Solid-phase Diffusion Research Articles

Laser doping mechanism of 4H-SiC by KrF excimer laser irradiation using SiNx thin films

In this study, nitrogen is doped into 4H-SiC by irradiating 4H-SiC with a SiNx thin film and a KrF excimer laser. The doping depth profile, crystal structure, electrical properties, and surface roughness results are analyzed to evaluate the excimer-laser doping mechanism. High-concentration doping is possible at a fluence of 2.5 J cm−2 and 10 shots, while maintaining the 4H-SiC crystal structure via solid-phase diffusion. However, changes in the 4H-SiC crystalline state are observed upon liquid-phase diffusion at a fluence of ≥2.8 J cm−2. At a fluence of 2.5 J cm−2 and 100 shots, nitrogen can be deeply diffused via solid-phase diffusion; however, an amorphous layer is formed on the surface and there is an increase in contact resistance.

Fast Identification of Micro-Health Parameters for Retired Batteries Based on a Simplified P2D Model by Using Padé Approximation

Better performance consistency of regrouped batteries retired from electric vehicles can guarantee the residual value maximized, which greatly improves the second-use application economy of retired batteries. This paper develops a fast identification approach for micro-health parameters characterizing negative electrode material and electrolyte in LiFePO4 batteries on the basis of a simplified pseudo two-dimensional model by using Padé approximation is developed. First, as the basis for accurately identifying micro-health parameters, the liquid-phase and solid-phase diffusion processes of pseudo two-dimensional model are simplified based on Padé approximation, especially according to enhanced boundary conditions of liquid-phase diffusion. Second, the reduced pseudo two-dimensional model with the lumped parameter is proposed, the target parameters characterizing negative electrode material (εn, Ds,n) and electrolyte (De, Ce) are grouped with other unknown but fixed parameters, which ensures that no matter whether the target parameters can be achieved, the corresponding varying traces is able to be effectively and independently monitored by lumped parameters. Third, the fast identification method for target micro-health parameters is developed based on the sensitivity of target parameters to constant-current charging voltage, which shortens the parameter identification time in comparison to that obtained by other approaches. Finally, the identification accuracy of the lumped micro-health parameters is verified under 1 C constant-current charging condition.

Efficient Reformulation of Linear and Nonlinear Solid-Phase Diffusion in Lithium-ion Battery Models using Symmetric Polynomials: Mass Conservation and Computational Efficiency

Lithium-ion batteries are typically modeled using porous electrode theory coupled with various transport and reaction mechanisms, along with suitable discretization or approximations for the solid-phase diffusion equation. The solid-phase diffusion equation represents the main computational burden for typical pseudo-2-dimensional (p2D) models since these equations in the pseudo r-dimension must be solved at each point in the computational grid. This substantially increases the complexity of the model as well as the computational time. Traditional approaches towards simplifying solid-phase diffusion possess certain significant limitations, especially in modeling emerging electrode materials which involve phase changes and variable diffusivities. A computationally efficient representation for solid-phase diffusion is discussed in this paper based on symmetric polynomials using Orthogonal Collocation and Galerkin formulation (weak form). A systematic approach is provided to increase the accuracy of the approximation (p form in finite element methods) to enable efficient simulation with a minimal number of semi-discretized equations, ensuring mass conservation even for non-linear diffusion problems involving variable diffusivities. These methods are then demonstrated by incorporation into the full p2D model, illustrating their advantages in simulating high C-rates and short-time dynamic operation of Lithium-ion batteries.

NMR study of the electrolyte diffusion in bituminous coal

The transfer of the electrolyte molecules (H2SO4 or H3PO4) into bituminous coal was studied by the method of solid-state NMR spectroscopy. The kinetic dependences of the electrolytes transfer into a coal membrane from an aqueous solution have been obtained. It was shown that the transfer of H2SO4 molecules into a coal thin layer is determined by the solid phase diffusion. The process was investigated in the framework of a mathematical model of diffusion in layered media. When the flow of electrolyte is directed perpendicular to the surface of the layer the diffusion coefficient of sulfuric acid in the coal equals 1∙10-13 m2/s. The diffusion coefficient of H2SO4 in the bituminous coal is four order of less than the self-diffusion coefficient of proton in aqueous solution. The diffusion process of the electrolyte delivery may be the rate-limiting stage preceding chemical transformations with the H2SO4 participation in bituminous coal.

Unveiling the role of water in enhancing the performance of zinc-ion batteries using dimethyl sulfoxide electrolyte and the manganese dioxide cathode

In dimethyl sulfoxide electrolytes, the existence of water can lead to changes occurring in the zinc-ionintercalated phase. A Zn-birnessite, when replaced by a super-hydrated Zn-buserite, enhanced solid-phase diffusion and surface kinetics.

