Characteristic Diffusion Length Research Articles

A Thermodynamically Based Modified Cam‐Clay Model for Post‐Bifurcation Behavior of Deformation Bands

AbstractCompaction bands are a type of localized deformation that can occur as diffuse or discrete bands in porous rocks. While modeling of shear bands can replicate discrete and diffusive bands, numerical models of compaction have so far only been able to describe the formation of discrete compaction bands. In this study, we present a new thermodynamic approach to model compaction bands that is able to capture both discrete and diffuse compaction band growth. The approach is based on a reaction‐diffusion formalism that includes an additional entropy flux. This entropic velocity regularizes the solution, by introducing a characteristic diffusion length scale and controlling the mode change from discrete to diffusive post‐localisation growth. The approach is used to model compaction band growth in highly porous carbonates. The model can replicate the areas of material damage exhibiting reduced porosity which are often observed as nuclei for the growth of compaction bands in experiments. The model also has the versatility to predict the formation of diffuse compaction bands, which is a significant advance in the field of compaction band modeling. The method can potentially be used for investigating the effect of material heterogeneities on compaction band growth and is heuristic for developing new methodologies for forecasting compaction band formation.

Impact of Morphology of Polycrystalline and Single Crystal Nickel Rich Cathode Particles on Performance

High nickel cathode material (NMC 811) is great candidate for high performance batteries. It has high specific capacity and lower utilization of cobalt. The morphology of the cathode particles is studied in a comprehensive manner, from the impact of synthesis parameters on primary particle size, to experimental characterization and replicating the key morphological features in computational model to elucidate the morphological features critical to the performance. The polycrystalline micron sized secondary particle is comprised of thousands of nanometers sized primary particles. The single crystal is generally 2 to 3 microns in size. The “single crystal” cathode particle may be cluster of few single crystals. The length scales of primary and secondary particles as well as internal porosity of polycrystalline cathode particles changes the characteristic diffusion length as well as surface area available for electrochemical reaction. Similarly, for single crystal, the size and the degree of clustering changes the diffusion characteristics and surface area. These variations are reflected in specific capacities obtained at different C-rates. Gaining an in-depth understanding of correlation of morphological features to performance would be helpful in directing the synthesis process. Figure 1

Position dependent microparticle charge in a spatiotemporal afterglow plasma

In the growing field of dusty afterglow plasma physics, the key parameter is the residual charge of dust particles. However, the particle (de)-charging process in afterglow plasmas is still far from fully understood and further development of a governing theoretical framework requires experimental data. In this work, the influence of the location of a microparticle in a spatiotemporal afterglow plasma, at the moment when the plasma was terminated, on its residual charge is investigated. It is found that the measured charge depends strongly on the local characteristic diffusion length scale of the system, while the plasma power prior to the start of the temporal afterglow phase is of much less influence. Our results contribute to an improved understanding of particle (de)-charging in afterglow plasmas and are highly relevant to the design of applications in which afterglow plasmas are present and where the charge of dust particles needs be controlled for the sake of (nano)contamination control.

Considering solid phase diffusion penetration depth to improve profile approximations: Towards accurate State estimations in lithium-ion batteries at low characteristic diffusion lengths

Lithium-ion batteries are typically modelled using the pseudo-2-dimensional (P2D) model, where a set of partial differential equations describing transport and electrochemical reactions are solved numerically to obtain battery state information. To improve computational efficiency and enable on-board implementation for state-estimation, reduced order models are developed, where one such model reduction technique includes using a profile approximation for solving solid phase diffusion inside electrode particles. While greatly reducing model complexity, the profile approximation also leads to reduced accuracy, especially at low characteristic diffusion lengths. We address this issue by developing an improved model, which recognizes the existence of a penetration depth and the solution is obtained by dividing the particle into diffusion-free core and a shell corresponding to the penetration depth. The time-scale for the diffusion front to reach the particle centre depends on the diffusivity and particle radius. A similarity solution for this period, leads to an expression for the State of charge (SOC) in the spatio-temporal domain. The predictions are compared to that from the benchmark P2D and experimental data, revealing accuracies >99%, while adding no computational cost. This improved model is particularly useful under high C-rate or low temperature operation, where the characteristic diffusion lengths are low.

