Temperature Dependence Of Diffusion Coefficient Research Articles

High-fidelity phase-field simulation of solid-state sintering enabled by Bayesian data assimilation using in situ electron tomography data

Experimental observation methods for understanding industrially important solid-state sintering are essential for the development of new materials and devices. To experimentally characterize solid-state sintering, the limitations posed by the complexity of target materials, experimental equipment, and observation conditions must be overcome. Therefore, hybrid techniques for predicting sintering behavior based on experimental datasets and physics-based simulation models are highly sought after. Herein, we propose a new technique for combining a physics-based model and experimental observation results from solid-state sintering using a nonsequential Bayesian data assimilation (DA) method. The proposed technique assimilates experimental data—obtained using in situ electron tomography/scanning transmission electron microscopy—into the corresponding phase-field (PF) model to enable high-fidelity PF simulations by estimating multiple material parameters included in the PF model. This study demonstrates the inverse estimation of seven parameters, including temperature-dependent diffusion coefficients, from the time-series information on the morphology of sintered nanoparticles observed in situ. The estimated parameters provide the high-fidelity PF simulation to capture the observed solid-state sintering of copper nanoparticles. Thus, this study contributes to the construction of digital twins for solid-state sintering based on DA-integrated PF simulations and in situ observation datasets and deepens our understanding of the sintering process.

Using Brownian model to study the effect of temperature on diffusion coefficient

This study employs molecular simulation techniques, particularly the Brownian motion model, to investigate the influence of temperature on diffusion coefficients. Leveraging Einsteins relationship for calculating diffusion coefficients and a one-dimensional random walk model, we systematically explore the impact of simulation direction, particle quantity, and simulation duration on diffusion behavior. The research extends its scope to three-dimensional Brownian motion simulations, offering insights into the stochastic motion of particles in a fluid. The primary objective is to analyze the relationship between temperature and diffusion coefficients. Through rigorous linear regression analysis, a significant and strong linear association is identified, demonstrating that an increase in temperature correlates with an increase in the diffusion coefficient. The research not only contributes to the fundamental understanding of molecular motion but also provides practical recommendations for simulation parameters, especially in resource-constrained computational environments. The study acknowledges certain limitations in the current Brownian motion algorithm and proposes avenues for future research to enhance computational efficiency and precision. This abstract encapsulates the key methodologies, findings, and implications of the research, laying the foundation for a comprehensive exploration of temperature-dependent diffusion coefficients in molecular systems.

Electrochemical behavior of aluminum in 1-ethyl-3-methylimidazolium chloroaluminate ionic liquids

The mechanism of electrochemical oxidation and reduction of aluminum in 1-ethyl-3-methylimidazolium-based (EMImCl) chloroaluminate ionic liquids is studied across the concentration range of N = 1.1–2.0 (N the molar ratio of AlCl3 to EMImCl) at temperatures between 303 K and 418 К. Anodic stationary polarization curves (SPCs) indicate that the process of anodic dissolution of aluminum is complicated by passivation. The current density in the passive region and the passivation potential decrease with a higher concentration of Al2Cl7– ion in the melt. To elucidate the processes taking place at the aluminum electrode, the relationship between the concentration of the ions in the vicinity of the electrode and the potential applied in the cathodic and anodic region was analyzed by in-situ Raman spectroscopy for the concentrations of N = 1.1 and 2.0. The resulting dependences of relative peak intensity vs. potential correlate with the cathodic and anodic polarization curves. In the anodic region the content of Al2Cl7– grows with the potential, while the concentration of AlCl4– ion decreases. In the cathodic region the opposite process is observed: the concentration of Al2Cl7– decreases and that of AlCl4–increases with growing potential. It is shown that a precipitate of AlCl3 forms on the electrode surface in the region of passive aluminum dissolution, which is responsible for the electrode passivation. Based on the results obtained, we propose a model for the process of aluminum oxidation/reduction preceded and followed by a chemical reaction of aluminum chloride formation for the cathodic and anodic process, respectively. Temperature dependences of diffusion coefficients are studied by chronopotentiometry. The results indicate that diffusion coefficients are not affected by the concentration across the temperature range studied. The activation energy for diffusion was found to be 13.65 kJ∙mol−1. Impedance spectroscopy was used to investigate the concentration and temperature dependences of exchange current density. The exchange currents increase with increasing aluminum chloride content in the melt. The transfer coefficient and electrochemical reaction rate constant were found to be α = 0.17 ± 0.04, ks = (1.7 ± 0.4)∙10−6 cm∙s−1, respectively. The activation energy for the electrochemical reaction rate constant does not depend on the concentration and was found to be 33.5 kJ∙mol−1.

