Diffusion Front Research Articles

Instabilities in cubic reaction–diffusion fronts advected by a Poiseuille flow

Instabilities in cubic reaction–diffusion fronts advected by a Poiseuille flow

High-power single-mode vertical-cavity surface-emitting lasers using strain-controlled disorder-defined apertures

Strain-engineered diffusion masks deposited via plasma-enhanced chemical vapor deposition are demonstrated to control the curvature of the zinc diffusion front and, hence, disordering front, in disorder-defined vertical-cavity surface-emitting lasers (VCSELs) for enhanced high-power single-mode operation. Tensilely strained silicon nitride diffusion masks are applied to limit the lateral undercut of the disordering front, thereby minimizing the interaction between the disordered region of the distributed Bragg reflector and the fundamental mode. This results in higher threshold modal gain and absorption losses from the disordered region for higher-order modes while enabling greater output powers for fundamental-mode operation in single-mode impurity-induced disordered VCSEL designs. Using this technique, 850 nm AlGaAs VCSELs are shown to operate in a single fundamental mode with record optical output powers in excess of 10 mW and side-mode suppression ratios greater than 35 dB. Electrical and optical performances of these devices are presented in addition to near-field images confirming single-fundamental-mode lasing.

Reactive Transport Modeling of Natural Gas Molecular and Isotopic Evolution During Diffusive Transport in the Subsurface

AbstractReactive transport modeling was employed to investigate the relative importance of fractionations associated with gas solubility, sorption and diffusive transport on dissolved methane, ethane and propane concentrations and the isotopic composition of carbon in methane (δ13C1) in groundwater. Temperature, pressure and salinity dependencies for the hydrocarbon gases were incorporated. Gas molecular ratios, C1/(C2 + C3), increased with diffusive transport, transitioning from thermogenic values to values typically indicative of biogenic gas sources, >1,000, at the leading edge of the diffusive front. Diffusive isotopic fractionation had a large effect on δ13C1 values, with fractionations ranging from −36‰ to −107‰, the difference being a function of the diffusive fractionation factor (αD0). Larger fractionations resulted from αD0 determined at relatively low pressures, 5–50 atm, and temperatures, 20°C–25°C. Less fractionation occurred with αD0 measured at higher pressures and temperature, 30–89 atm and 90°C. The extremely depleted δ13C1 values indicated from the modeling, less than −110‰, have not been observed in shallow groundwater, suggesting that diffusive fractionation of δ13C1 is offset by other processes such as microbial oxidation. 2k factorial analysis was used to assess the model sensitivity to specific parameters: estimations of hydrocarbon travel distance are most sensitive to porosity and tortuosity, while the molecular ratio was most sensitive to the free‐water diffusion coefficient, and the isotopic fractionation was most sensitive to αD0. The magnitude of diffusive fractionation on the molecular and isotopic composition of transported hydrocarbon gas may be similar to fractionations from microbial oxidation and mixing between different sources.

Strain-induced abnormal Ge/Si inter-diffusion during hetero-epitaxy process

In this work, strain-induced abnormal inter-diffusion at Ge/Si interface during the hetero-epitaxy process is reported. By mediating the residual strain in Ge epitaxial layer, we reveal an anisotropic inter-diffusion phenomenon during conventional two-step growth process of Ge film. The diffusion length of Ge in Si substrate is found to greatly exceed the theoretical value derived from generalized diffusion model, indicating that the inter-diffusion at the interface is considerably enhanced by the residual strain at growth temperature of 600 °C. The diffusion profiles are {111}-faceted, and a rather abrupt diffusion-front is pictured implying that the Fick's law becomes invalid during the inter-diffusion process. Extensive 60° mixed dislocation and stacking faults (SFs) are identified at the diffusion front signifying that the slip of {111} lattice plane is favored at the diffusion front. The net increase of inter-diffusivity at the Ge/Si interface is ascribed to the slip of {111} lattice plane and the preferential diffusion along the dislocation segments, both of which allow the Ge(Si) atoms to migrate across the diffusion front more easily. The findings in this study may cast light on the formation of micro-roughness at interface of Ge/Si hetero-structures during the epitaxy process.

