Diffusion of nickel in single- and polycrystalline Cr2O3

Chromia protective layers are formed on many industrial alloys to prevent corrosion by oxidation. Their role is to limit the inward diffusion of oxygen and the outward diffusion of cations. A number of chromia-forming alloys contain nickel as a component, such as steels, FeNiCr and NiCr alloys. To ascertain if chromia is a barrier to outward diffusion, nickel diffusion in chromia was studied in both single crystals and polycrystals in the temperature range 900–1100°C at an oxygen pressure of 10^?4 atm (argon + 100 ppm O₂). A nickel film of ～35 nm thick was deposited on the chromia surface and, after diffusing treatment, nickel penetration profiles were established by secondary ion mass spectrometry (SIMS). Two diffusion domains appear in polycrystals, the first domain is assigned to bulk diffusion and the second is due to diffusion along grain boundaries. For the bulk diffusion domain and diffusion in single crystals, using a solution of Fick's second law for diffusion from a thick film, bulk diffusion coefficients were determined at 900 and 1000°C. At the higher temperature, a solution of Fick's second law for diffusion from a thin film could be used. For the second domain in polycrystals, Le Claire's model allowed the grain boundary diffusion parameter (αD _gb δ) to be established. Nickel bulk diffusion does not vary significantly according to the microstructure of chromia. The activation energy of grain boundary diffusion is slightly greater than the activation energy of bulk diffusion, probably on account of segregation phenomena. Nickel diffusion was compared with cationic self-diffusion and with literature data on Fe and Mn heterodiffusion in the bulk and along grain boundaries. All results were analyzed in relation to the oxidation process of stainless steel.     

Diffusion in dislocation germanium and the model of a liquid dislocation core

Experimental data on the diffusion of ⁷¹Ge, ¹¹³Sn, ¹¹⁴In, and ¹²⁴Sb isotopes in dislocation germanium are discussed within the model of a liquid dislocation core and the filament model of diffusion along dislocations. The temperature dependences of the diffusion permeability along the dislocations are matched to the corresponding temperature dependences of the coefficient of diffusion in the melt in order to determine the absolute values of the coefficient of diffusion along dislocations and the effective diffusion radius of the dislocation core. The experimental results are discussed in terms of thermodynamic parameters of the liquid state and the parameters of diffusion in the melt. The results obtained are consistent with the cooperative diffusion mechanism and the mechanism of diffusion through relaxed vacancies.     

Photothermal deflection measurement of effective gas diffusion coefficient of a porous medium

In this work, an effective gas diffusion coefficient of a porous medium was measured using photothermal deflection (PD) technique. An in-house made Loschmidt diffusion cell with a photothermal-deflection probe were employed to measure the effective gas diffusion coefficient of a gas diffusion layer (GDL) with a porosity ε ≈ 0.7. The concentration evolutions of CO₂ in O₂ with and without the GDL were measured, respectively, using a transverse normal PD technique. The concentration variations were used to deduce the gas diffusion coefficients in the presence and absence of the GDL by solving mass diffusion equations. The effective gas diffusion coefficient of the GDL was calculated from the diffusion coefficients using a model of an equivalent resistance to diffusion and found to be 4.39 × 10^-6 m²s^-1, demonstrating that PD technique can be employed to determine the effective gas diffusion coefficient of a porous medium.     

Similarity solutions of reaction–diffusion equation with space- and time-dependent diffusion and reaction terms

We consider solvability of the generalized reaction–diffusion equation with both space- and time-dependent diffusion and reaction terms by means of the similarity method. By introducing the similarity variable, the reaction–diffusion equation is reduced to an ordinary differential equation. Matching the resulting ordinary differential equation with known exactly solvable equations, one can obtain corresponding exactly solvable reaction–diffusion systems. Several representative examples of exactly solvable reaction–diffusion equations are presented.     

On the analysis of coordinate-dependent diffusion

Coordinate-dependent diffusion in solids, in which case the probability of presence of a vacancy, φ, and the probability of migration, γ, depend on coordinate x is analyzed. The coordinate dependence of parameters φ and γ is shown to cause the drift component of the diffusion flux. In the presence of this component, the direction of atomic motion may coincide (enhanced diffusion) or not coincide (retarded diffusion and up-diffusion) with the direction of the diffusion component. The criteria of enhanced diffusion, retarded diffusion, and up-diffusion are established. These criteria are specified by the behavior of function F(x)=φ(x)/γ(x).     

