Predicting active material utilisation in LiFePO4 electrodes using a multi-scale mathematical model

A mathematical model is developed to simulate the discharge of a LiFePO4 cathode. This model contains 3 size scales, which match with experimental observations present in the literature on the multi-scale nature of LiFePO4 material. A shrinking-core is used on the smallest scale to represent the phase-transition of LiFePO4 during discharge. The model is then validated against existing experimental data and this validated model is then used to investigate parameters that influence active material utilisation. Specifically the size and composition of agglomerates of LiFePO4 crystals is discussed, and we investigate and quantify the relative effects that the ionic and electronic conductivities within the oxide have on oxide utilisation. We find that agglomerates of crystals can be tolerated under low discharge rates. The role of the electrolyte in limiting (cathodic) discharge is also discussed, and we show that electrolyte transport does limit performance at high discharge rates, confirming the conclusions of recent literature.

The persistence of phase-separation in LiFePO4 with two-dimensional Li+ transport : the Cahn-Hilliard-reaction equation and the role of defects

We examine the solution of the two-dimensional Cahn-Hilliard-reaction (CHR) equation in the xy plane as a model of Li+ intercalation into LiFePO4 material. We validate our numerical solution against the solution of the depth-averaged equation, which has been used to model intercalation in the limit of highly orthotropic diffusivity and gradient penalty tensors. We then examine the phase-change behaviour in the full CHR system as these parameters become more isotropic, and find that as the Li+ diffusivity is increased in the x direction, phase separation persists at high currents, even in small crystals with averaged coherency strain included. The resulting voltage curves decrease monotonically, which has previously been considered a hallmark of crystals that fill homogeneously.

Mathematical modelling of LiFePO4 cathodes

LiFePO4 is a commercially available battery material with good theoretical discharge capacity, excellent cycle life and increased safety compared with competing Li-ion chemistries. It has been the focus of considerable experimental and theoretical scrutiny in the past decade, resulting in LiFePO4 cathodes that perform well at high discharge rates. This scrutiny has raised several questions about the behaviour of LiFePO4 material during charge and discharge. In contrast to many other battery chemistries that intercalate homogeneously, LiFePO4 can phase-separate into highly and lowly lithiated phases, with intercalation proceeding by advancing an interface between these two phases. The main objective of this thesis is to construct mathematical models of LiFePO4 cathodes that can be validated against experimental discharge curves. This is in an attempt to understand some of the multi-scale dynamics of LiFePO4 cathodes that can be difficult to determine experimentally. The first section of this thesis constructs a three-scale mathematical model of LiFePO4 cathodes that uses a simple Stefan problem (which has been used previously in the literature) to describe the assumed phase-change. LiFePO4 crystals have been observed agglomerating in cathodes to form a porous collection of crystals and this morphology motivates the use of three size-scales in the model. The multi-scale model developed validates well against experimental data and this validated model is then used to examine the role of manufacturing parameters (including the agglomerate radius) on battery performance. The remainder of the thesis is concerned with investigating phase-field models as a replacement for the aforementioned Stefan problem. Phase-field models have recently been used in LiFePO4 and are a far more accurate representation of experimentally observed crystal-scale behaviour. They are based around the Cahn-Hilliard-reaction (CHR) IBVP, a fourth-order PDE with electrochemical (flux) boundary conditions that is very stiff and possesses multiple time and space scales. Numerical solutions to the CHR IBVP can be difficult to compute and hence a least-squares based Finite Volume Method (FVM) is developed for discretising both the full CHR IBVP and the more traditional Cahn-Hilliard IBVP. Phase-field models are subject to two main physicality constraints and the numerical scheme presented performs well under these constraints. This least-squares based FVM is then used to simulate the discharge of individual crystals of LiFePO4 in two dimensions. This discharge is subject to isotropic Li+ diffusion, based on experimental evidence that suggests the normally orthotropic transport of Li+ in LiFePO4 may become more isotropic in the presence of lattice defects. Numerical investigation shows that two-dimensional Li+ transport results in crystals that phase-separate, even at very high discharge rates. This is very different from results shown in the literature, where phase-separation in LiFePO4 crystals is suppressed during discharge with orthotropic Li+ transport. Finally, the three-scale cathodic model used at the beginning of the thesis is modified to simulate modern, high-rate LiFePO4 cathodes. High-rate cathodes typically do not contain (large) agglomerates and therefore a two-scale model is developed. The Stefan problem used previously is also replaced with the phase-field models examined in earlier chapters. The results from this model are then compared with experimental data and fit poorly, though a significant parameter regime could not be investigated numerically. Many-particle effects however, are evident in the simulated discharges, which match the conclusions of recent literature. These effects result in crystals that are subject to local currents very different from the discharge rate applied to the cathode, which impacts the phase-separating behaviour of the crystals and raises questions about the validity of using cathodic-scale experimental measurements in order to determine crystal-scale behaviour.

