Lithium Concentration Profiles Research Articles

(Invited) 3D Electrode Architectures for High Power and High Energy Lithium-Ion Battery Operation - Recent Approaches and Process Upscaling

During the next decades, combustion driven cars will be completely replaced by electrical vehicles (EVs) and it seems quite obvious that liquid electrolyte lithium-ion batteries (LIBs) will be the dominating energy storage system for the next at least 5 to 10 years. As a consequence, in Europe numerous Gigafactories have recently been planned with this state of technology. However, the current lithium-ion battery technology suffers so far from some restrictions like the inability to combine high power and high energy operations at the same time. This limitation is mainly attributed to the cathode architecture and respective mass loading. In addition, the further demand for a significantly enhanced fast charging mainly requires an optimization of the anode design flanked by a high areal capacity. Advanced 3D electrode architectures based on a thick film electrode concept seem to be the most promising approach to overcome the current limitations in battery performances. However, respective technology innovations need to provide a high compatibility grade to existing manufacturing routes in order to enable the required integration in existing and planned factories. For so-called “generation 3” materials, i.e., nickel-rich lithium nickel manganese cobalt oxide (NMC) cathode and silicon-based anode materials, structuring technologies using cutting edge ultrafast high power lasers, are being developed in order to manufacture 3D electrode architectures with high areal capacity. Multibeam laser processing using diffractive optical elements and dual scanner approaches were established in order to enable high processing speeds in roll-to-roll electrode handling systems. The technology readiness level (TRL 6) is demonstrated for pouch cells geometries. For water-based NMC 622 and silicon-graphite composites the laser structuring process was developed. Different structures including hole, grid, and line patterns, were studied regarding their impact on electrochemical performances such as high-rate capability and cell lifetime. Lithium concentration profiles of unstructured and structured electrodes were studied post mortem using laser-induced breakdown spectroscopy (LIBS) in order to evaluate lithium intercalation/deintercalation efficiencies and detect possible cell degradation processes. In comparison to unstructured electrodes, 3D electrodes could hereby always be identified as superior: unstructured thick film electrodes show a significant drop in capacity retention for high power operation and tend to form hot spots acting as starting point for cell failure. The upscaling process is flanked by a further improvement of electrode design. For this purpose very recently laser induced forward transfer (LIFT) is applied as printing technology to draw new concepts for sophisticated model electrode architectures with advanced electrochemical performances. Finally, the micro-/nano-scaled texturing of current collectors and separator material is discussed as further possible approaches for boosting the electrochemical performances of LIB pouch cells.

Computationally Efficient Quasi-3D Model of a Secondary Electrode Particle for Enhanced Prediction Capability of the Porous Electrode Model

Models of Li-ion batteries addressing a particular scale—from atomistic to continuum—have reached a certain level of maturity. Meanwhile, consistent multi-scale modelling approaches are still in their infancy despite their large potential to boost the accuracy and prediction capability of Li-ion battery models. As an answer to this challenge, the paper presents an advanced quasi-3D model of the active electrode material that tackles one of the main deficiencies of the porous-electrode theory (PET) based models which arises from a poor representation of the electrode topology. It is hypothesised that there exists a quasi-3D modelling representation of the active electrode material that adequately virtually replicates intra primary particle Li-distribution and features significantly shorter computational times compared to models featuring a fully 3D meshed electrode topology, which enables its full integration into the porous electrode model. An advanced quasi-3D model is constructed by the integration of the concentration and the chemical potential in each primary particle across its volume and by the introduction of the permeability parameter at the interfaces. Besides compatibility with PET and acceptable computational times, the model also exhibits results that are in good agreement with measured lithium concentration profiles inside secondary particles published in literature.

On the Diffusion-controlled Transport and Accumulation of Lithium in an Electrode of a Lithium-based Galvanic Cell

The presented formulation in this paper provides the information in the form of lithium concentration profiles and lithium accumulation in the solid-state active material particles of a porous bed cathode of a lithium based galvanic cell as a function of dimensionless time during the cell discharge period under the condition of lithium diffusion in the cathode active material being a predominant process affecting the cell voltage versus time performance. The computed data is deemed to be useful in the predetermination of required cell discharge time corresponding to a desired state-of-charge of a lithium-based galvanic cell under the above-mentioned condition.

