Tracer Diffusion Research Articles

Revealing Local Grain Boundary Chemistry and Correlating it with Local Mass Transport in Mixed-Conducting Perovskite Electrodes.

Grain boundary (GB) mass transport, and chemistry exert a pronounced influence on both the performance and stability of electrodes for solid oxide electrochemical cells. Lanthanum strontium cobalt ferrite (LSCF6428) is applied as a model mixed ionic and electronic conducting (MIEC) perovskite oxide. The cation-vacancy distribution at the GBs is studied at both single and multi-grain scales using high-resolution characterization techniques and computational approaches. The accumulation of oxygen vacancies ( ) in the GB region, rather than necessarily at the GB core, results in an enhancement of the oxygen diffusivity by 3 - 4 orders of magnitude along the GBs (Dgb). At 350°C, the oxygen tracer diffusion coefficient (D*) is measured as 2.5 × 10-14 cm2s-1. The Dgb is determined to be 2.8 × 10-10 cm2s-1 assuming a crystallographic GB width (δcrystal) of 1nm, and 2.5 × 10-11 cm2s-1 using a chemically measured δchem of 11.10nm by atom probe tomography (APT). The origin of the concomitant changes in the cation composition is also investigate. In addition to the host cations, strong Na segregation is detected at all the GBs examined. Despite the low (ppm) level of this impurity, its presence can affect the space charge potential (Φ0). This, in turn, will influence the evolution of GB chemistry.

Thermodynamics and kinetics of long-range ordering in FCC Ni-33at.%Cr alloys: Insights from atomic scale modeling

This study investigates the thermodynamics and kinetics of the Ni-Cr system, focusing specifically on the kinetics of the order–disorder phase transformation in the Ni-33at.%Cr alloy. Combining density functional theory, CALPHAD-type models, and experimental diffusion data, we introduce and validate an efficient pair interaction model (PIM) and use it in Monte Carlo simulations. Our results include a detailed phase diagram of Ni-Cr in face-centered cubic structure and kinetic models that delineate the behavior of solid solutions at high temperatures and ordered structures at low temperatures. The simulations shed light on tracer diffusion and ordering kinetics within Ni-33at.%Cr, demonstrating good agreement with existing experimental data. Furthermore, our simulation-driven insights prompt a reevaluation of certain aspects of related experimental studies concerning the apparent ordering activation enthalpies and growth kinetics. We also provide a thorough discussion on the strengths of our models and features for future improvement.

The effects of vacancy ordering on diffusion: a statistical study

In this paper we investigate the interconnection between vacancy-ordered phases and vacancy self-diffusion. Here, we investigate three ordered phases on a square lattice with energetics defined by two separate Hamiltonians. In the first case we used a classical antiferromagnetic Ising model Hamiltonian in order to generate a 'checkerboard' type ordered structure. In the second case, we used a modified Ising model with competing influence of second and third nearest-neighbors, which resulted in both 'hatch' and 'labyrinthine' structures, depending on concentration. To understand how vacancy-ordering affects diffusion, we determined the tracer diffusivity using rejection-free kinetic Monte Carlo and compared disordered and ordered structures. Finally, we developed an analytical model describing diffusion in the ordered 'checkerboard' structure and found that it was able to predict apparent activation energies in the ordered and disordered structures. Our results suggest that it is short-range order rather than long-range order that most significantly affects tracer diffusion.

An STM study on the diffusion of O atoms on a CO-covered Ru(0001) surface—The role of domain boundaries

We investigate tracer diffusion at the domain boundaries in an adsorption layer, an effect that corresponds to grain boundary diffusion in 3D polycrystalline solids. Experiments were performed on adsorbed O atoms on a Ru(0001) surface in a layer of CO molecules. The CO molecules form a (3x3)R30∘ structure which displays translational domains. High-speed scanning tunneling microscopy (STM) was used to image the motion of the O atoms. The data show that single O atoms preferentially move along the domain walls which in the STM movies appear as disordered, fluctuating stripes between the ordered domains. The diffusion coefficient of the O atoms is one order of magnitude higher than the diffusion coefficient in the ordered domains. By comparison with previous experiments on completely disordered CO layers, it is concluded that the diffusion is similarly promoted by the enhanced fluctuations in the disordered domain walls.