Zn diffusion technology for InP-InGaAs avalanche photodiodes

This paper presents a study of Zn diffusion process into InP and InGaAs/InP epitaxial heterostructures grown by molecular beam epitaxy. It was found that both diffusion systems: a resistively heated quartz reactor with a solid-state Zn vapor source placed inside and hydrogen or nitrogen as the carrier gas and MOCVD reactor with hydrogen as the carrier gas allow achieving similar dopant concentration above 2*10e18 cm-3. The depth of the diffusion front in the InP layer is located from 2 to 3.5 μm depending on the temperature and time of the diffusion process. The diffusion of Zn into InP through the intermediate InGaAs layer provides better surface quality comparing with direct zinc diffusion into InP surface.

Uniqueness of parameter estimates obtained from fitting free carrier absorption data of silicon wafers

In this paper, a data processing method is employed to improve the uniqueness of the electronic transport parameters (the carrier lifetime, carrier diffusion coefficient, and front and rear surface recombination velocities) obtained from fitting free carrier absorption data of silicon wafers. By employing the mean square variance graph or map, the influence of initial values on multi-parameter estimation greatly decreases. Theoretical simulations are performed to investigate the dependence of the uniqueness of the estimated parameters on the number of free parameters by choosing different initial values during multi-parameter fitting. Simulation and experimental results show that the proposed method can significantly improve the uniqueness of the fitted electronic transport parameters.

Carbon dioxide diffusions in Methane-Dissolved pore Fluids: Implications for geological carbon storage and utilization in tight formations

Fluid immobilizations in tight formations augment the importance of CO2 molecular diffusions in the processes of geological carbon utilization and storage. This study, for the first time, investigates the CO2 diffusions in unconventional tight formations which are saturated with in-situ gas-dissolved pore fluids, both experimentally and theoretically. A novel high-pressure high-temperature diffusion cell was designed to reproduce the actual CO2 diffusions in extremely low-permeability on-site geological cores saturated with methane-dissolved crude oils at the reservoir conditions and various scenarios (e.g., different gas–liquid ratios). On the other hand, a comprehensive mathematical model, which consists composition and diffusion models, was developed for quick predictions and in-depth evaluations. The CO2 diffusion coefficients at the pressure of 18.5 MPa and temperature of 80 °C with varying gas–liquid ratios were obtained from a genetic algorithm-fitting of the measured and calculated data. With the gas–liquid ratios increasing from 0 to 40 sm3/m3, the CO2 diffusion coefficient was found to decrease from 7.90 × 10−9 to 3.09 × 10−9 m2/s and the average velocity of diffusion front reduced from 0.0121 to 0.0050 m/d. This finding indicates methane dissolutions into the crude oil at the reservoir conditions would be detrimental for the CO2 diffusions. Hence, the methane amount is suggested to be well controlled in the processes of geological carbon storage and utilization for oil production. This study will support the foundation of more general application pertaining to geological CO2 utilization and storage, especially in the unconventional tight or shale oil reservoirs.

Plasma transport simulations of Rayleigh–Taylor instability in near-ICF deceleration regimes

Rayleigh–Taylor (R–T) instability between plasma species is examined in a kinetic test and near-inertial confinement fusion (ICF) regimes. A transport approximation to the plasma species kinetics is used to represent viscosity and species mass transport within a hydrodynamic fluid code (xRage). R–T simulation results are compared in a kinetic test regime with a fully kinetic particle-in-cell approach [vectorized particle-in-cell (VPIC)] and with an analytic model for the growth rate of R–T instability. Single-mode growth rates from both codes and the analytic model are in reasonable agreement over a range of initial wavelengths including the wavenumber of maximum growth rate. Both codes exhibit similar diffusive mixing fronts. Small code-to-code differences arise from the kinetics, while simulation-analytic model differences arise from several sources dominated by the choice of gradients establishing the hydrostatic equilibrium initial conditions. After demonstrating code agreement in the kinetic test regime, which is practically accessible to the VPIC code, then the xRage code, with the fluid plasma transport approximation, is applied to single mode R–T instability under deceleration conditions closer to an ICF implosion, approximated with a carbon (C) shell imploding on a deuterium (D) fuel. The analytic wavelength of maximum instability is limited by the kinetics, primarily in the viscosity, and is found to be ≈10 μm for an ion temperature near 1 keV at this C–D interface, with the most unstable wavelength increasing as temperature increases. The analytic viscous model agrees with simulation results over a range of initial perturbation wavelengths, provided the simulation results are analyzed over a sufficiently short duration (⪅0.2 ns in this case). Details of the fluid structure evolution during this R–T deceleration are compared between the inviscid Euler equations and cases, which include plasma transport over a range in initial wavelengths and initial perturbation amplitudes. The inviscid Euler solutions show a grid-dependent cascade to smaller scale structures often seen in the R–T instability, while simulations with plasma transport in this deceleration regime develop a single vortex roll-up, as the plasma transport smoothes all hydrodynamic fluid structures smaller than several micrometers. This leads to a grid-converged transient solution for the R–T instability when kinetic effects are included in the simulations, and thus represents a direct numerical simulation of the thermal ions during R–T unstable mixing in ICF relevant conditions.

