Multi-Scale Characterization Studies of Aged Li-Ion Large Format Cells for Improved Performance: An Overview

Lithium is an ideal anode material for Li-ion batteries, but because of the plating out of lithium during the charge/discharge cycle and subsequent formation of dendrites, there is a risk of the cell being short-circuited. Instead, carbonaceous materials are preferred for anodes in current commercial Li-ion batteries.²³ Studies have been conducted on graphite,²⁴ C-C composite, mesocarbon microbeads (MCMB),²⁵ carbon nanotubes^26,27 and carbon films. These anodes have a very good rate of lithium insertion/removal and thus improve the charge/discharge rate (power rating) of the battery, but the performance of the cell is limited due to the formation of a solid electrolyte interphase (SEI) during cycling of the cell.^23,28,29 The SEI is formed from the electrolyte decomposition products.³⁰ This SEI layer prevents the graphite surface from further exfoliation and also prevents further reduction of the electrolyte and consumption of active lithium. In the case of nanoparticulate graphite, the consumption of active lithium would be even higher, and the excessive charge developed between the graphite surface and the SEI would result in a loss of overall cell voltage. The SEI layer also reduces the active surface area and the porosity affecting the performance of the cell. Also, it is important to note that the lithium is intercalated into graphite at potentials less than 100 mV versus Li/Li⁺. There is always a risk of lithium depositing on the graphite surface resulting in dendrite formation and fatal short-circuiting of the cell.²⁴ The other classes of materials that are being pursued are the materials that can reversibly form alloys with lithium. As shown in Table I these alloys have much higher capacity than graphite. Since the equilibrium potential of these alloys with Li/Li⁺ is higher the possibility of plating and the reduction of electrolyte solvent is minimized. The drawback of these materials is the large volume change during the charging and discharging cycles that leads to cracking and mechanical disintegration of the anode structure. The last groups of materials that can be used as anode are certain lithium oxides that have low lithium equilibrium potential. TiO₂ is an example of such a material.³¹ These materials have the least risk of lithium plating and electrolyte reduction, but have very low energy capacity due to the low operating voltage when coupled with other cathode material.

The most common cathode materials are layered oxides LiMO₂, the spinels Li[M₂]O₄ and olivines LiMPO₄ where M is a transition metal atom.⁷

Layered oxide LiCoO₂, was developed as the cathode material for commercial Li-ion batteries,^7,24 but due to expensive and toxic cobalt they were later replaced by other layered oxides such as LiNi_0.8Co_0.15Al_0.05O₂, LiNi_0.8Co_0.2O₂, Li_1−xNi_1−yCo_yO₂, and LiMn_0.5Ni_0.5O₂ in commercial batteries.^7,32,33 These oxides have a high operating voltage, in the range of 2.75 V to 4.3 V.⁷ They have very high energy density and power density but they lack the necessary structural stability for deep discharge cycles, during which the host oxide structure collapses upon removal of more than 50% of the Li. The spinel structured LiMn₂O₄ has good structural stability.²⁴ They also have higher operating voltage and high charge/discharge rate but low energy density. The most recent among these cathode materials have been olivine-structured materials such as LiFePO₄. LiFePO₄ has a lower operating voltage of ∼3.3 V but demonstrates higher power and energy density along with good structural stability. Using nanosized particles helps mitigate the lower conductivity of LiFePO₄. Table II lists the properties of certain cathode materials. Battery manufacturers have also developed cathodes with multiple materials such as a mixed cathode with Li Ni_1/3Mn_1/3Co_1/3O₂ layered oxide and LiMn₂O₄ spinel.^34–40 They have high specific capacity and thermal stability, and they limit the dissolution of Mn that limits the cycle life.^{11,37–39,41,42}

This review focuses on the characterization of LiFePO₄ cathode material used in commercial cells. This material is extensively discussed in literature and it is preferred by some automobile makers due to its low cost and environmentally benign nature. The oxygen atoms in the phosphate have strong bonds and are not easily released, making the material incombustible in the event of overcharging. Thus the material is thermally and chemically stable and can provide thousands of charge/discharge cycles.^43–46

A separator is porous membrane with good ionic conductivity and good electronic insulation. The separator should allow a rapid flow of ions while preventing any electrical contact between the two electrodes of the cell. Until recently very little research and development has done to develop new separators as compared to other battery components. The separators should have the following features:⁴⁷

• Good electronic insulator
• Minimum electrolyte and ionic resistance
• Good mechanical, dimensional and physical stability
• Uniform thickness, and tortuosity
• Chemically stable and resistant to degradation by electrolyte, impurities and electrode reactants and products.
• Thermally stable
• Prevent migration of species between the two electrodes
• Easily wetted by the electrolyte

The most common type of separators in nonaqueous Li-ion batteries is microporous polyolefins. They can be a single layer of polyethylene (PE), polypropylene (PP) or laminates of PE and PP (Fig. 4).^47,48

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The function of the electrolyte is to provide a path for the ions while blocking any electronic charge flow. An electrolyte should have the following keys features⁴⁹

• Good ionic conductor and electronic insulator, to have better ion transport and minimum self-discharge
• Electrochemically inert with both, the oxidizing or reducing electrode surfaces within the operating range of the cell
• Should not react with other cell components such as cell separators, current collectors, etc.
• Environmentally benign

The combination of electrolyte and the electrode materials is responsible for the formation of the SEI that limits the life of the cell. The stability and quality of the film depends on the electrolyte composition, additives and impurities. Usually the electrolyte is composed of one or more liquid solvents and one or more salts. The most common electrolytes used in current generation lithium ion batteries are non-aqueous. The preferred solvent for the electrolyte in lithium-ion batteries is a combination of ethylene carbonate (EC) and dimethyl carbonate (DMC). EC is solid at room temperature and has low viscosity.⁴⁹ The EC:DMC mixture is liquid for range of compositions. The most common salt is LiPF₆. A 1 M LiPF₆ solution of EC:DMC 1:1 (wt) has a conductivity of 10⁷ mS cm⁻¹, and it is stable and safe in the temperature range between −20 and 50°C. The conductivity is quite high for a nonaqueous electrolyte, but is still too low to avoid non-homogeneous usage of thick electrodes when high power is required. Certain polymers and ionic liquids are being developed for future generations of lithium ion batteries.⁴⁹ Solid polymer electrolytes have very poor conductivity (<1 mS cm⁻¹).⁵⁰ Ionic liquids also need to be tested before they can be used in lithium ion batteries.⁴⁹ Table III lists the properties of certain solutes and solvent for lithium-ion battery electrolytes.

A side reaction that causes the decomposition of the reductive electrolyte and consumption of lithium ions takes place between the electrode and the electrolyte surface in the lithium-ion battery systems.³⁰ The decomposition products are deposited on the electrode surface. This deposited layer is termed as a solid electrolyte interphase (SEI). The SEI layer consumes the active lithium, and increases the impedance of the anode causing the capacity and power fade of the cell at the system level. Though SEI can be formed at both the anode and the cathode, it is more prominent at the anode surface due to the low potentials (vs Li/Li⁺) reached during the charging of the cell that are beyond the electrochemical stability window of most electrolyte solvents. As SEI is composed of the electrolyte decomposition products, it is understood that the chemical composition and properties of the SEI layer are dependent on the anode surface and the electrolyte solvents. Several electrolyte decomposition reactions have been reported in literature.⁷⁵ Since carbonate solvents are most common for the lithium-ion battery systems there exists several studies related to the reduction reactions and subsequent formation of the SEI layer for solvents such as propylene carbonate (PC), dimethyl carbonate (DMC), and diethyl carbonate (DEC) and ethylene carbonate (EC).^74–79

SEI once formed during the initial cycling of the cell is considered to limit the further reduction of the electrolyte and the corrosion of the anode surface. But the SEI layer conversion, stabilization and growth takes place steadily throughout the life of the battery although at a lower rate than at the initial stages.³⁰ The rate of the SEI growth is limited by the kinetics of the decomposition reaction or the diffusion of the solvent molecules through the SEI layer.¹¹ In general the growth of the SEI layer is accelerated at the elevated temperatures and the lower potentials of the anode.

The SEI formation, and growth is generally viewed as the primary reason behind the performance degradation of the lithium-ion cell by causing the capacity fade and the rise in the internal resistance. Several modeling efforts have demonstrated the loss of capacity due the SEI growth during the operation of the cell under various conditions.^76,80,81

Lithiation and delithiation of the host structure during each cycle of the cell causes the molar volume change of the host structure. This volume change in the crystal structure leads to the structural changes of the anode and cathode. Such a structural change affects the performance of the cathode more than the regular carbonaceous type anode. The structural changes can induce mechanical stresses and strains in the nanoparticles of the active cathode material, which subsequently act on the composite cathode structure.³⁰

During the lithiation and delithiation process some cathode oxides also undergo phase change. This phase change can cause the distortion of the crystal lattice further inducing mechanical stresses.³⁰ The misfit strains at the phase boundaries lead to discontinuities causing the cracking of the nanoparticles.³⁰ There have been several modeling efforts to understand the crack formation and propagation due to the mechanical stresses and strains in the cathode nanoparticles.^89–96

Thermography is used to measure the variations in temperatures through thermal imaging of the object. Here thermography by flash method is used as the first step in the multi-scale characterization of the LiFePO₄ cathode material. The flash method, which was introduced by Parker et al.,¹¹³ has been used extensively in the measurement of thermal characteristics such as thermal diffusivity, and thermal conductivity of various different kinds of materials. In this simple technique the front face of the sample with slab geometry receives a pulse of radiant energy coming from a laser or a flash lamp. The temperature rise of the opposite face is captured through high resolution, high frequency thermal imaging by an infrared (IR) camera. The average temperature rise in the sample is only few degrees above the initial value. This temperature rise curve is used for thermal characterization of the samples.^114,115