SENECA study: staging endometrial cancer based on molecular classification

ObjectiveManagement of endometrial cancer is advancing, with accurate staging crucial for guiding treatment decisions. Understanding sentinel lymph node (SLN) involvement rates across molecular subgroups is essential. To evaluate SLN involvement...

Fundamental Thermodynamic, Kinetic, and Mechanical Properties of Lithium and Its Alloys.

Lithium alloying reactions are beneficial in promoting uniform plating and stripping of lithium metal in all-solid-state batteries. First-principles calculations are performed to predict thermodynamic, kinetic, and mechanical properties of lithium and several important Li-M alloys (M = Mg, Ag, Zn, Al, Ga, In, Sn, Sb, and Bi). While the Li-Mg binary system forms a solid solution, most other lithium-metal alloys prefer stoichiometric intermetallic compounds with common local motifs that enable fast Li diffusion. Lithium and Li-rich alloys exhibit an unusually flat energy landscape along paths that connect BCC to close-packed structures like FCC and HCP, with important implications for mechanical properties. Very low migration barriers for Li diffusion that rival those of superion conductors are predicted, both in pure Li and in Li-M intermetallics. However, vacancy concentration, which is crucial for substitutional diffusion, is predicted to be low in metallic Li and most Li-M intermetallics. Compounds such as B32 LiAl and LiGa as well as D03 Li3Sb and Li3Bi exhibit structural vacancies at higher ends of their voltage windows, which together with low migration barriers leads to exceptionally high Li mobilities. In the Li-Mg solid solution, the addition of Mg is found to decrease the vacancy tracer diffusion coefficient by an order of magnitude.

A high-throughput flowless microfluidic single and multi-solute concentration gradient generator: Design and parametric study.

Microfluidic concentration gradient generators (μ-CGGs) are critical in various biochemical assays, including cell migration, drug screening, and antimicrobial susceptibility testing. However, current μ-CGGs rely on integration with flow systems, limiting their scalability and widespread adoption owing to limited infrastructure and technical expertise. Hence, there is a need for flowless diffusional gradient generators capable of standalone operation, thereby improving throughput and usability. In this study, we model such a diffusional μ-CGG as an infinite source-sink system to capture two characteristic timescales: (i) gradient generation dictated by the diffusion timescale and (ii) stability determined by the rate of change in reservoir concentrations. Through finite-element simulations, we explored the influence of various geometric parameters such as the channel length, cross-sectional area, node and reservoir volumes, and the solute diffusivity on these timescales, along with experimental confirmation using fluorescent tracer diffusion. Our results show that while the gradient stability strongly depends on the reservoir volumes, diffusion length, and solute diffusion coefficient, they are independent of the node shape or the shape of the channel cross section. However, gradient profiles were found to be the strong functions of the diffusion length, solute diffusivity, and the geometric pattern of the microfluidic grid. Additionally, we showcased the versatility of the design by generating discrete gradient profiles and combinatorial gradients of two and three solutes, thus improving throughput in a wide range of on-chip biological assays. These findings underscore the potential of our microfluidic device as an easy-to-use, inexpensive, efficient, and high-throughput platform for various on-chip biological assays.