Synergistic carbon and oxygen vacancy engineering on vanadium dioxide nanobelts for efficient aqueous zinc-ion batteries

This study proposes a synergistic engineering approach involving carbon and oxygen vacancy to improve the performance of VO2.

On the Feasibility of Electrode Concentration Distribution Estimation in Single-Particle Lithium-Ion Battery Models

This letter analyzes the observability of a nonlinear single particle model (SPM) of a lithium-ion battery. SPMs offer an attractive middle ground between the simplicity of equivalent circuit models (ECMs) and the fidelity of higher-order electrochemical models. This can enable individual electrode concentration estimation via algorithms such as interconnected observers. Limitations exist on the feasibility and accuracy of such estimation, and can be examined using metrics such as nonlinear observability. This letter presents a set of conditions under which one can estimate the spatial distribution of concentrations in a nonlinear SPM. Specifically, we examine a nonlinear SPM where terminal voltage and its resistive component are measured independently. Butler-Volmer polarization potentials are assumed to be concentration-dependent. Under these assumptions, we show that electrode spatial concentration distributions can be estimated if the Jacobian of the voltage measurements with respect to surface concentrations is full rank. This condition applies for an arbitrary finite difference discretization of solid-phase diffusion dynamics. This letter demonstrates this insight numerically, for a model of a nickel-manganese-cobalt (NMC) battery.

Dual-phase B-doped FeCoNiCuPd high-entropy alloys for nitrogen electroreduction to ammonia.

Dual-phase B-doped FeCoNiCuPd high-entropy alloy (DP-B-HEA) nanoparticles were synthesized via a strategy involving thermodynamically driven solid-phase diffusion. The DP-B-HEA/CNFs showed an outstanding electrochemical N2 reduction reaction (NRR) performance with an ammonia yield of 24.8 μmol h-1 cm-2 and NH3 faradaic efficiency (FE) of 39.2%. The optimized electronic structures of the HEA resulting from B doping led to the enhanced NRR activity and selectivity.

Effect of lemon essential oil on the microbial control, physicochemical properties, and aroma profiles of peeled shrimp

To extend the shelf-life of peeled shrimp, the risk of microbial contamination should be minimized. The aim of this study was to determine how the antimicrobial activity of citrus-based essential oils (EOs) benefits the shelf-life of peeled shrimp. Eight essential oils were screened for their inhibitory effects on shrimp spoilage bacteria in solid and vapor phase diffusion assays. The results indicated that folded lemon EO and grapefruit EO had relatively extensive and strong inhibitory effects on cell growth compared with the other EOs. Lemon EO was selected as a treatment for peeled shrimp in accelerated shelf-life testing at 30 °C. The final log CFU/g of total aerobic bacteria and lactic acid bacteria of the EO-treated groups was reduced by 20.7% and 21.6%, respectively, as compared with the control group. The TVB-N value in the EO-treated group was 9.03 mg/100 g at 72 h, whereas the one in the control group increased to 32.95 mg/100 g. The analysis of the physical characteristics and volatile compounds revealed that lemon oil retarded the deterioration of peeled shrimp during storage. Overall, this study supports the potential use of citrus EOs for the microbial control of peeled shrimp to help extend shelf-life.

Revealing the mechanism of stress rebound during discharging in lithium-ion batteries

Lithium-ion batteries especially with silicon-based anodes, exhibit high energy density but experience huge volume changes during charge and discharge. Research shows that multiple types of lithium-ion batteries undergo stress rise during the discharge process, which seems to contradict the sense that the battery volume ought to be reduced and the stress should decrease. To insight into this phenomenon, this work combines experimental measurements and an improved single-particle model to analyse the stress rise in detail. The results demonstrate that the large volume change of the anode material during (de)lithiation and the severe limitation of the solid phase diffusion of lithium-ion in the active particles lead to an uneven concentration distribution and cause anomalous stress changes. Accordingly, the diffusion coefficient of the anode material has a critical influence. Furthermore, the rupture of particles during cycling contributes to the increase in lithium-ion diffusion channels and the diffusion coefficient, making the stress characteristics show regular changes, which can be used as a means to predict the health state of the battery and reduce the complexity of prediction.