Carbon solute drag effect on the growth of carbon supersaturated bainitic ferrite: Modeling and experimental validations

The carbon partitioning and lengthening rate of bainitic ferrite (αb) are excellent experimental parameters to estimate our level of understanding of the mechanism of bainitic transformation from a continuum perspective and our ability to capture it in analytical expressions. For Fe-C alloys and relatively simple steels the classical Zener-Hillert theory captures the bainitic transformation rather well but mispredicts the level of carbon in solution in the bainite and overestimates the lengthening rates for transformations at lower temperatures. To address this issue, this paper presents a new thermo-kinetic model based on the Zener-Hillert theory and the Gibbs energy balance concept to simulate the lengthening behavior of αb in the Fe-C and low alloyed steels. The model incorporates the effect of the temperature dependent carbon diffusion within the migrating interface via a temperature dependent ferrite/austenite interfacial energy and a temperature dependent diffusion coefficient but does not impose local equilibrium across the interface. The good agreement between the model predictions and nine sets of published experiments indicates that both the carbon supersaturation in αb and the slower lengthening rate are caused by carbon diffusion within the migrating interface. It is found that the degree of carbon supersaturation in αb increases significantly with decreasing temperature. Consequently, the enhanced carbon solute drag effect, resulting from carbon diffusion within the interface, strongly retards the lengthening rates of αb at lower temperatures. Transformation strain is shown to have a modest effect on the lengthening rates but to lower the degree of carbon supersaturation.

Modeling of CO Oxidation by Diffusion of Oxygen Atoms in Ceria-Zirconia Particulates in a Three-Way Catalyst Particle Membrane Filter

In order to design a microporous membrane filter comprising Three-way Catalyst (TWC) particles with a size distribution of 1 to 2 microns, isothermal CO oxidation experiments and numerical simulations were conducted to investigate the transport of oxygen atoms within primary Ceria-Zirconia (CZ) particulates. These spherical TWC particles were fabricated through the agglomeration of primary CZ and alumina particulates, incorporating Pd and Rh catalysts. By comparing experimental CO2 emissions with simulation results over time, a temperature-dependent diffusion coefficient was determined. The simulation results reveal that the effective distance of oxygen atom transport within CZ particulates, heterogeneously distributed in the spherical TWC particle, is limited to approximately 100 nm from the surface of agglomerated spherical TWC particles within a temperature range of 175 to 225°C.

Enhanced nucleation of bimodal molecular weight distribution polymers: A molecular dynamics study

We perform coarse-grained molecular dynamics (CGMD) simulations to study the homogeneous nucleation of bimodal and unimodal molecular weight distribution polymers with equivalent average molecular weight. First, a statistical method is proposed to determine the critical nuclei and thus calculate the free energy barrier of nucleation. From the temperature dependence of diffusion coefficient, we also determine the activation energy of diffusion. Then we calculate the nucleation rate and find that it is consistent with the classical nucleation theory for homogeneous nucleation in semi-crystalline polymers. Compared with unimodal system, the bimodal system exhibits lower interfacial free energy and consequently lower free energy barrier for nucleation, while the two systems have similar activation energy for diffusion. This suggests that the promoted nucleation rate of bimodal molecular weight distribution polymer is a result of the reduction of interfacial free energy, which is eventually a consequence of chain-folding nucleation of long chain component.

Unified description for the temperature dependence of mobility in liquids.

The physical mechanisms governing molecular mobility in liquids remain unresolved. Whether distinct mechanisms govern mobility in the Arrhenian and super-cooled regions, and whether the mobility in these regions can be unified remain open questions. Here, molecular dynamics simulations were used to search for a structural property with a temperature dependence related by a simple functional form to the temperature dependent translational diffusion coefficient, Dtrans. The logarithm of Dtrans was found to be a two-parameter function of F2, where F2 is the mean squared-force per molecule. The relationship is demonstrated for all systems investigated: a three-bead model of ortho-terphenyl, an 80:20 binary mixture of Lennard-Jones spheres, and a system of Lennard-Jones dumbbells. For each system, the relationship holds for the entire range of temperatures under both constant pressure and constant density conditions. The same F2-based expression describes the translational diffusion coefficient in the Arrhenian, crossover, and super-Arrhenian regions.

