Phase Diffusion Coefficient Research Articles

System size synchronization.

In this paper we bring out the existence of a kind of synchronization associated with the size of a complex system. A dichotomic random jump process associated with the dynamics of an externally driven stochastic system with N coupled units is constructed. We define an output frequency and phase diffusion coefficient. System size synchronization occurs when the average output frequency is locked to the external one and the average phase diffusion coefficient shows a very deep minimum for a range of system sizes. Analytical and numerical procedures are introduced to study the phenomenon, and the results describe successfully the existence of system size synchronization.

Prediction of diffusion coefficients in fcc, bcc and hcp phases remained stable or metastable by the machine-learning methods

Diffusion coefficient play a crucial role in material designing, and physical phenomenon explaining during the material preparation and post-treatment. However, it is unavailable in some metallic systems. In this paper, based on basic physical properties (including atom properties, lattice parameters, melting temperature, elastic stiffness constant and etc.), the diffusion activate energy model were developed by machine-learning methods. First, the melting temperature (Tm) and elastic stiffness constant (Cij) models were built by machine-learning methods to fill the absent values in properties. Second, the diffusion activate energy (Q) model was built, and a hybrid features selection method was used to decrease features from 73 to 11 in the model. The Tm, Cij and Q models showed a good predictive ability and goodness of fit. Finally, features in the models were analyzed and compared with the parameters in various prior models. This work provides further understanding on the mechanism of the melting process, elastic deformation and diffusion process. Moreover, the models could be able to provide an easy and reliable method to obtain the diffusion coefficients in bcc, fcc, and hcp alloys when they are needed but unavailable.

Texture Analysis of Hepatocellular Carcinoma on Magnetic Resonance Imaging: Assessment for Performance in Predicting Histopathologic Grade.

The aim of the study was to evaluate the performance of texture analysis for discriminating the histopathological grade of hepatocellular carcinoma (HCC) on magnetic resonance imaging. Preoperative magnetic resonance imaging data from 101 patients with HCC, including T2-weighted imaging, arterial phase, and apparent diffusion coefficient mapping, were analyzed using texture analysis software (TexRAD). Differences among the histological groups were analyzed using the Mann-Whitney U test. The performance of texture features was evaluated using receiver operating characteristic analysis. Entropy was the most significantly relevant texture feature for distinguishing each histological grade group of HCC (P < 0.05). In ROC analysis, entropy with spatial scale filter 3 (area under curve the receiver operating characteristic curve [AUC], 0.778), mean with coarse filter (spatial scale filter 5; AUC, 0.670), and skewness without filtration (AUC, 0.760) had the highest AUC value on T2-weighted imaging, arterial phase, and apparent diffusion coefficient maps, respectively. Magnetic resonance imaging texture analysis demonstrated potential for predicting the histopathological grade of HCCs.

A Bayesian neural network methodology to predict the liquid phase diffusion coefficient

This paper deals with the development of an Artificial Neural Network methodology for the prediction of the liquid phase diffusion coefficient between species at infinite dilution in binary mixtures. The proposed methodology was implemented to estimate the diffusion coefficients with improved accuracy with respect to empirical correlations, which are widely used despite their significant errors, especially on organic mixtures. The final aim of the work is to propose a novel methodology to apply in industrial fields where the mass transport by diffusion between organic liquids plays a key role, e.g. the lubricant degradation and scraping due to the dilution with the liquid fuel in the engine combustion chamber and the dilution of heavy oils and bitumens with organic solvents. In spite of the classical use of Artificial Neural Networks, this work is based on the mutual support between a reference empirical correlation and the Neural Network model, where the former is used to directly calculate the diffusion coefficient while the latter is trained to correct the correlation's result depending on the bonds strength in the solvent and the solute. Moreover, since the prediction of the diffusion coefficient for new mixtures (i.e. where no experimental measures are available) with Artificial Neural Network models should not be taken blindly, a Bayesian Neural Network is implemented, since it is capable to provide the degree of uncertainty of its prediction. This Bayesian Neural Network, given a selection of fluid properties as input features, was trained on 263 experimental data collected from literature findings. The proposed methodology achieved the prediction of the 80% of the available data with absolute relative errors lower than 10%, while the most recognized empirical correlations predicted the same data with absolute relative errors from 30 to 45%. A proof of the reliability of this methodology is the fact that the experimental data corresponding to the points predicted with the higher errors however fall in the predicted uncertainty, whose average width is below the ±20% of the predicted mean.