On the down-sampling of diffusion MRI data along the angular dimension

BackgroundIt has been established that the diffusion gradient directions in diffusion MRI should be uniformly distributed in 3D spherical space, so that orientation-dependent diffusion properties (e.g., fractional anisotropy or FA) can be properly quantified. Sometimes the acquired data need to be down-sampled along the angular dimension before computing diffusion properties (e.g., to exclude data points corrupted by motion artifact; to harmonize data obtained with different protocols). It is important to quantitatively assess the impact of data down-sampling on measurement of diffusion properties.Materials and methodsHere we report 1) a numerical procedure for down-sampling diffusion MRI (e.g., for data harmonization), and 2) a spatial uniformity index of diffusion directions, aiming to predict the quality of the chosen down-sampling schemes (e.g., from data harmonization; or rejection of motion corrupted data points). We quantitatively evaluated human diffusion MRI data, which were down-sampled from 64 or 60 diffusion gradient directions to 30 directions, in terms of their 1) FA value accuracy (using fully-sampled data as the ground truth), 2) FA fitting residuals, and 3) spatial uniformity indices.ResultsOur experimental data show that the proposed spatial uniformity index is correlated with errors in FA obtained from down-sampled diffusion MRI data. The FA fitting residuals that are typically used to assess diffusion MRI quality are not correlated with either FA errors or spatial uniformity index.ConclusionsThese results suggest that the spatial uniformity index could be more valuable in assessing quality of down-sampled diffusion MRI data, as compared with FA fitting residual measures. We expect that our implemented software procedure should prove valuable for 1) guiding data harmonization for multi-site diffusion MRI studies, and 2) assessing the impact of rejecting motion corrupted data points on the accuracy of diffusion measures.     

Study of water diffusion in human dentin by optical coherent tomography

The diffusion of chemical agents in dental tissues is of interest for many problems of dental tissue physiology (diffusion of liquor and water), dental healing (diffusion of preparations), and cosmetic dental treatment (diffusion of whitening agents). The water diffusion in samples of human dentin was monitored using optical coherent tomography (OCT). This diffusion manifests itself as a change in the slope and amplitude of the OCT signal from the sample. It is shown that the average dentin permeability with respect to water is (15.11 ± 21.73) × 10⁻⁶ cm/s. These experimental results demonstrate the OCT efficiency for studying the diffusion in hard biological tissues.     

Oxygen diffusion in SrZrO3

Oxygen diffusion coefficients in SrZrO₃ polycrystals were determined using the isotopic exchange method with ¹⁸O as oxygen tracer. Diffusion treatments were performed at different temperatures between 1173 K and 1473 K. Oxygen diffusion profiles were established by secondary ion mass spectroscopy (SIMS). Classical diffusion equations were used to fit experimental results and to determine bulk diffusion (D_vol) and surface exchange (k) coefficients of oxygen in SrZrO₃ polycrystalline materials. From these values, bulk diffusion and grain boundary diffusion coefficients as well as oxygen surface exchange coefficients were determined. The activation energy of oxygen diffusion in the bulk is 2.1 eV, while for the diffusion in the grain boundary, 1.8 eV was found. The surface exchange reaction has an activation enthalpy of 1.2 eV.     

Simulations of anomalous ion diffusion in experimentally measured turbulent potential

The diffusion of plasma impurities in tokamak-edge-plasma turbulence is investigated numerically. The time-dependent potential governing particle motion was measured by 2D array of 8×8 Langmuir probes in edge region of CASTOR tokamak. The diffusion of particles is found to be classical in the radial direction, but it can be of an anomalous Lévy-walk type in the poloidal direction. The diffusion is found to be dependent on the ratio of particles’ mass and charge. When this ratio grows, the diffusion coefficient in radial direction grows as well, whereas poloidal diffusion coefficient drops down. Moreover, movement of particles in the time-frozen snapshot of this potential is investigated showing that also the time-independent potential is much more favorable for the particle diffusion in poloidal direction than in radial one. In the case of single ionized carbon ions the poloidal diffusion in time-independent potential transits to the Lévy-walk type for temperatures greater than 25 eV, for radial diffusion Lévy-walk was not observed even for 500 eV.     

