Solid-state Diffusion Coefficient Research Articles

An Efficient Methodology Combining K-Means Machine Learning and Electrochemical Modelling for the Determination of Ionic Diffusivity and Kinetic Properties in Battery Electrodes.

This paper presents an innovative and efficient methodology for the determination of the solid-state diffusion coefficient in electrode materials with phase transitions for which the assumption of applying the well-known formula from the work of Weppner et al. is not satisfied. This methodology includes a k-means machine learning screening of Galvanostatic Intermittent Titration Technique (GITT) steps, whose outcomes feed a physics-informed algorithm, the latter involving a pseudo-two-dimensional (P2D) electrochemical model for carrying out the numerical simulations. This methodology enables determining, for all of the 47 steps of the GITT characterization, the dependency of the Na+ diffusion coefficient as well as the reaction rate constant during the sodiation of an NVPF electrode to vary between 9 × 10-18 and 6.8 × 10-16 m2·s-1 and between 2.7 × 10-14 and 1.5 × 10-12 m2.5·mol-0.5·s-1, respectively. This methodology, also validated in this paper, is (a) innovative since it presents for the first time the successful application of unsupervised machine learning via k-means clustering for the categorization of GITT steps according to their characteristics in terms of voltage; (b) efficient given the considerable reduction in the number of iterations required with an average number of iterations equal to 8, and given the fact the entire experimental duration of each step should not be simulated anymore and hence can be simply restricted to the part with current and a small part of the rest period; (c) generically applicable since the methodology and its physics-informed algorithm only rely on "if" and "else" statements, i.e., no particular module/toolbox is required, which enables its replication and implementation for electrochemical models written in any programming language.

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

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

Rapid determination of solid-state diffusion coefficients in Li-based batteries via intermittent current interruption method

The galvanostatic intermittent titration technique (GITT) is considered the go-to method for determining the Li+ diffusion coefficients in insertion electrode materials. However, GITT-based methods are either time-consuming, prone to analysis pitfalls or require sophisticated interpretation models. Here, we propose the intermittent current interruption (ICI) method as a reliable, accurate and faster alternative to GITT-based methods. Using Fick’s laws, we prove that the ICI method renders the same information as the GITT within a certain duration of time since the current interruption. Via experimental measurements, we also demonstrate that the results from ICI and GITT methods match where the assumption of semi-infinite diffusion applies. Moreover, the benefit of the non-disruptive ICI method to operando materials characterization is exhibited by correlating the continuously monitored diffusion coefficient of Li+ in a LiNi0.8Mn0.1Co0.1O2-based electrode to its structural changes captured by operando X-ray diffraction measurements.

Improving the rate capability of LiNi0.5Mn1.3Ti0.2O4 by modifying the lithium insertion mechanism

Since lithium-ion batteries are becoming increasingly popular, we aimed to increase the power density of lithium-ion batteries by improving the rate capability of lithium insertion electrodes by controlling the reaction mechanism of lithium insertion materials. LiNi0.5Mn1.3Ti0.2O4 (Ti-LNMO), in which a part of Mn4+ in LiNi0.5Mn1.5O4 (LNMO) was replaced by Ti4+, was synthesized and proceeded in a single-phase reaction over the entire region. This resulted in two types of LNMOs with the same spinel structures and solid-state redox reactions of Ni2+/Ni4+, each with different reaction mechanisms. According to rate-capability tests of these two types of LNMOs, the Ti-LNMO exhibited superior rate capability than the LNMO without Ti-substitution, which demonstrated that high-power capabilities could be achieved by controlling the reaction mechanism. Furthermore, the solid-state Li-ion diffusion coefficient in the LNMOs was determined from the rate-capability using the diluted electrode method, and that of Ti-LNMO was more than three times greater than that of the LNMO. These results reveal that the lithium insertion mechanism is important for the kinetics of lithium insertion reaction.

