Estimation Of Diffusion Coefficient Research Articles

A diffusion-prepared reduced FOV sequence for prostate MRI near metallic implants.

To enable diffusion weighted imaging in prostate patients with metallic total hip replacements in clinically feasible scan times for prostate cancer screening, and avoid distortion and dropout artifacts present in the conventionally used Echo Planar Imaging (EPI). A reduced field of view (FOV) diffusion-prepared sequence that is robust to the B inhomogeneities produced by total hip replacements was achieved using high radiofrequency (RF) bandwidth pulses and manipulation for stimulated echo pathways. The reduced FOV along the A/P direction was obtained using slice-select gradient reversal, and the prepared magnetization was imaged with a three-dimensional RF-spoiled gradient echo readout. The sequence was validated in phantom experiments, in vivo in healthy volunteers with and without total hip replacements, and in vivo in patients undergoing a standard MRI prostate exam. The proposed sequence is robust to shading and distortion artifacts that are encountered by standard diffusion-weighted EPI in the presence of moderate off-resonance. Apparent diffusion coefficient estimates obtained by the proposed sequence were comparable to those obtained with diffusion-weighted EPI. Acquisition of distortionless diffusion weighted images of the prostate is feasible in patients with total hip replacements on conventional, whole-body 3T MRI, using a b-value of 800 and nominal resolution of 1.7 1.7 4 mm3 in scan times of 6 min.

A transition in diffusion behaviors of organic liquid mixtures in dense polymer membranes

Multi-component mass transfer frameworks, such as the Maxwell-Stefan approach, parameterized with the pure component diffusion and sorption behaviors of different substances in polymer materials have been used in predicting complex mixture permeation through polymer membranes. However, a change in the physical state of a polymer membrane (e.g., swelling) or the polymer dynamics (e.g., plasticization) is likely when the membrane is exposed to a high activity organic solvent mixture with strong chemical affinity for the polymer. These changes complicate the accurate estimation of diffusion coefficients for mixtures of solvents based on knowledge of pure component diffusivities within the polymer. Here, we present 120 organic solvent reverse osmosis (OSRO) permeation test results for hydrocarbon liquid mixtures with varying compositions in three different polymers and compare the experimental results to the predictions of a Flory-Huggins coupled Maxwell-Stefan model with two different diffusion modalities. The effect of the chemical affinity between the mixture and the membrane – estimated by the Hansen solubility difference – on the diffusion behaviors of individual solvents permeating through the membrane was investigated via the usage of this model. Our work demonstrates that polymer membranes undergo a reduction for the effectiveness of diffusion-based separation near a specific threshold level of solubility difference (8 MPa0.5) from the mixture and that this difference is consistent across several different membrane materials.

Measurements of diffusion coefficient and kinetic diameter of acetone vapor via molecular tagging

The Molecular Tagging (MT) technique is a promising methodology for locally measuring velocity and temperature fields in rarefied gas flows. Recently, Molecular Tagging Velocimetry (MTV) has been successfully applied to gas flows in mini-channels in the continuum regime at high pressure and early slip-flow regime at lower pressure. As the operating pressure decreases, diffusion effects become more pronounced, and in MTV, they hinder the extraction of the correct velocity profile by simply dividing the displacement profile of the tagged molecular line by time of flight. To address this issue, a reconstruction method that considers Taylor dispersion was previously developed to extract the velocity profile, considering the diffusion effects of the tracer molecules within the carrier gas. This reconstruction method successfully extracted the correct velocity profile in the continuum flow regime. However, the method still faces challenges in the slip-flow regime. Since there is currently no consensus in the literature regarding the kinetic diameter value of acetone vapor, the diffusion coefficient estimation is uncertain especially at low pressures. This is why, in this study, we propose an original optical method to measure the diffusion coefficient of acetone vapor. This is achieved by linking the temporal evolution of the spatial photoluminescence distribution of acetone vapor to the diffusion coefficient via the Chapman-Enskog theory. Our research provides measurements of these parameters for a wide range of pressures (0.5–10 kPa) at ambient temperature.