Effects of Soret diffusion on the laminar flame speed and Markstein length of syngas/air mixtures

The effects of Soret diffusion on premixed syngas/air flames at normal and elevated temperatures and pressures are investigated numerically including detailed chemistry and transport. The emphasis is placed on assessing and interpreting the influence of Soret diffusion on the unstretched and stretched laminar flame speed and Markstein length of syngas/air mixtures. The laminar flame speed and Markstein length are obtained by simulating the unstretched planar flame and positively-stretched spherical flame, respectively. The results indicate that at atmospheric pressure the laminar flame speed of syngas/air is mainly reduced by Soret diffusion of H radical while the influence of H₂ Soret diffusion is negligible. This is due to the facts that the main reaction zone and the Soret diffusion for H radical (H₂) are strongly (weakly) coupled, and that Soret diffusion reduces the H concentration in the reaction zone. Because of the enhancement in the Soret diffusion flux of H radical, the influence of Soret diffusion on the laminar burning flux increases with the initial temperature and pressure. Unlike the results at atmospheric pressure, at elevated pressures the laminar flame speed is shown to be affected by the Soret diffusion of H₂ as well as H radical. For stretched spherical flame, it is shown that the Soret diffusion of both H and H₂ should be included so that the stretched flame speed can be accurately predicted. Similar to the laminar flame speed, the Markstein length is also reduced by Soret diffusion. However, the reduction is found to be mainly caused by Soret diffusion of H₂ rather than that of H radical. Moreover, the influence of Soret diffusion on the Markstein length is demonstrated to decrease with the initial temperature and pressure.     

X-ray topography study of monocrystalline silicon wafers diffused with phosphorus by different methods

To reduce the cost of the emitter diffusion process, there has been increasing interest to substitute the standard process of batch POCl₃ emitter diffusion used in the silicon solar-cell manufacturing industry with in-line diffusion processes such as the spray-on and screen-printing process. For this reason, it is essential to study and compare the processes of different diffusion methods from the point of view of the crystalline quality of the final wafers. X-ray transmission topography was employed to characterize the possible precipitates and other microdefects generated in Czochralski-grown silicon (Cz Si) during the emitter diffusion process carried out by screen-printing, spray-on and the standard process, in which the emitter was provided by a liquid (POCl₃) source. The results indicate that the phosphorus diffusion process influences the crystalline quality of the wafers and the efficiency of the external gettering process that takes place during phosphorus diffusion depends on the diffusion method employed.     

Effect of Soret diffusion on lean hydrogen/air flames at normal and elevated pressure and temperature

The influence of Soret diffusion on lean premixed flames propagating in hydrogen/air mixtures is numerically investigated with a detailed chemical and transport models at normal and elevated pressure and temperature. The Soret diffusion influence on the one-dimensional (1D) flame mass burning rate and two-dimensional (2D) flame propagating characteristics is analysed, revealing a strong dependency on flame stretch rate, pressure and temperature. For 1D flames, at normal pressure and temperature, with an increase of Karlovitz number from 0 to 0.4, the mass burning rate is first reduced and then enhanced by Soret diffusion of H₂ while it is reduced by Soret diffusion of H. The influence of Soret diffusion of H₂ is enhanced by pressure and reduced by temperature. On the contrary, the influence of Soret diffusion of H is reduced by pressure and enhanced by temperature. For 2D flames, at normal pressure and temperature, during the early phase of flame evolution, flames with Soret diffusion display more curved flame cells. Pressure enhances this effect, while temperature reduces it. The influence of Soret diffusion of H₂ on the global consumption speed is enhanced at elevated pressure. The influence of Soret diffusion of H on the global consumption speed is enhanced at elevated temperature. The flame evolution is more affected by Soret diffusion in the early phase of propagation than in the long run due to the local enrichment of H₂ caused by flame curvature effects. The present study provides new insights into the Soret diffusion effect on the characteristics of lean hydrogen/air flames at conditions that are relevant to practical applications, e.g. gas engines and turbines.     