Unraveling The Role of Oxygen and Manganese Charge Compensation During Nucleation and Crystal Growth of Li-rich Layered Li1.2Mn0.8O2 Cathode Materials

The electrochemical performance of Li-rich layered manganese oxide (LMO) cathodes is greatly affected by the oxygen release and irreversible transition metal (TM) migration. Such structural instabilities are the driving force behind structural reconstruction, rapid voltage decay, and capacity fade in LMR cathodes. This is due to the inability to retain a layered-layered phase during cycling hence the inability to maintain a consistent conductive ion flow (lithiums). Herein, we report for the first time, exploration of manganese and oxygen-compensated nanostructures to investigate its role in the structural morphology and microstructure. The nanostructures were studied using the molecular dynamics simulation method owing to its ability to simulate nucleation and crystal growth. According to the analysis, the simulated nanospheres yielded multi-grained and single crystalline phases for Mn and O compensation, respectively. Further analysis illustrated severe Li/O loss in the structure when the role of oxygen is neglected. Moreover, the formation of layered-layered-spinel composites is demonstrated together with the comparison of temperature-dependent diffusion coefficients. This goes to show that both oxygen and manganese play a crucial role during the cycling process of Li-rich cathode materials. These findings can provide important insights into understanding diffusion and ageing mechanisms in cathode materials during the cycling processes.

Impurity influence on the hydrogen diffusivity in B2–TiFe

The projector augmented-wave method within the electron density functional theory is used for calculations of the hydrogen absorption energy and its migration barriers in the doped B2–TiFe. An analytical expression for the temperature-dependent diffusion coefficients of the hydrogen in the doped alloy is derived using Landman's method. An approach for estimation of the average jump rates of hydrogen that are necessary for calculations of the diffusion coefficient in the doped alloys is developed. The activation energy of hydrogen diffusion and the pre-exponential factor are estimated. The effect of impurities on the hydrogen diffusion in the alloy is discussed.

Measurement of the concentration- and temperature-dependent diffusion coefficient and activation energy via diffusion image analysis

Problems associated with obtaining measurements of the concentration- and temperature-dependent liquid diffusion coefficient, D(C, T), and the concentration-dependent diffusion activation energy, Ea(C), include large experimental workload and time consumption. To account for these, this paper introduces an optical method for rapidly measuring D(C, T) and Ea(C), based on the imagery of a liquid-core cylindrical lens (LCL) and numerical calculation. This method requires only one diffusion image obtained from the diffusion experiment, and D(C) is measured at a particular temperature. First, we measured the D(C) coefficients of glycerin solution at 288.0, 293.0, 298.0, 303.0, 308.0, 313.0, and 318.0 K. Then, the ray tracing theory was used to study the ray propagation law in the LCL composed of an inhomogeneous solution, which simulated the diffusion images of the entire experimental process and provided a method to verify the measured values of D(C). Finally, the law of diffusion activation energy varying with concentration was discussed based on the Arrhenius theory and the acquired values of D(C, T). This study further improves the measurement technology for D(C, T) and Ea(C) and provides an efficient methodology to build extensive D(C, T) and Ea(C) databases in the biochemical, medical, semiconductor, and environmental protection industries.

Simulation Investigation of Bulk and Surface Properties of Liquid Benzonitrile: Ring Stacking-Assessment and Deconvolution.

The content and the molecular dynamics (MD) simulation analysis here are inspired by our recent ab initio calculation on benzonitrile (BZN), whereas the present results are to expand and develop macroscopic documentation involving data verification. MD simulations of the bulk liquid BZN in the range of 293–323 K unravel the hydrogen bond (−C≡N···H) formation with strength in the order of ortho-H ≫ meta-H ∼> para-H. The possibility for ortho-Hs to get involved in the formation of two bonds simultaneously confirms each having σ- and π-bonding features. Accordingly, we used vast efforts for structural analysis particularly based on the deconvolution of the corresponding complex correlation functions. Specific angle-dependent correlation functions led to the recognition of the molecular stacking with a strict anti-parallel orientation. The in-plane dimer and trimer also take part in the structural recognition. A singularity, found in the trend of the simulated temperature-dependent viscosity and diffusion coefficient of liquid BZN, is centered at about 313 K and quite fascinatingly emulates the reported experiment viscosity. An interplay between a small change in the trend of density and a large change in the corresponding viscosity is a key factor in supporting the singularity. Deconvolution of the simulation results allows attributing the singularity to structural alteration involving H-bonding of different types and extent. Approaching the range of 308–313 K, an alteration between hydrogen bond formation involving mostly ortho-Hs and mixed ortho-Hs + meta-H is possible and supports the singularity.