Designing Cathode Morphology for Materials with Solid Transport Limitation

Lithium manganese rich (LMR-NMC) material is a great candidate for next generation high energy density cathodes. It has high specific capacity, low cost, and decreased usage of Cobalt. However, these materials display poor rate capabilities attributed in part due to low lithium diffusion in cathode particle. The LMR-NMC cathode particles (size ~ 5 to 15 microns) are agglomeration of nanoscale primary particles. In this work, we focus on the link between morphology and performance. There are two characteristic diffusion lengths associated with the morphology of LMR-NMC. The diffusion length associated with primary particle radius and the diffusion length associated with the agglomeration of primary particles. The agglomerate diffusion length varies significantly with how the primary particles agglomerate. Presence of intra-agglomerate closed pores results in higher agglomerate diffusion length compared to open and well dispersed arrangement of primary particles. The electrochemical performance is better with smaller primary and agglomerate diffusion lengths. Tailoring the synthesis of cathode particles to obtain the desired diffusion characteristics is promising avenue to optimize the performance of LMR-NMC cathode materials. Figure 1

Optical Detection of Long Electron Spin Transport Lengths in a Monolayer Semiconductor.

Using a spatially resolved optical pump-probe experiment, we measure the lateral transport of spin-valley polarized electrons over very long distances (tens of micrometers) in a single WSe_{2} monolayer. By locally pumping the Fermi sea of 2D electrons to a high degree of spin-valley polarization (up to 75%) using circularly polarized light, the lateral diffusion of the electron polarization can be mapped out via the photoluminescence induced by a spatially separated and linearly polarized probe laser. Up to 25% spin-valley polarization is observed at pump-probe separations up to 20 μm. Characteristic spin-valley diffusion lengths of 18±3 μm are revealed at low temperatures. The dependence on temperature, pump helicity, pump intensity, and electron density highlight the key roles played by spin relaxation time and pumping efficiency on polarized electron transport in monolayer semiconductors possessing spin-valley locking.

Theory of Electron Injection at Oblique Shock of Finite Thickness

Abstract A theory of electron injection into diffusive shock acceleration (DSA) for the generation of cosmic-ray electrons at collisionless shocks is presented. We consider a recently proposed particle acceleration mechanism called stochastic shock drift acceleration (SSDA). We find that SSDA may be understood as a diffusive particle acceleration mechanism at an oblique shock of finite thickness. More specifically, it is described by a solution to the diffusion–convection equation for particles with the characteristic diffusion length comparable to the shock thickness. On the other hand, the same equation yields the standard DSA if the diffusion length is much longer than the thickness. Although SSDA predicts, in general, a spectral index steeper than DSA, it is much more efficient for low-energy electron acceleration and is favorable for injection. The injection threshold energy corresponds to the transition energy between the two different regimes. It is of the order of 0.1–1 MeV in typical interstellar and interplanetary conditions if the dissipation scale of turbulence around the shock is determined by the ion inertial length. The electron injection is more efficient at high M A / cos θ Bn , where M A and θ Bn are the Alfvén Mach number and the shock obliquity, respectively. The theory suggests that efficient acceleration of electrons to ultrarelativistic energies will be more easily realized at high Mach number, young supernova remnant shocks, but not at weak or moderate shocks in the heliosphere unless the upstream magnetic field is nearly perpendicular to the shock normal.

Scanning Thermal Microscopy and Ballistic Phonon Transport in Lateral Spin Valves.

Using scanning thermal microscopy, we have mapped the spatial distribution of temperatures in an operating nanoscale device formed from a magnetic injector, an Ag connecting wire, and a magnetic detector. An analytical model explained the thermal diffusion over the measured temperature range (2-300K) and injector-detector separation (400-3000nm). The characteristic diffusion lengths of the Peltier and Joule heat differ remarkably below 60K, a fact that can be explained by the onset of ballistic phonon heat transfer in the substrate.

Performance comparison between washcoated and packed-bed monolithic reactors for the low-temperature Fischer-Tropsch synthesis

Washcoating and packing of Co-Re catalyst particles have been employed as structuring methods of parallel channel monoliths used in the low-temperature Fischer-Tropsch synthesis (FTS). These methods were compared with regard to catalyst hold-up, heat transfer properties and pressure drop. Reactors output was assessed in terms of CO conversion, CH4 selectivity and productivity of C5+ hydrocarbons. Washcoating led to much lower pressure drops, but also resulted in considerably lower catalyst inventory. As for the reactors performance (volumetric and per catalyst mass C5+ productivities), the washcoated monoliths were more effective than the packed-bed ones. This has been attributed to their more favorable hydrodynamic behavior that facilitates the drainage of the reaction products (liquids and waxes) through the central hollow of the channels thus reducing the extra-pellet diffusional limitations. For both catalyst configurations, it has been found that the productivity of C5+ per catalyst mass unit increases as the characteristic diffusion length increases within the range of values considered in this study (below 150 µm). This indicates that a moderate level of internal mass transport restrictions is beneficial for the low-temperature FTS, which has been explained in terms of the effects of diffusional limitations on the H2/CO molar ratio, and that of this ratio on the FTS kinetics. The possible influence of thermal effects on these results has been numerically and experimentally discarded.

