Jump diffusion coefficient of different cations intercalated into amorphous WO3

This work shows how the combination of quasi-equilibrium (chronopotentiometry) and kinetical measurements (electrochemical impedance) is able to extract ionic mobility values like the jump diffusion coefficient D_J. Results are presented on the jump diffusion coefficient variation with composition of several cations (Li⁺, Na⁺, and K⁺) intercalated into electron beam evaporation-prepared a-WO₃ thin films. D_J exhibits higher values for the smallest ion (Li⁺), and decreases as the ion size enlarges. In all cases D_J shows lower values for high intercalation levels. It is noted that the type of cation rather influences transport mechanisms than equilibrium properties (insertion thermodynamics). The energy barrier of ion hopping is analyzed in light of available microscopic diffusion models and theoretical simulations.     

The effect of zinc concentration on vacancies jump rate, diffusion coefficient and jump length in Cu-Zn ferrite

Samples with the chemical formula Cu_1−xZn_xFe₂O₄ (x=0.2, 0.4, 0.6, 0.8 and 1) were prepared by the standard ceramic method. The dielectric constant and dielectric loss tangent were studied as a function of vacancy jump rate. The results show that the dielectric constant and dielectric loss tangent decrease with increasing vacancy jump rate. In addition, the electron jump length in the octahedral sites was studied as a function of zinc concentration. The increase in jump length with Zn concentration has been attributed to the substitution of Fe⁺³ for Zn²⁺ at the A-sites, which increases the B-B interaction. The increase of diffusion coefficient with increasing Zn concentration was reinforced by the increase of jump rate.     

Computer simulation study of the Levy flight process

The random walk simulation of a Levy flight shows a linear relation between the mean square displacement 〈r²〉 and time. We have analyzed different aspects of this linearity. It is shown that the restriction of jump length to a maximum value (l_m) affects the diffusion coefficient, even though it remains constant for l_m greater than 1464. So, this factor has no effect on the linearity. In addition, it is shown that the number of samples does not affect the results. We have demonstrated that the relation between the mean square displacement and time remains linear in a continuous space, while continuous variables just reduce the diffusion coefficient. The results also imply that the movement of a Levy flight particle is similar to the case in which the particle moves in each time step with an average jump length 〈l〉. Finally, it is shown that the non-linear relation of the Levy flight will be satisfied if we use a time average instead of an ensemble average. The difference between the time average and ensemble average results shows that the Levy distribution may be a non-ergodic distribution.     

First principles calculation of boron diffusion in fcc-Fe

The diffusion mechanism of boron in fcc-Fe was studied by first-principles calculations. The sites where B atoms tend to occupy and the diffusion behavior were calculated. Results indicated that the main mechanism of boron diffusion in fcc-Fe was the B–monovacancy complex mechanism instead of the interstitial mechanism. The diffusion coefficient D₁ of the B–monovacancy complex mechanism was calculated without considering the backward jump of the B atoms. The calculated D₁ = 1.26 × 10⁻⁴ × exp(^–2.01eV/k_BT) m²·s⁻¹ is consistent with the reported results from experiments.     

On the thermal conductivity of glasses

We estimate the numerical contribution of the interaction between like defects in glasses for the linewidth (? T^?1₂) obtained in acoustical experiments. This interaction gives origin to a diffusion process with a very large diffusion constant (D = 10^?5 cm² sec^?1). The thermal conductivity due to this diffusion process is calculated. Its temperature dependence is also obtained.     

Sodium diffusion in cryolite at elevated temperatures studied by quasielastic neutron scattering

Quasielastic neutron scattering (QENS) has been applied to study the sodium mobility on nanosecond time scales in the perovskite fluoride cryolite, Na₃AlF₆, at high temperatures. Up to T = 1153 K the diffusion of Na ions is well described by a diffusion process of jumps between six and eight-fold coordinated sites. Above this temperature, where a step-like increase in the electrical conductivity occurs, the jump length increases, which indicates additional jumps over larger distances. The electrical conductivity derived from the self-diffusion coefficient via the Nernst–Einstein relation and the corresponding activation energy are in excellent agreement with the previous conductivity measurements. We conclude that the jump diffusion of sodium ions is the dominant mechanism for the electrical conductivity in cryolite at high temperatures up to T = 1153 K.     

Electrical conductivity and tracer diffusion in sodium germanate glasses

Measurements of the electrical conductivity using ac complex impedance techniques and the tracer diffusion coefficient of ²²Na have been performed in a series of (x)Na₂O(1?x) GeO₂ glasses (where 0.0006 ? x ? 0.156). The compositional form of the Haven ratios, calculated from these data, have been interpreted in terms of a single defect model which considers a number of distinctly different jump frequencies for the alkali ion; the magnitude of these different jump frequencies is determined by the proximity of the diffusing alkali ion to a charge-compensating center within the glass network. Attractive interactions between the positive alkali ions and the negative charge-compensating centers cause successive jump directions of the alkali ions to become correlated. In the sodium germanate glasses the negatively-charged centers probably correspond to the six-fold coordinated sites formed upon addition of alkali oxide to GeO₂. These negatively-charged trapping centers correspond to non-bridging oxygen sites in alkali silicate glasses.     