In Situ Observation of Pressurized Microcrack Growth in Silicon

The evolution of micrometer‐scale cracks in hydrogen‐ and helium‐implanted silicon during isothermal annealing is studied using confocal IR microscopy. Herein, it is demonstrated that the dominant mechanism of microcrack growth is crack coalescence. The coalescence of two cracks causes a sudden crack opening in silicon and leads to the formation of a larger crack. The surface of this large crack is equal to the sum of the surface areas of the two former cracks plus the opened zone. As a result, it has a less circular shape than both initial cracks. After the coalescence, the new pressurized crack surface evolves quickly and its shape circularizes again. Before their coalescence, the measurement of the distance between two microcracks reveals the increase of the gap closure velocity as two microcracks come closer due to the interaction of their stress fields. In addition, the growth of isolated cracks without coalescence due to implanted gas diffusion and crack front curvature effect on stress is detected. It is evidenced that two geometric parameters, the distance between neighboring cracks and the local curvature of the crack front, contribute to the growth of a pressurized crack.

Invasive-invaded system of non-Lipschitz porous medium equations with advection

This work provides analytical results towards applications in the field of invasive-invaded systems modeled with nonlinear diffusion and with advection. The results focus on showing regularity, existence and uniqueness of weak solutions using the condition of a nonlinear slightly positive parabolic operator and the reaction-absorption monotone properties. The coupling in the reaction-absorption terms, that characterizes the species interaction, impedes the formulation of a global comparison principle that is shown to exist locally. Additionally, this work provides analytical solutions obtained as selfsimilar minimal and maximal profiles. A propagating diffusive front is shown to exist until the invaded specie notes the existence of the invasive. When the desertion of the invaded starts, the diffusive front vanishes globally and the nonlinear diffusion concentrates only on the propagating tail which exhibits finite speed. Finally, the invaded specie is shown to exhibit an exponential decay along a characteristic curve. Such exponential decay is not trivial in the nonlinear diffusion case and confirms that the invasive continues to feed on the invaded during the desertion.

In‐Situ Observation of the Formation of NiSi/Ni2Si Heterojunction in SiGe Nanowire with Al2O3 Diffusion Barrier Layer

AbstractIn complementary metal‐oxide‐semiconductor technology, the metal silicides/germanides have prominent advantages such as low resistivity, high thermal and chemical stability. Here, a study to probe the phase transformations and the diffusion behaviors of Ni in Si1‐xGex nanowire (NW) by in situ transmission electron microscopy is conducted. The Si1‐xGex NWs are dispersed on Si3N4 membrane and contacted with Ni by E‐beam lithography process for in situ study. The sample is heated to 723 K, Ni is diffused into Si1‐xGex NW and Ni2Si is formed accordingly. The diffusion mechanism is confirmed to be reaction‐controlled and the activation energy can be extracted to be 0.708 eV. On the other hand, in this study Al2O3 layer‐coated Si1‐xGex NW is probed for comparison, while the Al2O3 layer serves as the diffusion barrier to modulate the diffusion rate of Ni. This increases the activation energy to 1.38 eV. Importantly, it is found that the NiSi/Ni2Si heterojunction is formed at the diffusion front. The results provide the insights for fabrication of semiconducting devices.

