Intrinsic Diffusion Research Articles

Solution of the fractional diffusion equation by using Caputo-Fabrizio derivative: application to intrinsic arsenic diffusion in germanium

In this work, we focused on solving the space-time fractional diffusion equation with an application on the intrinsic arsenic diffusion in germanium. At first we have treated the differential equation in a semi-infinite medium by using Caputo-Fabrizio fractional derivative. We have introduced the Laplace transform to solve this type of equations. Secondly, Based on the obtained solution, we have simulated an profile of arsenic diffusion in germanium under intrinsic conditions. Accurate simulations have been achieved showing that the fractional derivative orders affect on the estimation of the diffusion coefficient, where increasing the time fractional derivative order α reduces the value of the diffusion coefficient, while increasing the space fractional derivative order β increases the value of the diffusion coefficient.

Diffusion simulation based on atomistic model and mobility determination via Kirkendall experiment for multi-component systems

Currently the multi-component diffusion kinetic databases, one of the key inputs for successful predictions of microstructural evolution, are by no means reliable since they are developed mostly by only seeking interdiffusion properties via diffusion-couple experiments but without considering the indispensable tracer or intrinsic diffusion coefficients. Estimating interdiffusion coefficients becomes challenging with the increasing number of components. In the present work, a mobility-extraction method is presented to directly determine atomic mobilities, which is in turn used to develop kinetic databases and then calculate all sorts of diffusion coefficients. It requires only one single-phase diffusion couple with Kirkendall markers to obtain the atomic mobilities in the marker position, with no limit on the number of components. This novel idea is realized on the basis of a new simulation scheme to solve diffusion equations in line with the atomistic model, which takes the Kirkendall effect into account intrinsically and efficiently.

Langevin picture of subdiffusion in nonuniformly expanding medium.

Anomalous diffusion phenomena have been observed in many complex physical and biological systems. One significant advance recently is the physical extension of particle's motion in a static medium to a uniformly and even nonuniformly expanding medium. The dynamic mechanism of the anomalous diffusion in the nonuniformly expanding medium has only been investigated by the approach of continuous-time random walk. To study more physical observables and to supplement the physical models of the anomalous diffusion in the expanding mediums, we characterize the nonuniformly expanding medium with a spatiotemporal dependent scale factor a(x,t) and build the Langevin picture describing the particle's motion in the nonuniformly expanding medium. Besides the existing comoving and physical coordinates, by introducing a new coordinate and assuming that a(x,t) is separable at a long-time limit, we build the relation between the nonuniformly expanding medium and the uniformly expanding one and further obtain the moments of the comoving and physical coordinates. Different forms of the scale factor a(x,t) are considered to uncover the combined effects of the particle's intrinsic diffusion and the nonuniform expansion of medium. The theoretical analyses and simulations provide the foundation for studying more anomalous diffusion phenomena in the expanding mediums.

Binary and nanostructured Ni[sbnd]Mn perovskite fluorides as efficient electrocatalysts for urea oxidation reaction

Urea electrolysis holds tremendous promise to provide green and sustainable energy and environmental solutions, because it can simultaneously remedy urea–containing wastewater and provide energy–saving hydrogen. However, the development of this emerging technology remains challenging mainly due to a dearth of high–performance electrocatalysts for efficient urea oxidation reaction (UOR). Perovskite fluorides have the advantages of intrinsic 3D diffusion pathways, robust architecture, and tunable chemical composition, thus receiving increasing attention in many applications. In this work, the UOR performances of a series of ABF3 samples (A = K; B = Ni/Mn, Ni/Co, Co/Mn) with various compositions are investigated in a systematic fashion for the first time. Among the binary samples, KNMF41 (Ni/Mn atomic ratio = 4:1) is the optimal sample with reduced overpotential (reaching 100 mA cm−2 at 1.43 V), low Tafel slope (40 mV dec−1), enhanced reaction rate constant (6.3 × 105 cm3 mol−1 s−1), and high turnover frequency (TOF, 0.19 s−1 at 1.60 V) toward urea oxidation. By comparing with NiCo and CoMn samples, the binary NiMn design is confirmed to endow the perovskite fluoride with higher electrocatalytic activity, thanks to the directed adsorption of urea molecules on the adjacent NiMn active sites. This work presents a targeted synthetic strategy for obtaining efficient electrocatalysts.

