as low as 140 K, each Li⁺ ion jumps among four available positions. Its activation energies are 9.26 and 11.8 kJ mol^?1 for Li₅NI₂ and Li₅NI₂?0.77LiOH, respectively. Diffusive motion was observed in T₂ and T_1ρ above 240 K. The mode of the cation distribution and the diffusion mechanism are not affected by the presence of the OH^? anion. The most noticeable fact is that the OH^? ion is substituted selectively for the N^3? ion that is the nearest neighbour of the Li⁺ ion. This selective substitution increases the concentration of the Li⁺ vacancy most effectively up to 4.2% of the total Li positions. At the same time it diminishes the strong attractive force of the N^3? anion binding the Li⁺ ion to the position, and thus the activation energy. For the diffusion, an anomalously low attempt frequency of 3&#x0303; × 10⁹Hz was obtained from T_1ρ, while the normal value of 4.8 × 10¹²Hz was obtained from the ionic conductivity. The large discrepancy was attributed to the collective nature of the Li⁺ diffusive motion.     

Fourier transform spectroscopy on the 3ν2, 2ν2 + ν6 and ν3 + ν5 bands of H2CO

Fourier transform spectra covering the range from 1500 to 5400 cm^?1 with 0.02-cm^?1 resolution have been obtained for formaldehyde. A study of the region above 4000 cm^?1 has yielded rotational constants and other asymmetric rotor parameters for three bands: 3ν₂ (ν₀ = 5177.7611 ± 0.0005 cm^?1)2ν₂ + ν₆ (ν₀ = 4734.193 ± 0.004 cm^?1), and ν₃ + ν₅ (ν₀ = 4335.102 ± 0.001 cm^?1). An analysis of the A-type Coriolis interaction between the 2ν₂ + ν₆ state and the unobserved 2ν₂ + ν₄ state has yielded partially deperturbed rotational constants for the 2ν₂ + ν₆ state. Vibration-rotation interaction constants have been obtained for the ν₂ and ν₆ normal modes by combining the present results with those of previous workers.     

The relationship between chemical and tracer diffusion coefficients of aliovalent ions in an ionic lattice

The theoretical model developed by Lidiard was extended to describe the relationship between the chemical and tracer diffusion coefficients of aliovalent ions in an ionic lattice.It is shown that the relationship between the chemical diffusion coefficient, D, and the tracer diffusion coefficient, D¹, is D = 2D¹ if the migration of dimers is the principal mechanism of transport and for the migration of trimers D = 3D¹ if the concentration of impurity ion is relatively small. These relationships are valid regardless of the charge of the aliovalent or lattice ions.The chemical diffusion coefficients of Cr³⁺ in Cr-doped MgO were determined for three different temperatures, 1656, 1717 and 1768K, and for the concentration region 2.5×10^?2?2.8×10^?1 mole% Cr₂O₃. Using previously determined values for the tracer diffusion coefficient of ⁵¹Cr in Cr-doped MgO it was found that for the temperature and concentration region investigated D = (2.00±0.17)D¹ which indicates that diffusion proceeds primarily by the migration of dimers.     

Absolute intensity measurements of the CO2 bands 401III←000 and 411III←010

The absolute intensities of the transitions 401_III←000 and 411_III←010 of CO₂ have been measured from spectra obtained under high resolution. Both the vibration-rotation line intensities and the integrated band intensities are reported. The rotationless transition moment of 401_III←000 is deduced and a vibration-rotation interaction factor F(m) = 1+(4.92×10^?4)m+(4.4×10^?7)m² is determined. The values obtained are: S_Band(401_III←000) = (25.54±0.22)×10^?5 cm^?2atm_{(293 K)}^?1, |R₀₀₀^401_III| = (1.87±0.02)×10^?4D, and S_Band(411_III←010) = (1.83±0.13)×10^?5 cm^?2atm_{(293 K)}^?1.     