Simulating the distribution of electrochemical characteristics: A case study of 4.35 V LiCoO2/graphite pouch cell

Understanding the relationships between electrochemical characteristics and the corresponding parameters of the battery is crucial for optimizing cell design, which creates new ideas for safe management and optimized service life of lithium-ion batteries. Herein, a pseudo two-dimensional (P2D) electrochemical model of 4.35 V prismatically wound LiCoO2 pouch cell is established and optimized to predict its electrochemical behaviors. Based on the significant factors of cell design parameters by analysis of variance, the distribution characteristics of solid and electrolyte-phase Li+ concentration, potential of solid and electrolyte-phase, over-potential and local current density are investigated and verified, which is conducive to provide quantitative guidance for battery design and optimization. Simulation results show that the change of electrolyte-phase Li+ concentration gradient is 14.3% at 1C rate, and the concentration gradient decreases with the increase of the electrolyte phase diffusion coefficient and Li+ transference number. In addition, the particle size shows a positive correlation with the surface lithium ion concentration, while the electrode thickness, solid phase volume fraction and solid phase diffusion coefficient are negatively correlated with the surface lithium ion concentration. The model indicates that the polarization of anode is more than twice as larger as than that of the cathode at 1C discharge. Moreover, simulation results demonstrate that the peak of local current density moved from the separator interface to the current collector interface as discharge proceeded, which further reveal the non-uniform distribution of the electrochemical reaction rate in the cell.

Determination of the liquid diffusion coefficient of the Sn-Ni peritectic alloy through temperature gradient zone melting

In the present work, a new method determining the liquid phase diffusion coefficients DL in a binary peritectic alloy is presented. This method is based on the evolution in both the microstructure and melt concentrations which can be linked through liquid droplet migration in the mushy zone during thermal stabilization. The thermal stabilization experiments of different time (2 to 8 h) are performed on Sn–Ni peritectic alloy (L+Ni3Sn2→Ni3Sn4) in a Bridgman-type directional solidification furnace. Two different mushy zones are formed during thermal stabilization of samples which are kept still in the furnace. The diffusion-controlled liquid droplet migration is caused by remelting/resolidification by temperature gradient zone melting (TGZM). It leads to not only the variation of volume fractions of solid(fS)/liquid(fL) phases in the mushy zone but also the increase of the melt concentration in the complete-liquid zone C. Thus, based on the conservation of mass during thermal stabilization, fS and fL can be correlated to not only the liquid droplet migration velocity vm but also the melt concentration in the complete-liquid zone C during thermal stabilization. Since fS and fL can be easily obtained through microstructure analysis, the experimental value of vm at specific location/temperature is given. Then, the expression of vm which is function of DL is provided by an analytical model describing the remelting/resolidification process during the liquid migration. Finally, DL and the activation energy of the Sn-Ni peritectic alloy are obtained by equating the experimental values of vm with the expression of vm by this analytical model.

An integrated experimental and computational study of diffusion and atomic mobility of the aluminum–magnesium system

Diffusion between Al and Mg was investigated comprehensively using both high-throughput experiments and density functional theory (DFT) calculations. Experimental diffusion coefficients in fcc Al, hcp Mg, β–Mg17Al12, γ–Mg2Al3 andε−Mg23Al30 phases were collected by combining diffusion multiples with forward-simulation analysis together with a critical review of the experimental studies in the literature. The best settings to compute the dilute (impurity) diffusion coefficients of Al and Mg using DFT were tested by comparing the computed data using various DFT settings with the critically assessed experimental diffusion coefficients in stable phases (fcc Al and hcp Mg). The optimal DFT settings were employed to calculate the dilute diffusion coefficients of Al and Mg in metastable (hypothetical) phases (hcp Al and fcc Mg) where experimental measurements were impossible. The atomic mobilities of Al and Mg in the Al–Mg binary system across the entire composition range were then reliably optimized for both the fcc and hcp phases based on the comprehensive diffusion data obtained from both experimental measurements for the stable phases and DFT calculations for the metastable phases. This study demonstrates an efficient and reliable way to develop fundamental mobility databases using integrated experimental and computational methods.