Analytical solution for solute transport in a triple liner under non-isothermal conditions

Analytical solutions for the transport of contaminant through a 1D triple-layer composite liner system consisting of a geomembrane (GMB), a geosynthetic clay liner (GCL) and a compacted clay liner (CCL) under non-isothermal conditions are derived using the generalized integral transform technique. The proposed analytical solutions account for the combined effects of molecular diffusion, sorption and thermodiffusion as well as the temperature-dependent distribution coefficient and effective diffusion coefficient. The proposed analytical solutions are successfully validated against the experimental results of thermodiffusion tests and verified against an analytical solution available in the literature and a numerical model based on commercial finite element software. Using the verified analytical solutions, simulations are performed with representative geometry and material properties for a GMB/GCL/CCL liner system. The results indicate that neglecting the effect of non-isothermal condition can underestimate the benzene outflow rate by over 30% when the temperature difference between the surface and bottom of the liner system exceeds 10 K. The temperature-dependent CCL effective diffusion coefficient and CCL distribution coefficient have a significant effect on benzene transport through the GMB/GCL/CCL liner system, whereas the liner thermal conductivity and the temperature-dependent GCL effective diffusion coefficient and GCL distribution coefficient have a negligible effect.

Temperature-Dependent Constrained Diffusion of Micro-Confined Alkylimidazolium Chloride Ionic Liquids.

Alkylimidazolium chloride ionic liquids (ILs) have many uses in a variety of separation systems, including micro-confined separation systems. To understand the separation mechanism in these systems, the diffusion properties of analytes in ILs under relevant operating conditions, including micro-confinement dimension and temperature, should be known. For example, separation efficiencies for various IL-based microextraction techniques are dependent on the sample volume and temperature. Temperature-dependent (20-100 °C) fluorescence recovery after photobleaching (FRAP) was utilized to determine the diffusion properties of a zwitterionic, hydrophilic dye, ATTO 647, in alkylimidazolium chloride ILs in micro-confined geometries. These micro-confined geometries were generated by sandwiching the IL between glass substrates that were separated by ∼1 to 100 μm. From the measured temperature-dependent FRAP data, we note alkyl chain length-, thickness-, and temperature-dependent diffusion coefficients, with values ranging from 0.021 to 46 μm2/s. Deviations from Brownian diffusion are observed at lower temperatures and increasingly less so at elevated temperatures; the differences are attributed to alterations in intermolecular interactions that reduce temperature-dependent nanoscale structural heterogeneities. The temperature- and thickness-dependent data provide a useful foundation for efficient design of micro-confined IL separation systems.

Oxygen absorption and diffusion in Ti5Si3

The oxygen absorption energy and its migration barriers in titanium silicide with composition Ti5Si3 and hexagonal structure have been calculated by using the projector augmented-wave method within the electron density functional theory. We have derived analytical expressions for the temperature-dependent diffusion coefficients along two crystallographic directions using Landman's method and calculated the activation energies and the pre-exponential factor. The mechanism of oxygen diffusion in the bulk Ti5Si3 is discussed. It is shown that the obtained diffusion coefficient of oxygen in this silicide is comparable with experimental ones for metal oxides such as Al2O3, SiO2, Cr2O3.

Microscopic Dynamics of Inverse Wormlike Micelles Probed Using X-ray Photon Correlation Spectroscopy.

Wormlike micelles (WLMs) are ubiquitous viscoelastic modifiers that share properties with polymer solutions. While their macroscopic rheology is well-understood, their microscopic dynamics remain difficult to measure because they span a large range of time and length scales. In this work, we demonstrate the use of X-ray photon correlation spectroscopy to interrogate the segmental dynamics of inverse WLM solutions swollen with a rubidium chloride solution. We observe a diffusive scaling of the dynamics and extract a temperature-dependent diffusion coefficient, which we associate with the thermal interactions of the slow segmental dynamics near entanglement points. We probe this relaxation process across the unbranched to branched topological transition and find no microstructural evidence of branch formation in the slow mode. Instead, we observe that the dynamics become more homogeneous and prominent as the temperature is reduced and water content increases.