Investigating liquid fronts during spontaneous imbibition of liquids in industrial wicks. Part I: Experimental studies

AbstractA large set of industrial wicks made from sintered polymer beads and fibrous materials were studied. Three types of liquid fronts were observed: sharp, semi‐sharp, and diffuse. The bead‐like microstructure with lower porosity is found to support sharp fronts, while the aligned‐fiber microstructure with higher porosities leads to a smudging/diffusing of the fronts. The previously developed sharp‐front model is found to predict the front height as a function of time quite well in the sintered‐bead wicks and the two “semi‐sharp” fibrous wicks. The liquid‐front height calculated from the liquid mass‐gain data was validated through visual observations for all but the two fibrous wicks generating the diffuse fronts. These latter cases, observed to start off as a sharp fronts, faded with time.

Simulation of the growth of sucrose crystals in a sugar-containing solution

Crystallization is one of the most important steps in the technological flow of commodity sugar. By its nature, it develops in a fairly wide temperature range, conditions of varying concentration of the solution, its peptization and other mass-exchange process of formation and growth of sugar crystals in a sugar solution by diffusion transfer in it sucrose molecules. To this it is necessary to add such complicating physical and mathematical formalization phenomena, affecting crystallization, such as the shape of the crystal, purity, viscous properties and surface tension of the solution, the presence of non-sugars, etc. Therefore, among the factors that determine the whole process, the factors usually take place, keeping among them only priority and most important from the point of view of the study. The article, unlike known analogues, provides justification and quantitative analysis of the kinetics of the sucrose crystallization process, taking into account the features of the crystal shape and diffusion properties of the solution. From the point of view of classical diffusion theory, the phenomenon of crystallization is interpreted as molecular with infinite rate of perilation from the source of diffusion transfer in the solution of sucrose molecules, so that the concentration in the sugar-containing liquid system is also supposed to change instantly at each point. However, since in the real world this effect is not observed, in order to resolve this contradiction, introduce the concepts of the indignant and unperturbed, separated by the diffusion front of the concentration of the regions of these phase states. Using the kinematic characteristics of the front, determine the time of the crystallization process in general in both phases. This allows us to calculate the processing period of the solution with greater accuracy than the results obtained on the basis of classical theory.

Swelling and Diffusion in Polymerized Ionic Liquids-Based Hydrogels.

Hydrogels are one of the emerging classes of materials in current research. Besides their numerous applications in the medical sector as a drug delivery system or in tissue replacement, they are also suitable as irrigation components or as immobilization matrices in catalysis. For optimal application of these compounds, knowledge of the swelling properties and the diffusion mechanisms occurring in the gels is mandatory. This study is focused on hydrogels synthesized by radical polymerization of imidazolium-based ionic liquids. Both the swelling and diffusion behavior of these hydrogels were investigated via gravimetric swelling as well as sorption experiments implemented in water, ethanol, n-heptane, and tetrahydrofuran. In water and ethanol, strong swelling was observed while the transport mechanism deviated from Fickian-type behavior. By varying the counterion and the chain length of the cation, their influences on the processes were observed. The calculation of the diffusion coefficients delivered values in the range of 10−10 to 10−12 m2 s−1. The gravimetric results were supported by apparent diffusion coefficients measured through diffusion-weighted magnetic resonance imaging. A visualization of the water diffusion front within the hydrogel should help to further elucidate the diffusion processes in the imidazolium-based hydrogels.