(Invited) Comprehensive Analysis of Exciton Diffusion with Time-Resolved Fluorescence Spectroscopy, Anisotropy and Imaging

Excitons produced in materials play a crucial role in photo-energy conversion such as photovoltaics and electroluminescence devices. The temporal and spatial diffusion of excitons is a key factor for dominating the fundamental performance of optoelectronic materials. In this context, analysis of the exciton diffusion dynamics is an important issue for obtaining the rational design of the materials. Excitons diffusing in materials can be characterized by several parameters such as the energy level, orientation of the transition dipole moment and spatial distribution, and the detection of these properties is required for the comprehensive analysis. In the present study, we show time-resolved fluorescence methods for detecting the above relevant properties of excitons.First, time-resolved fluorescence spectroscopy is a basic technique for analyzing the exciton diffusion dynamics. Fluorescence intensity is detected as functions of observation wavelength and time, and the spectral intensity and shift of fluorescence bands provide information on the population of excitons and their energy level. For example, dynamic Stokes shift indicates downhill energy migration and excitons are trapped by the defective site in molecular aggregates. Second, fluorescence anisotropy can be a good indicator for tracking the exciton diffusion in amorphous materials. Fluorescence anisotropy is sensitive to orientation change in transition dipole moments (TDMs) between absorption and fluorescence. In systems where the relative orientation of adjacent molecules is different from each other, such as amorphous solids, the exciton diffusion is accompanied with the change in TDM. Thus, appropriate modeling of molecular alignment enables quantitative estimation of the exciton diffusion coefficient and diffusion length from the anisotropy signal. Finally, time-resolved imaging is a combination of time-resolved spectroscopy and super-resolution microscopy, and an emergent technique for visualizing real-space propagation of excitons in materials. The diffraction-limited excitation beam produces excitons in several hundreds of nanometers and the subsequent exciton diffusion is evaluated by the spatial width of the fluorescence spot. The temporal broadening of the fluorescence spot directly reflects the exciton distribution and we can intuitively obtain the diffusion coefficient and length. Unlike the conventional methods for bulk materials, the advantage of the time-resolved imaging is the applicability to materials with nano- and meso-scale heterogeneous structure and it enables site-selective evaluation of the exciton transport capability. In the conference site, we will also show the application of the above methods to supramolecular polymers and thermally activated delayed fluorescence materials. Figure 1

Mathematical Models for Estimating Diffusion Coefficients in Concentrated Polymer Solutions from Experimental Data

Diffusion processes in operations involving polymeric materials are of significant interest. Determining experimental values for diffusion coefficients is often challenging. Estimating these coefficients in concentrated polymer solution, polymer films, and membranes relies on experimental tests where the polymer is brought into contact with certain components/solvents. The diffusion coefficient values depend on the diffusion type, which is affected mainly by the nature of the polymer, concentration, and temperature. The literature presents an extensive amount of information regarding the diffusion phenomenon. This paper makes a particular contribution by showing how experimental data obtained from different applications can be processed to determine diffusion coefficients. The manuscript addresses some aspects regarding solvent diffusion in polymers, and illustrates how to determine the diffusion coefficients from experimental data. For specific cases of diffusion, several models for the predictive estimation of diffusion coefficients are also presented. Polymer–solvent systems such as polyvinyl alcohol (PVA)–water, cellulose acetate (CA)–tetrahydrofuran (THF) and cellulose triacetate (CTA)–dichloromethane (DCM) are investigated, with their diffusion mechanisms influenced by changes in structure caused by variations in concentration and temperature. The experimental data obtained through a gravitational technique allow for the highlighting of the diffusion mechanism and the selection of an appropriate mathematical model. A change in the structure of the polymer during the experiment leads to diffusion anomalies. Modeling the experimental data yielded diffusion coefficient values that vary based on the type of system investigated, composition and temperature. Thus, in the case of the CTA-DCM system, the diffusion coefficient at 303 K, at various concentration values, is in the range of 4.5 and 8·10−11 m2/s; for the PVA-H2O system, D = 4.1·10−12 m2/s at 303 K, and D = 6.5·10−12 m2/s at 333 K; while for the CA-THF system, the solvent–polymer diffusion coefficient has a value of 2.5∙10−12 m2/s at 303 K, and D = 1.75∙10−11 m2/s at 323 K. Mathematical models can be useful in studies regarding the drying of polymer films with complex structures, providing knowledge for designing or selecting suitable equipment.