Several authors have successfully applied this technique for several different materials. Lafond-Huot and Bransier,¹¹⁶ Luc and Balageas,¹¹⁷ Philippi et al.,¹¹⁸ Degiovanni et al.,¹¹⁹ and Krapez¹²⁰ used it to study anisotropic materials. Batsale et al.¹²¹ and Ramond et al.^122,123 used it to study complex heterogeneous media. Moyne et al.^124,125 and Azizi et al.¹²⁶ studied porous materials. André and Degiovanni,¹²⁷ Hahn et al.,¹²⁸ and Lazard et al.¹²⁹ applied it to study semi-transparent materials. Coquard and Panel¹³⁰ used it to study liquids or pasty materials. There are also several reviews published about the theoretical and practical applications of this technique by Righini and Cezairliyan,¹³¹ Degiovanni,¹³² Taylor,¹³³ Balageas,¹³⁴ Taylor and Maglić,¹³⁵ Maglić and Taylor,¹³⁶ Sheindlin et al.,¹³⁷ Baba and Ono,¹³⁸ and Vozár and Hohenauer.^115,139

As large areas can be easily scanned with this technique, it becomes an ideal choice to scan the long cathode strips for any physical and/or morphological damages. Nagpure et al.⁶⁵ have demonstrated the application of this technique in battery research by capturing 2D thermographs of the cathode strips harvested from unaged and aged commercial cells. The setup to capture the thermal maps of the samples is discussed in ASTM 1461 92 standard¹⁴⁰ and is shown in Fig. 9. The main features of this setup are the flash lamp, sample mount, high-resolution IR camera, and data acquisition system. The high energy pulse required in this experiment was generated by Profoto, Acute 2, flash lamp with a 2400 W-s capacity. The flash lamp was operated to deliver a finite pulse of energy at 300 W-s. The sample mount was a custom made hollow box with a square slot of approximately 63.5 mm × 63.5 mm on one face. The flash lamp was centered over this slot. A circular hole of approximately 90 mm was cut on the opposite face. The IR camera lens was inserted through this hole and focused on the sample. The thermal maps were taken with an IR camera from Indigo Systems, Phoenix Mid-wave IR Camera, with a 320 × 256 pixel resolution and InSb focal plane array. The frequency of the camera is set at 346 Hz. The data acquisition system was built into the IR camera equipment.

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The long cathode strip was divided into five equally spaced sections each ∼65 mm (2.5 in) wide. The sample was mounted flushed on the face with the square slot on the sample mount. The center of the flash lamp coincides approximately with the center of the sample so that the heat pulse is uniformly incident on the sample. The IR camera lens was focused on the opposite face of the sample with the center of the lens aligned approximately with the center of the sample. The finite heat pulse from the flash lamp was incident on the front face of the sample. The heat gained by the sample from this pulse is conducted through its thickness to the rear face. As such the rear face of the sample is heated and its temperature increases. The IR camera captures this heat gained by the rear face at a frequency of 346 frames per second. The experimental setup was under ambient conditions and as such all the thermal maps were obtained under ambient conditions.

The thermal maps of the aged and unaged sample for all five sections (Fig. 10a), shown in Fig. 10, were taken when the temperature of the rear face of the sample reached the maximum value. In these thermal maps the dark spots represent the cold areas while the bright spots represent the hot areas. The dark spots are more prominent in the aged sample (right side) as compared to the unaged sample (left side).

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The dark spots are mostly in areas where the spalling of the cathode material from the current collector was observed. The spalling could be attributed to the disbonding, cracking or buildup of residual stress and strain between the current collector and the cathode material interface. The spalling could also be attributed to the shocks and vibrations during disassembling of cells and/or handling of the long cathode strip. Thus the reason for spalling could not be conclusively attributed to any specific damage mechanism. Since spalling was a result or effect of certain underlying damage mechanism the aging studies were focused on areas without any visible damage.

Thermal diffusivity was used as a damage metric in the areas without any visible damage (no spalling). Figure 11a shows the temperature rise of the rear face of the sample in terms of IR counts. The temperature rise shown here is for section # 4 of the aged and the unaged cathode samples shown in Fig. 11b. An area with a uniform IR intensity was randomly chosen in the thermal map of the aged and unaged sample for thermal diffusivity analyzes. The IR counts are obtained over this area from the instant the heat pulse was incident on the sample until the temperature of the sample reaches a steady state value. A baseline temperature was identified in these plots as the temperature just before the pulse is incident on the sample (T_ini). Then the maximum temperature was measured as the steady state temperature of the rear face of the sample (T_max). The half rise time (t_1/2), i.e. the time required from the initiation of the pulse on the front face of the sample to the time at which the temperature of the rear face of the sample reached half the difference between T_ini and T_max, was calculated. The thermal diffusivity for the sample was then calculated using the following formula:¹⁴⁰

where α is the thermal diffusivity (m/s), L is the thickness of the sample (m), and t_1/2 is the half rise time (s). It is important to note that the Eq. 5.1 is not dependent on the absolute value of T_max. Therefore, the observed differences in maximum IR counts between aged and unaged samples as seen in Fig. 11a are not important in these analyzes.

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Figure 11b shows a comparison of the thermal diffusivity between the unaged and the aged sample over all 5 sections. As can be seen in this figure the thermal diffusivity of the aged sample was more than the unaged sample in all 5 sections. This indicates that the rate of heat conduction in aged samples is higher than the unaged sample, which can be attributed to the change in the porosity of the cathode material. The differences in the thermal diffusivity values between aged and unaged samples are significantly less in sections 1 and 5. These sections are near the core of the cylinder and near the outer edge of the cylinder, respectively. The differences in the thermal diffusivity are more prominent in sections 2, 3, and 4 of the samples. Nagpure et al.⁶⁵ believed that the different rate of change in the porosity in various sections leads to the non-uniform change in the thermal diffusivity across the sections.

Theoretically, thermal diffusivity is given as the ratio of the thermal conductivity to volumetric heat capacity as follows:

where α is the thermal diffusivity (m²/s), k is the thermal conductivity (W/m-K), and ρC_p is the volumetric heat capacity (J/m³K). The Eq. 5.2 is strictly applicable only to monolithic material. Since, the cathode material is a composite, Nagpure et al.⁶⁵ associated the increase in thermal diffusivity with a change in k, ρ and/or C_p.

Figure 12 shows the schematic of a proposed mechanism explaining the increase in the thermal diffusivity of a LiFePO₄ cathode due to aging.⁶⁵ As a first order approximation the cathode can be considered as a porous medium. Also, it can be assumed here that the heat diffuses through the cathode only due to conduction. As the cathode ages the nanoparticles tend to coarsen by sintering. Due to this sintering of the nanoparticles, the effective surface area per unit volume decreases,¹⁴¹ with an associated decrease in the porosity of the cathode. The decrease in the porosity can also expose a larger area of the aluminum current collector. Since aluminum has high thermal diffusivity (8.418 × 10⁻⁵ m²s⁻¹), the overall thermal diffusivity of the aged sample may show an apparent increase.^142–144 It is interesting to note that the sintering of oxide particles takes place at high temperatures. The onset of sintering in the cathode material may be attributed to the high surface energy of the LiFePO₄ nanoparticles Zhang and Miser¹⁴⁵ has observed coalescence of oxide particles with no external heating. In general, as the porosity of the medium decreases, the thermal conductivity increases, and hence, the aged sample shows increase in thermal diffusivity.^146,147

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In summary thermography bridges the gap between different length scales and proves to be an effective technique to relate the damage mechanisms of the cathode at mm length scale to micro/nanoscale. The thermal diffusivity increases as the cathode ages during the cycling of the batteries. The increase in the thermal diffusivity was attributed to the decreased porosity of the cathode samples due to the coarsening of the LiFePO₄ nanoparticles. The 2D thermal maps and the thermal diffusivity calculations help in making samples for further micro/nano level characterization studies.

Advances in the lens design and manufacturing has helped the development of the high-resolution optical microscope. Issues such as optical aberrations, and blurring of the images have been overcome in modern optical microscopes. Coupled with these advances, the advances in digital imaging have led to the development of the digital microscope. In digital microscopes the eyepiece of an optical microscope is replaced with a charged coupled device camera. Digital microscopes provide added advantages of precise computer control and greater flexibility in image analysis and processing. They have been used regularly in the fields of biological sciences, nanotechnology, as well as material science and metallography. They are very useful in imaging the texture of samples for metallographic analysis.

Digital microscopy has not been used as widely as other techniques in the study of battery materials. Figure 13 shows the digital micrographs of the unaged and aged anode and cathode taken along the cross-section (thickness) of the electrode strips. They are very useful in understanding the basic construction and layout of the electrode strips. In Fig. 13a the middle vertical region represents the copper current collector. The graphite coating is seen on either side of this current collector. Similarly, in the case of Fig. 13b the middle shiny vertical region in the images is the aluminum current collector. The active material (LiFePO₄) is coated on either side of this current collector substrate. Due to the dense packing of the active material the nanoparticles structure is not visible at the resolution available in these images. The edges of the current collector have been smeared off and the coating of the active material is not uniform on either side in the case of the aged sample. Using the digital image processing technique on these micrographs the thickness of the current collector and the coatings on each side is measured as ∼10 μm and ∼75 μm respectively. This data is a very useful input to the battery performance electrochemical models.¹⁴⁸

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When lithium intercalates into the graphite anode it changes color, and this behavior has been used to characterize the graphite anode with optical microscopy. Maire et al.¹⁴⁹ have used calorimetery in combination with optical microscopy to determine the local state of charge and lithium distribution with the anodes of the Li-ion cell. Harris et al.⁸³ have used optical microscopy to study lithium transport in the anodes and have suggested that the transport phenomena could be controlled by liquid-phase diffusion. Qi and Harris¹⁵⁰ have used optical microscopy to study the strains in the graphite anode during the lithiation process and explained the stiffening of the graphite upon lithiation.