Tunnel-Structured ζ-V2O5 as a Redox-Active Insertion Host for Hybrid Capacitive Deionization

Much of the earth's water has a salt content that is too high for human consumption or agricultural use. Enhanced oil recovery operations generate massive volumes of produced water waste with a high mineral content that can substantially exacerbate water distress. Current deionization techniques such as reverse osmosis function by removing the water (majority phase) from the salt (minority phase) and are thus exceedingly energy-intensive. Furthermore, these methods are limited in their ability to selectively extract high-value ions from produced water waste and brine streams. Hybrid capacitive deionization holds promise for enabling both desalination and resource recovery. In this work, we demonstrate the construction of a hybrid capacitive deionization cell that makes use of tunnel-structured ζ-V2O5 as a redox-active positive electrode material. By augmenting surface adsorption with Faradaic insertion processes, a 50% improvement in the ion removal capacity for K and Li ions is obtained as compared to a capacitive high-surface-area carbon electrode. The extracted ions are accommodated in surface sites and interstitial sites within the one-dimensional tunnel framework of ζ-V2O5. The kinetics of ion removal depend on the free energy of hydration, which governs the ease of desolvation at the electrode/electrolyte interface. The overall ion removal capacity additionally depends on the solid-state diffusion coefficient. ζ-V2O5 positive electrodes show substantial selectivity for Li+ removal from mixed flow streams and enrichment of the Li-ion concentration from produced water waste derived from the Permian Basin.

Analysis of Graphite Lithiation Behaviour in Li-Ion Full Cells Using a Novel Cross-Sectional in Situ Optical Microscopy Method

In Li-Ion batteries, the graphite anode undergoes chromatic changes from grey (unlithiated graphite) to blue (LiC18) to red (LiC12) to gold (LiC6) during lithiation.1 When charged with high current rates, lithiation gradients are observable due to mass transport limitations within the anode.2 Due to high lithiation degrees at the surface, the anode potential decreases locally and the possibility of Li deposition is increased.3 We introduce a new in situ optical microscopy set-up, which allows a direct observation of the cross-section of Li-ion full cells in combination with simultaneous recording of electrochemical data (Figure 1). Extensive analysis of the chromatic changes from the graphite electrode surface to the current collector gives insights into the lithiation processes on electrode and particle level. The set-up was validated by comparing the electrochemical results with data from coin full cells. The propagation of lithiation fronts for LiC12 (~ 3300 µm2 min-1) and LiC6 (~1260 µm2 min-1) at 1C through the graphite electrode coating were determined as well as the estimation of apparent solid-state diffusion coefficients in the order of 10-10 cm2 s-1 from analyzing the phase propagation within single particles at C/10. Additionally, the expansion of all components of the whole cell can be observed individually. We found that the graphite contributes mainly to the cell expansion, both irreversibly (4%) and reversibly (4-13%). Directly observing the described phenomena in the full cell can give insights into aging mechanisms of the materials.Figure 1 Exemplary image from the video at the end of charge of an in situ measurement (cycling at C/10) of a graphite-NMC 622 full cell cross-sections.References P. Maire, A. Evans, H. Kaiser, W. Scheifele and P. Novák, J. Power Sources, 155(11), A862 (2008).M. Weiss, R. Ruess, J. Kasnatscheew, Y. Levartovsky, N. R. Levy, P. Minnmann, L. Stolz, T. Waldmann, M. Wohlfahrt-Mehrens, D. Aurbach, M. Winter, Y. Ein-Eli and J. Janek, Adv. Energy Mater., 11(n/a), 2101126 (2021).T. Gao, Y. Han, D. Fraggedakis, S. Das, T. Zhou, C.-N. Yeh, S. Xu, W. C. Chueh, J. Li and M. Z. Bazant, Joule (2021). Figure 1

Liquid Processing of Interfacially Grown Iron-Oxide Flowers into 2D-Platelets Yields Lithium-Ion Battery Anodes with Capacities of Twice the Theoretical Value.

Iron oxide (Fe2 O3 )is an abundant and potentially low-cost material for fabricating lithium-ion battery anodes. Here, the growth of α-Fe2 O3 nano-flowers at an electrified liquid-liquid interface is demonstrated. Sonication is used to convert these flowers into quasi-2D platelets with lateral sizes in the range of hundreds of nanometers and thicknesses in the range of tens of nanometers. These nanoplatelets can be combined with carbon nanotubes to form porous, conductive composites which can be used as electrodes in lithium-ion batteries. Using a standard activation process, these anodes display good cycling stability, reasonable rate performance and low-rate capacities approaching 1500 mAh g-1 , consistent with the current state-of-the-art for Fe2 O3 . However, by using an extended activation process, it is found that the morphology of these composites can be significantly changed, rendering the iron oxide amorphous and significantly increasing the porosity and internal surface area. These morphological changes yield anodes with very good cycling stability and low-rate capacity exceeding 2000 mAh g-1 , which is competitive with the best anode materials in the literature. However, the data implies that, after activation, the iron oxide displays a reduced solid-state lithium-ion diffusion coefficient resulting in somewhat degraded rate performance.