Introducing concepts of estimating tracer and intrinsic diffusion coefficients in a ternary system: a case study in the FCC Fe-Mn-Cr solid solution

ABSTRACT Estimating tracer and intrinsic diffusion coefficients following the diffusion couple method with systematic composition variation can be challenging because of the diffusion paths’ serpentine or double serpentine nature on the Gibbs triangle. Moreover, the possibility of estimating these diffusion coefficients from a single diffusion profile can have immense benefits. We have demonstrated four ways of estimating tracer and impurity diffusion coefficients in the FCC Fe-Mn-Cr solid solution: (i) We have shown that these can be estimated directly at the Kirkendall marker plane from a single conventional ternary diffusion profile. (ii) We have, for the first time, demonstrated that the estimation at the intersection of a conventional ternary and constrained pseudo-binary diffusion path is helpful for systematically generating composition-dependent tracer diffusion coefficients. (iii) We have followed the Kirkaldy-Lane method for estimating these diffusion coefficients at the intersection of two conventional ternary diffusion couples (for comparison of the data measured by new methods), although for data generation at random compositions. This was proposed a long time ago but practised occasionally. It helps to compare with the estimated data following other methods. (iv) Additionally, we have estimated the impurity diffusion coefficients of Cr and Mn in Fe following the Hall method, which helps in understanding the variation of the diffusion coefficients in Fe-Mn-Cr alloys compared to pure Fe. The sensitivity of data estimation following different methods, i.e. different equation schemes, is discussed, explaining the strategic design of diffusion couple for a small error range.

Prediction of diffusion coefficients in aqueous systems by machine learning models

Currently there are no accurate models for the prediction of diffusion coefficients at infinite dilution in aqueous systems. Frequently, models that work well for polar solvents often perform worse in the case of water. At the same time, experimental data of tracer diffusion coefficients are scarce and can be impractical to measure when information on this important transport property is required. In this work, machine learning models were developed to predict the tracer diffusion coefficient of any solute in water at atmospheric pressure. Several approaches were carried out to construct the model, using different types of input parameters: pure component properties and theoretical molecular descriptors, such as atom counts, structural fragments and fingerprints, computed using different sources. A database of 126 systems (1192 data points) was used for training and the best model showed a global average absolute relative deviation (AARD) of 3.92%, with a maximum deviation of 24.27% on the test set. This model uses as inputs the temperature and 195 molecular descriptors computed using the RDKit cheminformatics package, which can be automatically calculated from a molecular identifier thus making the model very simple to use. In comparison, the well-known Wilke-Chang equation provided an AARD of 13.03% in the same test set, demonstrating the improved accuracy of the proposed solution. The models developed in this work are provided at github.com/EgiChem/ml-D12-water-app.

Do Entangled Polymer Chains Reptate?

AbstractNeutron spin echo spectroscopy of entangled polymer melts [M. Zamponi, et al. J. Phys. Chem. B 2008, 112, 16220], and of tracer diffusion of short polymer chains in highly entangled polymer melt [M. Zamponi et al. Phys. Rev. Lett. 2021, 126, 187801.] and [M. Kruteva et al. Macromolecules 2021, 54, 11384] found the center‐of‐mass mean‐square displacements at shorter times are subdiffusive, heterogeneous, non‐Gaussian, and cooperative. These properties contradict the assumption of reptation within the tube in the tube‐reptation (TR) model, but are in accord with the predictions from the many‐chain cooperative dynamics in the theory of Guenza. The inadequacy of the TR model revealed by the microscopic experiments and theory motivates the author to reexamine previously published data of diffusion of entangled polymer chains from experiments and simulations used to test the TR model. The results reported in this study lead to the conclusion that the key predictions of the TR model are at variance with experimental and simulation data. The cause lies in the reptation hypothesis contradicting the cooperative nature of entangled chain diffusion proven by its dynamics being isomorphic to cooperative diffusion in other materials. The Coupling Model has predictions consistent with the cooperative diffusion properties in interacting materials [Prog. Mater. Sci., 2023, 139, 101130.]. Applied to the entangled polymers, the predictions successfully explain the data, especially those contradicting the TR model. Thus, diffusion of entangled polymer chains is a cooperative many‐chain process in having the universal properties of many‐body cooperative diffusion established in many other interacting materials, and the reptation hypothesis is unwarranted.