Studies of Defect Structure in Epitaxial AlN/GaN Films Grown on (111) 3C-SiC.

Several aspects such as the growth relation between the layers of the GaN/AlN/SiC heterostructure, the consistency of the interfaces, and elemental diffusion are achieved by High Resolution Transmission Electron Microscopy (HR-TEM). In addition, the dislocation densities together with the defect correlation lengths are investigated via High-Resolution X-ray Diffraction (HR-XRD) and the characteristic positron diffusion length is achieved by Doppler Broadening Spectroscopy (DBS). Moreover, a comparative analysis with our previous work (i.e., GaN/AlN/Si and GaN/AlN/Al2O3) has been carried out. Within the epitaxial GaN layer defined by the relationship (111) 3C-SiC || (0002) AlN || (0002) GaN, the total dislocation density has been assessed as being 1.47 × 1010 cm−2. Compared with previously investigated heterostructures (on Si and Al2O3 substrates), the obtained dislocation correlation lengths (Le = 171 nm and Ls =288 nm) and the mean distance between two dislocations (rd = 82 nm) are higher. This reveals an improved crystal quality of the GaN with SiC as a growth template. In addition, the DBS measurements upheld the aforementioned results with a higher effective positron diffusion length = 75 ± 20 nm for the GaN layer.

Extremely bias stress stable enhancement mode sol–gel-processed SnO2 thin-film transistors with Y2O3 passivation layers

Herein, a new combination of high-performance and bias-stress-stable SnO2 thin-film transistors (TFTs) with Y2O3 passivation layers is introduced. The Y2O3 layers on SnO2 semiconductors function suitably as passivation layers to minimize H2O adsorption and to avoid free carrier trapping by creating physical gaps that are larger than the characteristic diffusion length. Yttrium is observed to partially diffuse into SnO2, suppressing the formation of oxygen vacancies in the SnO2 semiconductor because of its low electronegativity and standard electrode potential. The SnO2 TFTs with Y2O3 passivation layers exhibit a mobility of 5.7 ± 0.3 cm2/Vs, subthreshold swing of 1.1 ± 0.2 V/decade, threshold voltage (VTH) of + 6.8 ± 0.4 V, and on/off current ratio of 6.1 (±0.3) × 107. The fabricated sol–gel-processed SnO2 TFTs with Y2O3 passivation layers revealed remarkable negative and positive bias stress stabilities without hysteresis and consistently delivered high performance with enhancement mode operations. Owing to this high performance, the SnO2/Y2O3 combination reported herein has potential as a commercial-product-level TFT for next-generation displays.

Understanding How Degree of Crystallinity Affects Electrochemical Kinetics of Sodium‐Ion in Brown TiO2 Nanotubes

AbstractSodium‐ion batteries (SIBs) have attracted significant attention as an emerging alternative to lithium‐ion batteries (LIBs). The charge and discharge performance of the electrode material are affected by various intrinsic parameters, including Na‐ion diffusion coefficient, ionic conductivity, concentration, etc., which are further related to the structure and crystallinity of the material. Herein, the kinetics of Na‐ion intercalation into low and high crystalline brown TiO2 nanotubes are studied by using galvanostatic intermittent titration technique (GITT) and electrochemical impedance spectroscopy (EIS) techniques. Various parameters such as intercalation capacity, partial sodium ion conductivity , diffusion time constant ( ), characteristic diffusion length ), etc., are analyzed during sodiation/de‐sodiation, and the dependence of these parameters with the degree of crystallinity of the material is discussed. The chemical diffusion coefficients ( ) are determined at different intercalation and de‐intercalation potentials, which showed similar behaviour within a range of 10−15–10−18 cm2 s−1, with a slightly higher value for high crystalline brown TiO2. The correlation between the diffusion behavior of Na‐ions in high and low crystalline brown TiO2 nanotubes and their degree of crystallinity provides insights into the electrochemical performance of TiO2 anodes.