In summary, digital microscopy contributes very little toward identifying the degradation mechanisms of the cathode material. It is unclear if the uneven active material coating thickness is a manufacturing defect or an aging effect. Nonetheless these studies provide important information about the physical dimension of the cathode and anode, which are useful in the electrochemical modeling of the battery performance.

SEM is widely used as a non-destructive tool for characterization and analysis of materials. The focused high-energy electron beam incident on the sample generates signals that are analyzed for the morphology. A SEM with electron back scattering detector can also be applied to study the crystal structure, chemical composition, and material orientation. SEM is widely used in lithium ion battery research to produce high magnification images of the nanostructured active materials. It is often used to understand the morphology of the synthesized cathode material and to verify the nanostructure of the material.⁷¹ SEM can be used to identify the major physical and or morphological structures in the active materials. Such studies can reveal any particle cracking, particle separation, and particle agglomeration.¹⁵³

Figure 15 shows the SEM micrographs of the samples harvested from the unaged and aged cells obtained by Nagpure et al.⁶⁵ The SEM micrographs reveal the coarsening of the nanoparticles in the aged samples as compared to the unaged sample. The particles in the unaged sample are of the order 40–50 nm while in the aged sample the particles are of the order 240–350 nm. As can be seen in the Fig. 15, in commercial batteries the active material is densely packed on the current collector. Thus higher resolution and magnification SEM images would be necessary to analyze the particle size and its distribution on the cathode surface to study the effect of the coarsening on the overall performance characteristics of the battery.

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The coarsening of the particles leads to a decrease in the effective surface area of the particles affecting the rate of the reaction. The change in the particle size would also affect the diffusion kinetics of the lithium ions during charging and discharging cycles. The coarsening phenomenon can also lead to the disbonding of these particles from the aluminum substrate causing physical failure or cracking of the active material and to the increase in the internal resistance due to loss of contact. The coarsening can also lead to the separation of particles, leading to the loss of contact between particles.

Since its development by Binnig et al.,¹⁵⁴ AFM has played a vital role in surface characterization of various different materials such as semiconductors, insulators, bio-materials, etc. A sharp tip at the free end of a flexible cantilever scans the surface of the sample to measure the surface topography of the sample.¹⁵⁵

A brief review of the AFM techniques used in Li-ion battery research has been pro- vided by Nagpure and Bhushan.¹⁵⁶ This technique provides surface morphology maps of the cathode samples with micron to nm resolution. These maps are useful in studying the grain coarsening phenomena.^66,157 Figure 16 shows the AFM surface height image of the LiFePO₄ cathode sample harvested from the unaged and aged cells. As can be seen from the images, the LiFePO₄ nanoparticles tend to coarsen in the aged samples as compared to the unaged samples. The same phenomenon was observed with SEM micrographs at micron length scales. The AFM surface height images have higher spatial resolution than the SEM micrographs. Hence they might be more useful in statistical quantification of the particle size distribution. Along with this standard measurement, AFM modules are also helpful in measuring surface electrical properties.

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TEM is a highly effective and versatile electron microscope technique to image, analyze and characterize the materials at length scales of the order of nanometers.¹⁵⁸ Some of the application of TEM in lithium ion battery research has been for studying nanoparticle morphology, and phase change in the nano particles.^159–161 In a multi-scale characterization plan TEM is used to provide high-resolution images of the cathode samples for understanding the particle morphology at nanometer length scale.

TEM, though very useful for high-resolution imaging, requires a very careful sample preparation, which should be thin so that they are electron transparent. The TEM samples were prepared on a FEI Helios 600 -Dual beam, focused ion beam system (FIB). The TEM samples were extracted from the surface through the thickness of the sample using lift-out technique. The lift-out technique used here has been discussed in Giannuzzi et al.¹⁶² and Giannuzzi and Stevie.¹⁶³ The steps followed in the lift-out technique used by Nagpure et al.⁶⁸ are shown in Fig. 17 and briefly discussed here. A clean area is found on the sample and imaged with the ion beam (1). Then Pt is deposited on the surface using a very small current of 2.8 nA (2). The sample is turned by 20deg in one direction, and the area around the Pt deposit is milled away using a milling current of 9.3 nA. A similar step is repeated to mill the area on the other side of the Pt deposit (3). The sample is then turned by 7°, and a trench is cut along the depth of the sample (4) to extract the TEM foil. In step 5 the omniprobe is attached to the foil, and the foil is pulled from the rest of the sample. The foil is then welded onto a TEM Cu grid (GRD-0001.01.01) using Pt (6) and detached from the omniprobe. Finally, the foil is further thinned to approximately ∼200 nm using the ion beam to make it electron transparent.

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Morphologies and nanostructures of the LiFePO₄ samples are shown in the TEM images (Fig. 18). They have the same global morphologies. Particles of the aged sample were bigger than the particles of the unaged samples. The samples have several layers of nanoparticles and, as such, contrast exists among the overlapping particles. This makes particle size analysis difficult, but the coarsening phenomenon is clearly visible in Figure 18b. Good statistical analysis of the coarsening and the particle size variation can only be achieved with a more subtle TEM sample extraction process that would allow quantitative measurement of the relative fractions of agglomeration and sintering, without destroying the configurations observed in the Figure 18.

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Recently, in situ TEM methodology was developed for studying the processes and aging effects that cannot be captured by ex-situ studies. The critical part of such studies was to operate the LI-ion system inside the ultra-high vacuum column of a TEM. To mitigate this situation, the liquid electrolytes are replaced with either the ceramic or polymer electrolytes to construct an all solid-state "nano-battery". The electrode/electrolyte interface can then be easily probed with TEM. Significant research efforts are underway for developing such in situ TEM techniques to probe the electrochemical behavior of the materials at nanoscale. Some of the earlier work in this area has been published by Brazier et al.,¹⁶⁴ Huang et al.,¹⁶⁵ Wang et al.,^166,167 and Yamamoto et al.¹⁶⁸ But these studies were focused on anode materials for lithium batteries. As such authors would leave this up to the reader to investigate it further, but would point out that such a study is also viable and important for the cathode materials within the lithium ion batteries.

Advances in AFM instrumentation has led to the development of a technique known as scanning spreading resistance microscopy (SSRM).^155,169 The SSRM module used in AFM measures the surface resistance between the conductive tip and the sample while the tip is scanned in contact mode across the sample surface. The most important application of the SSRM technique can be found in the mapping of carrier concentration inside a semiconductor device.¹⁷⁰ In contrast to SSRM, there also exists a method called current sensing AFM (CSAFM) to measure the surface current between the conductive tip and the sample. This has been previously used in lithium ion battery research. A review of AFM techniques used in electrical characterization of battery materials has been presented by Nagpure and Bhushan.¹⁷⁰

The nanoscale surface resistance measurements were taken by Nagpure et al.¹⁵⁶ with a Nanoscope IIIa Dimension 3000 AFM equipped with the SSRM application module. The conductive SCM PIT (Veeco Instruments) probes used in this study were coated with platinum-Iridium on front and back side and had a nominal tip radius of 20 nm. A known DC bias voltage of +1 V was applied between the sample and the conductive tip, and the current was monitored using a logarithmic current amplifier built into the SSRM sensor, as shown in the schematic in Fig. 22.

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The module applies the same bias to the 1 MΩ reference resistor mounted inside the module. The resistance is then measured by a comparator that compares the current flowing through the sample to the current flowing through the reference resistor. The output of the SSRM module is in volts. The module is calibrated by connecting several resistances of known value in the module instead of the tip-sample. For example, if 1 MΩ resistance is connected instead of the tip-sample, the output of the comparator is 0 V as the same current flows from the sample resistance and the reference resistor. Thus a 0 V output corresponds to a 1 MΩ resistance between the tip and the sample. When a positive bias is applied between the tip and the sample, the output voltage is inversely proportional to the surface resistance while it is directly proportional to the surface resistance if a negative bias is applied. The total resistance between the tip and the sample depends on the contact resistance, the spreading resistance, and the bulk resistance. One of the resistances dominates the total resistance depending on the contact force applied on the tip, the applied bias and the condition of the sample material. Depending upon the material, when a high enough contact force and a suitable bias is applied, a stable electrical contact is established between the tip and the sample, and the total resistance measured will be the surface resistance dominated by the contact resistance and the spreading resistance.¹⁷¹

Figure 23 shows the SSRM surface resistance image of the LiFePO₄ cathode sample harvested from the unaged and aged cells. As the module configuration when +1 V is applied between the tip and the sample, the higher voltage reading represents lower surface resistance. The surface resistance scale on the unaged sample is 0–2 V, while the scale on the aged sample is 0–20 mV. The lower voltage output in the case of aged samples indicates higher surface resistance as compared to unaged sample. Thus surface resistance increases as the cells are aged.

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Based on their results, Nagpure et al.⁶⁴ have proposed a mechanism that leads to the increase in the surface resistance of the LiFePO₄ cathode sample, shown in Fig. 24. When the tip scans over the surface of the sample a circular contact is formed between the LiFePO₄ nanoparticles and the tip. As mentioned earlier, the LiFePO₄ nanoparticles have very poor conductivity (σ = 2 × 10⁻⁹ S cm⁻¹),^70,71 and hence to increase their conductivity, they are coated with carbon.⁷ In the case of the unaged sample the total surface resistance measured is the resistance of the carbon-coated LiFePO₄ nanoparticles (R_u). Due to the coarsening of the nanoparticles the overall resistance increases to (R_a).