Quantification of membrane fluidity in bacteria using TIR-FCS

Plasma membrane fluidity is an important phenotypic feature that regulates the diffusion, function, and folding of transmembrane and membrane-associated proteins. In bacterial cells, variations in membrane fluidity are known to affect respiration, transport, and antibiotic resistance. Membrane fluidity must therefore be tightly regulated to adapt to environmental variations and stresses such as temperature fluctuations or osmotic shocks. Quantitative investigation of bacterial membrane fluidity has been, however, limited due to the lack of available tools, primarily due to the small size and membrane curvature of bacteria that preclude most conventional analysis methods used in eukaryotes. Here, we develop an assay based on total internal reflection-fluorescence correlation spectroscopy (TIR-FCS) to directly measure membrane fluidity in live bacteria via the diffusivity of fluorescent membrane markers. With simulations validated by experiments, we could determine how the small size, high curvature, and geometry of bacteria affect diffusion measurements and correct subsequent measurements for unbiased diffusion coefficient estimation. We used this assay to quantify the fluidity of the cytoplasmic membranes of the Gram-positive bacteria Bacillus subtilis (rod-shaped) and Staphylococcus aureus (coccus) at high (37°C) and low (20°C) temperatures in a steady state and in response to a cold shock, caused by a shift from high to low temperature. The steady-state fluidity was lower at 20°C than at 37°C, yet differed between B. subtilis and S. aureus at 37°C. Upon cold shock, the membrane fluidity decreased further below the steady-state fluidity at 20°C and recovered within 30 min in both bacterial species. Our minimally invasive assay opens up exciting perspectives for the study of a wide range of phenomena affecting the bacterial membrane, from disruption by chemicals or antibiotics to viral infection or change in nutrient availability.

The influence of thermal diffusion on water migration through a porous insulation material

Excess water on pipes and equipment under porous insulation materials can lead to undesired corrosion. This work aims to clarify to what extent thermal diffusion affects the migration of water inside insulation materials subject to large temperature gradients. Since no experimental data is available on the thermal diffusion coefficients of humid air, revised Enskog theory for Mie fluids is used to estimate transport properties. Comparison to experimental data from literature shows that the theory reproduces the diffusion coefficient, viscosity and thermal conductivity of humid air within 8.7%, 5.0% and 3.5% respectively. The small discrepancies suggest that the theory can also provide reliable estimates of the thermal diffusion coefficients. In the investigated composition and temperature range, the theory predicts the Soret coefficient of water to be approximately ▪, while the Soret coefficient of oxygen varies from ▪ to +▪. A case study with heating of glass wool insulation containing humid air, encapsulating a cylindrical pipe is investigated. Non-equilibrium thermodynamics is used to consistently incorporate the Soret coefficients into the flux equations in a dynamic, non-isothermal model that includes diffusion, convection, thermal conduction and water sorption in the porous medium. With 50 K temperature difference across 5 cm of insulation, we find that at steady-state, thermal diffusion leads to a mole fraction of water in the gas phase that is about 1.5% higher at the hot location than if thermal diffusion is neglected.

Assessment of fitting methods and variability of IVIM parameters in muscles of the lumbar spine at rest.

Intravoxel incoherent motion (IVIM) MRI provides insight into tissue diffusion and perfusion. Here, estimates of perfusion fraction ( ), pseudo-diffusion coefficient ( ), and diffusion coefficient ( ) obtained via different fitting methods are compared to ascertain (1) the optimal analysis strategy for muscles of the lumbar spine and (2) repeatability of IVIM parameters in skeletal muscle at rest. Diffusion-weighted images were acquired in the lumbar spine at rest in 15 healthy participants. Data were fit to the bi-exponential IVIM model to estimate and using three variably segmented approaches based on non-linear least squares fitting, and a Bayesian fitting method. Assuming that perfusion and diffusion are temporally stable in skeletal muscle at rest, and spatially uniform within a spinal segment, the optimal analysis strategy was determined as the approach with the lowest temporal or spatial variation and smallest residual between measured and fit data. Inter-session repeatability of IVIM parameters was evaluated in a subset of 11 people. Finally, simulated IVIM signal at varying signal to noise ratio were evaluated to understand precision and bias. Experimental results showed that IVIM parameter values differed depending on the fitting method. A three-step non-linear least squares fitting approach, where , and were estimated sequentially, generally yielded the lowest spatial and temporal variation. Solving all parameters simultaneously yielded the lowest residual between measured and fit data, however there was substantial spatial and temporal variability. Results obtained by Bayesian fitting had high spatial and temporal variability in addition to a large residual between measured and fit data. Simulations showed that all fitting methods can fit the IVIM data at signal to noise ratios >35, and that was the most challenging to accurately obtain. Overall, this study motivates use of a three-step non-linear least squares fitting strategy to quantify IVIM parameters in skeletal muscle.