Thermal Swing Evaluation of Thermal Barrier Coatings for Diesel Engines

“Thermal swing” coatings have recently been of great interest to automotive researchers for their potential to insulate internal combustion engines, reduce cooling requirements, and increase their efficiency. Plasma-sprayed yttria-stabilized zirconia, ceramics in the MgO-Al2O3-SiO2 system (cordierite, mullite, and steatite), and silicate-yttria-stabilized zirconia composite thermal barriers have been investigated in this context with thermophysical properties measured using a thermal flash method and further screened by thermal swing using a custom laboratory developed functional test. Correlations between microstructure and thermal properties are developed and their combined impact on thermal swing assessed. The coatings thermal effusivity dominates these considerations for coatings above the characteristic thermal diffusion length of periodic exposure, with substrate thermal properties quickly becoming important below this thickness. Plasma-sprayed cordierite and its composites are determined to be the most promising materials for this application, exhibiting the highest thermal swing and effusivities as low as 373 Ws1/2/m2K. Performance testing in a heavy-duty single-cylinder diesel engine is ongoing with preliminary data suggesting that thermal swing alone may not provide efficiency benefits. Coating thickness, roughness, and dynamic interactions in the engine may play a role in this, highlighting that many potential nuances need consideration for the successful applications of these coatings.

Tip dynamics for equiaxed Al-Cu dendrites in thin samples : Phase-field study of thermodynamic effects

We test the influence of two thermodynamic effects on the dynamics of equiaxed Al-Cu dendrites growth and interactions in thin samples. The first effect results from the nonlinearity of the phase diagram with the copper concentration and the second effect is due to temperature fluctuations. The study relies on three-dimensional phase-field simulations of isothermal solidification in confined samples, for which thickness is of the order of the characteristic diffusion length. We compare the present results with those of a previous study that did not take these thermodynamic effects into account [A.K. Boukellal et al., Materialia 1, (2018)]. We show that including these effects does not affect the scaling laws derived previously. This result strengthens the conclusions already drawn and encourages the application of these scaling laws to predict the behaviour of dendrite tips in more physical situations.

Electron density profile inside a cylindrical plasma with elliptical cross section in a microwave discharge

In a microwave discharge, the profile of electron number density inside a cylindrical plasma with elliptic cross section is analytically calculated. Using separation of variables way for the electron continuity equation (as function of position and time) and so solving it, the electron number density profile is calculated. It is shown that the profile of electron number density in a cylindrical plasma with elliptical cross section is in the form of Mathieu functions. The characteristic diffusion length for the elliptical cylinder plasma is obtained, and it is seen that it is different with the characteristic diffusion length for the circular cylinder plasma. In the steady state, the normalized density profiles of lowest even and odd modes are plotted. Furthermore, the components of normalized electron number density gradient are plotted. In the limit that plasma cylinder with elliptical cross section being converted to plasma cylinder with circular cross section, the obtained results are confirmed.

Indenter–Foam Dampers Inspired by Cartilage: Dynamic Mechanical Analyses and Design

Abstract Articular cartilage is a thin layer of a solid matrix swollen by fluid, and it protects joints from damage via poroviscoelastic damping. Our previous experimental and simulation studies showed that cartilage-like poroviscoelastic damping could widen the range of damping methods in a low-frequency range (<100 Hz). Thus, the current study aimed to realize cartilage-like damping capacity by single- and two-indenter–foam poroviscoelastic dampers in a low-frequency range. Multiple single-indenter–foam dampers were designed by combining foam sheets with different pore diameters and indenters with different radii. Their damping capacity was investigated by dynamic mechanical analysis in a frequency range of 0.5–100 Hz. Single-indenter–foam dampers delivered peak damping frequencies that depended on the foam’s pore diameter and characteristic diffusion length (contact radii). Those dampers maximize the damping capacity at the desired frequency (narrowband performance). A mechanical model combined with simple scaling laws was shown to relate poroelasticity to the peak damping frequencies reasonably well. Finally, combinations of single-indenter–foam dampers were optimized to obtain a two-indenter–foam damper that delivered nearly rate-independent damping capacity within 0.5–100 Hz (broadband performance). These findings suggested that cartilage-like poroviscoelastic dampers can be an effective mean of passive damping for narrowband and broadband applications.

Estimation of homogenisation time for superalloys based on a new diffusional model

The inter-diffusion of segregating elements (Nb, Mo, and Ti) in the cast ingot of Inconel 718 superalloy during homogenisation at elevated temperature was studied by a new model based on the characteristic diffusion length. The proposed simple method was used for obtaining the homogenisation time required for back-diffusion of each element. Therefore, the developed model can be used for both studying the diffusion of alloying elements and estimation of homogenisation time, where the latter is important from the industrial standpoint.