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The coarsening may also causes loss of the carbon coating, which leads to a further increase in the resistance of these particles. In addition to this, the total surface resistance of the aged sample could increase due to the additional resistance from the nano crystalline deposit (NCD) formed on the cathode surface. The NCD is formed due to the chemical reactions taking place at the surface of the cathode. Further experiments are needed to investigate the details of the NCD on the LiFePO₄ cathode surface, but it was observed by Zhang et al.¹⁷² and Kostecki and McLarnon³² on LiNi_0.8Co_0.2O₂ cathode surface.

Ramdon and Bhushan¹⁵⁷ have used the current sensing capabilities of AFM to determine the effect of differences in surface morphology on the surface conductance of unaged and aged cathodes. They used Agilent 5500 AFM equipped with a current sensing preamplifier having a sensitivity of 1 nA/V. The experiments were conducted in the contact mode of the AFM with the tip coated with conductive material. CSAFM involves a bias voltage applied between the sample and the tip, which creates a current, and this current is used to construct a conductivity map. The voltage used in their experiment was 3 V.

Figure 25 shows the results of their experiment. There were greater occurrences of higher conducting regions within the sample for both 5 μm × 5 μm and 2 μm × 2 μm for the unaged cathodes. In the aged sample it was observed that the overall conductivity was lower and only the edges of some particles showed conductivity.

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Fig. 25b shows a profile extraction that was done for the unaged and the aged cathodes, and it can be seen that there are higher currents in the unaged sample going up to 2 nA for that section as compared to the aged with the highest reading being 0.01 nA. The 2 μm profile of the unaged sample showed that the particles had higher current reading as compared to the aged samples that had very low conductance. The histogram in Fig. 25c shows the current data extracted from the current maps. The unaged sample showed that 20% of the values fall between 1 to 10 nA while the other 80% are distributed from 0 to 1 nA. The majority of the aged cathode current values were between 0 and 0.1 nA. They have attributed the change in the surface conductivity to the active material losing contact with the current collector, poor conductivity of the PVDF binder, and the rearrangement of the carbon additive.

Another technique of interest is Kelvin probe microscopy (KPM), which has been used in a variety of applications to measure surface potential. Because of the sensitive nature of silicon to charge buildup and subsequent discharge which can damage small silicon parts, surface potential measurements have been of interest in the semiconductor industry. The technique has also been used successfully to detect wear precursors from wear at very low loads using AFM based Kelvin probe methods.^155,169,173

The use of the Kelvin probe method was extended to the study of Li-ion batteries by Nagpure et al.⁶⁶ The KPM technique is based on the contact potential difference method for measuring the electronic work function (EWF).¹⁷⁴ Since EWF is strongly influenced by the surface chemical composition and Fermi level of the material KPM can detect the structural and chemical changes of the surface and provide vital information about the onset of damage. Using KPM large areas of the entire cathode electrode can be scanned quickly giving spatial information of its surface. In this study, KPM was used for the first time to characterize aging of the cathode surfaces by measuring the change in the surface potential that can be attributed to physical and chemical changes of the surface.

Nanoscale surface potential measurements have been made by Nagpure et al.⁶⁶ to study aged cathode samples. A schematic of this instrument with KPM setup is shown in Fig. 26. The KPM measures the surface potential of the samples in interleave mode. Along one scan line on the sample, in first pass, the surface height image is obtained in tapping mode. In second pass the tip is lifted off the sample surface and a surface potential map is obtained. Both images are obtained simultaneously.¹⁷⁵ During the first pass, the cantilever is mechanically vibrated by the X-Y-Z piezo near its resonance frequency. The amplitude of the tip vibrations (not shown) is maintained at a constant value by the feedback loop as the tip scans the surface of the sample. The signal from the feedback loop is used to construct the height map of the sample surface (Fig. 26a). During the interleaved scan, the X-Y-Z piezo is switched off. Instead, an AC signal is applied directly to the conductive tip that generates an oscillating electrostatic force on the tip. The tip is scanned along the surface topography line obtained in the tapping mode with a certain lift off the sample (dotted line in Fig. 26a).

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To briefly describe the operating principle of KPM, consider a tip and sample interaction as seen in Fig. 26b–26d. When the tip and sample are electrically connected (Fig. 26b) electrons flow from the material with the lower work function to the material with the higher work function. Due to the difference in the work function of the electrically connected tip and the sample, an electrostatic contact potential difference (or surface potential difference) is created between the tip and the sample.¹⁷⁴ The value of this surface potential (ΔΦ) is given by the following equation

where Φ_tip and Φ_sample are work functions of the tip and the sample, respectively, and e is the magnitude of the charge of one electron. ΔΦ will be affected by any adsorption layer and the phase of the material near the surface. Electrostatic force is created between the tip and sample under the influence of this surface potential difference and the separation dependent local capacitance C of the tip and sample. This force is given by

where z is the distance between the tip and sample.

Along with ΔΦ, in the operation of the KPM a compensating DC voltage signal (V_DC) and AC voltage signal, V_ACsin (ωt) (Fig. 26c and Fig. 26d), is applied directly to the tip. Thus the electrostatic force between the tip and the sample becomes:

The cantilever responds only to the forces at or very near its resonance frequency. Thus, only the oscillating electric force at ω acts as a sinusoidal driving force that can excite oscillations in the cantilever. The DC and the 2ω terms do not cause any significant oscillations of the cantilever. In tapping mode, the cantilever response (RMS amplitude) is directly proportional to the drive amplitude of the tapping piezo. Here in the interleave mode the response is directly proportional to the amplitude of the ω term.¹⁷⁵ The servo controller applies a DC voltage signal equal and out of phase with ΔΦ so that the amplitude of the tip becomes zero (F = 0). This compensating signal from the servo controller creates the surface potential map of the sample.¹⁷⁶

The conductive AFM tip is necessary for the KPM experiments. The tips used in these experiments had an electrically conductive 5 nm thick chromium coating and 25 nm thick platinum coating on both sides of the cantilever (Budget Sensors, Model # Multi75E-G). The resonant frequency of the tips was 75 kHz, and the radius was less than 25 nm. The interleave height was optimized to 150 nm for a good surface potential signal.

The surface potential maps of the unaged and aged LiFePO₄ cathode samples are shown in Fig. 27. The maps were collected by applying +1.0 V and +3.3 V from the external DC voltage source. Maps for samples without an externally applied voltage are shown for comparison. Within each surface potential map for both the unaged and aged sample, Nagpure et al.⁶⁶ observed no large difference in the contrast, suggesting an almost uniform dissipation of charge over the surface of the samples under the externally applied voltage. This indicates that under the external source the sample tends to charge uniformly even in an aged condition. The uniform charging is good for the cell as it avoids large local currents and subsequent damage to the cathode.

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The surface potential image discussed above is generated by a matrix of 256 × 256 data points. The last column of Fig. 27 also shows the distribution of these data points in unaged and aged cathodes. For each case a histogram is created with 17 equally spaced bins. The bin size was optimized using Sturges rule,¹⁷⁷

where k is the number of bins, and n is total number of data points. Then a normal probability density function as shown below is used to fit the data.¹⁷⁸

where μ is the mean, and σ is the standard deviation of the data points. The unaged sample had mean values of the surface potential almost equivalent to the external applied voltage. The mean values of surface potential on the aged sample are lower than that of the unaged sample. Thus, even though the externally applied voltage was the same for the unaged and aged samples the charge sustained on the surface of the aged cathode is less than that sustained on the unaged cathode.

The surface potential measured using KPM is the difference between the work functions of the tip and sample surface. Since the same kind of tip is used in these experiments, the work function of the tip is constant in each surface potential map. Figure 27 shows the change in the work function of the aged sample as compared to the unaged sample. The work function is the property of the structure near the surface of the sample along with the chemical potential of the surface. The decreased surface potential in the aged sample is the indication of the surface modification and could occur due to one or all of the factors discussed below.

A phase change of the cathode material occurs from LiFePO₄ to FePO₄ and back to LiFePO₄ during respective charging and discharging cycles of the battery. During charging, the Li-ions from the LiFePO₄ cathode are intercalated in the graphite anode. During discharging, the Li-ions move out of the graphite anode and are intercalated back in the cathode. The olivine structured LiFePO₄ has a different work function than that of the metastable FePO₄. The change in the surface potential map of the aged sample indicates that one of the phases might be growing in the cathode sample during the battery aging. Andersson and Thomas¹⁷⁹ have demonstrated this phase change as a source of initial capacity loss using neutron diffraction data. Based on their experiments they have proposed a radial model and a mosaic model for the phase change between LiFePO₄ and FePO₄. In either of their models they have suggested unconverted inactive regions of LiFePO₄ entrapped by the FePO₄ phase. They concluded that, in reality, the superposition of the essential features of the two models might be occurring.

X-ray diffraction is a non-destructive technique mainly used for studying long range structural ordering of materials and phase identification. It is also used for quantitative analysis of phases, residual stress measurement, crystal structure and three-dimensional material properties. In lithium ion battery research it has been used for ex-situ phase identification of the cathode materials after being charged and discharged. Recently in situ XRD has been demonstrated to analyze the crystalline structure of the cathode material during charging and discharging cycles.¹⁹⁵

Li et al.¹⁹⁵ have used Rietveld fitting and quantitative phase analysis to analyze the phase fractions. The two-phase fitting was performed using LiFePO₄ and FePO₄ as end-members and the structural data given by Anderson et al.¹⁹⁶ and Channagiri et al.¹⁵² The results of quantitative phase analysis demonstrate an increase in FePO₄ phase fraction with aging at a given location on the cathode as seen in Fig. 31. The increase in FePO₄ phase with aging was explained by considering separation at the Carbon-LiFePO₄ interface with aging. This separation would result in fewer regions of the cathode where a three phase boundary is present (Active material/Carbon/Electrolyte), reducing the efficiency of Li intercalation into the solid nanoparticles. The change in the volumetric concentration of the active material would be a very important input parameter in the electrochemical and performance models of the Li-ion batteries.