Thermodynamic uncertainty relations in the presence of non-linear friction and memory

A new thermodynamic uncertainty relation (TUR) is derived for systems described by linearly coupled Langevin equations in the presence of non-linear frictional forces. In our scheme, the main variable represents the velocity of a particle, while the other coupled variables describe memory effects which may arise from strongly correlated degrees of freedom with several time-scales and, in general, are associated with thermal baths at different temperatures. The new TUR gives a lower bound for the mean-squared displacement of the position of the particle, including its asymptotic diffusion coefficient. This bound, in several examples worked out here, appears to be a good analytical estimate of the real diffusion coefficient. The new TUR can be also applied in the absence of any external force (with or without thermal equilibrium between the baths), a case which usually goes beyond the scope of original TURs. We show applications to non-linear frictional models with memory, such as the Coulomb and the Prandtl-Tomlinson models, usually representative of friction at the nano-scale and within atomic-force microscopy experiments.

Diffusion-controlled growth and microstructural evolution between Pt and Pd containing B2-NiAl bondcoats and Ni-based single crystal superalloy

Pt-modified NiAl bond coats are used to extend the lifetime of blades in gas turbine engine applications. However, they suffer from the growth of deleterious precipitates within the interdiffusion zone. Partial substitution of Pt by Pd is advantageous in reducing the interdiffusion zone thickness between the bond coat and the superalloy, providing comparable oxidation properties, and critically reducing the propensity to form brittle (Pt,Ni)Al2 precipitates. In this study, we utilize the pseudo-binary diffusion couple method to estimate the interdiffusion coefficients of Ni and Al in Pd, Pd-Pt and Pt-modified nickel aluminides. Additionally, the main and cross-interdiffusion coefficients are estimated in the ternary diffusion couples. The estimated diffusion coefficients in the β-NiAl phase reflect on the thickness of the β phase in the superalloy bond coat interdiffusion zone. Pd reduces the pseudo-binary interdiffusion coefficients of Ni–Al and also decreases the main and cross-ternary interdiffusion coefficients. This correlates with the reduction of the interdiffusion zone thickness by Pd. The diffusion process is strongly assisted by point defects in this phase. Ab initio-informed defect calculations are done to explain diffusion retardation in the presence of Pd (compared to Pt) with decreased defect concentrations. Furthermore, through in-depth microstructure characterization performed by electron probe micro analyser, transmission electron microscopy, and atom probe tomography, the presence of σ, R and μ phases as TCP precipitates in the interdiffusion zone are identified. The results give insights into the coatings’ diffusional properties that influence the service life of the product.

Investigation of hydrothermal activity in the South West Indian ridge region using Ra isotopes and 227Ac as tracers

Hydrothermal vents have been shown to be important vectors for various chemical elements into the ocean. However, both the intensity of the chemical fluxes associated with these systems and the fate of the chemical elements along the plume are still largely overlooked. At two stations located above the South West Indian Ridge (SWIR), we investigate the distributions of the Ra quartet (223Ra, 224Ra, 226Ra and 228Ra) and 227Ac that have been used as tracers of hydrothermal activity. While the vertical distributions of 226Ra, 228Ra and 227Ac do not show a clear enrichment at depth, unusual signatures of excess 223Ra and 224Ra near the seafloor are attributed to the presence of a hydrothermal activity. The discrepancy observed between the different isotopes is attributed to different chemical reactivity when seawater circulates within the crust and/or to different regeneration rates within the fluid. A 1D diffusion model applied to the vertical profiles of short-lived Ra isotopes provided an estimation of the vertical eddy diffusivity coefficients (KZ) between 38 cm2 s−1 and 149 cm2 s−1. These high values suggest strong mixing likely favored by the complex bathymetry in the region. By combining these KZ with the vertical gradient of dissolved Fe (dFe), we estimate a vertical flux of dFe that ranges from 139 to 1173 nmol m−2 d-1. These results confirm that low-expansion-rate ridges could be significant sources of dFe to the deep ocean.