High performance all-solid-state lithium battery: Assessment of the temperature dependence of Li diffusion

All-solid-state silicon/LiPON/lithium model batteries are assembled via magnetron sputtering followed by a lithium evaporation process. The cells were characterized via cyclic voltammetry, linear sweep voltammetry and impedance spectroscopy. Cyclic voltammetry confirms a long-term stability and high coulombic efficiency of the solid cells. Also, the assembled batteries were tested at extraordinary high scan rates, showing remarkably high output currents and an exceptional fast-cycling capability. Further rate-dependent investigations via linear sweep voltammetry indicate clearly two different ion-transport mechanisms in the silicon electrode at low and high scan rates. While a diffusion-controlled mechanism is suggested at high scan rates, a homogenous concentration profile is expected at extremely low rates. As a decisive advantage of solid-state cells, electrochemical cycling can be performed at elevated temperatures. This is used to determine the temperature dependence of the diffusion coefficients of lithium in the silicon electrode from room temperature to 165 °C. The effective activation energy of the lithium-ion migration in silicon is obtained to 0.1 eV, which is remarkably lower than that of inside LiPON, i.e. 0.55 eV. Complementary impedance data reveal that the kinetics of transport in the solid-state setup at very high output currents and low temperatures is controlled by lithium-ion migration in the LiPON film. • High rate capability and temperature durability of solid-state battery are shown. • Long-term stability and high coulombic efficiency are demonstrated. • Lithiation of silicon exhibits different kinetic regimes at low and high scan rates. • Temperature dependence of diffusion coefficients of lithium in Si was determined.

Evaluation of a Moisture Diffusion Model for Analyzing the Convective Drying Kinetics of Lavandula x allardii Leaves

In the present case study, a moisture diffusion model is developed to simulate the drying kinetics of Lavandula x allardii leaves for non-stationary convective drying regimes. Increasing temperature profiles are applied over the drying duration and the influence of temperature advancing rates on the moisture removal and the drying rate is investigated. The model assumes a one-dimensional moisture transfer under transient conditions, which occurs from the leaf center to the surface by liquid diffusion due to the concentration gradient developed by the surface water evaporation caused by the difference of water vapor partial pressure between the drying medium and the leaf surface. A numerical solution of Fick’s 2nd law is obtained by an in-house code using the finite volume method, including shrinkage and a variable temperature-dependent effective moisture diffusion coefficient. The numerical results have been validated against experimental data for selected cases using statistical indices and the predicted dehydration curves presented a good agreement for the higher temperature advancing rates. The examined modeling approach was found stable and can output, in a computationally efficient way, the temporal changes of moisture and drying rate. Thus, the present model could be used for engineering applications involving the design, optimization and development of drying equipment and drying schedules for the examined type of non-stationary drying patterns.

On the two-dimensional Boussinesq equations with temperature-dependent thermal and viscosity diffusions in general Sobolev spaces

We study the existence, uniqueness as well as regularity issues for the two-dimensional incompressible Boussinesq equations with temperature-dependent thermal and viscosity diffusion coefficients in general Sobolev spaces. The optimal regularity exponent ranges are considered.

Slow‐Moving Phase Boundary in Li4/3+xTi5/3O4 (Small Methods 10/2021)

Inside Back Cover In article number 2100532, Joshi and co-workers developed a methodology to study lithium transport using optical microscopy. It unravels temperature dependent diffusion and barrier coefficients for the two phases and the phase boundary. Electrode-size dependent, slow/linear migration of the phase boundary, in the initial stages of lithiation, is observed. It is postulated that such migration is controlled by the concentration gradient in the Li4/3+δTi5/3O4 phase formed ahead of the phase boundary.

Pressure- and temperature-dependent diffusion from first-principles: A case study of V and Ti in a TiN matrix

We present a first-principles study of pressure- and temperature-dependent diffusion barriers and coefficients for vacancy-mediated and interstitial V impurity and Ti self-diffusion in TiN. The thus obtained diffusion coefficients were fitted with an Arrhenius-type relation yielding pre-exponential coefficients and activation energies. Our results suggest that (i) V diffuses faster than Ti, (ii) vacancy-mediated mechanism is dominating over the interstitial one, and (iii) impact of pressure is much weaker than the impact of temperature. • V diffusion in TiN for knowledge-based design of novel tribological coatings • Pressure decreases diffusion rate, the effect is weaker than impact of temperature. • Vanadium impurities diffuse faster than titanium matrix atoms. • Interstitial diffusion leads to much smaller mass transport than vacancy-mediated.