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Electron energy loss spectrometry (EELS) is based on the analysis of the energy distribution of electrons that have interacted inelastically with the specimen. These inelastic collisions carry information about the electronic structure of the specimen, which helps in understanding the electronic bonding between the various elements of the specimen. EELS studies can also help identify the thickness of the sample. The technique can be applied to any amorphous as well as crystalline sample. The EELS spectrum is gathered with the help of a magnetic prism spectrometer that is often interfaced into TEM.¹⁹⁷

So far, in lithium ion battery research, EELS has been used to study the local electron structure of the host material, the intercalation/deintercalation process of the Li within the host material and the subsequent phase changes.^58,160 In the multi-scale characterization plan EELS was included to analyze the local electronic bonding of the Li with its neighboring atoms and to identify the changes in these electronic bonding schemes between the LiFePO₄ cathode samples harvested from the unaged and aged batteries. Such studies were conducted along with the high-resolution TEM imaging studies reported in morphological studies by Nagpure et al.⁶⁸ The sample preparation process has already been discussed earlier.

Figure 32 shows the microstructure and the corresponding EELS measurements for the unaged and aged samples. The areas were chosen for a single particle analysis. Due to the uncertainty in establishing the absolute value for the energy loss scale all the spectra were aligned at O K edge (532 eV). All the spectra were normalized to the intensity of the O K edge peak. As shown in Fig. 32b, a significant difference in the shape of the O K edge peak is observed. The peaks in the data were fitted with a Gaussian function. The O K edge peak is at 532 eV, with a pre-peak at ∼528 eV found in the aged sample which is almost negligible in the unaged sample. Figure 32c shows changes in the Fe L_2,3 edge with aging. It can be seen in this figure that the main difference between the aged and unaged sample is the position of the Fe L_2,3 edge. The onset of the Fe L_2,3 edge for the aged sample is ∼2 eV higher than for the unaged sample. The EELS measurements were conducted from the periphery to the core of the LiFePO₄ particle in both the unaged and aged sample. But note that in Fig. 32b and 32c not all spectra are shown, and only a representative of the phenomena is presented. As can be seen in Fig. 32b, the intensity of the O K edge pre-peak is higher at the core than at the periphery of the large particle in the aged sample. Thus the ratio of the pre-peak to the main feature of O K edge peak was less at the core of the larger particle in the aged sample than at the periphery. It is also interesting to note that if the EELS spectra are obtained at the core and the periphery of a large particle in the aged sample, there is a shift of the Fe L_2,3 edge to a higher energy.

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The differences in the shape of the O K edge and the position of the Fe L_2,3 edge have been explained in previous spectroscopy work by Laffont et al.¹⁶⁰ and Miao et al.⁵⁸ The pre-peak at the O K edge and the shift to higher energy of the Fe L_2,3 edge observed in the aged sample is characteristic of a highly delithiated LiFePO₄ (a charged cell), while the spectra observed in the unaged sample is characteristic of a well lithiated LiFePO₄ (a discharged cell). Since in this study both samples were discharged before disassembly, it is believed the phenomena observed here is due to the aging of the cells. The measurements suggest that the core of the larger, coarsened LiFePO₄ particle in the aged sample has a different lithium composition than the periphery. It is thus believed that during aging the LiFePO₄ nanoparticles sinter together resulting in coarsening of the particles. This coarsening is expected to increase the Li-ion diffusion length through the particles, and thus the transformation of nanoparticles during discharging of the cell from FePO₄ back to LiFePO₄ is expected to be incomplete, leaving an FePO₄ (or low Li-concentration) core and a LiFePO₄ shell around the core in large particles. As the cell ages the FePO₄ (or low Li concentration) core increases and the LiFePO₄ shell decreases. This leads to the conclusion that the aging has caused significant compositional changes in the LiFePO₄ nanoparticles. The active lithium is lost from the host cathode material, thus reducing its capacity. The diminished levels of Li in the cathode can be expected to lead to a compromised capability of the overall cell to recharge.

The electronic structure calculations were performed on supercells containing six formula units of Li_xFePO₄ with x = 0, 0.25, 0.5, 0.75, and 1 for detailed analysis and interpretation of the experimental results. The structural data for the starting materials in these calculations were adapted from Tang and Holzwarth.¹⁹⁸ LiFePO₄ forms an orthorhombic olivine structure with a slightly distorted hexagonal close packed oxygen array belonging to the symmetry group Pnma,¹⁹⁹ listed as no. 62 in the International Tables for Crystallography.²⁰⁰ Figure 33 shows the crystal structure of this material with one unit cell constructed with Materials Studio. The O atoms are located at the tetrahedral sites around each P atom. The divalent Fe ions form an octahedral arrangement with the O atoms. The Li atoms are located in channels along the b axis of the orthorhombic structure.¹⁹⁸

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The density functional theory (DFT), as implemented in the Vienna Ab-initio Simulation Package (VASP)^201,202 was employed to perform the electronic structure calculations within the generalized gradient approximation (GGA) with a PW91²⁰³ type projector augmented wave (PAW) potentials using a cutoff energy of 500 eV, enhanced by a coulombic term U²⁰⁴ to include strong correlation effects (GGA + U) for the Fe d orbitals. Within this framework the exchange term U is combined with the coulomb term U and (U − J), an effective value of U referred to as U_eff, is used. A value of 4.3 eV was chosen for U_eff following Miao et al.⁵⁸ All the calculations here have been performed for the ferro-magnetic configuration for consistency. An energy convergence of better than 10⁻⁶ eV was achieved when relaxing the geometry. The initial and relaxed lattice parameters for structures with varying lithium contents calculated with the GGA + U approximation are shown in Table VII.

Following Duscher et al.,²⁰⁵ the Z + 1 approximation method has been applied to simulate the electron energy loss near edge structure (ELNES). The ELNES onset was set up at the Fermi energy of the different structures. This approximation has been shown to model core hole excitation spectra in oxides well if dipole selection rules are used (change in orbital angular momentum quantum number by one).^205,206 Integration for the angular momentum resolved conduction band density of states (DOS) has been performed using the tetrahedron method with Blöchl corrections for 6 formula unit supercells created from the geometrically relaxed unit cells, with a 4 × 4 × 4 Monkhorst-Pack k-point mesh for Brillouin zone sampling for the supercells.²⁰⁷

Figure 34 shows ELNES for the O K edge and Fe L_2,3 edge obtained by the first-principles calculations. A small pre-peak for the O K edge is found for FePO₄, which is not found in structures with Li_xFePO₄ (x > 0). This is in agreement with the observed experimental trend presented in Fig. 32b. For the Fe L_2,3 edge (Fig. 34b) a peak shift toward higher energies can be observed with decreasing lithium content, which has also been observed in the experimental results (Fig. 32c). For FePO₄ with no lithium, the calculated EELS shows a reverse shift in the Fe L_2,3 edge, in agreement with Miao et al.,⁵⁸ which the band structure calculations suggest could potentially be due to the fact that Li acts as a donor in FePO₄, causing a shift in the Fermi level.

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Figure 35 shows O p states, Fe d states, and P s and p states and their hybridization based on band structure calculations. In a perfectly ionic state the O ions in FePO₄ could be expected to have a valence of 2 with fully filled 2p states. Covalent bonding, however, leads to hybridization between the Fe 3d, O 2p, and P 3s and 3p states, giving rise to empty states (above the Fermi level) with some O 2p states. This can be seen from Fig. 35, where the atom resolved DOS, obtained from first-principles calculations, has been plotted for three compositions: FePO₄, Li_0.5FePO₄, and FePO₄. In all three compounds the valence band just below the Fermi level (region 1 in Fig. 35) has major contributions from the O 2p states with some Fe 3d states. The conduction band just above the Fermi level (region 2 in Fig. 35), on the other hand, is dominated by Fe 3d states with small contributions from O 2p states. Moving to higher energy bands (>10 eV, region 3 in Fig. 35), antibonding states are found with O 2p, 3s, and 3p states. In FePO₄ the contribution of O 2p states in region 2 is significant and gives rise to the pre-peak A observed in the simulated O K edge EELS spectra, shown in Fig. 34a, due to transitions from the 1s core orbital of oxygen. The O 2p states present in region 3 gives rise to peaks B and C seen in Fig. 34a, after core hole corrections which shift these states toward lower energies by approximately 3 eV.

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While Li addition does not affect the positions of peaks B and C, it does lead to a continuous decrease in the intensity of pre-peak A, as observed in both the experimental (Fig. 32b) and simulated (Fig. 34a) O K edge EELS spectra. This can be attributed to the following two causes. Firstly, on addition of Li the Fe 3d states shift to higher energies (from ∼3–5 eV in FePO₄ to ∼6–8 eV in LiFePO₄) because of the reduction in the oxidation state of Fe from Fe³⁺ to Fe2+ (region 2 in Fig. 35). Secondly, it leads to a continuous decrease in the extent of hybridization between Fe 3d and O 2p states, such that the contribution of O 2p states in region 2 becomes negligible in LiFePO₄. This analysis is similar to the arguments put forward by Kinyanjui et al.,²⁰⁸ who studied only the end compounds. Based on the decrease in intensity of pre-peak A with Li addition, the pre-peak is expected to be completely absent for Li concentrations greater than ∼75%. Similarly, in the case of Fe L edges the intensities of the sharp lines themselves scale with the number of unoccupied 3d states of the Fe atom. In the aged sample the shift is ∼2 eV. According to the first principles simulations presented, this would correspond to a reduction in Li content of ∼80%. Thus, the FePO₄ core and LiFePO₄ shell, co-exist within large particles, and as the cell ages the FePO₄ (low Li content) core expands while the LiFePO₄ shell decreases.