Membrane Functionalization Approaches toward Per- and Polyfluoroalkyl Substances and Selected Metal Ion Separations.

Adsorption and ion exchange technologies are two of the most widely used approaches to separate pollutants from water; however, their intrinsic diffusion limitations continue to be a challenge. Pore functionalized membranes are a promising technology that can help overcome these challenges, but the extents of their competitive benefits and broad applicability have not been systematically evaluated. Herein, three types of adsorptive/ion exchange (IX) polymers containing strong/weak acid, strong base, and iron-chitosan complex groups were synthesized in the pores and partially on the surface of microfiltration (MF) membranes and tested for the removal of organic and inorganic cations and anions from water, including arsenic, per- and polyfluoroalkyl substances (PFAS), and calcium (hardness). When directly compared with beads (0.5-6 mm) and crushed resins (0.05 mm), adsorptive/IX pore-functionalized membranes demonstrated an increased relative sorption capacity, up to 2 orders of magnitude faster kinetics and the ability to regenerate up to 70-100% of their capacity while concentrating the initial solution concentration up to 12 times. The simple and versatile synthesis approach used to functionalize membranes, notably independent of the polymer type of the MF membrane, utilized pores throughout the entire cross section of the membrane to immobilize the polymers that contain the functional groups. Utilizing the pore volume of commercial membranes (6-112 mL/m2), the scientific weight capacity of the polymer (3.1-11.5 mequiv/g), and the synthesis conditions (e.g., monomer concentration), the theoretical adsorption/IX capacities per area of the membranes were calculated to be as high as 550 mequiv/m2, substantially higher than the 175 mequiv/m2 value needed to compete with commercially available IX resins. This work therefore shows that pore functionalized membranes are a promising path to tackle water contamination challenges, lowering separation diffusion limitations.

Estimation of diffusion coefficients in NiCoFeCrAl multi-principal element alloy following an inventive design strategy of diffusion couples

An inventive design strategy of producing the diffusion couples for intersecting the diffusion paths in multicomponent space is described in Ni-Co-Fe-Cr-Al multi-principal element alloy. This, for the first time, facilitates the estimation of the tracer, intrinsic, and interdiffusion coefficients of all the elements purely experimentally in this quinary system. This was not possible until now following any other experimental methods. The tracer diffusion coefficients estimated in this quinary system are compared with the impurity and tracer diffusion coefficients in pure Ni, and at (or near) equiatomic compositions of binary Ni-Co, ternary Ni-Co-Cr, and quaternary Ni-Co-Fe-Cr systems. The relative mobilities of the elements are found to follow the trend DNi*≤DCo*<DFe*≤DCr*<DAl* in all the systems. However, the tracer diffusion coefficients of the elements first decrease and then increase with the increasing order of the systems. The contribution of the vacancy wind effect on certain cross-intrinsic diffusion coefficients is found to be very significant and cannot be ignored. The influence of the vacancy wind effect on interdiffusion coefficients is less significant than the intrinsic diffusion coefficients since interdiffusion coefficients are the average of multiple intrinsic diffusion coefficients. This may lead to the wrong statement that the vacancy wind effects are negligible. We have further shown that describing the relative diffusion rates of the elements with main interdiffusion coefficients instead of the tracer diffusion coefficients can be misleading or confusing. Different elements as the dependent variables of interdiffusion coefficients indicate a very different or even opposite trend of relative diffusivities in this system.