New prospects in studying Li diffusion—two-time stimulated echo NMR of spin-3/2 nuclei

The measurement of diffusion parameters like activation energies and translational jump rates of small cations plays a key role in materials science. Especially the in-depth investigation of Li diffusion in ionic conductors is of great interest, because suitable ionic conductors are needed for, e.g., the development of new secondary ion battery systems. As the standard tracer method is not applicable to study Li diffusion due to the lack of a suitable radioactive isotope, Li diffusion is alternatively probed by solid state NMR techniques. With the different NMR methods being available, diffusion processes can be studied on different length- and timescales. In the present paper we use two-time spin-alignment echo (SAE) NMR for the direct, i.e., model independent, measurement of extremely small translational Li jump rates. To this end, different crystalline and glassy ion conductors like Li_xTiS₂, Li₄SiO₄ as well as LiNbO₃ served as model substances to reveal the special features of this technique. SAE-NMR, which was originally developed for deuterons, has also been applied in a few cases to spin-3/2 nuclei, like ⁷Li, before. The corresponding correlation functions yield not only information about diffusion parameters but also about geometric properties of the diffusion pathways, making SAE-NMR a powerful method which complements well-established NMR techniques.     

Silver-tracer diffusion in Cu2O

The diffusion of¹¹⁰Ag in Cu₂O has been measured by a serial-sectioning technique as a function of temperature (700–1132°C) and oxygen partial pressure (6 × 10^?6 ?8 × 10^?2 atm). The data are fit to the defect model for Cu₂O developed by the authors in the preceding paper. Silver ions have a larger impurity-vacancy binding free energy and/or a larger jump frequency for the singly charged cation vacancies relative to that for the neutral cation vacancies. The activation enthalpies for the diffusion of copper and silver ions in Cu₂O are nearly equal, but the absolute value of D¹_Ag is about three times larger than D¹_Cu even though the silver ion is 31% larger than the copper ion.     

Fast diffusion of copper(I) ions in NaI

Results are presented for nmr investigations into the diffusion of Cu⁺ in NaI. The nmr results show that a considerable amount of the copper(I) ions is incorporated interstitially and that the mean jump frequency ν_Cu of the Cu⁺ ions is much higher than that of the host cations: ν_Cu/ν_Na ≈ 820 at 320 °C. Two values for the temperature dependence of ν_Cu are found: E₁ = 1.63 eV (T < 300 °C) and E₂ = 0.61 eV (T > 300 °C). The nature of the mechanism of the Cu⁺-migration in NaI is discussed and a model proposed. The interstitial incorporation and fast diffusion of the Cu⁺ ions is confirmed by a comparison with the results for CdI₂ doped NaI. CdI₂ is incorporated substitutionally and the mean jump frequency ν_Cd is lower than that of the host ions: ν_Cd < 10⁸ s^-1 at 650 °C.For the pure substance conductivity measurements were performed too, for vomparison. The agreement of nmr and conductivity data is good. From both δH_m = 0.59 eV and δH_s = 2.08 eV were calculated in excellent agreement with recently reported data. It is shown that the presence of oxygen in the samples leads to wrong data. A method for removing this impurity is described.     

Analytical solution for the57Fe Mössbauer spectra for octahedral cage hopping and correlated electric field gradient fluctuations

We derive an analytical solution for the Mössbauer relaxation spectra of⁵⁷Fe in the case of correlated jump diffusion and electric field gradient rotation in an octahedral cage.     

New model for tracer-diffusion in amorphous solid

The tracer-diffusion and structure of polymorphic states of amorphous solid is studied by mean of the statistic relaxation technique and simplex analysis. Several different metastable states of amorphous iron have been constructed based on the model containing 2 × 10⁵ atoms. All models have almost the same pair radial distribution functions, but they differ in the potential energy per atom and the density. We found a large number of vacancy-simplexes which varies according to the relaxation and serves as a diffusion vehicle. New diffusion mechanism for tracer-diffusion is found of which the elementary diffusion process likes a collapse of “microscopic bubble” in amorphous matrix. This includes a jump of diffusing atom and the collective movement of a large number of neighboring atoms. The diffusion constant D determined in accordance with considered diffusion mechanism is in reasonable agreement with experimental data. The decrease in diffusion constant D upon thermal annealing is explained by the reducing vacancy-simplex concentration which is caused by both the local atomic rearrangement and the elimination of excess free volume.     