The energy at the Fe L_2,3 edge peak obtained from first-principles calculations was plotted against the Li concentration in Li_xFePO₄ in Fig. 36. The shift to higher energy in the location of the Fe L_2,3 edge peak follows a linear trend with an approximate slope of −1.9 eV with increasing Li concentration. Considering the experimental shift of ∼2 eV between the unaged and aged samples, this would indicate a Li loss of ∼80% in the aged sample. Since complete Li depletion from LiFePO₄ would lead to a downward rather than the observed upward peak shift, the calculation here indicates that the aged sample is not completely Li depleted, but rather remains at a low Li content of ∼20%.

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To summarize, the EELS measurement showed that the density of states for O changes as the cell ages. This was evident in the presence of the pre-peak in the case of the O K edge. The increase in the ratio of the pre-peak to the O K edge peak in the EELS data from the core to the surface of the large LiFePO₄ particle indicates different lithium composition within the particle. There is also a shift of almost 2 eV for the L_2,3 edge of Fe in the aged sample. At a certain age of the cell the particles start to coarsen. The ion diffusion length is expected to increase in the coarser particles, and this is expected to lead to an incomplete transformation between LiFePO₄ and FePO₄ while charging and discharging. The FePO₄ core is expected to expand in subsequent cycles, thus reducing the capacity of the host cathode material.

The experimental results were analyzed with the help of simulated ELNES spectra for the olivine structure (space group Pnma) of Li_xFePO₄ with x = 0, 0.25, 0.5, 0.75, and 1. The nature of the O pre-peak was confirmed by comparing the position of the O 2p bands arising due to strong hybridization among the O p states, Fe d states, and P s and p states with the Fermi level position. The Li loss was quantified by these calculations as 80%, suggesting a strongly Li depleted, but not completely Li free, core region in the coarsened particles.

Solid state NMR is extremely useful for studying the local structure in ordered and disordered materials. Solid state Li NMR in particular is very useful due to its high sensitivity toward the atomic and electronic environment at the lithium site within the host cathode structure.²¹³ NMR can distinguish between the metallic and semiconductor behavior of the materials. While probing the local and electronic environment of the nuclear probe it can also monitor the electronic structure of the surrounding cations.²¹² In NMR spectroscopy it is also possible to quantify the species taking part in battery charging and discharging, and monitor the effect on the local structural changes of these species as the function of the aging of the battery. Due to its sensitivity toward the local electronic structure it can also distinguish between diamagnetic and paramagnetic behavior of materials. Most of the materials used as cathode in lithium-ion batteries show paramagnetic behavior in charged and discharged state.²¹⁴

The naturally abundant ⁷Li isotope (93%) has larger quadruple and gyromagnetic moments as compared to the less abundant ⁶Li (7%) isotope. The quadruple interactions result from the interactions between the quadruple nucleus and the electric field gradient at the nucleus. The quadruple interactions of ⁶Li are smaller compared with ⁷Li but they result in higher resolution spectrum that is easier to interpret.²¹⁴ Thus the coupling between the lithium nucleus and the unpaired electrons can be exploited in magic angle spinning (MAS) NMR to study the changes in the local electronic structures as the function of the battery aging in the paramagnetic cathode materials.

Given these advantages of NMR, it has been used by several researchers to study different types of cathode materials. Layered oxides such as LiCoO₂ and LiNiO₂ have been studied by Dahn et al.,²¹⁵ Marichal et al.,²¹⁶ Levasseur et al.,²¹⁷ and Carlier et al.^218,219 The spinel structured materials, such as LiMn₂O₄, have been studied by Morgan et al.,²²⁰ Gee et al.,²²¹ Lee et al.,^222,223 Lee and Gray,²²⁴ Tucker et al.,²²⁵ and Verhoeven et al.²²⁶ The spinel structured materials, such as LiFePO₄, have also been studied by Gaubicher et al.,²²⁷ Tucker et al.,^213,225,228 and Arrabito et al.²²⁹ The goal in these studies has been to understand and predict the effect of local and electronic structure on lithium NMR shift in these battery materials. In situ NMR studies using a toroid detector with limited resolution have also been conducted by Gerald et al.²³⁰ Chevallier et al.²³¹ have also shown that NMR signals from plastic bag batteries can be successfully obtained for analysis.

In the multi-scale characterization plan a magic angle spinning (MAS) nuclear magnetic resonance (NMR) with ⁷Li probe was used to probe the presence of lithium in the unaged and aged cells by Nagpure et al.⁶⁹ Since Li is vital in charging and discharging of the batteries, NMR can provide a vital understanding about its local environment within the host structure and any changes to the structure due to aging during cycling of the cells.

A Bruker DSX 300 MHz NMR spectrometer was used to probe the lithium in LiFePO₄ nanoparticles. A 7 mm triple resonance MAS probe was tuned to the ⁷Li frequency of 38.9 MHz. The shifts in the ⁷Li were referenced with 1 M LiCl(aq) solution. The Bloch Decay experiment method was used with relaxation delay of 10 s and spin rate of 10 kHz.

Figure 37 shows the NMR spectra for C0 and C6 samples. In the case of the C0 sample a single isotropic ⁷Li peak is observed while this peak is absent in the case of the C6 sample. The NMR spectra of C0 shows a small chemical shift of ∼8 ppm. There is also considerable broadening of the peak. The multiple spinning side bands accompanying the isotropic peak observed by Tucker et al.^213,228 are not observed in this case. The single isotropic band indicates one local environment for the lithium in the case of C0. The crystal structure of the LiFePO₄ was shown in Fig. 33. LiFePO₄ shows a paramagnetic behavior and the single isotropic peak in C0 is as expected for paramagnetic materials containing a single type of Li site. Lithium NMR spectra for paramagnetic materials are dominated by series of larger interactions, such as quadruple coupling (⁶Li, I = 1; ⁷Li, I = 3/2) and hyperfine interactions between nucleus and the unpaired electrons.²¹⁴ The possibility of a Knight shift in the battery materials is excluded due to their electronic insulating character.²²⁸

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According to Tucker et al.^213,228 the shift in the case of LiFePO₄ can be attributed to the hyperfine interactions through-bond transfer (specifically Li-Fe-O bond) of the unpaired electron density via the oxygen p-orbitals to the Li s-orbitals. Since LiFePO₄ is electronically less conductive the Knight shift characteristic of metal conductors is ignored for this material. The broadening of the peak can be attributed to the considerable local disorder in the coordination sphere of Li in LiFePO₄.²¹³ The absence of a peak in the case of the C6 samples indicates the presence of FePO₄ instead of the LiFePO₄ phase. This is consistent with an observation by Nagpure et al.,⁶⁸ using EELNS. The Li depletion in the case of the aged samples caused the changes in the local electronic structure of the sample. The Li depletion in the aged sample caused the transitions from the 1s core orbital of oxygen and strong hybridization between the Fe 3d, O 2p, and P 3s and 3p states, giving rise to empty states (above the Fermi level) with some O 2p states. The lithium starved FePO₄ phase indicates loss of cycling capability of the battery.

In summary NMR was used to probe the local Li environment of the LiFePO₄ nanoparticles. The solid state ⁷Li NMR is very critical in studying the local environment and electronic structure of the LiFePO₄ nanoparticles as it directly probes the Li within the sample. An isotropic peak with a small chemical shift, a characteristic of paramagnetic materials, is observed in the unaged LiFePO₄ sample. The absence of such a peak in the aged sample indicates the Li starved FePO₄ phase. The loss of active Li directly affects the loss of cycling capacity of the battery.

NDP is a very useful technique in studying the concentration of lithium within the sample. It is a non-destructive analytical technique based on the nuclear fission reaction between beams of neutrons with certain elements, such as lithium, throughout the sample. The cold neutrons are delivered through a neutron guide to the NDP chamber. In this work, the cold neutrons refer to neutrons with energy less than 5 meV. Since cold neutrons have extremely low energy and momentum, there is no center-of-mass motion in the neutron-lithium reaction. Furthermore, the neutron event rate is insufficient to cause significant temperature rise in the sample, nor is there significant radiation damage to the sample during the measurement period.

Ziegler et al.²³² for the first time used the nuclear reaction experiment to determine the concentration of boron impurity in silicon wafers. The sample was bombarded with a well-collimated beam of low energy neutrons in a vacuum, and the emitted energized particles were analyzed using a charged-particle spectroscopy for the concentration profile of the ¹⁰B in the sample. Later, Downing et al.²³³ coined the term neutron depth profiling (NDP) for this technique. Since then there have been several applications of this technique to other neutron sensitive light-weight isotopes, some of which are listed by Downing et al.²³⁴ Biersack and Fink²³⁵ were first to study the implantation of lithium in semiconductors using NDP. Later on Krings et al.²³⁶ studied lithium diffusion in electrochromic WO₃ films using NDP. They compared the secondary ion mass spectrometry (SIMS), elastic recoil detection (ERD), and NDP techniques while profiling the lithium concentration along the depth of lithium intercalated thin electrochromic WO₃ films. They concluded that the NDP technique has a very good depth resolution with high sensitivity, and proves to be very useful over the other techniques because of its non-destructiveness. Lamaze et al.²³⁷ have demonstrated the use of NDP in two thin film battery materials. They profiled the lithium concentration in ion beam assisted deposition (IBAD) thin lithium phosphorus oxynitride films and thin lithium cobalt oxide films. The main advantage was again the non-destructive nature of the NDP technique. The study was limited to the deposited thin films rather than electrodes extracted from actual lithium ion cell.