A novel method to design Nb(W)–Ti–Co(Fe) alloy membrane with high hydrogen permeability and strong resistance to hydrogen embrittlement

A hydrogen permeable Nb43W5Ti27Co20Fe5 alloy membrane was designed and its microstructure and hydrogen transportation performances were systematically studied. W mainly dissolves into primary body-centered cubic (bcc)-(Nb) phases, while Fe is captured in eutectic structures. Substituting Nb with W leads to a substantial reduction in hydrogen solubility and substituting Co with Fe negligibly affects hydrogen solubility. The W and Fe substitutions contribute to an enhanced intrinsic hydrogen diffusion coefficient D∗. The designed Nb43W5Ti27Co20Fe5 alloy membrane exhibits lower hydrogen solubility and higher hydrogen permeability at temperatures below 623 K than that of the original Nb48Ti27Co25 alloy membrane. No hydrogen-induced failures were found for the designed Nb43W5Ti27Co20Fe5 alloy membrane during cooling to room temperature and under long-term hydrogen permeation at 673 K for 72 h, whereas the original alloy membrane failed at 444 K during cooling to room temperature and after 19 h during hydrogen permeation at 673 K. The designed Nb43W5Ti27Co20Fe5 alloy membrane exhibits high hydrogen permeability and strong resistance to hydrogen embrittlement.

Recent Advances in Synergistic Modulation of Transition-Metal-Based Electrocatalysts for Water Oxidation: A Mini Review

Synergistic modulation has been extensively explored to develop highly efficient transition-metal-based electrocatalysts for oxygen evolution reaction (OER) because coupling effects among intrinsic activity, conductivity, mass transfer, mass diffusion, and intermediates adsorption can further promote catalytic activity. In this review, recent progress in both experimental and theoretical research on synergistic modulation for transition-metal-based alkaline OER electrocatalysts is focused. Specifically, synergistic effects will be presented in the following aspects: (1) metal reactive sites and heterogeneous atoms; (2) heterogeneous atoms and crystallographic structure; (3) electronic structure and morphology; (4) elementary reaction steps; and (5) external fields. Finally, the remaining challenges and prospects of synergistic modulation for efficient OER are further proposed.

Utilising physics-informed neural networks for optimisation of diffusion coefficients in pseudo-binary diffusion couples

ABSTRACT We propose a numerical inverse method based on physics-informed neural networks (PINN) for calculating composition-dependent diffusion coefficients in pseudo-binary (PB) diffusion couples in multicomponent alloys. Traditional methods rely solely on experimental diffusion profiles as design targets, which can lead to unreliable estimates. In contrast, PINN uses a combination of available data and physics-based constraints to obtain optimised design parameters and exact solutions for constrained governing differential equations. The constraints in PINN include governing partial differential equations, initial and boundary conditions, and any other equality/inequality relations obeyed by physical parameters. Our study shows the necessity of experimentally estimated intrinsic diffusion coefficients for the prediction of reliable composition-dependent mobility data. In the absence of such data, different combinations of unknown intrinsic diffusion coefficients can also produce reasonable approximations of diffusion profiles and interdiffusion coefficients while wrongly predicting more fundamental quantities (i.e. intrinsic diffusivities). Our method utilises PINN to simultaneously obtain optimised design parameters (diffusion coefficients) and exact solutions for governing diffusion equations. The implementation of PINN uses experimentally estimated diffusion coefficients obtained by the PB diffusion couple method, in addition to diffusion profiles, as design targets. The method is extended to non-ideal PB diffusion profiles, such as conventional diffusion couples in which all the components develop diffusion profiles, by incorporating additional constraints such as zero composition gradient of certain component(s) and experimentally estimated interdiffusion coefficients at extrema in the composition profiles. PINN is found to be a promising approach for obtaining reliable estimates of diffusion coefficients in multicomponent alloys.

The development of ultrafine grain structure in an additively manufactured titanium alloy via high-temperature microscopy

Microstructures dominated by acicular α' martensitic phase, such as in the case of Ti-6Al-4V fabricated by laser powder-bed fusion (PBF-LB), are known to suffer from reduced ductility and low toughness. The decomposition of such metastable microstructures into α+β lamellar structures during PBF-LB requires either specific laser regimes that are often challenging to be attained or post-process heat treatments which might lead, instead, to undesirable coarsening of the grain structure. Here we propose a novel route for the formation of ultrafine lamellar α+β microstructures and demonstrate the associated advantages in terms of tensile strength and ductility. Our approach is based on a suitable modification of constitution of Ti-6Al-4V with additions of Fe, a known potent β stabiliser of high intrinsic diffusivity. After printing, this alloy presents a microstructure dominated by metastable β phase. We investigate the details of its decomposition using a combination of in-situ high-energy synchrotron X-ray diffraction and high temperature microscopy up to the β transus temperature. The microstructure evolution is comprised by homogeneous decomposition of the metastable β phase via ω-assisted nucleation of α phase, α grain growth sustained by early diffusion of Fe in the β phase followed by a conventional partitioning of V. The understanding of this transformation pathway enables the development of ultrafine grained α+β lamellar microstructures that exhibit outstanding tensile behaviour. The presented approach is machine-agnostic and offers a novel alloy design strategy for development of high-strength alloys in additive manufacturing.