Phase equilibria and diffusion coefficients in the Fe-Zn binary system

Phase diagram and diffusion coefficients of the Fe-Zn binary system are required to predict and control the microstructure of galvanized zinc coatings and thus were systematically investigated in the temperature range from 700 to 1100 °C using nine novel Fe/Zn liquid-solid diffusion couples (LSDCs). The equilibrium compositions of the α and Γ phases of the Fe-Zn system were determined and agree well with the recently established Fe-Zn phase diagram. The extracted interdiffusion coefficients in α-Fe at temperatures between 700 and 1100 °C and in Γ at 750 and 700 °C using the forward-simulation analysis (FSA) extend the experimental interdiffusivity measurements to the whole solubility range of these two phases. Three impurity diffusion coefficients of Zn in paramagnetic α-Fe were also determined by the FSA and show good agreement with the literature data. The temperature dependence of the Zn impurity diffusion coefficients in both the paramagnetic and ferromagnetic α-Fe phases across the Curie temperature TC was established by analyzing the reliable experimental results as well as by density functional theory (DFT) calculations. The newly measured phase equilibrium and diffusivity data provide reliable inputs for future thermodynamic and kinetic modeling of the Fe-Zn system.

Ruelle–Pollicott Resonances of Stochastic Systems in Reduced State Space. Part III: Application to the Cane–Zebiak Model of the El Niño–Southern Oscillation

The response of a low-frequency mode of climate variability, El Nino–Southern Oscillation, to stochastic forcing is studied in a high-dimensional model of intermediate complexity, the fully-coupled Cane–Zebiak model (Zebiak and Cane 1987), from the spectral analysis of Markov operators governing the decay of correlations and resonances in the power spectrum. Noise-induced oscillations excited before a supercritical Hopf bifurcation are examined by means of complex resonances, the reduced Ruelle–Pollicott (RP) resonances, via a numerical application of the reduction approach of the first part of this contribution (Chekroun et al. 2019) to model simulations. The oscillations manifest themselves as peaks in the power spectrum which are associated with RP resonances organized along parabolas, as the bifurcation is neared. These resonances and the associated eigenvectors are furthermore well described by the small-noise expansion formulas obtained by Gaspard (2002) and made explicit in the second part of this contribution (Tantet et al. 2019). Beyond the bifurcation, the spectral gap between the imaginary axis and the real part of the leading resonances quantifies the diffusion of phase of the noise-induced oscillations and can be computed from the linearization of the model and from the diffusion matrix of the noise. In this model, the phase diffusion coefficient thus gives a measure of the predictability of oscillatory events representing ENSO. ENSO events being known to be locked to the seasonal cycle, these results should be extended to the non-autonomous case. More generally, the reduction approach theorized in Chekroun et al. (2019), complemented by our understanding of the spectral properties of reference systems such as the stochastic Hopf bifurcation, provides a promising methodology for the analysis of low-frequency variability in high-dimensional stochastic systems.

Phase Equilibria and Diffusion in the Ni-Cr-Pt System at 1200 °C

Pt modified NiAl, which is often simply called Pt aluminide, is widely used in jet engines as a protective coating against oxidation and hot corrosion as well as a bond coat for thermal barrier coatings. Phase equilibria and diffusion coefficients in the Ni-Cr-Pt ternary system are thus valuable data for modeling the behavior of Pt aluminide coatings on Ni-based superalloys in which Cr is an essential alloying element. A Ni-Cr-Pt diffusion multiple was made and annealed at 1200 °C for 100 h to obtain the first reliable isothermal section phase diagram for this ternary system. Interdiffusion coefficients were extracted from the measured diffusion concentration profiles using a forward simulation analysis for all the single-phase regions of the Ni-Cr, Ni-Pt and Cr-Pt binary systems. The impurity diffusion coefficient data obtained from this study are combined with literature data to assess reliable Arrhenius equations for the impurity diffusion coefficients of Pt in Ni, Ni in Pt, and Cr in Ni. An Arrhenius equation for the impurity diffusion coefficient of Cr in Pt is recommended for the first time by combining a fitted prefactor from experimental data and an activation energy value from first principles calculations.