Investigation of Fast-Charging and Degradation Processes in 3D Silicon-Graphite Anodes.

The 3D battery concept applied on silicon–graphite electrodes (Si/C) has revealed a significant improvement of battery performances, including high-rate capability, cycle stability, and cell lifetime. 3D architectures provide free spaces for volume expansion as well as additional lithium diffusion pathways into the electrodes. Therefore, the cell degradation induced by the volume change of silicon as active material can be significantly reduced, and the high-rate capability can be achieved. In order to better understand the impact of 3D electrode architectures on rate capability and degradation process of the thick film silicon–graphite electrodes, we applied laser-induced breakdown spectroscopy (LIBS). A calibration curve was established that enables the quantitative determination of the elemental concentrations in the electrodes. The structured silicon–graphite electrode, which was lithiated by 1C, revealed a homogeneous lithium distribution within the entire electrode. In contrast, a lithium concentration gradient was observed on the unstructured electrode. The lithium concentration was reduced gradually from the top to the button of the electrode, which indicated an inhibited diffusion kinetic at high C-rates. In addition, the LIBS applied on a model electrode with micropillars revealed that the lithium-ions principally diffused along the contour of laser-generated structures into the electrodes at elevated C-rates. The rate capability and electrochemical degradation observed in lithium-ion cells can be correlated to lithium concentration profiles in the electrodes measured by LIBS.

Thermo-chemo-mechanical stress analysis in a thin-electrolyte plate of all-solid-state battery

Stress fields of the electrolytes of all-solid-state batteries can be induced by several factors, such as temperature variations, lithium-ion distributions, and mechanical constraints. In this study, the thermo-chemo-mechanical stress field in an electrolyte was formulated using plate theory, assuming an infinite thin-electrolyte plate in a planar battery system. The stress fields were successfully calculated with consideration of property variations with temperature and lithium concentration under various conditions of temperature gradients, lithium concentration profiles, and mechanical boundary constraints. The extent to which the property variations affected the stress fields was also demonstrated. From these calculated stress distributions, an estimation method of the critical conditions for safe operation was proposed to limit maximum stress induced in electrolytes.

Impact of Silicon Content within Silicon-Graphite Anodes on Performance and Li Concentration Profiles of Li-Ion Cells using Neutron Depth Profiling

Due to its high specific capacity, silicon is a promising candidate to substitute conventional graphite as anode material in lithium-ion batteries. However, pure silicon-based anodes suffer from poor capacity retention, mainly due to a large volume change during cycling, which results in material pulverization and other side reactions. Therefore, alternative compositions with lowered silicon content and a similar working voltage as graphite are favored, e.g. silicon-graphite (SiG), as they can reduce these volume change and side reactions while maintaining a high capacity. Here, neutron depth profiling (NDP) offers the unique possibility to quantify non-destructively the lithium concentration profile over the depth of these electrodes. In this study, the (de-)intercalation phenomena during (de-)lithiation in SiG porous anodes with silicon contents ranging from 0 wt% to 20 wt% is investigated for the first time using ex situ NDP during the initial discharge at defined depths of discharge (DODs) states. These findings are complemented by a conventional electrochemical analysis of the first full cycle with a charge/discharge rate of C/20. While the specific capacity is observed to increase with higher silicon content, NDP directly reveals a homogeneous irreversible lithium accumulation within the entire electrode depth.

A Liquid Electrolyte-Based Lithium-Ion Battery Cell Design for Operando Neutron Depth Profiling

In this study, we present a novel cell design for liquid electrolyte-based lithium-ion batteries (LIBs) to detect the lithium distribution across an electrode by neutron depth profiling (NDP). This newly developed cell design allows to obtain electrochemical data comparable to a standard laboratory cell making use of 500 μm diameter holes to assure a homogeneous compression over the entire electrode area. We present operando NDP data recorded during the formation of a porous graphite electrode where we can both distinguish between irreversibly bound lithium within the solid electrolyte interphase (SEI) and reversibly intercalated lithium into graphite, and quantify the lithium concentration profile across the electrode. The amount of lithium reversibly intercalated into the graphite electrode (≈LiC6), based on one lithium per electron of charge (1 Li/e−), was found to corroborate well with the lithium amount quantified using operando NDP. However, comparing the irreversible capacity with the amount of lithium detected as SEI within the graphite anode, a significantly smaller Li/e− ratio was observed. Furthermore, we confirm that small amounts of lithium alloy into the copper current collector, using NDP and complementary ex situ X-ray photoelectron spectroscopy (XPS).