Whitney et al.²³⁸ used NDP to profile the lithium concentration in a cathode of the Li-ion lab cells and in an anode of the off-the-shelf Li-ion cells. The lithium transportation was studied for storage of cells at different temperatures and cycling of the cells at different rates. They demonstrated a method to determine the thickness of the solid electrolyte interface on a graphite anode in a LiFePO₄ cell when stored for different lengths of time under different temperatures. They also profiled the lithium concentration in LiFePO₄ and LiNi_1/3Mn_1/3Co_1/3O₂ cathodes after cycling for only 100 cycles. This helped to understand the lithium distribution in initial cycles, but did not address the issue of lithium transportation during the end of life of the cells.

Nagpure et al.⁶⁷ used the NDP technique in the multi-scale characterization plan for detailed analysis of the lithium concentration in the commercial cells. The effect of C-rate on the lithium concentration toward the EOL of the battery was measured. All NDP experiments discussed here were conducted at the NIST Center for Neutron Research (NCNR). A schematic of the NDP facility is shown in Fig. 38. The sample is attached to an aluminum disk (Fig. 38) which is held vertically at the center of a vacuum chamber by the grooves provided on the sample mount. The sample mount is oriented such that the sample faces the surface-barrier type charged particle detector. The detector has an active area of 150 mm² and is placed slightly more than 10 cm from the neutron beam-spot on the sample. An area of ∼0.8 cm² of the sample is illuminated by the cold neutron beam entering the vacuum chamber. Upon the absorption of the neutron by the elemental atom in the sample, monoenergetically charged alpha and triton particles are emitted and travel diametrically opposite from the site of the reaction. More specifically, when the neutron reacts with the ⁶Li atom in this sample, monoenergetically charged alpha (⁴He) and triton (³H) particles are emitted as shown in the reaction below,

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The energy of the ⁴He and ³H particles at the reaction site is known to be at 2055 keV and 2727 keV, respectively.²³⁴ These heavy charged particles lose energy via a stochastic collision with electrons along the path traveling outwards. Both, the count rate and the residual energy are simultaneously measured from all depths for the particle species emerging in the direction of the detector (Fig. 38). The charged particles do not lose any energy after leaving the surface of the sample traveling to the detectors, since the sample chamber is maintained at a vacuum less than 1.33 mPa (10⁻⁶ Torr). Calibration performed prior to the experiment determined the full width half maximum (FWHM) energy resolution of 18 keV for the charged particle detector. The samples were exposed to the neutron beam for various time lengths ranging between 3 to 4 hours. The exposure time was not fixed so the data was normalized with respect to the run time, but the samples were exposed long enough so that the statistical error in counting of the ⁴He or ³H particles is no higher than 3%.

The reaction center of mass coincides with the site of the lithium atom. Thus the ⁴He and triton ³H particles originate from the same location as that of the original lithium atom, and their respective energies are directly related to the location of the lithium atom in the sample. The energy loss of the charged particle per unit length traveled through the sample is given by the stopping power function of the sample. Mathematically, to the first-order approximation, the depth is related to the stopping power by Braggs law given as

Here x is the path length traveled by the particle through the material, E₀ is the initial energy of the particle, E(x) is the energy of the particle emerging from the surface, and S(E) is the stopping power of the sample material.²³² The Stopping and Range of Ions in Matter (SRIM) code developed by Ziegler et al.²³⁹ is then used to obtain the stopping power of the LiFePO₄ cathode and the graphite anode and to assign the residual energies of the charged particle to the corresponding depth in the sample. The concentration of ⁶Li within the sample is determined by comparing the count rate observed from the sample with that of a well characterized boron concentration standard, labeled as N6.²⁴⁰ Since the natural abundance of ⁶Li in the sample is only 7.5%, the total Li elemental concentration is obtained by dividing the determined ⁶Li concentration by 0.075.

The energy spectrum of the 2727 keV ³H particle is used here because of its two advantages over the corresponding energy spectrum of the 2055 keV ⁴He particle. First, since the ³H particle has higher energy and less mass, the concentration profiles can be obtained to greater depth in the sample. Second, the ³H energy spectrum is not overlapped by the ⁴He energy spectrum, but the ³H energy spectrum interferes with the ⁴He energy spectrum at low energies, i.e., by the charged particles from greater depths below the sample's surface.

Figure 39 shows the lithium concentration profile in the anode and cathode of the various cells aged with different C-rates. The lithium profile obtained from cell C0 is established as the baseline for comparison. In the left column the lithium concentration profiles of the anode can be seen changing from section # 1 to section # 5 at the same C-rate. The surface concentration increases across the different cells with the C-rate. The right column shows the lithium concentration profile in the cathode. The profiles remain identical from sections 1 to 5 at the same C-rate, but the slope of the profile decreases with increasing C-rate.

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Figure 40 shows the effect of the SOC combined with the C-rate on the lithium concentration profile. Fig. 40a shows the lithium concentration profile in the cell cycled between 60 and 70% SOC with ∼6 C-rate (C6) for sections # 1, 3, and 5. The lithium concentration profile in cell C4 (same as in Fig. 39) is shown again in this figure for comparison. In C6, even though the C-rate is high, the amount of lithium buildup near the surface of the anode is less as compared to C4. The prominent change of lithium concentration profiles in the anode from section # 1 to section # 5 observed in C4 is also absent in C6 except for minor deviations near the sub-surface. Similar to C4, the lithium concentration profiles in sections # 1, 3, and 5 of cell C6 are identical to each other. However the lithium concentration profile for C6 has dropped below the concentration profile in C4. Thus, the overall lithium concentration in the cathode has dropped significantly in C6 as compared to C4. Thus at a higher SOC and moderate C-rate, the lithium buildup on the surface of the anode is contained, but lithium is lost from the host cathode material. In Fig. 40b the lithium concentration profile in section # 5 of C16 is compared with C0. In this case cell C16 is cycled between 45 and 55%, but with a very high C-rate of 16C. It should be noted that cells C0 and C16 in this data were chosen from a different batch than the earlier cells. The basic chemistry was the same, but the initial lithium concentration in the cathode was much higher in these cells. The lithium buildup on the surface of the anode was very high in C16 compared to any other cell in this study. The concentration in the anode dropped across its thickness with a steep slope. The lithium concentration profile in the cathodes of cells C0 and C16 are identical, but the concentration of lithium in the cathode was significantly lower than in C0. Thus, at moderate SOC but very high C-rate the process of lithium buildup on the surface of the anode is enhanced while there is significant loss of lithium from the host cathode. These results suggest that a cell operating at high SOC and moderate C-rate has the least amount of lithium build up on the anode surface, and also the least amount of lithium is lost from the host cathode.

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Figure 41 shows the lithium concentration profiles obtained on section # 3 of cell C0 and C6 at various locations within the same section. The aim here was to identify any change in the lithium concentration profiles measured at spots away from the center of the given section. The lithium concentration profiles in the anode shown in the left column of Fig. 41 are similar for both cells at various locations on section # 3. This indicates that the lithium concentration in the anode does not vary along the height of the anode. The right column shows the lithium concentration profile in the cathode from both cells. The profiles for C0 measured at various locations on section # 3 are identical, but the profile measured at the center spot on the front side has a higher surface concentration and shows a higher gradient along the thickness than at any other location on the section # 3. The profiles for C6 measured at various locations on section # 3 are identical. Since the intensity and change in the lithium concentration in the unaged cell (C0) were greater at the center of the section, the measurements were taken at the center of each section throughout this study.

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As expected for a completely discharged unaged cell (C0) (Fig. 39), the lithium concentration in the anode is significantly lower with little buildup of lithium at the surface, while most of the lithium is concentrated in the cathode. The lithium concentration profiles in the anode show higher surface concentration as the C-rate increases. The lithium concentration is at a maximum near the surface, and it decays exponentially with the depth (thickness) of the sample. The lithium buildup on the anode surface from a cell cycled at higher SOC is less, but increases with increasing C-rate. The lithium concentration drops in the cathode with higher SOC and higher C-rate. The lithium concentration profiles in the cathode show a uniform gradient, but the concentration decreases with increasing C-rate.

The analysis of the surface lithium concentration in the anode is shown in Fig. 42. As seen in Fig. 42a the surface lithium concentration is nearly constant over all the sections for C0 and C1. In the case of C3 and C4 the surface lithium concentration increases from section # 1 to section # 5. Thus the buildup of lithium on the surface of the anode is greater toward the core of the cylindrical cell than against the outer edge. For example, in the case of cell C4 where the highest change is observed, the concentration increases from 1.36 × 10²⁰ to 3.74 × 10²⁰ atoms/cm³ from edge to core. In Fig. 42b the effect of C-rate on the lithium concentration gradient in the anode is shown. The lithium concentration gradient increases with the C-rate. The lithium concentration gradient is very small in the case of cells C0 and C1 and is very prominent in the case of cells C3 and C4. The lithium concentration gradient in all cells exists only for a certain depth from the surface of the anode. The depth up to which the lithium concentration gradient exists in the anode also increases with the C-rate. In the case of cell C4 the lithium concentration gradient exists up to ∼1 μm in the anode. Thus with increasing C-rate not only does the lithium buildup on the surface increase, but the lithium build up in the sub-surface area also increases.