Experimental study of zeolitic diffusion by use of a concentration-dependent surface diffusion model

Surface diffusivity in adsorption and ion exchange processes is probably the most important property studied expensively in the literature but some aspects, especially its dependence on solid phase concentration, is still an open subject to discussion. In this study a new concentration-dependent surface diffusion model, equipped with a flexible double selectivity equilibrium relationship is applied on the removal of Pb2+, Cr3+, Fe3+ and Cu2+ from aqueous solutions using a natural zeolite. The model incorporates the Chen-Yang surface diffusivity correlation able to deal with positive and negative dependence with surface coverage. The double selectivity equilibrium relationship successfully represents the experimental equilibrium data, which follow Langmurian isotherm type for Pb2+, sigmoidal for Cr3+ and Fe3+ and linear for Cu2+. The concentration-dependent surface diffusion model was compared with the constant diffusivity surface diffusion model and found to be moderately more accurate but considerably more useful as it provides more insights into the diffusion mechanism. The application of the model resulted in an average deviation of 8.56 ± 6.74% from the experimental data and an average solid phase diffusion coefficients between 10−9 and 10−10 cm2/s. The results showed that the diffusion of metal ions in the zeolite structure is unhindered following the surface diffusion mass transfer mechanism.

Formation of hierarchical porosity in oxidation of Ag films by reactive sputtering deposition of metal oxides via the Kirkendall effect.

In this work, the conversion of Ag films to silver oxide nanorod arrays with hierarchical porosity which was realized in an oxidation environment by reactive sputtering deposition of metal oxides was reported. The mechanisms from the oxidation of Ag films to the formation of hierarchical porosity were investigated by varying the deposition parameters with the determination of phase structure, hierarchical porosity, diffusion coefficient, and chemical states of elements as well as by a comparison with the oxidation of Ag films by direct exposure to plasma. The oxidation of Ag films can be ascribed to the atomic oxygen in the environment. The formation of silver oxide nanorods and the creation of hierarchical porosity were substantiated to be due to the Kirkendall effect occurring between the oxidized Ag films and the deposited metal oxides with the assistance of the shading effect in deposition. In addition, the sample temperature and the attributes of metal oxides were found to have significant effects on the formation of hierarchically structured porous silver oxide films. The principle revealed in this work is of significance for the synthesis of porous materials with hierarchical porosity, especially for fabrication of hierarchically porous silver oxide films with improved properties, which are needed in the research fields of solid-state thin film batteries, photocatalysts, bactericides, gas sensors, etc.

Quasi-Isothermal External Short Circuit Tests Applied to Lithium-Ion Cells: Part II. Modeling and Simulation

Measurement data gained from quasi-isothermal external short circuit tests on single-layered pouch-type Li-ion cells presented in the first part of this combined work was used to validate a well-known homogenized physical-chemical model for different electrode loadings, cell temperatures, initial cell voltages, and external short circuit resistances. Accounting for diffusion-limited reaction kinetics, effective solid phase diffusion coefficients, and one representative active material particle size within each electrode, the model is capable of describing the experimentally observed characteristic change in magnitudes of current and heat generation rate throughout the short circuit. Underlying mechanisms for the observed characteristics are studied by evaluating the predicted concentration distribution across the electrodes and separator and by calculating the cell polarization due to ohmic losses, diffusion processes, and reaction kinetics. The importance of mass transport in the solid and liquid phase limiting reaction kinetics is discussed and evaluated in the context of a sensitivity analysis. Concentration dependent transport properties, electrode tortuosity, particle size, and electrode energy density are affecting different stages of a short circuit. Simulation results suggest a strong impact of electrode design on the short circuit dynamics allowing for an optimization regarding a cell’s energy and power characteristics whilst guaranteeing a high short circuit tolerance.