Lithium Distribution in Structured Graphite Anodes Investigated by Laser-Induced Breakdown Spectroscopy

For the development of thick film graphite electrodes, a 3D battery concept is applied, which significantly improves lithium-ion diffusion kinetics, high-rate capability, and cell lifetime and reduces mechanical tensions. Our current research indicates that 3D architectures of anode materials can prevent cells from capacity fading at high C-rates and improve cell lifespan. For the further research and development of 3D battery concepts, it is important to scientifically understand the influence of laser-generated 3D anode architectures on lithium distribution during charging and discharging at elevated C-rates. Laser-induced breakdown spectroscopy (LIBS) is applied post-mortem for quantitatively studying the lithium concentration profiles within the entire structured and unstructured graphite electrodes. Space-resolved LIBS measurements revealed that less lithium-ion content could be detected in structured electrodes at delithiated state in comparison to unstructured electrodes. This result indicates that 3D architectures established on anode electrodes can accelerate the lithium-ion extraction process and reduce the formation of inactive materials during electrochemical cycling. Furthermore, LIBS measurements showed that at high C-rates, lithium-ion concentration is increased along the contour of laser-generated structures indicating enhanced lithium-ion diffusion kinetics for 3D anode materials. This result is correlated with significantly increased capacity retention. Moreover, the lithium-ion distribution profiles provide meaningful information about optimizing the electrode architecture with respect to film thickness, pitch distance, and battery usage scenario.

Monitoring the Lithium Concentration across the Thickness of Silicon-Graphite Electrodes during the First (De-)Lithiation

Progressing from graphite to silicon-based anodes for lithium-ion batteries increases the importance of a depth-resolved understanding of the reversible and irreversible processes across the thickness of the anode electrode. Considerable changes in electrode volume and mass loading upon (de–)lithiation make silicon electrodes more susceptible to continuous side reactions and to the isolation of active material particles, leading to non-uniform and accelerated electrode degradation. Here, we investigate the evolution of lithium concentration profiles across the thickness of porous silicon-graphite (SiG) electrodes (∼20 μm thickness, ∼1.7 mAh cm−2) with 35 wt% silicon nanoparticles during the first (de–)lithiation cycle. Using ex situ neutron depth profiling (NDP), we monitor depth- and quantity-resolved (i) the solid-electrolyte-interphase (SEI) formation, (ii) the (de–)lithiation of the active materials, as well as (iii) the changes in the total lithium content as a function of the state-of-charge (SOC) and depth-of-discharge (DOD). The results provide depth–resolved information about reversible and irreversible processes occurring during the formation of SiG electrodes, and thus offer insight into the formation process of silicon-based electrodes.

Laser-induced breakdown spectroscopy for the quantitative measurement of lithium concentration profiles in structured and unstructured electrodes

An advanced battery concept providing new diffusion pathways along the contour of electrode microstructures proved by 3D lithium elemental mapping.

Partitioning and isotopic fractionation of lithium in mineral phases of hot, dry rhyolites: The case of the Mesa Falls Tuff, Yellowstone