Microstructures and hot cracking formed at the interface of Zircaloy-4/stainless-steel-304L junctions

ABSTRACT Dissimilar junctions between the zirconium alloy (Zy-4) and 304L stainless steel (SS) are prepared via two bonding processes: solid-phase diffusion at T1 = 1223 K and in transient liquid phase (TLP) at T2 = 1293 K and T3 = 1323 K for an identical isothermal hold time of 2700 s. The formed layers and phases at the interface were characterised by the combination of EDS-EBSD-ESEM, EPMA and X-RD and impact fracturing tests. The Zy-4/SS interface is formed of three layers containing Cr-rich α-Fe and Zr(Fe,Cr)2 and Zr2(Fe,Ni) intermetallic compounds. We establish the relationship between the interface microstructures and hot cracking formation which are of thermo-mechanical and solidification origin. The knowledge of the solidification path of the TLP obtained in LIII layer at T2 and T3 makes it possible to explain the formation of micro-pores. The fracture is for both bonding processes, takes place in the brittle mode, of the intergranular type by cleavage and is in the LIII layer of the junction.

Hexic Polynomial Approximation for Spherical Diffusion to Accelerate Accurate Lithium-Ion Battery Simulation

There is a need for proper estimates of various vital internal states of Li-ion batteries in a battery management system like state of charge, state of health, state of power, and available energy for a better lifetime and user experience. These estimates Require electrochemical models that are generally coupled partial differential equations (PDEs) which are computationally expensive. This work proposes hexic polynomial-based models to provide better accuracy than the lower order polynomial-based models (parabolic and quartic models) while providing comparable computational efficiency in solving the PDE-based models for solid phase diffusion. While the constant current discharge behavior of a battery can be captured reasonably well using parabolic profile approximation, for a time-varying current (especially having high-frequency components), such lower order approximations lead to significant errors hence a hexic polynomial approximation is proposed. To compare the accuracy of different approximations for battery simulation, a single-particle model with thermal effects and an isothermal pseudo-2D model are simulated in this paper. The voltage response for the time-varying current profile in SPM shows the superiority of the hexic polynomial approximation over other lower-order approximations in providing a balance between computational efficiency and accuracy.

Are Three-Dimensional Batteries Beneficial? Analyzing Historical Data to Elucidate Performance Advantages

Conventional lithium-ion batteries (LIBs) are composed of planar stacks of anodes, cathodes, and separators, all immersed in electrolyte and sandwiched between current collectors. However, planar LIBs have a performance trade-off where increasing electrode thickness leads to higher capacity but lower rate capability. Three-dimensional (3D) batteries circumvent this issue with 3D electrode architecture. Herein, we systematically analyze 3D LIBs from experimental publications over the past 20 years. Using a previously developed empirical model, we obtain parameters to quantify the rate capability and rate-limiting mechanisms of 3D LIBs. Compared to conventional LIBs, 3D LIBs exhibit better rate capability─confirming their expected performance benefit. To provide further insight, we investigate the impact of liquid-phase and solid-phase diffusion mechanisms on this performance benefit. Lastly, we discuss the design landscape of 3D LIBs across multiple electrode designs and material sets and highlight our perspective on the applicability of 3D LIBs at different application scales.

High Thermoelectric Performance in Polycrystalline GeSiSn Ternary Alloy Thin Films.

Group IV materials are promising candidates for highly reliable and human-friendly thin-film thermoelectric generators, used for micro-energy harvesting. In this study, we investigated the synthesis and thermoelectric applications of a Ge-based ternary alloy thin film, Ge1-x-ySixSny. The solid-phase crystallization of the highly densified amorphous precursors allowed the formation of high-quality polycrystalline Ge1-x-ySixSny layers on an insulating substrate. The small compositions of Si and Sn in Ge1-x-ySixSny (x < 0.15 and y < 0.05) lowered the thermal conductivity (3.1 W m-1 K-1) owing to the alloy scattering of phonons, while maintaining a high carrier mobility (approximately 200 cm2 V-1 s-1). The solid-phase diffusion of Ga and P allowed us to control the carrier concentration to the order of 1019 cm-3 for holes and 1018 cm-3 for electrons. For both p- and n-type Ge1-x-ySixSny, the power factor peaked at x = 0.06 and y = 0.02, reaching 1160 μW m-1 K-2 for p-type and 2040 μW m-1 K-2 for n-type. The resulting dimensionless figure of merits (0.12 for p-type and 0.20 for n-type) are higher than those of most environmentally friendly thermoelectric thin films. These results indicate that group IV alloys are promising candidates for high-performance, reliable thin-film thermoelectric generators.