Stroke-GFCN: ischemic stroke lesion prediction with a fully convolutional graph network.

The interpretation of image data plays a critical role during acute brain stroke diagnosis, and promptly defining the requirement of a surgical intervention will drastically impact the patient's outcome. However, determining stroke lesions purely from images can be a daunting task. Many studies proposed automatic segmentation methods for brain stroke lesions from medical images in different modalities, though heretofore results do not satisfy the requirements to be clinically reliable. We investigate the segmentation of brain stroke lesions using a geometric deep learning model that takes advantage of the intrinsic interconnected diffusion features in a set of multi-modal inputs consisting of computer tomography (CT) perfusion parameters. We propose a geometric deep learning model for the segmentation of ischemic stroke brain lesions that employs spline convolutions and unpooling/pooling operators on graphs to excerpt graph-structured features in a fully convolutional network architecture. In addition, we seek to understand the underlying principles governing the different components of our model. Accordingly, we structure the experiments in two parts: an evaluation of different architecture hyperparameters and a comparison with state-of-the-art methods. The ablation study shows that deeper layers obtain a higher Dice coefficient score (DCS) of up to 0.3654. Comparing different pooling and unpooling methods shows that the best performing unpooling method is the proportional approach, yet it often smooths the segmentation border. Unpooling achieves segmentation results more adapted to the lesion boundary corroborated with systematic lower values of Hausdorff distance. The model performs at the level of state-of-the-art models without optimized training methods, such as augmentation or patches, with a DCS of . We proposed and evaluated an end-to-end trainable fully convolutional graph network architecture using spline convolutional layers for the ischemic stroke lesion prediction. We propose a model that employs graph-based operations to predict acute stroke brain lesions from CT perfusion parameters. Our results prove the feasibility of using geometric deep learning to solve segmentation problems, and our model shows a better performance than other models evaluated. The proposed model achieves improved metric values for the DCS metric, ranging from 8.61% to 69.05%, compared with other models trained under the same conditions. Next, we compare different pooling and unpooling operations in relation to their segmentation results, and we show that the model can produce segmentation outputs that adapt to irregular segmentation boundaries when using simple heuristic unpooling operations.

Quantitative estimation of coarsening behavior of L12 domains in Ni–Al–V alloys by a first-principles calculation

Ni–Al–V based alloys possess superior creep resistance at higher temperatures because of the sluggish interdiffusion of constituent elements within the L12-Ni3(Al, V) matrix. In this study, intrinsic diffusion coefficients of Ni, Al and V in quasi-binary Ni3Al1-xVx (x = 0, 0.125, 0.25, 0.5) were quantified based on a first-principles calculation for elucidating the effect of V concentration on the coarsening behavior of L12 domains. From the results of the estimated formation energies, migration energies and activation energies, it was found that intrinsic diffusion coefficients of Ni and Al are decreased by the addition of V, while intrinsic diffusion coefficient of V remains two or three orders of magnitude smaller than them. Such a suppressed diffusion of Ni and Al by V addition well explains the experimentally obtained lower coarsening rates of L12 domains in Ni3Al0.58V0.42 and Ni3Al0.48V0.52 alloys.