Surface diffusion of k-mers in one-dimensional systems

The surface diffusion of interacting k-mers is studied both through analytical and Monte Carlo simulation methods in one-dimensional systems. Adsorption isotherms, jump diffusion coefficients and collective diffusion coefficients are obtained for attractive and repulsive k-mers, showing a variety of behaviors as a function of the size of particles, k. The following main results are found: (a) diffusion coefficients increase with k for non-interacting particles; (b) for fixed k, diffusion coefficients increase as the interaction energy increases from negative (attractive) to positive (repulsive) values; (c) for attractive interactions diffusion coefficients increase with k in the whole range of coverage; (d) for repulsive interactions diffusion coefficients decrease with k up to moderately high coverage and increase with k at high coverage. Results are rationalized in terms of the behavior of the vacancy probability distribution.     

Diffusion of Cu in β-phase CuI

Measurements of ionic diffusion of Cu⁺ in solid CuI in the β-phase is carried out with a non-destructive radioactive tracer technique, utilizing coincidence counting of the annihilation gammas from the positron decay of ⁶⁴Cu. The diffusion coefficient and the activation energy for diffusion are evaluated. The experimental results show distinct diffusion character in the β-phase which differs from those in the γ-and -phases. The β-phase diffusion properties together with the previous results for γ-and -phases will provide valuable guidance for MD calculations, in which the diffusion coefficients and activation energies have been overestimated and the γ-β phase transition does not appear. The ionic conductivity of CuI estimated from tracer diffusion results and the Nernst-Einstein relation are compared with values from electrochemical methods. In all three phases the conductivities obtained from electrochemical methods are much lower than those calculated from the measured tracer diffusion coefficients.     

Gold and platinum diffusion: The key to the understanding of intrinsic point defect behavior in silicon

The study of gold and platinum diffusion is found to allow the separate observation of the intrinsic point defects, i.e., of silicon self-interstitials and of vacancies. The diffusion of gold in float zone (FZ) silicon is found to be dominated by the kick-out mechanism for temperatures of 800° C and higher. The diffusion of platinum in FZ silicon is described by the kick-out mechanism for temperatures above approximately 900° C, whereas for temperatures below approximately 850° C the dissociative mechanism governs platinum diffusion. As a result of numerical simulations, we suggest a complete and consistent set of parameters which describes the diffusion of platinum in silicon in the temperature range from 700° C to 950° C and the diffusion of gold in the temperature range from 800° C to 1100° C. The generation or recombination of self-interstitials and vacancies is found to be ineffective at least below 850° C. The concentration of substitutional platinum is determined by the initial concentration of vacancies at diffusion temperatures below 850° C. Platinum diffusion below 850°C can be used to measure vacancy distributions in silicon quantitatively.     

Removal of partial volume averaging with free water in MR diffusion tensor imaging using inversion recovery for b0 image

Purpose

To remove the partial volume averaging effect of free water in MR diffusion imaging of neural tissues by use of the fluid attenuated inversion recovery (FLAIR) without the penalty of an extended scan time.

Materials and methods

The magnetic resonance images were obtained from a normal volunteer in a coronal slice orientation at 3 T with the 20-channel rf coil. In diffusion imaging only the b0 images were obtained with the FLAIR contrast while the diffusion weighted images were obtained without the FLAIR contrast. A composition of FLAIR b0 and non-FLAIR diffusion weighted images was used in calculating the diffusion tensor and fractional anisotropy after compensating the reduced signal amplitude due to the inversion recovery in the FLAIR b0 images. The fractional anisotropy of the non-FLAIR, FLAIR, and the composite methods were analyzed for the mean and histogram in the corpus callosum, cervical spine, and the fornix tracts.

Results

The partial volume averaging effect was observed in the corpus callosum, the cervical spine, and the fornix tracts in the non-FLAIR b0 and diffusion images. The partial volume averaging effect was removed in the FLAIR diffusion images which took more than twice the scan time than the non-FLAIR diffusion imaging. The proposed composite FLAIR diffusion imaging removed the partial volume averaging effect as in the FLAIR diffusion imaging. The distribution of the FA histogram was very different between the non-FLAIR and FLAIR diffusion images, while it was very similar between the FLAIR and the composite FLAIR after correcting the white matter signal in the FLAIR b0 images.