Studying the inventory and distribution of lithium (Li) in rhyolitic magmas, and the potential Li isotope fractionation during progressive crystallisation is crucial to understand the formation of economic Li deposits. Lithium concentrations and isotopic compositions of co-existing groundmass glass, quartz, sanidine, plagioclase, clinopyroxene, fayalite, and orthopyroxene from the Mesa Falls Tuff (Yellowstone) were determined using LA-ICP-MS and MC-ICP-MS. The highest Li contents were obtained from quartz-hosted melt inclusions (avg. 244 ppm) and groundmass glass (avg. 43 ppm). Lithium concentrations are lower in mineral phases, decreasing from quartz (avg. 18 ppm), plagioclase (avg. 17 ppm), fayalite (avg. 16 ppm), clinopyroxene (avg. 11 ppm), orthopyroxene (avg. 8 ppm) to sanidine (avg. 6 ppm). Lithium isotopic compositions of bulk tuff samples and major mineral phases reveal a range in δ7Li values (per mil deviation of 7Li/6Li ratio relative to L-SVEC reference material), spanning ~10‰ between the co-existing phases and decreasing from groundmass glass (6.5–7.5‰) to feldspars (plagioclase from −2.3 to −1.4‰; sanidine from −0.6 to −0.1‰). Lithium concentration profiles across sanidine and plagioclase crystals show a decrease towards the crystal rims, which is not observed in the other mineral phases of the Mesa Falls Tuff. The variations identified in feldspar are decoupled from both the major and all other trace element compositions, precluding an origin related to mafic recharge and magma mixing. We propose that they result from Li loss from the melt to a vapour or fluid phase taking place immediately prior to, or synchronously with, eruption. This is supported by the observation that Li contents in quartz-hosted melt inclusions are a factor of six greater than those found in groundmass glass while the concentrations of immobile trace elements are identical. The low-Li rims on sanidine and plagioclase crystals observed in the high-silica Mesa Falls Tuff rhyolite are potential candidates to preserve Li isotopic disequilibrium as has been observed in less evolved systems. The variation in Li abundances within feldspar crystals hints at the potential for kinetic isotopic fractionation to play a role in the reported isotopic compositions of bulk separates. The large elemental database of Li concentrations from the MFT allows us to calculate apparent partition coefficients between groundmass glass and co-existing minerals. These data are compared to fifteen other ignimbrites from the Yellowstone-Snake River Plain province to provide a coherent picture of Li partitioning in hot and dry rhyolites with Li most compatible in quartz and olivine, and least compatible in sanidine.

Lithium Trapping in Alloy Forming Electrodes and Current Collectors for Lithium Based Batteries

The next generation of lithium based batteries can be expected to be based on lithium alloy forming anode materials which can store up to ten times more charge than the currently used graphite anodes. This increase in the charge storage capability has motivated significant research towards the commercialization of anode materials such as Si, Sn and Al. These alloy forming anode materials are, however, known to exhibit significant capacity losses during cycling. These are typically ascribed to the volume expansion associated with the formation of the lithium alloys (the volume expansion is e.g. about 280 % for Li3.75Si) resulting in electrode pulverization as well as continuous solid electrolyte interphase (SEI) layer formation [1-3]. While significant progress has been made to decrease the volume expansion problems by the use of e.g. nanoparticles, nanorods and thin films, and/or capacity limitations [1-3], capacity losses are still generally seen [4,5]. This and previously published data suggest that the phenomenon may be due to another effect, possibly as a result of lithium trapping in the electrodes [6-8]. In the present work it is demonstrated (based on e.g. elemental analyses of cycled Sn, Al and Si electrodes) that lithium trapping can account for the capacity losses seen when alloy forming anode materials are cycled versus lithium electrodes, see Figure 1. It is shown that small amounts of elemental lithium are trapped within the electrode material during the cycling as a result of a two-way diffusion process [8] causing the lithium to move into the bulk material even during the delithiation step. This phenomenon, which can be explained by the lithium concentration profiles in the electrodes, makes a complete delithiation process very time consuming. As a result of the lithium trapping effect, the lithium concentration in the electrode increases continuously during the cycling. The experimental results also show that a similar effect can be seen also for commonly used current collector metals such as Cu, Ni and Ti. The latter means that these metals are unsuitable as current collector materials for lithium alloy forming materials in the absence of a thin layer of boron doped diamond serving as a lithium diffusion barrier layer [8]. References 1 M. N. Obrovac and V. L. Chevrier, Chem. Rev., 2014, 114, 11444. 2 X. Su, Q. Wu, J. Li, X. Xiao, A. Lott, W. Lu, B. W. Sheldon and J. Wu, Adv. Energy Mater., 2014, 4, 1300882. 3 J. R. Szczech and S. Jin, Energy Environ. Sci., 2011, 4, 56. 4 G. Zheng, S. W. Lee, Z. Liang, H-W. Lee, K. Yan, H. Yao, H. Wang, W. Li, S. Chu and Y. Cui, Nat. Nanotechnol., 2014, 9, 618. 5 K. Yan, H-W. Lee, T. Gao, G. Zheng, H. Yao, H. Wang, Z. Lu, Y. Zhou, Z. Liang, Z. Liu, S. Chu and Y. Cui, Nano Letters, 2014, 14, 6016. 6 G. Oltean, C-W. Tai, K. Edström and L. Nyholm, J. Power Sources, 2014, 269, 266. 7 A. L. Michan, G. Divitini, A. J. Pell, M. Leskes, C. Ducati and C. P. Grey, J. Am. Chem. Soc., 2016, 138, 7918. 8 D. Rehnlund, F. Lindgren, S. Böhme, T. Nordh, Y. Zou, J. Pettersson, U. Bexell, M. Boman, K. Edström and L. Nyholm, Energy Environ. Sci., 10 (2017) 1350. Figure 1