Melt Synthesis of Lithium Manganese Iron Phosphate: Part I. Composition, Physical Properties, Structural Analysis, and Charge/Discharge Cycling

Melt synthesis is a fast and simple process to make dense LiMnyFe1-yPO4 (LMFP with 0 ≤ y ≤ 1) from all-dry, low-cost precursors with zero waste. This study characterizes melt LMFP materials with 0%–100% Mn after particle size reduction by planetary milling and carbon coating with glucose. The melt LMFP samples show higher electrical conductivity at similar pellet density than LFP (0% Mn) and LMFP (79% Mn) reference samples made by traditional methods. The melt LMFP samples exhibit higher crystallinity than the reference samples and show no crystalline impurities. Their unit cell volume and crystallographic density scale with Mn content; the percentage of Fe and/or Mn in Li positions is below 1.5%, which is comparable to reference samples. Crystallite sizes of at least 100 to 175 nm are observed for melt LMFP, which is larger than the fine ∼50 nm crystallites of reference LMFP. Melt LFP shows specific discharge capacity and cycling stability comparable to reference LFP, but the melt LMFP samples with 25%–100% Mn shows worse performance than reference LMFP (79% Mn). Part two of this study will quantify the solid-state lithium diffusion coefficient in melt LMFP materials and correlate it to their electrochemical performance.

Multi-material additive-manufacturing of tungsten - copper alloy bimetallic structure with a stainless-steel interlayer and associated bonding mechanisms

Copper alloy–tungsten (CuA-W) material combination offers high-temperature damage resistance and excellent plasma radiation resistance. At present, there is a lack of knowledge on laser-based powder bed fusion (LPBF) additive manufacturing of CuA-W bimetallic structures. Here we show the influence of the build strategies (including directly bonding, using CuA-W powder mixture, and using the stainless steel (SS) interlayer) on the bonding of CuA to W. The experimental results show that pure CuA became spherical on the surface of solid W. The powder layers composed of the CuA-W mixture are thermally deformed after printing several layers. Using a SS transition layer between CuA and W, good bonding between the materials is achieved due to solid-state diffusion and grain boundary diffusion. We have also found that if the melting points of the two materials are significantly different, the printing of the high melting point material first will most likely make the material interface unmelted in multi-material LPBF. The material combination must have good wettability and a high element solid-state diffusion coefficient to achieve good bonding in such a condition. This study would be helpful for future investigation on multi-material AM involving a metallic material combination with significant difference in their melting points.

Validity of solid-state Li[formula omitted] diffusion coefficient estimation by electrochemical approaches for lithium-ion batteries

The solid-state diffusion coefficient of the electrode active material is one of the key parameters in lithium-ion battery modelling. Conventionally, this diffusion coefficient is estimated through the galvanostatic intermittent titration technique (GITT). In this work, the validity of GITT and a faster alternative technique, intermittent current interruption (ICI), are investigated regarding their effectiveness through a black-box testing approach. A Doyle-Fuller-Newman model with parameters for a LiNi0.8Mn0.1Co0.1O2 electrode is used as a fairly faithful representation as a real battery system, and the GITT and ICI experiments are simulated to extract the diffusion coefficient. With the parameters used in this work, the results show that both the GITT and ICI methods can identify the solid-state diffusion coefficient very well compared to the value used as input into the simulation model. The ICI method allows more frequent measurement but the experiment time is 85% less than what takes to perform a GITT test. Different fitting approaches and fitting length affected the estimation accuracy, however not significantly. Moreover, a thinner electrode, a higher C-rate and a greater electrolyte diffusion coefficient will lead to an estimation of a higher solid-state diffusion coefficient, generally closer to the target value.

Electrochemical Modeling of GITT Measurements for Improved Solid-State Diffusion Coefficient Evaluation

Galvanostatic Intermittent Titration Technique (GITT) is widely used to evaluate solid-state diffusion coefficients in electrochemical systems. However, the existing analysis methods for GITT data require numerous assumptions, and the derived diffusion coefficients typically are not independently validated. To investigate the validity of the assumptions and derived diffusion coefficients, we employ a direct pulse fitting method for interpreting GITT data that involves numerically fitting an electrochemical pulse and subsequent relaxation to a one-dimensional, single-particle, electrochemical model coupled with non-ideal transport to directly evaluate diffusion coefficients that are independently verified through cycling predictions. Extracted from GITT measurements of the intercalation regime of FeS2 and used to predict the discharge behavior, our non-ideal diffusion coefficients prove to be two orders of magnitude more accurate than ideal diffusion coefficients extracted using conventional methods. We further extend our model to a polydisperse set of particles to show the validity of a single-particle approach when the modeled radius is proportional to the total volume-to-surface-area ratio of the system.