NMR study of hydrogen diffusion in uranium hydride

The diffusion of hydrogen in uranium hydride is studied employing the NMR technique. From measurements of spin-spin relaxation time T₂, the activation energy for hydrogen diffusion in β-UH₃ is determined to be $\text{E}{}_{\mathrm{a}}\text{= (19.25 ± 0.4)}\text{kcal}\text{mole}$ and the preexponential factor to be A₀ ≈ 5 × 10¹⁴ Hz. It is shown that these results are in fair agreement with spin-lattice relaxation time T₁ data. Assuming that hydrogen diffusion proceeds via vacancies whose concentration is temperature dependent, it is concluded that E_a is the sum of the energies of vacancy formation and barrier height, and that A₀ contains an entropy change factor. Using vacancy concentration data calculated by Libowitz, we estimate the barrier height energy to be E_b ≈7 kcal/mole. Using a value for the frequency of hydrogen vibration v₀ determined from inelastic neutron scattering by Rush et al., we estimate the entropy change due to vacancy formation and the hydrogen atom jump to be about $\text{S}\text{k}{}_{\mathrm{B}}\text{≈3}$. Similar measurements on samples containing less hydrogen than is needed to compose stoichiometric UH₃, show that the rate of diffusion is enhanced by the presence of excess metal in the sample. The jump frequency at 500°K in UH₃ is found to be approximately 10⁶ Hz while for the two-phase samples of H/U = 2.8 and 2.5, it is larger by a factor of about 3 and 3.5, respectively.     

Dynamics of different molecules adsorbed in porous media

We present in this paper a comparative study on the dynamics of benzene, cyclohexane, and methanol molecules, confined in the pores of MCM-41 molecular sieve and HZSM-5 zeolite. The quasi-elastic neutron scattering (QENS) measurements revealed that the physical state of these adsorbed molecules depended not only on the structural characteristics of the host matrix but also on the chemical properties, such as dipole moment, of the guest molecules. Thus, while no motion was observed in the time-scale of 10⁻¹⁰−10⁻¹² s in the case of methanol, the larger size benzene and cyclohexane molecules are found to perform six-fold and three-fold jump rotation, respectively, when adsorbed inside the cages of HZSM-5 at room temperature. At the same time, all the three molecules are found to undergo a translational motion inside the pores of MCM-41 molecular sieves, the value of diffusion constant being the lowest in case of methanol because of its higher polarity. Translationl motion of the guest molecules inside the pores of MCM-41 can be satisfactorily described by Chudley-Eliott fixed jump length diffusion and accordingly the residence time, jump length and diffusion constant are estimated.     

Thermal neutron scattering from a hydrogen-metal system in terms of a general multi-sublattice jump diffusion model—I: Theory

A Multi-Sublattice Jump Diffusion Model (MSJD) for hydrogen diffusion through interstitial-site lattices is presented. The MSJD approach may, in principle, be considered as an extension of the Rowe et al.[1] model. Jump diffusion to any neighbours with different jump times which may be asymmetric in space is discussed. On the basis of the model a new method of calculating the diffusion tensor is advanced. The quasielastic, double differential cross section for thermal neutron scattering is obtained in terms of the MSJD model. The model can be used for systems in which interstitial jump diffusion of impurity particles occurs. In Part II the theoretical results are compared with those for quasielastic neutron scattering from the αNbH_x system.     

Neutron scattering study of NH4+ Motion in NH4+ β-alumina

Incoherent inelastic neutron scattering has been used to study the motion of NH₄⁺ ions in NH₄⁺ β-alumina. The results establish that jump reorientation of NH₄⁺ ions is rapid compared to translational diffusion: The data are consistent with thermally activated jumps between equivalent NH₄⁺ orientations with a proton jump frequency of $\text{~1.0 × 10}{}^{12}\text{sec}$ at room temperature.The data are inconsistent with either free rotation or unrestricted rotational diffusion. The residence time between translational diffusion jumps is >6 × 10^?11 sec at temperatures less than 473°K.     

Effect of the ionic radius on jump frequencies of alkaline earth cations in NaCl crystals

By comparing diffusion coefficientsD of bivalent cations Ba²⁺, Ca²⁺, Sr²⁺ in NaCl crystals it was shown that in the temperature range above 550 °CD (Ba²⁺)>D (Sr²⁺)>D (Ca²⁺) is valid. Temperature dependences of jump frequenciesw ₂ of these cations are described byw ₂ (Ba²⁺)=(2·15±0·55) × 10¹² × exp {?(0·817±0.007)/kT};w ₂ (Sr²⁺)=(2·9±1·1) × 10¹² × exp {?(0·84±0.02)/kT} andw ₂ (Ca²⁺)=(5·5±6·5) × 10¹⁰ × exp {?(0·51±0·07)/kT}. It was demonstrated that in NaCl crystals the activation enthalpy and the preexponential factor of the jump frequencyw ₂ increase with increasing ionic radius and mass of the bivalent alkaline earth cation.