First coarse grain then scale: How to estimate diffusion coefficients of confined molecules.

An approach for approximating position and orientation dependent translational and rotational diffusion coefficients of rigid molecules of any shape suspended in a viscous fluid under geometric confinement is proposed. It is an extension of the previously developed scheme for evaluating near-wall diffusion of macromolecules, now applied to any geometry of boundaries. The method relies on shape based coarse-graining combined with scaling of mobility matrix components by factors derived based on energy dissipation arguments for Stokes flows. Tests performed for a capsule shaped molecule and its coarse-grained model, a dumbbell, for three different types of boundaries (a sphere, an open cylinder, and two parallel planes) are described. An almost perfect agreement between mobility functions of the detailed and coarse-grained models, even close to boundary surfaces, is obtained. The proposed method can be used to simplify hydrodynamic calculations and reduce errors introduced due to coarse-graining of molecular shapes.

Diffusion kinetics of ionic charge carriers across Ti3C2Tx MXene-aqueous electrochemical interfaces

Titanium carbide MXene -Ti3C2Tx - is a representative and well-employed electrode material for a variety of electrochemical energy storage applications. Despite exhibiting metal-like electronic conductivity, restacked Ti3C2Tx films show mediocre rate performance. Here, we report on the estimation of diffusion coefficients of aqueous cations (H+, Li+, Na+and Ca+2) across Ti3C2Tx MXene interlayer spaces by employing electrochemical impedance spectroscopy. Proton diffusivity across 2D slits is found to be 2.2 * 10−8 ± 0.4 * 10−8 cm2/s, which is three orders of magnitude slower than in bulk water. Such a sluggish diffusive behavior is attributed to interfacial confinement effects in the 2D space. It is found that protons diffuse three times faster than hydrated metal cations (Li+, Na+and Ca+2) through Ti3C2Tx slits and exhibit strong potential dependent behavior. Therefore, the rate performance of Ti3C2Tx MXene electrodes is limited by the ionic transportation in the 2D slits rather than electronic transport. This study provides insights into the engineering of open 2D electrode architectures for better ionic diffusive pathways towards the design of high rate MXene based energy storage devices.

Space and time on the membrane: modelling Type VI secretion system dynamics as a state-dependent random walk.

The type six secretion system (T6SS) is a transmembrane protein complex that mediates bacterial cell killing. The T6SS comprises three main components (transmembrane, baseplate and sheath/tube complexes) that are sequentially assembled in order to enable an attacking cell to transport payloads into neighbouring cells. A T6SS attack disrupts the function of essential cellular components of target cells, typically resulting in their death. While the assembled T6SS adopts a fixed position in the cell membrane of the attacking cell, the location of the firing site varies between firing events. In Serratia marcescens, a post-translational regulatory network regulates the assembly and firing kinetics of the T6SS in a manner that affects the attacking cell's ability to kill target cells. Moreover, when the ability of membrane complexes to reorient is reduced, an attacking cell's competitiveness is also reduced. In this study, we will develop a mathematical model that describes both the spatial motion and assembly/disassembly of a firing T6SS. The model represents the motion of a T6SS on the cell membrane as a state-dependent random walk. Using the model, we will explore how both spatial and temporal effects can combine to give rise to different firing phenotypes. Using parameters inferred from the available literature, we show that variation in estimated diffusion coefficients is sufficient to give rise to either spatially local or global firers.