A robust numerical treatment of solid-phase diffusion in pseudo two-dimensional lithium-ion battery models

Solid-phase diffusion in active materials of lithium-ion batteries significantly affects charging and safety-related behavior of lithium-ion batteries. Therefore, it is essential to develop an efficient and robust numerical algorithm for solving solid-phase diffusion equations in physics-based battery models. In this work, we discuss the origins of numerical instabilities that can occur when solving the solid-phase diffusion equations using iterative methods. Then, in order to resolve such issues, we propose a simple numerical treatment to the surface flux term of discretized solid-phase diffusion equations. To demonstrate its numerical robustness, the proposed method is implemented into a pseudo two-dimensional (P2D) physics-based battery model and simulations are conducted at wide ranges of operating conditions. Even with extremely poor initial guesses for the Li+ concentrations of the active materials, computations using the proposed method do not diverge and the their computational speeds are comparable to those with conventional initial guesses. Comprehensive tests of the proposed method are also performed with a dynamic current profile based on US06 driving profile and a multi-stage charging profile with very high initial C-rate (12C).

Considering solid phase diffusion penetration depth to improve profile approximations: Towards accurate State estimations in lithium-ion batteries at low characteristic diffusion lengths

Lithium-ion batteries are typically modelled using the pseudo-2-dimensional (P2D) model, where a set of partial differential equations describing transport and electrochemical reactions are solved numerically to obtain battery state information. To improve computational efficiency and enable on-board implementation for state-estimation, reduced order models are developed, where one such model reduction technique includes using a profile approximation for solving solid phase diffusion inside electrode particles. While greatly reducing model complexity, the profile approximation also leads to reduced accuracy, especially at low characteristic diffusion lengths. We address this issue by developing an improved model, which recognizes the existence of a penetration depth and the solution is obtained by dividing the particle into diffusion-free core and a shell corresponding to the penetration depth. The time-scale for the diffusion front to reach the particle centre depends on the diffusivity and particle radius. A similarity solution for this period, leads to an expression for the State of charge (SOC) in the spatio-temporal domain. The predictions are compared to that from the benchmark P2D and experimental data, revealing accuracies >99%, while adding no computational cost. This improved model is particularly useful under high C-rate or low temperature operation, where the characteristic diffusion lengths are low.

Disturbances Due to Short- and Long-Term Diffusion Equalization Effects in Self-Discharge Measurements of Lithium-Ion Batteries

Quality assurance is essential for controlling lithium-ion cell properties during and after manufacturing. The largest contributors to process manufacturing costs of lithium-ion batteries are the cell formation and aging, when cell quality parameters are determined [1]. While voltage, capacity and impedance are determined reasonably fast, cell aging and self-discharge monitoring may take two to three weeks [2]. Apart from economical aspects for manufacturing and cell aging, accurately measuring the self-discharge may take up to several month [3, 4].The main reason for the long duration of electrical self-discharge measurements are disturbances due to short-term and long-term diffusion equalization effects [5]. Short-term effects up to several hours include solid phase and liquid phase diffusion, leading to open circuit voltage relaxation [6]. Long-term effects up to several weeks are mainly based on the same diffusion phenomena in conjunction with inactive anode overhang areas [7]. Therefore, the storage condition has significant impact on the state-of-charge of the anode overhang, inducing anomalies with regard to capacity [8] and coulombic efficiency [9]. Consequently, it is expected that the aforementioned disturbances might have a similar effect on the electrical measurement of self-discharge.In this work, various cell preconditionings were applied to different methods for electrical self-discharge measurement, such as the capacity loss, the voltage decay and the voltage hold methods. The preconditioning allowed a distinction between undisturbed cells, short-term and long-term disturbed cells, or cells affected by a combination of disturbances. The investigated cells were commercial Samsung INR21700-50E cylindrical cells (NCA/silicon-graphite) and non-commercial pouch cells (NMC622/graphite) with comparable capacity and anode overhang areas.The results showed significant impact of preconditioning on the self-discharge measurements. Self-discharge of undisturbed cells was accurately measured within a few days. Short-term disturbances subsided after several hours, which is in good agreement with the findings from open circuit voltage relaxation [6]. Long-term disturbances due to the anode overhang areas decreased over the measurement period even though the self-discharge current was still many times higher than the undisturbed self-discharge after several weeks. Comparison to initial testing of non-commercial cells showed an equivalence of voltage decay method for fresh cells after formation and long-term disturbed cells, indicating anode overhang charge equalization as the main contributor to self-discharge measurements during cell aging step.The utilized non-commercial pouch cells were designed and produced within the scope of the project “FormEL”, funded by the German Federal Ministry of Education and Research (BMBF) under grant number 03XP0296D.Literature[1] Liu, Y.; Zhang, R.; Wang, J.; Wang, Y.: Current and future lithium-ion battery manufacturing, In: iScience 24 (4), p. 102332–102332, 2021[2] Kwade, A.; Haselrieder, W.; Leithoff, R.; Modlinger, A.; Dietrich, F.; Droeder, K.: Current status and challenges for automotive battery production technologies, In: Nature Energy 3 (4), pp. 290–300, 2018[3] Zilberman, I.; Sturm, J.; Jossen, A.: Reversible self-discharge and calendar aging of 18650 nickel-rich, silicon-graphite lithium-ion cells, In: Journal of Power Sources 425 (9), pp. 217–226, 2019[4] Theiler, M.; Endisch, C.; Lewerenz, M.: Float Current Analysis for Fast Calendar Aging Assessment of 18650 Li(NiCoAl)O2/Graphite Cells, In: Batteries 7 (2), p. 22–22, 2021[5] Deutschen, T.; Gasser, S.; Schaller, M.; Siehr, J.: Modeling the self-discharge by voltage decay of a NMC/graphite lithium-ion cell, In: Journal of Energy Storage 19 (8), pp. 113–119, 2018[6] Kindermann, F.M.; Noel, A.; Erhard, S.V.; Jossen, A.: Long-term equalization effects in Li-ion batteries due to local state of charge inhomogeneities and their impact on impedance measurements, In: Electrochimica Acta 185, pp. 107–116, 2015[7] Wilhelm, J.; Seidlmayer, S.; Keil, P.; Schuster, J.; Kriele, A.; Gilles, R.; Jossen, A.: Cycling capacity recovery effect: A coulombic efficiency and post-mortem study, In: Journal of Power Sources 365, pp. 327–338, 2017[8] Burrell, R.; Zulke, A.; Keil, P.; Hoster, H.: Communication—Identifying and Managing Reversible Capacity Losses that Falsify Cycle Ageing Tests of Lithium-Ion Cells, In: Journal of The Electrochemical Society 167 (13), p. 130544–130544, 2020[9] Gyenes, B.; Stevens, D.A.; Chevrier, V.L.; Dahn, J.R.: Understanding Anomalous Behavior in Coulombic Efficiency Measurements on Li-Ion Batteries, In: Journal of The Electrochemical Society 162 (3), A278-A283, 2015