Fault Triggering Mechanisms for Hydraulic Fracturing-Induced Seismicity From the Preston New Road, UK Case Study

We investigate the physical mechanisms governing the activation of faults during hydraulic fracturing. Recent studies have debated the varying importance of different fault reactivation mechanisms in different settings. Pore pressure increase caused by injection is generally considered to be the primary driver of induced seismicity. However, in very tight reservoir rocks, unless a fracture network exists to act as a hydraulic conduit, the rate of diffusion may be too low to explain the spatio-temporal evolution of some microseismic sequences. Thus, elastic and poroelastic stress transfer and aseismic slip have been invoked to explain observations of events occurring beyond the expected distance of a reasonable diffusive front. In this study we use the high quality microseismic data acquired during hydraulic fracturing at the Preston New Road (PNR) wells, Lancashire, UK, to examine fault triggering mechanisms. Injection through both wells generated felt induced seismicity—an ML 1.6 during PNR-1z injection in 2018 and an ML 2.9 during PNR-2 in 2019—and the microseismic observations show that each operation activated different faults with different orientations. Previous studies have already shown that PNR-1z seismicity was triggered by a combination of both direct hydraulic effects and elastic stress transfer generated by hydraulic fracture opening. Here we perform a similar analysis of the PNR-2 seismicity, finding that the PNR-2 fault triggering was mostly likely dominated by the diffusion of increased fluid pressure through a secondary zone of hydraulic fractures. However, elastic stress transfer caused by hydraulic fracture opening would have also acted to promote slip. It is significant that no microseismicity was observed on the previously activated fault during PNR-2 operations. This dataset therefore provides a unique opportunity to estimate the minimum perturbation required to activate the fault. As it appears that there was no hydraulic connection between them during each stimulation, any perturbation caused to the PNR-1z fault by PNR-2 stimulation must be through elastic or poroelastic stress transfer. As such, by computing the stress transfer created by PNR-2 stimulation onto the PNR-1z fault, we are able to approximate the minimum bound for the required stress perturbation: in excess of 0.1 MPa, orders of magnitude larger than stated estimates of a generalized triggering threshold.

A Floating Mold Technique for the Programmed Assembly of Protocells into Protocellular Materials Capable of Non-Equilibrium Biochemical Sensing.

Despite important breakthroughs in bottom-up synthetic biology, a major challenge still remains the construction of free-standing, macroscopic, and robust materials from protocell building blocks that are stable in water and capable of emergent behaviors. Herein, a new floating mold technique for the fabrication of millimeter- to centimeter-sized protocellular materials (PCMs) of any shape that overcomes most of the current challenges in prototissue engineering is reported. Significantly, this technique also allows for the generation of 2D periodic arrays of PCMs that display an emergent non-equilibrium spatiotemporal sensing behavior. These arrays are capable of collectively translating the information provided by the external environment and are encoded in the form of propagating reaction-diffusion fronts into a readable dynamic signal output. Overall, the methodology opens up a route to the fabrication of macroscopic and robust tissue-like materials with emergent behaviors, providing a new paradigm of bottom-up synthetic biology and biomimetic materials science.

Theoretical Analysis of Experimental Data of Sodium Diffusion in Oxidized Molybdenum Thin Films

In this work, the diffusion process of sodium (Na) in molybdenum (Mo) thin films while it was deposited on soda lime glass (SLG) was studied. A small amount of oxygen was present in the chamber while the direct-current (DC) magnetron sputtering was used for the deposition. The substrate temperatures were varied to observe its effect. Such molybdenum films, with or without oxidations, are often used in thin film solar cells, either as back contact or as hole transport layers. Secondary ion mass spectrometry (SIMS) was used to quantify the concentration of the species. A grain diffusion mechanistic model incorporating the effect of grain and grain boundary geometrical shape and size was developed. The model was used to provide an in-depth theoretical analysis of the sodium diffusion in molybdenum thin films that lead to the measured SIMS data. It was observed that not only diffusion coefficients should be considered when analyzing diffusion processes in thin films but also the ratio of grain boundary size to grain size. Both depend on substrate temperature and directly affect the amount of diffused species in the film. The data were analyzed under the light of the film growth speed versus diffusion front speed, the effect of oxygen content, and the effect of substrate temperature on the overall diffusion process. The temperature inversely affects the ratio of grain boundary size and grain size and directly affects the diffusion coefficient, which leads to a preferable temperature at which the highest amount of alkali can be found in the film.