A comparison of mathematical models for phase separation in high-rate LiFePO4 cathodes

We construct a two-scale mathematical model for modern, high-rate LiFePO4cathodes. We attempt to validate against experimental data using two forms of the phase-field model developed recently to represent the concentration of Li+ in nano-sized LiFePO4crystals. We also compare this with the shrinking-core based model we developed previously. Validating against high-rate experimental data, in which electronic and electrolytic resistances have been reduced is an excellent test of the validity of the crystal-scale model used to represent the phase-change that may occur in LiFePO4material. We obtain poor fits with the shrinking-core based model, even with fitting based on “effective” parameter values. Surprisingly, using the more sophisticated phase-field models on the crystal-scale results in poorer fits, though a significant parameter regime could not be investigated due to numerical difficulties. Separate to the fits obtained, using phase-field based models embedded in a two-scale cathodic model results in “many-particle” effects consistent with those reported recently.

Single-Shot Preparation of Crystalline Nanoplate LiFePO4 by a Simple Polyol Route

Nanoplate LiFePO4 is synthesized by a polyol route starting from only two reactants, namely, FePO4 and LiOH. The crystalline compound forms by refluxing a tetraethylene glycol solution consisting of FePO4 and LiOH at 335 degrees C without further heating of the reaction product.The nanoplates have average dimensions of 30 nm width and 160 nm length, as measured from transmission electron microscopy micrographs.The surface area of the LiFePO4 sample is 38 m(2) g(-1). Also, the sample is porous with a broadly distributed pore around 50 nm. The electrodes fabricated out of the nanoplate of LiFePO4 exhibit a high electrochemical activity. Discharge capacity values measured are 160 and 100 mAh g(-1) at 0.15C and 3.45C, respectively. A stable capacity of about 155 mAh g(-1) is measured at 0.2C over a 50 charge-discharge cycle. (C) 2010 The Electrochemical Society. [DOI: 10.1149/1.3425730] All rights reserved.

High Rate Capability of a Dual-Porosity LiFePO4/C Composite

Mesoporous intercalation compounds consisting of two differentdistributions of pores represent a potentially attractive material for high-rate cathodes. A mesoporous LiFePO4/C composite with two sizes of pores is prepared for the first time via a solution-based polymer templating technique. The precursor of the LiFePO4/C composite is heated at different temperatures in the range from 600 to 800 degrees C to study the effect of crystallinity, porosity, and morphology on the electrochemical performance. The composite is found to attain reduction in the surface area, carbon content, and porosity upon increasing temperature. Nonetheless, the composite prepared at 700 degrees C with pore-size distributions of around 4 and 50 nm exhibits a high rate capability and stable capacity retention upon cycling.