An experimental estimation method of diffusion coefficients in ternary and multicomponent systems from a single diffusion profile

Until recently, it was textbook knowledge that the diffusion coefficients could not be estimated in a multi-component system following the widely practised diffusion couple method. The recently proposed constrained diffusion couple method largely solved the problems. The need to produce two intersecting diffusion paths in a multi-component space with very well-controlled compositions of the diffusion couple end members may be tricky in certain situations, depending on the complications of diffusion paths. In this study, we have shown the estimation of all types of diffusion coefficients from a single diffusion profile without neglecting Onsager's cross terms in concentrated ternary Ni-Co-Fe, Fe-rich quaternary Fe-Ni-Co-Cr and concentrated Ni-Co-Fe-Cr-Al quinary alloys. This is applicable in ternary and multicomponent component systems (n≥3) at a stable Kirkendall marker plane position. One can even estimate the impurity diffusion coefficients utilizing the composition profiles at the ends of the diffusion couples following the Hall method, which has been rarely practised in multicomponent systems until now. We have further demonstrated the importance of estimating the tracer and intrinsic diffusion coefficients in a concentrated or multi-principal element alloy in which interdiffusion coefficients can be vague and misleading for understanding the elements' diffusional interactions and relative mobilities. We have also shown the importance of considering the vacancy wind effect in concentrated alloys. The method proposed in this study will help to generate a mobility database with relative ease in various multicomponent systems important for various applications, which was considered impossible until recently.

Impact of sulfur addition on the structure and dynamics of Ni–Nb alloy melts

We investigated the change in the structure and dynamics of a Ni–Nb bulk metallic glass upon sulfur addition on both microscopic and macroscopic scales. With the sulfur concentration of 3 at. %, where the composition Ni58Nb39S3 exhibits the best glass forming ability in the investigated sulfur concentration range, both the equilibrium and undercooled melt dynamics remain almost unchanged. Only in the glassy state does sulfur seem to result in mass transport less decoupled to the viscosity of the undercooled liquid, where the measured Ag tracer diffusion coefficient is slower in the ternary alloy. With the structural disorder introduced by the alloying sulfur, the improved glass forming ability is attributed to geometrical frustration, where crystal nucleation requires a depletion of sulfur and hence long range diffusion, as long as no primary sulfur-containing crystalline phase is involved.

High-throughput approach for investigating interdiffusion in medium- and high-entropy alloys

Interdiffusion experiments are usually time-consuming and tedious since diffusion couples must be annealed at several temperatures for a long time. The efforts required to study interdiffusion in multicomponent alloys increase dramatically as multiple diffusion couples are required to cover broad composition ranges and determine the diffusivities of individual elements in different chemical environments. To circumvent this challenge, we present a high-throughput approach applicable to single-phase and compositionally complex alloys, which are assumed to approximate ideal solid solutions. Here, a simple diffusion-multiple experiment combined with a physically based kinetic model is proposed to efficiently determine the diffusion coefficients of the constituent elements in quaternary CrFeCoNi alloys. Compared with tracer diffusivities reported in the literature, the results, thus, obtained do not differ by more than a factor of 2 and were obtained from a single interdiffusion experiment. In contrast, the diffusivities simulated with commercial mobility and thermodynamic databases are strongly overestimated by a factor ranging from 1 to 16. Therefore, our approach enables high-throughput determination of diffusivities and can help in the design of alloys for high-temperature applications where diffusion plays a key role.

An investigation of self-interstitial diffusion in α-zirconium by an on-the-fly machine learning force field

The on-the-fly machine learning force field approach, based on the Gaussian approximation potential and Bayesian error estimation, was used to study the diffusion of self-interstitial atoms in α-zirconium. Ab initio molecular dynamics simulations of lattice vibration and interstitial diffusion at different temperatures were employed to develop the force field. The radial and angular descriptors of the potential were further optimized to achieve better agreement with first-principles results. Subsequent long-term diffusion simulations were performed to assess the diffusion behavior based on the obtained force field. Tracer diffusion coefficients and diffusion anisotropy were studied at temperatures of 600–1200 K, and the Bayesian errors were estimated throughout the diffusion simulations. The mean and maximum estimated Bayesian errors of atomic force were approximately twice as large as those observed during the learning period. The basal diffusion was greatly favored compared to the interstitial diffusion along the c-axis, consistent with previous simulations based on first-principles results and classical potentials. The accuracy and applicability of the current on-the-fly machine learning approach were critically evaluated.