With a Little Help from 31P NMR: The Complete Picture on Localized and Long-Range Li+ Diffusion in Li6PS5I.

Li6PS5I acts as a perfect model substance to study length scale-dependent diffusion parameters in an ordered matrix. It provides Li-rich cages which offer rapid but localized Li+ translational jump processes. As jumps between these cages are assumed to be much less frequent, long-range ion transport is sluggish, resulting in ionic conductivities in the order of 10–6 S cm–1 at room temperature. In contrast, the site disordered analogues Li6PS5X (X = Br, Cl) are known as fast ion conductors because structural disorder facilities intercage dynamics. As yet, the two extremely distinct jump processes in Li6PS5I have not been visualized separately. Here, we used a combination of 31P and 7Li NMR relaxation measurements to probe this bimodal dynamic behavior, that is, ultrafast intracage Li+ hopping and the much slower Li+intercage exchange process. While the first is to be characterized by an activation energy of ca. 0.2 eV as directly measured by 7Li NMR, the latter is best observed by 31P NMR and follows the Arrhenius law determined by 0.44 eV. This activation energy perfectly agrees with that seen by direct current conductivity spectroscopy being sensitive to long-range ion transport for which the intercage jumps are the rate limiting step. Moreover, quantitative agreement in terms of diffusion coefficients is also observed. The solid-state diffusion coefficient Dσ obtained from conductivity spectroscopy agrees very well with that from 31P NMR (DNMR ≈ 4.6 × 10–15 cm2 s–1). DNMR was directly extracted from the pronounced diffusion-controlled 31P NMR spin-lock spin–lattice relaxation peak appearing at 366 K.

Determination of state-of-charge dependent diffusion coefficients and kinetic rate constants of phase changing electrode materials using physics-based models

The simplified gravimetric intermittent titration technique (GITT) model, which was first proposed by Weppner and Huggins in 1977, remains a popular method to determine the solid-state diffusion coefficient ( D 1 ) and the electrochemical kinetic rate constant ( k ). This is despite the model having been developed on the premise of a single-slab electrode and other gross simplification which are not applicable to modern-day porous battery electrodes. Recently however, more realistic and conceptually descriptive models have emerged, which make use of the increased availability of computational power. Chief among them is the P2D model developed by Newman et al., which has been validated for various porous battery electrodes. Herein, a P2D GITT model is presented and coupled with grid search optimization to determine state-of-charge (SOC) dependent D 1 and k parameters for a sodium-ion battery (SIB) cathode. Using this approach, experimental GITT steps could be well fitted and thus validated at different SOC points. This work demonstrates the first usage of the P2D GITT model coupled with optimization as an analytical method to derive and validate physically meaningful parameters. The accurate knowledge of D 1 and k as a function of the SOC gives further insight into the SIB intercalation dynamics and rate capability. • A P2D model and GITT experiments on a Na// sodium-ion battery half-cell are presented. • SOC dependent diffusion coefficient and kinetic rate constant are derived from the P2D model and grid search optimization. • The model accurately matches the experimental voltage profiles in the solid-solution and phase transition regions. • This approach is a departure from usual analytical models and provides physically meaningful electrochemical parameters.

Full Parametrisation and Newman Modelling of the Mixed Niobium Oxide - NMC System: Unveiling the Limiting Factor and Tackling Problems with Solid State Diffusion Parametrisation