Semi-analytical estimates for the chaotic diffusion in the Second Fundamental Model of Resonance. Application to Earth’s navigation satellites

We discuss the applicability of the Melnikov and Landau–Teller theories in obtaining semi-analytical estimates of the speed of chaotic diffusion in systems driven by the separatrix-like stochastic layers of a resonance belonging to the ‘second fundamental model’ (SFM) (Henrard and Lemaitre, 1983). Stemming from the analytic solution for the SFM in terms of Weierstrass elliptic functions, we introduce stochastic Melnikov and Landau–Teller models allowing to locally approximate chaotic diffusion as a sequence of uncorrelated ‘jumps’ observed in the time series yielding the slow evolution of an ensemble of trajectories in the space of the adiabatic actions of the system. Such jumps occur in steps of one per homoclinic loop. We show how a semi-analytical determination of the probability distribution of the size of the jumps can be arrived at by the Melnikov and Landau–Teller approximate theories. Computing also the mean time required per homoclinic loop, we arrive at estimates of the chaotic diffusion coefficient in such systems. As a concrete example, we refer to the long-term diffusion of a small object (e.g. Earth navigation satellite or space debris) within the chaotic layers of the so-called 2g+h lunisolar resonance, which is of the SFM type. After a suitable normal form reduction of the Hamiltonian, we compute estimates of the speed of diffusion of these objects, which compare well with the results of numerical experiments.

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.

Concepts for estimating all types of diffusion coefficients of NiCoFeCr multi-principal element alloys using two dissimilar or a combination of ideal and non-ideal pseudo-ternary diffusion couples

The estimation of diffusion coefficients in multicomponent system is facilitated by strategically designing diffusion couples with constrained diffusion paths. We have demonstrated methods of estimating tracer diffusion coefficients following three different combinations of diffusion profiles: (i) By intersecting a pseudo-ternary diffusion path with a rectilinear pseudo-binary diffusion path, (ii) by considering a combination of two dissimilar pseudo-ternary diffusion paths, and (iii) considering a combination of ideal and non-ideal pseudo-ternary diffusion paths with uphill diffusion characteristics. Equation schemes required for such analyses depending on the type of diffusion profiles are explained in detail. This approach relies on the availability of reliable thermodynamic data for the estimation of the tracer diffusion coefficients. Following, as demonstrated, one can calculate the intrinsic and interdiffusion coefficients of all the elements for a conventional diffusion couple in which all the elements would produce the diffusion profiles.

Diffusion-controlled growth mechanism of phases and the microstructural evolution in the Ni-Zn system

The diffusion-controlled growth mechanism of the phases and microstructural evolution in correlation to estimated diffusion coefficients are described in solid Ni-solid Zn and solid Ni-liquid Zn diffusion couples that mimic the hot-dip galvanization of Ni pre-coated steel. Contrary to earlier belief, the location of the Kirkendall marker plane is detected not at the δ-NiZn8/Zn interface but inside the δ-NiZn8 phase indicating the role of both the diffusing elements Ni and Zn on the evolution of duplex morphology in this phase. Further, the growth of γ1-NiZn3, and γ-Ni2Zn11 phase layers with distinct microstructures are identified contrary to the belief that there is only one intermediate phase γ-Ni2Zn11 over this composition range. This study explains the role of relative mobilities of the elements behind the characteristic microstructural evolution in this system of technological importance.

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.

Comparison of Lithium Diffusion Coefficient Measurements in Tellurium Electrodes via Different Electrochemical Techniques

Both thin (55 μm) composite and thick (350 μm) all active material battery porous electrodes were prepared for estimating the diffusion coefficient of Li+ ( in tellurium (Te) during electrochemical lithiation. Galvanostatic intermittent titration technique (GITT), cyclic voltammetry (CV), and electrochemical impedance spectroscopy (EIS) were applied to quantify the chemical lithium solid-state diffusion coefficient within the Te active material in the electrodes. Multiple methods of GITT and EIS were assessed. For the composite Te electrodes, the was on the order of 10−11 cm2 s−1 from both CV and GITT methods, but 10−9 cm2 s−1 from EIS. For the thick tellurium electrodes, both GITT and EIS resulted in lithium diffusion coefficient estimates in the range of 10−11–10−12 cm2 s−1. The general trend across all methods that quantified the diffusion coefficient as a function of lithiation of tellurium was that the decreased rapidly when the Te material was initially lithiated. The at the phase transition voltage plateau (∼1.7 V, vs Li/Li+, where both Te and Li2Te were expected) had the lowest while the both before and after the plateau was generally higher. Among all the electrochemical measurements of the modified GITT method with modelling the relaxation region resulted in relatively low scatter in the data, provided values as a function of lithiation, and was well suited to thick electrodes with a flat discharge plateau as was the case herein.