Geometry-Defined Response Time and Sensitivity for Microneedle-Based Amperometric Sensors

Smart, ultra-scaled, always-on wearable (and implantable) sensors are an exciting frontier of modern medicine. Among them, minimally invasive microneedles (MN) is an emerging technology platform for theragnostic applications. Compared to traditional continuous glucose measurement (CGM) devices, these MNs offer pain-less insertion and simple operation. These MN systems, however, rely on analyte diffusion from the interstitial fluid (ISF) to the sensing site, and thus, (a) introduce a substantial and intrinsic diffusion delay in sensor response, and (b) reduce the analyte concentration to which the sensor must respond. A diversity of experimental platforms has been proposed to improve performance, but their optimization relies on empirical iterative approaches. Here, we integrate the theory of transient flux balance and the biomimetic concepts from ion uptake by bacteria to derive a generalized physics-guided model for MN sensors. The framework suggests strategies to minimize response time and maximize extracted analyte concentration in terms of the geometric and physical properties of the system. Our results show that there exists an intrinsic trade-off between response time and extracted analyte concentration. Our model, validated against numerical simulations and experiment data, offers a predictive design framework that would significantly reduce the optimization time for MN-based sensor platforms.

Microstructure and micromechanical responses of bulk nanostructured high entropy alloy after heavy-ion irradiation at 500°C

Nanocrystalline materials possess high defect-sink density, but often experience radiation-enhanced grain coarsening. With the intrinsic sluggish diffusion and radiation tolerance, high entropy alloys (HEA) may have superior radiation tolerance in their nanocrystalline form. In this study, CoCrFeNiMn HEA samples were processed via high-pressure torsion (HPT) under 6 GPa at room temperature for 1 (1T) and 8 (8T) turns to form nanograins with unsaturated and saturated plastic deformation, respectively. After 3.4MeV Ni ion irradiation at 500 °C, grain growth was observed in both HPT-processed samples. The microstructural evolution is dependent on pre-irradiation HPT processing, with the 8T sample showing stronger radiation tolerance against dislocation development and hardness changes, observed through transmission electron microscopy and nanoindentation, respectively. This radiation resistance is attributed to a unique nanodomain microstructure formed within the radiation-coarsened grains of the 8T sample. Microstructural and microchemical analysis suggested both HPT process and the alloy chemistry played roles in the nanodomain formation.

Preventing Hydrogen Embrittlement: The Role of Barrier Coatings for the Hydrogen Economy

Hydrogen barrier coatings are protective layers consisting of materials with a low intrinsic hydrogen diffusivity and solubility, showing the potential to delay, reduce or hinder hydrogen permeation. Hydrogen barrier coatings are expected to enable steels, which are susceptible to hydrogen embrittlement, specifically cost-effective low alloy-steels or light-weight high-strength steels, for applications in a hydrogen economy. Predominantly, ceramic coating materials have been investigated for this purpose, including oxides, nitrides and carbides. In this review, the state of the art with respect to hydrogen permeation is discussed for a variety of coatings. Al2O3, TiAlN and TiC appear to be the most promising candidates from a large pool of ceramic materials. Coating methods are compared with respect to their ability to produce layers with suitable quality and their potential for scaling up for industrial use. Different setups for the characterisation of hydrogen permeability are discussed, using both gaseous hydrogen and hydrogen originating from an electrochemical reaction. Finally, possible pathways for improvement and optimisation of hydrogen barrier coatings are outlined.

Assessment of Thermodynamic and Structural Properties of Al–Er liquid Alloy at Different Temperatures

Theoretical expressions of quasi–lattice model were used to assess the thermodynamic and structural properties of Al–Er liquid alloy at different temperatures. The model fit parameters were optimised using the available literature data of the thermodynamic properties for the system at 1873 K. The computed values of thermodynamic properties such as excess Gibbs free energy of mixing, enthalpy of mixing, entropy of mixing and activities of Er and Al using the model fit parameters were found to be consistent with the reference data–set. Therefore, the same parameters were used to compute the structural properties such as concentration fluctuation in long wavelength limit, Warren–Cowley short range–order parameter and ratio of mutual to intrinsic diffusion coefficients. Assuming the model fit parameters to be linear temperature–dependent, the above mentioned properties were also assessed in the temperature range 1873–2173 K. The compound forming tendency of the system was found to decrease gradually with increase in temperature.