Multi-Species, Multi-Reaction Model for Porous Intercalation Electrodes: Part II. Model-Experiment Comparisons for Linear-Sweep Voltammetry of Spinel Lithium Manganese Oxide Electrodes

In Part 1 of this series, we formulated a porous electrode model including multiple lithium-insertion species and associated electrochemical and homogenous reactions. In this paper, the multi-species multi-reaction (MSMR) model is used to simulate linear-sweep voltammetry (LSV) data of a porous electrode of spinel lithium manganese oxide (LMO) at different scan rates, and values of transport, kinetic, and thermodynamic parameters are fit to the measured data. Twenty model parameters are optimized to simultaneously fit the slowest and fastest sweep rates. The optimization is computationally intensive, but the calculation times were reduced by almost one half using a perturbation formula valid at the lowest sweep rate, developed in Part 1, together with numerical solutions at higher sweep rates. A sensitivity analysis determines the importance of different model parameters on the results. The fitting is most sensitive to the values of the Open Circuit Voltage (OCV) and it was necessary include a small amount of hysteresis, so that the OCV is slightly different on forward and backward scans. The next most important fitting parameter was the solid phase diffusion coefficient. Of smaller importance are the kinetic parameters and ohmic losses in the solid and liquid phases of the electrode.

The Influence of Bond Angle on Thermophysical Properties of Three-Center Lennard-Jones Fluids: Computer Simulation and Theory

Abstract We carry out extensive computer simulations to study the phase equilibrium, thermodynamics, and diffusion coefficient of three-center Lennard-Jones (3CLJ) fluids with an emphasis on the effects of bond angle on these properties. We take into account several bond angles ranging from θ 0 = 60 to 180 degrees and two equilibrium bond elongations le = 1.0 and 0.5 (in Lennard-Jones length unit). Moreover, we study the fully flexible (FF) 3CLJ fluids for molecules with bond length 1.0. Gibbs ensemble Monte Carlo (MC) simulations are performed to compute the densities of the vapor-liquid coexisting phases and the vapor pressure, and direct three-phase (vapor-liquid-vapor) molecular dynamics (MD) simulations are carried out to calculate the surface tension. We then apply constant NVT MC simulations to obtain the internal energy, the pressure, and the pair correlation function, and utilize equilibrium MD simulations to compute the diffusion coefficient of systems with le = 1.0. In addition to MD simulations, the modified Cohen-Turnbull (mCT) theory is used to to compute the diffusion coefficient and the mean free volume appearing in the mCT relation is provided by the results of the Generic van der Waals (GvdW) theory. We show that the mCT theory is capable of reproducing the MD simulation values quite well over a wide range of density with slight overestimations at medium range. The angle dependence of different thermophysical properties are analyzed and discussed in details.

Estimates of parameters for formaldehyde emission model from plywood panel under various temperature and relative humidity conditions

The initial emittable concentration, Cm,0, the material phase diffusion coefficient, Dm, and the air/material partition coefficient, K, are the key parameters used to predict the formaldehyde emissions from indoor building materials. This work presents formaldehyde emission experiments of plywood panels in a climatic chamber under various environmental conditions, which provides information on how relative humidity, temperature, and loading degree affect the formaldehyde emission. The experimental results showed that formaldehyde concentration in the climatic chamber increased rapidly during the initial 3 h, and then reached equilibrium after 7 h. The equilibrium concentration of formaldehyde in the closed chamber was increased by 1.1–1.3 times with the relative humidity increased by 20%, and 1.3–2.5 times with the temperature increased by 5 °C, respectively. In agreement with the experimental treatment, a new method of estimating parameters was carried out in a theoretical model from formaldehyde emission, opening the way to a factorial analysis of the relevant parameters for relative humidity and temperature. The theoretical model with estimated parameters was further validated by experiments with different environmental conditions, which should help to quickly determine the parameters needed to predict formaldehyde emissions.

Compilation and evaluation of gas phase diffusion coefficients of halogenated organic compounds.