Over the last decade, Mixed Niobium Oxide (MNO) materials have been widely researched as new lithium-ion battery anode material[1]. Their MO3-x perovskite-like host structure enables faster lithium-ion transport than graphite with higher specific capacities than LTO, while it also has excellent cycle life and voltage window respectively. Recent DFT modelling and in-situ material studies have greatly improved understanding at the material level[2]. However, for full scale implementation, more holistic parametrisation and modelling is needed to further interpret MNO behaviour in full cells, to perform sensitivity analysis for increased life and rate performance, and to design NMC/MNO battery systems. Here, we present one of the first full parametrisations and physics-based Newman models of the NMC/MNO system based on experimental data. The main governing mechanisms in the model are illustrated in Fig. 1.In particular we focus on parametrisation and modelling of the particle size and solid-state lithium-ion diffusion coefficient. While these are shown to be crucial controlling factors in performance, there is considerable disagreement on definitions and measurement methods of the solid-state lithium-ion diffusion coefficient in literature. Values attained through DFT, PFG-NMR, GITT, EIS and Cyclic Voltammetry differ by orders of magnitude[3,4,5], and there is a knowledge gap between diffusion coefficients determined at the crystal level and at the cell level[6]. Literature on solid-state lithium-ion diffusion theory and measurement techniques is reviewed, and a better approach to parametrisation of solid-state lithium-ion diffusion is presented to improve cell modelling.The resulting model helps in a more complete understanding of the NMC/MNO system and provides insights in why the NMC/MNO cell has superior properties compared to other cell configurations. It reveals what processes control NMC/MNO cell performance parameters such as polarisation, and therefore directs further research. Finally, it is shown how the model can be used to design new battery applications.

Determination of Solid-State Li Diffusion Coefficient of Lithium Insertion Materials from Rate Capability Tests on Diluted Electrode

To establish the kinetics of the lithium insertion materials used as the electrodes in lithium-ion batteries, it is important to clarify the diffusion phenomena of lithium ions in the solid phase. Since there are two variations of the rate-determining step of a lithium insertion electrode (Li-ion diffusion in solid particles and that in the electrolyte solution), these have to be differentiated in any investigation of the diffusion phenomena of Li ions in a solid. In this study, we calculated the rate capability of diluted electrodes using a charge–discharge simulation program and proved that the transport of Li ions in the solid phase is the rate-determining step for a diluted electrode with an extremely low active material content. In addition, the solid-state Li-ion diffusion coefficient can be calculated by analyzing the results of the rate capability tests. These results reveal that the diluted electrode method is very useful for elucidating the solid-state Li ion diffusion phenomena of lithium insertion materials. As such, the rate capability tests provide a new means of analyzing the solid-state diffusion coefficient.

Solid-State Diffusion Coefficient of Li Ions in Li[Ni1/2Mn3/2]O4 Determined By the Diluted Electrode Method

The input- and output-power of lithium-ion batteries strongly depend on the rate capability of the lithium insertion electrode used as positive and negative electrodes. In our previous studies, the rate capability of the electrodes have revealed that the diffusion of Li ions in the electrolyte inside the electrode is a rate-determining step [1]. Recently, the use of a dilute electrode in which a part of the active material is replaced with a spectator material makes the Li ion transport process in the solid phase rate-determining. In other words, the diluted electrode method allows to measure the rate capability of the material and to determine the solid-state Li-ion diffusion coefficient in an active material.In this study, we investigate the dependence of the rate capability of materials on the particle size. The material used was Li[Ni1/2Mn3/2]O4 (LiNiMO), which is a 5V class positive electrode material whose rate capability have been variously changed depending on the crystal structure, particle size, and reaction mechanism. LiNiMO with different particle size was synthesized by changing the synthesis temperature from 800 ℃ to 1100 ℃. The particle size of LiNiMO increased with rising the synthesis temperature. Dilute electrodes containing 10 wt% of LiNiMO active material was prepared and the rate capability tests were carried out. The lower the synthesis temperature, the better the rate capability. The sample with the smallest particle size (> 1㎛) synthesized at 800 ℃ showed 4 times higher rate capability compared to the sample with the largest particle size (7 ㎛) synthesized at 1100 ℃. This result suggests that the smaller the particle size of the material, the shorter the diffusion distance of lithium ions in the solid phase, and thus the superior rate capability was exhibited.In the presentation, based on the results of these rate tests, the solid-state diffusion coefficient of Li ions in the LiNiMO was determined, and the relationship between physicochemical properties such as particle size, crystal structure, and reaction mechanism of LiNiMO and the diffusion coefficient was investigated.[1] K. Ariyoshi et al., J. Electrochem. Soc., 165, A3965-A3970 (2018). Figure 1

Mesoscale Effects in the Extraction of the Solid-State Lithium Diffusion Coefficient Values of Battery Active Materials: Physical Insights from 3D Modeling.