Lithium isotope fractionation by diffusion in minerals Part 2: Olivine

Recent experiments have shown that lithium isotopes can be significantly fractionated by diffusion in silicate liquids and in augite. Here we report new laboratory experiments that document similarly large lithium isotopic fractionation by diffusion in olivine. Two types of experiments were used. A powder-source method where lithium from finely ground spodumene (LiAlSi2O6) diffused into oriented San Carlos olivine, and piston cylinder annealing experiments where Kunlun clinopyroxene (∼30ppm lithium) and oriented San Carlos olivine (∼2ppm lithium) were juxtaposed. The lithium concentration along traverses across the run products was measured using both laser ablation asa source for a Varian 820-MS quadrupole mass spectrometer and a CAMECA 1270 secondary ion mass spectrometer. The CAMECA 1270 was also used to measure the lithium isotopic fractionation across olivine grains recovered from the experiments. The lithium isotopes were found to be fractionationed by many tens of permil in the diffusion boundary layer at the grain edges asa result of 6Li diffusing significantly faster than 7Li. The lithium concentration and isotopic fractionation data across the olivine recovered from the different experiments were modeled using calculations in which lithium was assumed to be of two distinct types – one being fast diffusing interstitial lithium, the other much less mobile lithium on a metal site. The two-site diffusion model involves a large number of independent parameters and we found that different choices of the parameters can produce very comparable fits to the lithium concentration profiles and associated isotopic fractionation. Because of this nonuniqueness we are able to determine only a range for the relative diffusivity of 6Li compared to 7Li. When the mass dependence of lithium diffusion is parameterized as D6Li/D7Li=(7/6)β, the isotope fractionation for diffusion along the a and c crystallographic direction of olivine can be fit by β=0.4±0.1 while the fractionation in the b direction appears to be somewhat lower. Model calculations were also used to fit the lithium concentration and isotopic fractionation across a natural olivine grain from a peridotite xenolith from the Eastern North China Craton. The isotopic data were fit using β values (0.3–0.36) similar to that of the laboratory experiments. This, along with the fact that the isotopic fractionation is restricted to that part of the mineral with a gradient in lithium concentration, is strong evidence that the lithium zoning of this mineral grain is the result of lithium loss by diffusion and thus that it can be used, as illustrated, to constrain the cooling history.

Mechanical Modeling of Particles with Active Core–Shell Structures for Lithium-Ion Battery Electrodes

Active particles with a core–shell structure exhibit superior physical, electrochemical, and mechanical properties over their single-component counterparts in lithium-ion battery electrodes. Modeling plays an important role in providing insights into the design and utilization of this structure. However, previous models typically assume a shell without electrochemical activity. Inaccurate interfacial conditions have been used to bridge the core and the shell in several studies. This work develops a physically rigorous model to describe the diffusion and stress inside the core–shell structure based on a generalized chemical potential. Including both chemical and mechanical effects, the generalized chemical potential governs the diffusion in both the shell and the core. The stress is calculated using the lithium concentration profile. Our simulations reveal a lithium concentration jump forming at the core–shell interface, which is only possible to capture by modeling the shell as electrochemically active. I...

Multiscale Imaging and Spectroscopy on a Lithium-Ion Pouch Cell : Experiments and Modelling