Enhanced cycling performance and high energy density of LiFePO4 based lithium ion batteries

LiFePO4 attracts a lot of attention as cathode materials for the next generation of lithium ion batteries. However, LiFePO4 has a poor rate capability attributed to low electronic conductivity and low density. There is seldom data reported on lithium ion batteries with LiFePO4 as cathode and graphite as anode. According to our experimental results, the capacity fading on cycling is surprisingly negligible at 1664 cycles for the cell type 042040. It delivers a capacity of 1170 mAh for 18650 cell type at 4.5C discharge rate. It is confirmed that lithium ion batteries with LiFePO4 as cathode are suitable for electric vehicle application. (c) 2007 Elsevier B.V. All rights reserved.

Facile synthesis of nanocrystalline LiFePO4/graphene composite as cathode material for high power lithium ion batteries

We describe a simple strategy, which is based on the idea of space confinement, for the synthesis of carbon coating on LiFePO₄ nanoparticles/graphene nanosheets composites in a water-in-oil emulsion system. The prepared composite displayed high performance as a cathode material for lithium-ion battery, such as high reversible lithium storage capacity (158 mA h g^-1 after 100 cycles), high coulombic efficiency (over 97%), excellent cycling stability and high rate capability (as high as 83 mA h g ^-1 at 60 C). Very significantly, the preparation method employed can be easily adapted and be extended as a general approach to sophisticated compositions and structures for the preparation of highly dispersed nanosized structure on graphene. 

Synthèse du LiXFePO4 par voie fondue et l’étude de la couche de carbone sur LiFePO4

Le LiFePO4 est un matériau prometteur pour les cathodes des batteries au lithium. Il possède une bonne stabilité à haute température et les précurseurs utilisés pour la synthèse sont peu couteux. Malheureusement, sa faible conductivité nuit aux performances électrochimiques. Le fait de diminuer la taille des particules ou d’enrober les particules d’une couche de carbone permet d’augmenter la conductivité. Nous avons utilisé une nouvelle méthode appelée « synthèse par voie fondue » pour synthétiser le LiFePO4. Cette synthèse donne des gros cristaux et aucune impureté n’est détectée par analyse Rayon-X. En revanche, la synthèse de LiXFePO4 donne un mélange de LiFePO4 pur et d’impureté à base de lithium ou de fer selon l’excès de fer ou de lithium utilisé. La taille des particules de LiFePO4 est réduite à l’aide d’un broyeur planétaire et plusieurs paramètres de broyage sont étudiés. Une couche de carbone est ensuite déposée sur la surface des particules broyées par un traitement thermique sur le LiFePO4 avec du -lactose. L’influence de plusieurs paramètres comme la température du traitement thermique ou la durée du chauffage sont étudiés. Ces expériences sont réalisées avec un appareil d’analyse thermogravimétrique (ATG) qui donne la quantité de chaleur ainsi que la variation de masse durant le chauffage de l’échantillon. Ce nouveau chauffage pour la couche de carbone donne des échantillons dont les performances électrochimiques sont similaires à celles obtenues précédemment avec la méthode de chauffage pour la couche de carbone utilisant le four tubulaire.

Effect of magnetic treatment on microstructure and cycle performance of LiFePO4/C cathode material

LiFePO4/C composite was prepared by hydrothermal synthesis along with a magnetic treatment method. The LiFePO4/C composite synthesized without magnetic treatment is an integrated rhombic shape crystal, whereas the LiFePO4/C material synthesized with magnetic treatment presents a rhombus shape which is self-assembled by a number of small crystal particles with an average size of about 100 nms. The capacity retention for the LiFePO4/C cathode material synthesized without magnetic treatment is only 77% after 30 charge-discharge cycles at 0.2 C, but the LiFePO4/C composite synthesized with magnetic treatment has a capacity retention of 100% after 100 charge-discharge cycles at 1 C and 5 C. It suggests that magnetic treatment can remove Fe3+ cations effectively during the preparation process and enhance the cycle performance of the LiFePO4/C material.