Laser assisted diffusion bonding of TC4 titanium alloy to 301 stainless steel using a Ni interlayer

Ni interlayer was applied in the lap welding of Ti6Al4V titanium (Ti) alloy and 301 stainless steel (SS). By adjusting the welding parameters, the SS irradiated by the laser was not completely penetrated. The SS/Ni and Ni/Ti interfaces were metallurgically bonded due to indirect heating. Two bonding interfaces formed based on solid phase diffusion bonding and eutectic reaction. As the laser power increased, the thickness of the remaining Ni interlayer gradually decreased. A Ni transition layer, as barrier to mixing of the two base materials can prevent the formation of Ti–Fe IMCs. The shear test results showed that the shear strength of the joint increased first and then decreased with the increase of laser power, and the maximum shear strength of joint was 269.8 MPa.

Investigation of the diffusion phenomena in lithium-ion batteries with distribution of relaxation times

The distribution of relaxation times method (DRT) has been widely used to quantify the numbers and characterize the properties of the physico-chemical processes inside the Li-ion battery (LIB). While most of the published works focused on the mid-high frequency range, the processes in the low frequency area, such as diffusion, have garnered less attention. The difficulties of applying the DRT to the diffusion processes include the more complicated mathematical treatment involved, the unknown influence of the porous electrode on the DRT spectra and the evaluation of the measured impedance with the developed theory. The galvanostatic intermittent titration technique (GITT) has been widely applied to determine the solid diffusion coefficient for the LIB. However, the GITT does not consider the geometry of the active material particles and cannot effectively separate the contribution of the solid diffusion from other processes, such as liquid diffusion. In the present work, a comprehensive theory is developed to investigate the DRT spectra of a LIB with a physics-based impedance model. Furthermore, an analytical expression is developed for the DRT spectra and analyzed in detail. The developed theory can help to determine the solid phase diffusion coefficient with a firm physico-chemical background. Based on the developed theory, the solid diffusion coefficients of the silicon graphite (SiC) and NMC811 are determined with a commercial cell. Besides, the galvanostatic intermittent titration technique (GITT) has been applied to the same cells and the measurement results are compared with that using the DRT method. The comparison indicates that GITT cannot exclude the influence of the liquid diffusion and the solid diffusion coefficients will be underestimated.

Developing a new model connecting solid phase diffusion and solid surface adsorption to simulate behavior of toxic substances in geomaterials

Developing a new model connecting solid phase diffusion and solid surface adsorption to simulate behavior of toxic substances in geomaterials