Majority of electrode materials used for advanced lithium based batteries have well defined chemical composition and particle morphology. The chemistry as well as the microstructure can undergo reversible or irreversible changes under continuous electrochemical charge-discharge cycles. These could have measurable impact on the battery capacity and life. Combining multi-length scale characterization with electrochemical modelling can provide vital information regarding battery electrode degradation and inomogeneity. The talk will cover our recent work related to applying a number of neutron, X-ray and laser based spectroscopy and imaging methods to a number of relvant battery chemistries such as NMC and multi-lithium transition metal based compostions. These techniques covers from meso to micron length scale truly providing the mulit-scale nature of transport in batteries. Specifcally, we demonstrate lithiation in graphitic anodes using insitu neutron imaging in a pouch cell format. The neutron absorption contrast shows a direct correlation between degree of lithiation and the discharge voltage plateau at various time steps. We further provide a semi-quantitative comparison between the observed spatial variations of neutron absorption contrast in graphite with the calculated lithium concentration profiles computed using a 3D electrochemical transport model. In conjunction with imaging, in situ neutron diffraction of a similar pouch cell under identical test protocol was carried to obtain information about the local phase changes upon lithiation. Combined in-situ radiography and diffraction opens up a powerful nondestructive method to understand the multi-scale nature of lithium transport and degradation in practical lithium-ion cells.

Probing Multiscale Transport and Inhomogeneity in a Lithium-Ion Pouch Cell Using In Situ Neutron Methods

We demonstrate the lithiation process in graphitic anodes using in situ neutron radiography and diffraction in a single-layer pouch cell. The variation in neutron absorption contrast in graphite shows a direct correlation between the degree of lithiation and the discharge potential. The experimental neutron attenuation line profiles across the graphite electrode at various discharge times (potentials) were compared with lithium concentration profiles computed using a 3D electrochemical transport model. In conjunction with imaging/radiography, in situ neutron diffraction was carried out to obtain information about the local structural changes during various stages of lithiation in carbon. Combined in situ radiography and diffraction supported by 3D multiscale electrochemical modeling opens up a powerful nondestructive tool that can be utilized to understand the multiscale nature of lithium transport as well as observe various inhomogeneities at a cell level.

Inverse Modelling Approach to the Determination of Concentration-Dependent Transport Properties in Electrolytes: The Effect of Ion Pairing

The goal of the present investigation was to extend the recently proposed inverse modelling approach for determining concentration-dependent transport properties (salt diffusivity and Li+ cation transference number) to concentrated lithium salt solutions in solvents with relatively low permittivity. We demonstrated in our previous studies that NMR concentration profiles can be used for estimating the concentration dependent transport properties of LiTFSI solution in propylene carbonate (PC) under minimal assumption, including that of negligible ion pairing (simplified transport model) [1], which is valid for solvents with relative high permittivity [2] (εr ≈ 65 for PC). Herein we consider the case where ion paring effects cannot be neglected, due to the low permittivity of the solvent, as is the case for concentrated solutions of Li salts in mixed organic carbonate solvents (εr≈ 26 for EC:DMC 1:1). The data for the present study was obtained in the form of NMR intensity images of the 19F nuclei in the PF6 - anions of LiPF6 dissolved in a binary mixture of ethylene carbonate (EC) and dimethyl carbonate (DMC), recorded under galvanostatic conditions. The NMR images were then post-processed to obtain lithium concentration profiles. The formation of non-negligible amounts of ion pairs in the present work significantly affects the estimation of transport properties of the system. As a result, the simplified transport model produces thermodynamically inconsistent results, manifested as negative transference numbers obtained from the inverse modelling analysis (Fig. 1). To remedy this situation, we considered an extended transport model which assumes that oppositely charged ions combine to form neutral ion pairs and which tracks the concentration of neutral ion pairs in addition to the concentration of free ions. However, due to the presence of a reaction term describing the formation and disintegration of ion pairs, the resulting PDE system is extremely stiff. Using methods of asymptotic analysis, corresponding to the limit of fast reaction rates, we have reduced the modeling problem to a more simple system describing the evolution of the total lithium concentration, which is computationally tractable. As this reduced system may not satisfy all boundary conditions of the original extended system, an additional material property called boundary transference number was introduced and its optimal dependence on the total concentration was identified via inverse analysis. The unknown material properties are concentration dependent (except for the equilibrium constant K) and are reconstructed with minimal assumptions using methods of variational optimization, to minimize the least-square error between the experimentally determined and simulated concentration values. The optimization problem is solved using a gradient-based method with a careful treatment of uncertainties resulting from the presence of noise in the experimental data. A key element of our computational approach is identification of the sensitivity of the PDE system solutions to perturbations of the constitutive relations, which is achieved through a novel adjoint-based approach. As shown in Fig. 2, the reconstruction produces thermodynamically consistent results for the Li+transference number under conditions when ion pairing effects cannot be neglected.