Organic halogens are of great environmental and climatic concern. In this work, we have compiled their gas phase diffusivities (pressure-normalized diffusion coefficients) in a variety of bath gases experimentally measured by previous studies. It is found that diffusivities estimated using Fuller's semi-empirical method agree very well with measured values for organic halogens. In addition, we find that at a given temperature and pressure, different molecules exhibit very similar mean free paths in the same bath gas, and then propose a method to estimate mean free paths in different bath gases. For example, the pressure-normalized mean free paths are estimated to be 90, 350, 90, 80, 120 nm atm in air (and N2/O2), He, argon, CO2 and CH4, respectively, with estimated errors of around ±25%. A generic method, which requires less input parameter than Fuller's method, is proposed to calculate gas phase diffusivities. We find that gas phase diffusivities in He (and air as well) calculated using our method show fairly good agreement with those measured experimentally and estimated using Fuller's method. Our method is particularly useful for the estimation of gas phase diffusivities when the trace gas contains atoms whose diffusion volumes are not known.

Differentiating malignant from benign hyperintense nodules on unenhanced T1-weighted images in patients with chronic liver disease: using gadoxetic acid-enhanced and diffusion-weighted MR imaging.

To evaluate value of gadoxetic acid-enhanced and diffusion-weighted (DW) MRI for distinguishing malignant from benign hyperintense nodules on unenhanced T1-weighted images (T1WIs) in patients with chronic liver disease. Forty-two patients with 37 malignant and 41 benign hyperintense nodules on unenhanced T1WIs who underwent gadoxetic acid-enhanced and DW MRI, followed by histopathological examination, were included. Qualitativeand quantitative analyses were conducted. Significant findings on univariate and multivariate analyses were identified and their diagnostic performances were analyzed for predicting hyperintense hepatocellular carcinomas (HCCs). In univariate analysis, hyperintensity on T2WI, arterial enhancement, washout, hypointensity on hepatobiliary phase, and diffusion restriction were more frequently observed (P < 0.05) in hyperintense HCCs. Tumor-to-liver SI ratio on hepatobiliary phase and minimum apparent diffusion coefficient (ADCmin) were significantly lower in hyperintense HCCs (P < 0.05). In multivariate analysis, hyperintensity on T2WI (OR, 13.58; P = 0.02), arterial enhancement (OR, 8.21; P = 0.002), and ADCmin ≤ 0.83 × 10-3mm2/s (OR, 6.88; P = 0.008) were independently significant factors for predicting hyperintense HCCs. When two of three criteria were combined, 75.7% (28/37) of hyperintense HCCs were identified with a specificity of 92.7%, and when all three criteria were satisfied, the specificity was 97.6%. Gadoxetic acid-enhanced and DW MRI may be helpful for differentiating malignant from benign hyperintense nodules on unenhanced T1WI.

Effect of Source on the Properties and Behavior of Cellulose Nanocrystal Suspensions

Sulfuric acid hydrolysis of native cellulose fibers results in colloidally stable suspensions of cellulose nanocrystals (CNCs). We have investigated the effect of the cellulose source on the suspension properties of CNCs extracted from cotton and wood sources using a comparable preparation strategy. The structural properties were revealed to be similar within the given standard deviation and prevalent polydispersity, whereas other properties such as liquid crystalline phase behavior, viscosity, diffusion coefficients, and surface tension were found to differ significantly. This study shows that ostensibly similar suspensions may exhibit rather differing behaviors and attempts to interpret this phenomenon. This finding shows that full characterization and a detailed description of the preparation of the nanocrystals used in publications are extremely important and should be reported in detail in all instances.

Two-phase homogeneous diffusion model for the fixed bed sorption of heavy metals on natural zeolites

In this work, the fixed bed removal kinetics of Pb2+, Zn2+, Mn2+, Cr3+, Fe3+ and Cu2+ from aqueous solutions on natural zeolites was studied. For this aim, a non-dimensional two-phase homogeneous solid diffusion model including axial dispersion and equipped with a universal double-selectivity equilibrium model is developed and applied. In total 9 isotherms, representing 128 experimental points and 25 breakthrough curves, representing 764 experimental points are used in modeling. The application of the model is satisfactory resulted in an average deviation from the experimental data of 11.19 ± 5.53%. The solid phase diffusion coefficients are between 10−7 and 10−9 cm2/s depending on the metal, flow rate and particle size in the decreasing order of Cu > Fe, Cr > Zn, Pb > Mn. The study is supplemented by an extended literature review on fixed bed models and experimentally derived solid phase diffusion coefficients in zeolites.