Biotemplated fabrication of a novel hierarchical porous C/LiFePO4/C composite for Li-ion batteries

Hierarchical porous composites are a potentially attractive material for high-rate cathode. This work presents a facile sol-gel process for the fabrication of a hierarchical porous C/LiFePO4/bio-C composite by using artemia cyst shells as natural biological carbon templates. The C/LiFePO4/bio-C composite exhibits a superior electrochemical performance with discharge capacities of 105 mA h g-1, 93 mA h g-1 and 80 mA h g-1 at 5 C, 10 C and 20 C, respectively. Remarkably, it produces a high discharge capacity of 69.1 mA h g-1 and no fading after 50 cycles even at a high current density of 6800 mA g-1. This journal is

Synthesis of single-crystalline LiFePO4 with rhombus-like morphology

In this investigation, carbon-coated LiFePO4 cathode materials were synthesized with a facile hydrothermal method. The structure and electrochemical properties of the materials were investigated by X-ray diffraction (XRD), Roman, transmission electron microscopy-energy dispersive spectroscopy (TEM-EDS), and electrochemical impedance spectroscopy (EIS). By adjusting the mixing concentration of starting materials, a single-crystalline LiFePO4 with an anisotropic rhombus morphology (Space Group: Pmnb No. 62) were successfully synthesized. In addition, the carbon coated on the surface of LiFePO4 material prepared has a lower ID/IG (0.80), which indicates an optimized carbon structure with an increased amount of sp2-type carbon. Electrochemical performance test shows that the carbon-coated LiFePO4 cathode materials have an initial discharge capacity of 146 mAh g−1 at 0.2C.

Effect of different carbon-coating ways on the microstructure and electrochemical performance of LiFePO4/C cathodes

Through comparative studying on LiFePO4/C preparation process of adding carbon source in precursor and pre-sintered material, marked as LFP-1 (in-situ carbon coating) and LFP-2 respectively, by means of C-S test, XRD, SEM, BET, Raman, the effects of carbon content, morphology, particle size and surface carbon structure on the electrochemical performance of LiFePO4/C cathodes were investigated. SEM images showed that particle sizes of LFP-1 and LFP-2 are about 10μm and 100nm respectively. The EIS and galvnostatic charge-discharge tests indicated that LFP-1 has lower charge transfer resistance (Rct), better rate and cycle performance than that of LFP-2, which can be attributed to the different microstructure and the higher degree of graphitized carbon of LiFePO4/C. Raman spectroscopic analysis showed that the ratio of the ID/IG and Asp3/Asp2 of LFP-1 is lower that of LFP-2, which means the degree of graphitized carbon of LFP-1 is higher than that of LEP-2. These results have important significance for improving the overall performance of olivine cathode materials for lithium ion batteries.

Improved Real-time State-of-Charge Estimation of LiFePO4 Battery Based on a Novel Thermoelectric Model

Li-ion batteries have been widely used in electric vehicles, and battery internal state estimation plays an important role in the battery management system. However, it is technically challenging, in particular, for the estimation of the battery internal temperature and state-ofcharge (SOC), which are two key state variables affecting the battery performance. In this paper, a novel method is proposed for realtime simultaneous estimation of these two internal states, thus leading to a significantly improved battery model for realtime SOC estimation. To achieve this, a simplified battery thermoelectric model is firstly built, which couples a thermal submodel and an electrical submodel. The interactions between the battery thermal and electrical behaviours are captured, thus offering a comprehensive description of the battery thermal and electrical behaviour. To achieve more accurate internal state estimations, the model is trained by the simulation error minimization method, and model parameters are optimized by a hybrid optimization method combining a meta-heuristic algorithm and the least square approach. Further, timevarying model parameters under different heat dissipation conditions are considered, and a joint extended Kalman filter is used to simultaneously estimate both the battery internal states and time-varying model parameters in realtime. Experimental results based on the testing data of LiFePO4 batteries confirm the efficacy of the proposed method.