Influence of salinity gradients on the diffusion of water and ionic species in dual porosity clay samples

Most of the available data on diffusion in natural clayey rocks consider tracer diffusion in the absence of a salinity gradient despite the fact that such gradients are frequently found in natural and engineered subsurface environments. To assess the role of such gradients on the diffusion properties of clayey materials, through-diffusion experiments were carried out in the presence and absence of a salinity gradient using salt-diffusion and radioisotope tracer techniques. The experiments were carried out with vermiculite samples that contained equal proportions of interparticle and interlayer porosities so as to assess also the role played by the two types of porosities on the diffusion of water and ions. Data were interpreted using both a classical Fickian diffusion model and with a reactive transport code, CrunchClay that can handle multi-porosity diffusion processes in the presence of charged surfaces. By combining experimental and simulated data, we demonstrated that (i) the flux of water diffusing through vermiculite interlayer porosity was minor compared to that diffusing through the interparticle porosity, and (ii) a model considering at least three types of porous volumes (interlayer, interparticle diffuse layer, and bulk interparticle) was necessary to reproduce consistently the variations of neutral and charged species diffusion as a function of salinity gradient conditions.

Size Sensitivity of Metabolite Diffusion in Macromolecular Crowds.

Metabolites play crucial roles in cellular processes, yet their diffusion in the densely packed interiors of cells remains poorly understood, compounded by conflicting reports in existing studies. Here, we employ pulsed-gradient stimulated-echo NMR and Brownian/Stokesian dynamics simulations to elucidate the behavior of nano- and subnanometer-sized tracers in crowded environments. Using Ficoll as a crowder, we observe a linear decrease in tracer diffusivity with increasing occupied volume fraction, persisting─somewhat surprisingly─up to volume fractions of 30-40%. While simulations suggest a linear correlation between diffusivity slowdown and particle size, experimental findings hint at a more intricate relationship, possibly influenced by Ficoll's porosity. Simulations and numerical calculations of tracer diffusivity in the E. coli cytoplasm show a nonlinear yet monotonic diffusion slowdown with particle size. We discuss our results in the context of nanoviscosity and discrepancies with existing studies.

Inferring Tracer Diffusivity From Coherent Mesoscale Eddies

AbstractMixing along isopycnals plays an important role in the transport and uptake of oceanic tracers. Isopycnal mixing is commonly quantified by a tracer diffusivity. Previous studies have estimated the tracer diffusivity using the rate of dispersion of surface drifters, subsurface floats, or numerical particles advected by satellite‐derived velocity fields. This study shows that the diffusivity can be more efficiently estimated from the dispersion of coherent mesoscale eddies. Coherent eddies are identified and tracked as the persistent sea surface height extrema in both a two‐layer quasigeostrophic (QG) model and an idealized primitive equation (PE) model. The Lagrangian diffusivity is estimated using the tracks of these coherent eddies and compared to the diagnosed Eulerian diffusivity. It is found that the meridional coherent eddy diffusivity approaches a stable value within about 20–40 days in both models. In the QG model, the coherent eddy diffusivity is a good approximation to the upper‐layer tracer diffusivity in a broad range of flow regimes, except for small values of bottom friction or planetary vorticity gradient, where the motions of same‐sign eddies are correlated over long distances. In the PE model, the tracer diffusivity has a complicated vertical structure and the coherent eddy diffusivity is correlated with the tracer diffusivity at the e‐folding depth of the energy‐containing eddies where the intrinsic speed of the coherent eddies matches the rms eddy velocity. These results suggest that the oceanic tracer diffusivity at depth can be estimated from the movements of coherent mesoscale eddies, which are routinely tracked from satellite observations.