During the screening of active materials (AMs) for lithium-ion batteries, the solid-state lithium diffusion coefficient (DLi) is one of the most relevant descriptors used to evaluate the relevance of an AM candidate. However, for a given compound, the DLi values reported in literature span over several orders of magnitude. Therefore, through the case study of LiNi1/3Mn1/3Co1/3O2 cathode AM, new physical insights are provided to explain the dispersion of DLi values obtained through galvanostatic intermittent titration technique (GITT) . For the first time, a 3D electrochemical model (accounting for the carbon-binder domain) fed with experimental inputs is capable of highlighting the limitations of the most widely used equation for deriving DLi. Through our model, we show that these limitations arise from the influence of the carbon-binder domain location throughout the electrode and the non-homogeneous AM phasedistribution and particle size.

Sulfur-nitrogen rich carbon as stable high capacity potassium ion battery anode: Performance and storage mechanisms

Combined sulfur and nitrogen (S ​= ​12.9 ​at.%, N ​= ​9.9 ​at.%) rich carbons are synthesized for potassium ion anode applications. The low-surface-area carbons (56 ​m2 ​g−1) have sulfur covalently bonded to the structure, with minimum unbound “free” sulfur. This allows for exceptional rate capability and stability: Capacities of 437, 234 and 72 mAh g−1 are achieved at 0.1, 1 and 10 ​A ​g−1, with 75% retention at 2 ​A ​g−1 after 3000 cycles. These are among the most favorable capacity-cyclability combinations reported in potassium ion battery carbon literature. As a proof of principle, the carbons are incorporated into a potassium ion capacitor with state-of-the-art energy and power (e.g. 110 ​W ​h ​kg−1 at 244 ​W ​kg −1). According to XPS analysis, the reaction of nitrogen with K+ is distinct from that of K+ with sulfur. The N and N–O moieties undergo a series of complex multi-voltage reactions that result in both reversible and irreversible changes to their structure. The K–S reactions involve a combination of reversible adsorption and reversible formation of sulfides, thiosulfate and sulfate. GITT and EIS analysis indicate that incorporation of S into the N-rich carbon increases the K+ solid-state diffusion coefficient by factors ranging from ~3 to 8, depending on the voltage. The diffusivities are asymmetric with charging vs. discharging, signifying distinct reaction pathways. The covalently bound sulfur also has a positive influence on the solid electrolyte interphase (SEI) formation, at early and at prolonged cycling.

How solution chemistry affects the electrochemical behavior of cathodes for Mg batteries, a classical electroanalytical study

Mo6S8 Chevrel phase (CP) is still the most effective magnesium ions insertion material that was examined in cathodes for rechargeable Mg battery model systems. Its synthesis includes CuMo6S8 as an intermediate which undergoes Cu ions leaching. Thereby, CP materials may contain small amounts of copper. CuxMo6S8 undergoes complex magnesium insertion processes that include reversible displacement of copper. We report herein on a study of Cu0.09Mo6S8 electrodes in two electrolyte solutions which are important for secondary Mg batteries: C6H6MgCl/AlCl3/THF (all phenyl complex solutions, APC) and MgTFSI2/MgCl2/DME (Mg imide/chloride/DME solutions, ICD). There systems are ideal playgrounds for studying the nature of complex magnesium insertion processes into inorganic hosts. The analysis reported herein shows how the electroanalytical behavior of CP electrodes is affected by the electrolyte solution identity. For instance, the main Mg ions insertion process from the APC solutions occurs at 160 mV lower than from the ICD ones; the heterogeneous rate constant for charge transfer across the interface are significantly higher in APC solutions; in turn, the conversion processes related to the Cu residue in the CP electrodes are kinetically and thermodynamically favorable in the ICD solutions. As expected, the magnesium solid-state diffusion coefficient was found to be solutions independent. The study demonstrates the sensitivity of electroanalytical tools such as slow scanning rate voltammetry for reflecting fine structural changes during intercalation processes and can be generalized to other systems.

A Hybrid Backward Euler Control Volume Method to Solve the Concentration-Dependent Solid-State Diffusion Problem in Battery Modeling

Several efficient analytical methods have been developed to solve the solid-state diffusion problem, for constant diffusion coefficient problems. However, these methods cannot be applied for concentration-dependent diffusion coefficient problems and numerical methods are used instead. Herein, grid-based numerical methods derived from the control volume discretization are presented to resolve the characteristic nonlinear system of partial differential equations. A novel hybrid backward Euler control volume (HBECV) method is presented which requires only one iteration to reach an implicit solution. The HBECV results are shown to be stable and accurate for a moderate number of grid points. The computational speed and accuracy of the HBECV, justify its use in battery simulations, in which the solid-state diffusion coefficient is a strong function of the concentration.