Stress intensity factors of a Griffith crack in a porous medium subjected to a time-harmonic stress wave

In many practices, cracks are filled with fluid and their background materials can be modelled within the framework of poroelasticity. Understanding the crack-tip mechanical behaviors of such a cracked medium subjected to dynamic loads is of importance for prediction of fracture failure. In this paper, based on Biot’s theory of poroelastodynamics, solutions of mode-I and mode-II dynamic stress intensity factors (SIFs) of a Griffith crack are derived for the scattering problem of oblique incidence of in-plane time-harmonic P-SV waves. The crack surfaces are assumed to be permeable, and the crack is saturated by fluid. With the aid of Fourier integral transforms, the problem is reduced to a system of coupled Fredholm integral equations with special emphasis placed on finding the near-field solution. Impacts of incident wave type, material permeability and incident angle on the frequency-dependent behaviors of the SIFs have been shown graphically. It is found that the induced fluid pressure inside the crack can significantly change the effective normal stress so that the magnitude of mode-I SIF is much lower than that of a dry impermeable crack. Furthermore, the diffusion-type fluid flow (scattered slow P wave) can greatly lower the magnitude of mode-I SIF at low frequencies (much smaller than the resonance frequency). The characteristic frequency at which the curves of SIFs decline strongest occurs when the characteristic diffusion length is of the same order of the crack size. The fluid flow can also lower mode-II SIF at low frequencies and the effects are strong in the low permeability case. Specifically, in the case of scattering of SV waves, it is shown that the maximum drop of mode-II SIF in peak with respect to that of the corresponding dry crack in an elastic medium is about 10%. The obtained results reveal significant influences of the presence of pore fluid upon the SIFs, both magnitudes and frequency-dependent trends. Such information is useful in predicting the fracture strength of saturated porous materials subjected to oscillating loads.

Volume-Averaged Electrochemical Performance Modeling of 3D Interpenetrating Battery Electrode Architectures

Recent advancements in micro-scale additive manufacturing techniques have created opportunities for design of novel electrode geometries that improve battery performance by deviating from the traditional layered battery design. These 3D batteries typically exhibit interpenetrating anode and cathode materials throughout the design space, but the existing well-established porous electrode theory models assume only one type of electrode is present in each battery layer. We therefore develop and demonstrate a multi-electrode volume-averaged electrochemical transport model to simulate transient discharge performance of these new interpenetrating electrode architectures. We implement the new reduced-order model in the PETSc framework and asses its accuracy by comparing predictions to corresponding mesoscale-resolved simulations that are orders of magnitude more computationally-intensive. For simple electrode designs such as alternating plates or cylinders, the volume-averaged model predicts performance within ∼2% for electrode feature sizes comparable to traditional particle sizes (5-10μm) at discharge rates up to 3C. When considering more complex geometries such as minimal surface designs (i.e. gyroid, Schwarz P), we show that using calibrated characteristic diffusion lengths for each design results in errors below 3% for discharge rates up to 3C. These comparisons verify that this novel model has made reliable cell-scale simulations of interpenetrating electrode designs possible.

Adsorptive Nature of Surface Barriers in MFI Nanocrystals.

Zeolite nanocrystals with characteristic diffusion lengths of nanometers are widely used in molecular applications to overcome diffusion limitations. However, with a large fraction of external surface area, mass transport in these materials is often limited by the presence of a surface barrier, which limits their overall potential in catalytic or separation applications. Herein, silicalite-1 crystals of varying sizes were synthesized, and the adsorption and diffusion characteristics of four molecules (ethylcyclohexane, methylcyclohexane, cyclohexane, and cis-1,4-dimethylcyclohexane) were measured to mechanistically evaluate the mass transfer surface barrier. The results observed in this study support the presence of a nonstructural surface resistance associated with the strong enthalpic interaction between the diffusing molecule and zeolite surface. Further analysis indicates that the contributions of structural and nonstructural surface barriers to the mass transport vary greatly with the heat of adsorption. This work suggests that when diffusing molecules have a weak heat of adsorption on the zeolite surface, strategies to mitigate the surface barrier should focus on the structural modification of the zeolite surface using methods such as surface etching to remove pore blockages. When the heat of adsorption is strong, strategies should focus on tuning the adsorbate/adsorbent surface interaction by methods such as depositing a mesoporous silica overlayer to reduce surface adsorption or adding a secondary external surface to minimize re-entering of the micropores.