Tracer dynamics in polymer networks: Generalized Langevin description.

Tracer diffusion in polymer networks and hydrogels is relevant in biology and technology, while it also constitutes an interesting model process for the dynamics of molecules in fluctuating, heterogeneous soft matter. Here, we systematically study the time-dependent dynamics and (non-Markovian) memory effects of tracers in polymer networks based on (Markovian) implicit-solvent Langevin simulations. In particular, we consider spherical tracer solutes at high dilution in regular, tetrafunctional bead-spring polymer networks and control the tracer-network Lennard-Jones (LJ) interactions and the polymer density. Based on the analysis of the memory (friction) kernels, we recover the expected long-time transport coefficients and demonstrate how the short-time tracer dynamics, polymer fluctuations, and the viscoelastic response are interlinked. Furthermore, we fit the characteristic memory modes of the tracers with damped harmonic oscillations and identify LJ contributions, bond vibrations, and slow network relaxations. Tuned by the LJ interaction parameter, these modes enter the kernel with an approximately linear to quadratic scaling, which we incorporate into a reduced functional form for convenient tracer memory interpolation and extrapolation. This eventually leads to highly efficient simulations utilizing the generalized Langevin equation, in which the polymer network acts as an additional thermal bath with a tunable intensity.

Diffusion in ultra-fine-grained CoCrFeNiMn high entropy alloy processed by equal-channel angular pressing

Grain boundary diffusion in severely plastically deformed (SPD) CoCrFeMnNi high entropy alloy (HEA) has been studied by applying the tracer diffusion technique. After two passes of equal channel angular pressing (ECAP), three untra-fast diffusion paths in ECAP-processed CoCrFeMnNi HEA were distinguished, which were identified with twin boundaries, high-angle grain boundaries and porosity defects. The enhanced diffusivity is induced by a high strain localization in the vicinity of interfaces in a deformation-induced non-equilibrium state that is correlated with the pronounced deformation twinning due to the low stacking fault energy of the material.

Activation energy and molecular weight dependence of cooperative tracer chains diffusion in highly entangled polymer melts

AbstractThe generalized Langevin equation for cooperative dynamics of Guenza predicts the dynamics of chains in entangled polymers is cooperative with anomalous properties, and at variance with the tube‐reptation model. The center‐of‐mass mean‐square displacements at shorter times are subdiffusive with with β < 1, contradicting the common assumption of reptation within the tube. At some longer time the subdiffusive dynamics exhibits the crossover to free diffusion with . Moreover the subdiffusive dynamics is heterogeneous, non‐Gaussian, and cooperative. These predictions have been confirmed by using neutron spin echo spectroscopy in entangled polyethylene melts [M. Zamponi, et al. J. Phys. Chem. B 2008, 112, 16220], and in tracer diffusion of short polyethylene chains in a highly entangled polyethylene melt [M. Zamponi et al. Phys. Rev. Lett. 2021, 126, 187801]. The latter was confirmed in poly(ethylene oxide) tracer diffusion in highly entangled poly(ethylene oxide) melt [M. Kruteva et al. Macromolecules 2021, 54, 11384]. Notwithstanding, there are other important data sets obtained in the NSE experiments but were left unexplained. One set consists of the activation energies of the Arrhenius temperature dependence of D for each tracer. Another is the molecular weight dependence of D of the tracers determined at the same temperature. In this article the predictions of the Coupling Model are applied to these two sets of data. Good quantitative agreements of the CM predictions with experimental data provide additional support to the cooperativity dynamics of entangled polymers as concluded by others. Additionally, all the properties of cooperative diffusion of entangled polymer chains are shown to be isomorphic to those found in cooperative diffusions in totally different systems. Diffusion in all are governed by interaction between the diffusing units, and from which the universal properties originate.