Nuclear spin relaxation of Xe in liquid Te

By the method of time differential perturbed angular distribution following a nuclear reaction, the relaxation rateT _r ^?1 of the 8 msI ^π=10⁺ isomer of¹³²Xe has been measured in liquid Te. Between 670 °K (supercooled liquid) and 1,000 °K the rate decreases from about 720/s by about a factor of two. From existing experimental material it is concluded thatT _r ^?1 is mainly due to quadrupolar interaction (T _r ^?1 ≈T _Q ^?1 ). Its magnitude is discussed considering the metallic and the noble gas limit as models for the Xe-Te-interactions. The temperature dependenceT _Q(T) apparently does not correlate with the diffusion constant of Te in contrast to a simplified theoretical treatment. — The nuclearg value of the isomer has been determined to be g=(?)0.195(5) thus confirming the configuration (vh_11/2)².     

Doping of polyacetylene by diffusion of iodine

The solubility limit and diffusion coefficient of I₂ in (CH)_x polymer have been measured with a radiotracer technique. The concentration of iodine in the polymer is a function of the surrounding concentration outside the film at equilibrium (free enthalpy of solubility = ? 0.20 eV). The data are consistent with the following mechanism: liquid state diffusion of the solution in between the fibrils and solid state diffusion of iodine inside the fibrils. The macroscopic diffusion coefficient throughout the film is equal to 10^?9cm²sec^?1. These results restrict the present (CH)_x polymer to heterolithic device applications after encapsulation. Monolithic substrate application will require a further inhibition of diffusion.     

Diffusion and compressibility of sodium on the (110) plane of tungsten

The surface diffusion parameters and the compressibility of sodium on the (110) plane of tungsten have been measured using the field emission fluctuation method for sodium coverages from 0.2 to 3 × 10¹⁴ atoms cm^?2 and for temperatures from 170 to 500 K. Two temperature regimes can be defined. In the high temperature regime (? 300 K) the diffusion is essentially normal with an activation energy ranging from 0.28 to 0.58 eV and a preexponential coefficient D₀ from 10^?8.1 to 10^?2.7 cm² s^?1. In this regime the compressibility increases with temperature indicating an effective repulsive adatoms interaction. In the low temperature regime (? 300 K) the diffusion coefficient decreases with temperature at high coverage and slowly increases with temperature at lower coverage. The transition between both regimes appears on the compressibility versus temperature curve as an inflection point. The comparison of the present results with slow electron diffraction results furnishes strong evidence that the observed transition corresponds to a continuous short-range order-disorder transition.     

Lithium mobility in the layered oxide Li1−xCoO2

The Li⁺-ion chemical diffusion coefficient in the layered oxide Li_0.65CoO₂ has been measured to be $\text{D}\text{?}\text{= 5 × 10}{}^{\mathrm{?12}}$ m² s^?1 by three independent techniques: (1) from the Warburg prefactor, (2) from the transition frequency for semi-infinite to finite diffusion lengths in steady-state ac-impedence measurements and (3) from a modified Tubandt method that uses ac-impedance data to distinguish interfacial and surface-layer resistances from the bulk resistance of the sample. This value and a small increase in D? with (1 ? x) in Li_1?xCoO₂, 0.45 < (1 ? x) < 0.80, compare favorably with the $\text{D}\text{?}\text{= 5}\text{to}\text{7 × 10}{}^{-12}\text{m}{}^2\text{s}{}^{-1}$ obtained by Honders for this system with pulse techniques. A qualitative discussion is presented as to why this composition dependence and why D? for this system is a factor of five larger than that for Li⁺-ion diffusion in Li_xTiS₂.     

Absolute coverage and isostemc heat of adsorption of deuterium on Pt(111) studied by nuclear microanalysis

The absolute coverage (θ) of deuterium adsorbed on Pt(111) in the ranges 180< T<440 K and 5 × 10^?6 < P < 5 × 10^?2 Pa D₂ has been determined by nuclear microanalysis using the D(³He, p)⁴He reaction. From these data, the isosteric heat of adsorption (E_a) has been determined to be 67 ± 7 kJ mol^?1 at θ ? 0.3. This heat of adsorption yields values of the pre-exponential for desorption (10^?5 to 10^?2 cm² atom^?1 s^?1) that lie much closer to the normal range for a second order process than those determined from previous isosteric heat measurements. The E_a versus θ relationship indicates that the adsorbed D atoms are mobile and that there is a repulsive interaction of 6–8 kJ mol^?1 at nearest neighbour distances. At 300 K the coverage decreases to ? 0.05 monolayer (? 8 × 10¹³ D atoms cm^?2) as P→ 0, apparently invalidating a recent model of site exchange in the adsorbed layer.