Exploring the Nature of EUV Waves in a Radiative Magnetohydrodynamic Simulation

Abstract Coronal extreme-ultraviolet (EUV) waves are large-scale disturbances propagating in the corona, whose physical nature and origin have been discussed for decades. We report the first three-dimensional (3D) radiative magnetohydrodynamic simulation of a coronal EUV wave and the accompanying quasi-periodic wave trains. The numerical experiment is conducted with the MURaM code and simulates the formation of solar active regions through magnetic flux emergence from the convection zone to the corona. The coronal EUV wave is driven by the eruption of a magnetic flux rope that also gives rise to a C-class flare. It propagates in a semicircular shape with an initial speed ranging from about 550 to 700 km s−1, which corresponds to an average Mach number (relative to fast magnetoacoustic waves) of about 1.2. Furthermore, the abrupt increase of the plasma density, pressure, and tangential magnetic field at the wave front confirms fast-mode shock nature of the coronal EUV wave. Quasi-periodic wave trains with a period of about 30 s are found as multiple secondary wavefronts propagating behind the leading wave front and ahead of the erupting magnetic flux rope. We also note that the true wave front in the 3D space can be very inhomogeneous; however, the line-of-sight integration of EUV emission significantly smoothes the sharp structures in 3D and leads to a more diffuse wave front.

Mobility of selenium oxyanions in clay-rich media: A combined batch and diffusion experiments and synchrotron-based spectroscopic investigation

Selenium-79 is considered as a critical radionuclide in safety assessment of high-level radioactive waste deep geological repository in clay-rich formations, owing to its long half-life and its anionic form in three relevant oxidation states (VI, IV,-II). An in-depth understanding of the diffusive transport properties of Se is therefore essential, especially due to its high sensitivity to oxido-reduction conditions. Here, the mobility of selenite and selenate in claystone samples (Callovo-Oxfordian, East of Paris Basin, France) under anoxic conditions is assessed by combining batch and diffusion experiments, and synchrotron-based spectroscopic mapping of diffusion fronts.Results showed that selenite and selenate behaved distinctly. Selenate diffused similarly to the reference anionic tracer, 36Cl−, without significant sorption or reduction. Selenite showed a sorption behaviour that increased with the decrease of the initial concentration from 10−3 to 10−6 mol L−1, values of distribution ratio (Rd) from batch experiments ranging from 10 to about 250 mL g−1. Selenite in-diffusion experiments showed that a pure diffusion model with reversible sorption was able to roughly reproduce the evolution of dissolved selenite in solution over time. However, additional reactions were required to properly describe the irregular shape of the selenite diffusion profiles in the solid. Mapping of Se oxidation state in diffusion fronts within the claystone coupons showed the presence of reduced Se (Se (0), Se(-I) and/or Se(-II)) along a fringe located at about 2 mm beneath the surface, possibly explaining the irregular shape of diffusion profiles. In the superficial zone (0–2 mm), oxidizing perturbations are assumed to account for the preservation of selenite under this oxidation state. These perturbations would also bias batch results in the same manner. Deeper in the claystone sample, diffusing selenite was observed, with a content steadily decreasing up to 7 mm from the inlet. The results suggest that, even after more than 500 days of diffusion, Se reduction would occur progressively along the diffusion pathways.

High-temperature diffusion in couple of electrodeposited iridium/rhenium

Ir coated Re (Ir/Re), combining the outstanding high-temperature mechanical property of Re and excellent high-temperature oxygen permeability resistance of Ir, is a promising high-temperature material in high temperature applications, such as rocket engine combustion chambers and crucibles for crystal growth, etc. The elemental diffusion behaviors in the Ir/Re material are closely related to its failure mode and lifetime. Therefore, the diffusion behavior investigation on the Ir/Re material is essential for understanding the failure mechanism and building the lifetime prediction model of this material. In this work, a three-layered CVD Re/ED Ir/ED Re sample was fabricated and its diffusion behaviors at the temperatures ranging from 1400 to 2000 °C were investigated. The diffusion coefficients and activation energy of ED Re diffusing into Ir using a semi-infinite diffusion model were obtained and compared with those of the CVD Re. The obviously lower diffusion activation energy of ED Re (0.98 eV) compared with the CVD Re is due to their microstructure difference. The higher defect concentration, thermodynamically unstable grain structure and preferred orientation of the ED Re layer promotes the dominant diffusion of Ir into Re, resulting in a thicker diffusion layer with a frame-shaped diffusion front.