Global dynamics of a Leslie–Gower predator–prey model in open advective environments

This paper investigates the global dynamics of a reaction–diffusion–advection Leslie–Gower predator–prey model in open advective environments. We find that there exist critical advection rates, intrinsic growth rates, diffusion rates and length of the domain, which classify the global dynamics of the Leslie–Gower predator–prey system into three scenarios: coexistence, persistence of prey only and extinction of both species. The results reveal some significant differences with the classical specialist and generalist predator–prey systems. In particular, it is found that the critical advection rates of prey and predator are independent of each other and the parameters about predation rate have no influence on the dynamics of system. The theoretical results provide some interesting highlights in ecological protection in streams or rivers.

Novel porous CoS1.097@carbon nanofibers as flexible and binder-free anode material for sodium-ion batteries

Transition metal sulfides (TMSs) have received numerous attention as anode materials for sodium-ion batteries because of the high theoretical capacity. So far, the Na-storage performance of TMSs is still unsatisfactory due to the structural degeneration that induced by the volume change upon redox process. Herein, a novel flexible and binder-free anode material of porous CoS1.097@carbon nanofibers was facilely constructed by means of the electrospinning, carbonization and sulfidation processes. The porous CoS1.097@carbon nanofibers display unique structure with CoS1.097 nanoparticles confined into porous N-doped carbon nanofibers, and can provide sufficient active sites, high electrical conductivity, reduced ion diffusion distance, abundant ion migration pathways, desirable voids for alleviating the volume variation, and rigid structural stability for efficient Na-storage. In consequence, the flexible and binder-free electrode material delivers high initial discharge capacity, enhanced rate capability and long-term cycling life. Besides, intrinsic diffusion and electrochemical storage behavior of Na+ ions were emphatically disclosed. This work paves a facile route for the synthesis of flexible and binder-free TMSs-based anode materials, promoting the practical application of wearable sodium-ion batteries.

Space–time upscaling of reactive transport in porous media

Reactive transport in saturated/unsaturated porous media is numerically upscaled to the space–time scale of a hypothetical measurement through coarse-grained space–time (CGST) averages. The reactive transport is modeled at the fine-grained Darcy scale by the actual number of molecules involved in reactions which undergo advective and diffusive movements described by global random walk (GRW) simulations. The CGST averages verify identities similar to a local balance equation which allow us to derive expressions for the flow velocity and the intrinsic diffusion coefficient in terms of averaged microscopic quantities. The latter are further used to verify the CGST-GRW numerical approach. The upscaling approach is applied to biodegradation processes in saturated aquifers and variably saturated soils and the CGST averages are compared to classical volume averages. One finds that if the process is characterized by slow variations in time, as in homogeneous reaction systems, the differences between the two averages are negligible. Instead, the differences are significant and can be extremely large in simulations of time-dependent biodegradation processes in both variably saturated soils and saturated aquifers.

Diagnosing and Correcting the Failure of the Solid-State Polymer Electrolyte for Enhancing Solid-State Lithium-Sulfur Batteries.

Solid-state polymer electrolytes (SPEs) attract great interest in developing high-performance yet reliable solid-state batteries. However, understanding of the failure mechanism of the SPE and SPE-based solid-state batteries remains in its infancy, posing a great barrier to practical solid-state batteries. Herein, the high accumulation and clogging of "dead" lithium polysulfides (LiPS) on the interface between the cathode and SPE with intrinsic diffusion limitation is identified as a critical failure cause of SPE-based solid-state Li-S batteries. It induces a poorly reversible chemical environment with retarded kinetics on the cathode-SPE interface and in bulk SPEs, starving the Li-S redox in solid-state cells. This observation is different from the case in liquid electrolytes with free solvent and charge carriers, where LiPS dissolve but remain alive for electrochemical/chemical redox without interfacial clogging. Electrocatalysis demonstrates the feasibility of tailoring the chemical environment in diffusion-restricted reaction media for reducing Li-S redox failure in the SPE. It enables Ah-level solid-state Li-S pouch cells with a high specific energy of 343Whkg-1 on the cell level. This work may shed new light on the understanding of the failure mechanism of SPE for bottom-up improvement of solid-state Li-S batteries.