Reassessing the cooling rate and geologic setting of Martian meteorites MIL 03346 and NWA 817

Lithium concentration and isotopic fractionation profiles across augite grains from two Martian meteorites – MIL 03346 and NWA 817 – were used to determine their thermal history and implications for their geologic setting. The iron–magnesium zoning and associated magnesium isotopic fractionation of olivine grains from NWA 817 were also measured and provide a separate estimate of the cooling rate. The observed correlation of concentration with isotopic fractionation provides the essential evidence that the zoning of these grains was in fact due to diffusion and thus can be used as a measure of their cooling rate. The diffusion rate of lithium in augite depends on the oxygen fugacity, which has to be taken into account when determining a cooling rate based on the lithium zoning. The Fe–Mg exchange in olivine is much less sensitive to oxygen fugacity, but it is significantly anisotropic and for this reason we determined the direction relative to crystallographic axes of the line along which the Fe–Mg zoning was measured. We found that the cooling rate of NWA 817 determined from the lithium zoning in augite grains and that based on the Fe–Mg zoning of olivines are in good agreement at an oxygen fugacity close to that of quartz–fayalite–magnetite oxygen buffer. The cooling rate of MIL 03346 was found to be resolvably faster than that of NWA 817 – of the order of 1°C/h for the former and of the order of 0.2°C/h for the latter. An important observation regarding the history of MIL 03346 and NWA 817 is that the lithium and Fe–Mg zoning are only observed where the augite or olivine is in contact with the mesostasis, which implies that they were already about 80% crystallized at the time diffusion began. The augite and olivine core compositions while very homogeneous are not in equilibrium with each other, which we interpret to imply that prior to the rapid cooling there must have been a protracted period of the order of years above the solidus, during which the much faster Fe–Mg exchange in olivine compared to that in augite allowed the olivine to maintain equilibrium with a changing melt composition while the augite was not significantly affected. We suggest two possible geological settings for the origin and evolution of MIL 03346 and NWA 817: (1) a slow cooling stage in a crystallization front in a crustal magma chamber, followed by eruption of melt plus portions of the crystallization front onto the surface where the final fast cooling took place at the bottom of a lava flow or melt pond, and (2) eruption of a crystal laden melt as a thick long-lived lava flow where the crystals continued to grow as a cumulate and were rapidly cooled when the overlying lava layer was suddenly drained.

Simplification of pseudo two dimensional battery model using dynamic profile of lithium concentration

A sophisticated BMS often requires an accurate yet simple battery model. Simplified models such as the single particle model (SPM), however, provide limited insight because lithium concentration variations over the cell thickness dimension are often neglected. In this study, we propose a simplified electrochemical model that, by reviving the lithium concentration variation across the cell thickness, provides significantly improved prediction power over the SPM. The lithium concentration profiles are first derived according to the electrochemistry-based pseudo-two dimensions (P2D) model under the steady-state assumption, they are then relaxed into a dynamic model. By employing steady-state concentration profiles coupled with averaged dynamics, the proposed model predicts electrolyte and solid surface concentrations (ce and css, respectively) and potential variations across the cell during both transients and stead-state conditions. The proposed model is validated by comparing the cell voltage, ce, and css concentration RMS errors with respect to the P2D model under pulse and constant current inputs. The simulation shows that the proposed model achieves at least 74%, 77%, and 65% RMS error reductions for cell voltage, css and ce, respectively, when compared to SPM in constant current simulation. Finally, the presented model is used to predict and detect local lithium plating, which the SPM is not capable of doing; our method yields predictions similar to those of the original P2D model at computational loads comparable to SPM.

The Role of Solid Mechanics in Electrochemical Energy Systems such as Lithium-ion Batteries

The effect of stress on storage particles within a lithium-ion battery, while acknowledged, is not fully understood. In this study we identify the importance of solid mechanics in the performance and reliability of the system. We identify three non-dimensional parameters that govern the stress response within a spherical storage particle, and we describe the results of numerical simulations that characterize particle stresses. The non-dimensional groups contain system parameters such as the diffusion coefficient, the particle radius, the lithium partial molar volume and the host material's Young's modulus. Stress maps are presented for various values of these parameters for fixed rates of insertion and extraction, with boundary conditions applied to particles similar to those found in a battery. Stress and lithium concentration profiles for various values of these parameters show that the coupling between stress and concentration is magnified depending on the values of the parameters.