Conclusions

The proposed composite FLAIR diffusion imaging method was equally effective in removing the partial volume averaging effect as the FLAIR diffusion imaging at a limited increase of the scan time since only a small number of b0 images needed to be obtained with the FLAIR contrast.     

Fractional Brownian Motions and Enhanced Diffusion in a Unidirectional Wave-Like Turbulence

We study transport in random undirectional wave-like velocity fields with nonlinear dispersion relations. For this simple model, we have several interesting findings: (1) In the absence of molecular diffusion the entire family of fractional Brownian motions (FBMs), persistent or anti-persistent, can arise in the scaling limit. (2) The infrared cutoff may alter the scaling limit depending on whether the cutoff exceeds certain critical value or not. (3) Small, but nonzero, molecular diffusion can drastically change the scaling limit. As a result, some regimes stay intact; some (persistent) FBM regimes become non-Gaussian and some other FBM regimes become Brownian motions with enhanced diffusion coefficients. Moreover, in the particular regime where the scaling limit is a Brownian motion in the absence of molecular diffusion, the vanishing molecular diffusion limit of the enhanced diffusion coefficient is strictly larger than the diffusion coefficient with zero molecular diffusion. This is the first such example that we are aware of to demonstrate rigorously a nonperturbative effect of vanishing molecular diffusion on turbulent diffusion coefficient.     

Adsorption and diffusion of argon confined in ordered and disordered microporous carbons

We use a combination of grand canonical Monte Carlo and microcanonical molecular dynamics simulations to study the adsorption and diffusion of argon at 77 K and 120 K confined in previously generated models of a disordered bituminous coal-based carbon, BPL, and an ordered carbon replica of Faujasite zeolite (C-FAU). Both materials exhibit a maximum in the diffusion coefficient as well as anomalous (sub-diffusive) behavior in the mean-squared displacements at short times at some relative pressures. In BPL, the anomalous diffusion occurs at low relative pressures, due to the trapping of argon atoms in small pores. In C-FAU, the anomalous diffusion occurs at high relative pressures, due to competitive diffusion of atoms traveling through windows and constrictions which interconnect the pores. All diffusion eventually tends to Fickian diffusion at longer times.     

Microstructure and oxidation of hot-dip aluminized titanium at high temperature

High-temperature diffusion of a hot-dip aluminized titanium is conducted to study microstructure changes and oxidation behavior of the aluminized titanium. After aluminizing, the titanium substrate is covered by a black layer in which tiny block-shaped TiAl₃ particles are scattered in aluminum matrix. Based on the diffusion experiment results, the thickness of the aluminum diffusion layer at 800 °C increases with diffusion time. However, the aluminum diffusion layer at 900 °C grows and reaches its maximum thickness in 6 h, and then the thickness of the aluminum diffusion layer is reduced with prolonged diffusion time. An inversion of the diffusion layer thickness versus time appears for the aluminized titanium treated at 1000 °C, and the thickness of the diffusion layer keeps declining with diffusion time. The phases present in the outer and middle sublayers are titanium-rich TiAl₃ and equilibrium TiAl₃, respectively. However, the phase in inner sublayer changes from titanium-rich TiAl₃ to TiAl₂ and TiAl as diffusion temperature and time increase. Through energy-dispersive X-ray and X-ray diffraction analysis, the oxides formed in the oxidation process are Al₂O₃ and Al₂TiO₅. Although the oxide scale formed on the surface of the aluminized titanium has an insufficient stability and integrity, the thermal oxidation resistance of the aluminized titanium is still improved by over 5 times compared with that of the pure titanium.     

Random walk on hierarchical comb structures

This paper examines random walks on an exactly solvable comb model of percolation clusters. The study shows that diffusion along the structure’s axis is anomalous. Generalized diffusion equations with fractional-order time derivatives are derived, and a generalization to the multidimensional case is carried out. The relationship between this problem and that of diffusion in a medium with traps is examined, and equations that describe diffusion in a medium with traps are derived. The paper also discusses the transition to ordinary diffusion due to the introduction of comb teeth of finite length, and analyzes the case of N teeth of different length. It is shown that the solution of this problem leads to the emergence of an N-channel diffusion equation. Finally, equations describing the diffusion of interacting electrons are derived. Zh. éksp. Teor. Fiz. 115, 1285–1296 (April 1999)