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It is well known that a solid electrolyte layer (SEI) composed of the decomposition products of the electrolyte salt and the solvent is formed on the surface of the anode.³⁰ The thickness of the SEI is usually of the order of tens of nanometer.^241,242 This thickness of the SEI on a given type of anode varies depending on the electrolyte components, mode of cycling, overpotential, temperature, etc.^243–246 The lithium concentration profiles for the anode presented here not only indicate higher lithium content in the SEI layer at higher C-rate, but also show that the lithium concentration in the SEI layer is changing from the outer edge to the core of the cylindrical cell aged at a certain C-rate. This has never been reported before in literature. This study reveals that the anode-electrolyte interphase cannot be assumed to be alike over the length of the anode in a cylindrical cell as is the common practice adapted in Li-ion cell modeling.

The analysis of the surface lithium concentration was also conducted and is presented in Fig. 43. A buildup of lithium on the surface as seen in the anode is not observed in cathode samples from different cells. Since there is no buildup, it is certain that there is no lithium plating occurring at the cathode surface. The initial expectation was a decrease in the lithium concentration in the aged sample as compared to the unaged sample. The decrease in the lithium concentration in the case of cells C1, C3, and C4 (Fig. 39) is not very prominent, but the results in Fig. 40 are in good agreement with this hypothesis. Therefore, there is a critical C-rate beyond which the drop in the lithium concentration from the cathode is noticeable. In Fig. 43, the analysis of the lithium concentration gradient along the depth of the cathode is shown for section # 3 of different cells. The lithium concentration gradient observed on a particular section decreases exponentially with the C-rate, as shown by the curve in Fig. 43. For example, in the case of cells C0 and C4 the gradients are −1.63 × 10¹⁸ atoms/cm³/μm and −0.46 × 10¹⁸ atoms/cm³/μm. For a higher C-rate the concentration gradient is lower, indicating that the flux available for diffusion of lithium into the cathode particles is decreasing. Thus the further cycling of the cells at still higher C-rate will be strongly affected. Since the concentration gradient has a negative slope, it indicates that the lithium diffusion within the LiFePO₄ is restricted as the diffusion front moves toward the current collector. No fluctuations were observed in the concentration profile as were observed by Whitney et al.²³⁸ Thus there is no structural breakdown of the cathode material, unlike that concluded by Whitney et al.²³⁸

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The decrease in the lithium concentration can be explained by a change in the particle size or coarsening of the LiFePO₄ nanoparticles observed in physical/morphological studies. Due to the coarsening of the nanoparticles, the diffusion length for the lithium increases within each particle. As a result, the net uptake of lithium during the discharging processes is low. During each charge cycle lithium diffuses out of the LiFePO₄, and phase change occurs from LiFePO₄ to FePO₄. In the discharge cycle the lithium diffuses back in the host FePO₄ particle, and the phase changes from FePO₄ to LiFePO₄. During the early life of the battery the phase change from LiFePO₄ to FePO₄ and back to LiFePO₄ might be complete, but as the particle size increases due to coarsening, the diffusion length changes, and this will affect the phase change. The incomplete phase change continues to occur in subsequent cycles while the particle size tends to increase. Thus the lithium retaining capacity of the particle drops in each subsequent cycle. The loss of active lithium in the cathode is directly related to the drop in capacity of the battery while the increase in the particle size and the subsequent increase in the diffusion length are directly related to the rate capabilities of the battery.

In summary, The Li concentration profile across the electrodes of the cells at the end of life is affected by the C-rate of the charge/discharge cycle and SOC of the battery. The Li concentration profile changes along the length of the electrode from outer edge to the core of the cylindrical cell, but it remains constant along the height of the electrode. In the case of the anode, the lithium concentration profile decays exponentially along the thickness of the anode. The Li builds up on the surface of the anode, and the buildup rate increases along the length of the anode and also with the C-rate. This buildup below the surface extends to a higher depth in cells cycled at higher C-rate. There is no buildup of the lithium near the cathode surface. Beyond a certain critical C-rate the lithium concentration drops with increasing C-rate, and it has a constant gradient along the depth of the cathode. The gradient of the lithium concentration profile in the cathode decreases with increasing C-rate. While the coarsening of the LiFePO₄ particles limits the diffusion of the lithium in the cathode, the surface concentration of the lithium on the anode increases with the C-rate. The quantitative measurement of the lithium profiles for the anode and cathode can prove instrumental in calibrating the diffusion models of the Li-ion cells.

Oudenhoven et al.,²⁴⁷ have demonstrated that lithium depth profiles can be measured in situ inside all solid state thin-film micro-batteries to monitor the charging and discharging processes. Since NDP is only sensitive for the ⁶Li isotope, a thin-film battery that contained a ⁶Li-enriched LiCoO₂ cathode was analyzed, resulting in enhanced signals. They claim that depending on the materials composition and density an analysis depth of up to 50 μm from the top surface can be obtained.

The battery that was analyzed in this measurement consisted of a monocrystalline silicon substrate with a 200 nm Pt bottom current collector, a 500 nm LiCoO2 cathode, a solid-state electrolyte consisting of 1.5 μm nitrogen doped Li₃PO₄ (LiPON) and a 150 nm Cu top current collector. The LiCoO₂ and LiPON films were deposited using magnetron sputtering. The sputter chamber contained a LiCoO2 and a lithium phosphate target. The lithium-metal anode is formed during the first charge cycle by in situ lithium plating. On top of the copper current collector a thick protective coating was deposited to protect the battery stack. The material of the protective coating is not mentioned.

It is possible to in situ monitor the charge-discharge profile by integrating the difference between the continuously measured NDP spectra and the spectrum of the as-deposited (discharged) battery in the energy range of the cathode (475–960 keV) and the anode (1510–1625 keV). The amount of lithium removed or stored on both sides can, with this difference, be determined accurately, even when the depth profile is relatively inaccurate. With this improved tolerance toward depth inaccuracy, the NDP measurement time for each spectrum can be reduced to less than 10 minutes, short enough with respect to the ∼3 hour (dis)charging time to follow these processes in situ.

It was concluded that the (initial) exchange rate is very low, for example, due to the absence of required Li vacancies in the electrode or electrolyte, or due to a high activation energy for the ion conductivity mechanism in these materials. During the charging process, the necessary exchange of lithium occurs between the cathode and electrolyte. Oudenhoven et al.,²⁴⁷ claim that when the packaging is sufficiently thin, it can also be applied to analyze classical liquid electrolyte micro-batteries.

Nagpure et al.²⁴⁸ have studied copper current collectors with NDP. Figure 44a shows the high-resolution optical microscopy image of the anode cross-section. The copper current collector (CCC) of ∼6μm in thickness is visible between graphite coatings on either side. The lithium concentration is measured for this thin CCC from both faces. Figure 44b shows the measured Li concentration profile from the two surfaces of the CCC. The profiles from each surfaces resembles a classic diffusion profile from surfaces similar to metalliding or carburization. The profile was reproducible for different CCC samples. The profile from the front face has a maximum of 0.025% atomic Li and the profile from the back face has a Li concentration of 0.08% atomic Li. The measured profiles do not have the same maximum at the surface, but show similar exponential decay along the thickness of the CCC. The data should not be confused with a plating of Li on the CCC surface as the NDP measurements indicate that Li has penetrated into the copper sub-surface.

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The first principle calculations by Van de Walle et al.²⁴⁹ have shown enhanced Li solubility (30 at.%) in FCC copper at 400 K. Also, the calculated phase diagram using differential thermal analysis and electromotive force measurements from high temperature have suggested 18 at.% solubility of Li in copper.²⁵⁰ Therefore, the tendency for Li diffusion into the CCC should be expected. During operation of the battery there exists a high concentration of Li atoms at the CCC surface, especially when the battery is fully charged. However, at the operating temperature of the batteries diffusion of Li to form copper alloys is not expected due to high activation energies.²⁵¹ Suzuki et al.²⁵² have concluded that it is possible for mass transfer across a copper film coated on a carbon fiber using electrochemical insertion and extraction mechanisms. However, they have not reported measurements showing the presence of Li within the CCC films.

Presence of Li in the CCC indicates the loss of cyclable Li. Among losses of active Li, the loss into the CCC is responsible for the loss of electrical capacity of the battery. The diffusion of Li into the CCC can alter its both electrical and thermal behavior. The increased levels of Li in Cu would change battery impedance and eventually degrade battery performance through ohmic losses. The residual resistivity of the CCC will be affected due to the Li impurity, as given by Nordheim's rule:²⁵³

where ρ_r(x)is the residual resistivity of Cu due to Li impurity, A is a constant and the x is the impurity concentration. Also, change in the thermal properties and local heating due to increased impedance can cause delamination between the CCC and the active graphite coating, leading to a further increase in the overall battery impedance. These effects, now evident from these measurements, should be given consideration while building battery performance and aging models. Only then can accurate estimates of the performance and aging of the Li-ion battery be established to guide the successful deployment in electric vehicles. Even though a specific mechanism for the above phenomena eludes us, the discovery is significant for aging studies of Li-ion batteries.

In summary, neutron depth profiling has been used to characterize the copper current collector used in the real life Li-ion battery. The data shows the presence of lithium in the CCC with a profile similar to a metalliding or carburization process. The presence of lithium in the CCC will affect its thermal and electrical behavior during the operation of the battery. The presence of lithium beyond the active material and in the CCC suggests that the degradation and loss of active Li in the current collectors cannot be ignored in efforts for the overall understanding of the aging mechanisms predicting the life and performance of the batteries.

The most simple battery model can be thought of as an electrical circuit with a resistance in series with an ideal voltage source, as shown in Fig. 45a.^255,256 The ideal voltage represents an ideal battery with open circuit voltage (E₀). The actual battery terminal voltage (V_b) is then given by the voltage drop across the constant resistance (R_b). This resistance represents the internal resistance of the battery. But the model fails to account for the true internal resistance of the battery as the internal resistance is assumed to be constant in this model, while the actual resistance is a function of the state of charge, and electrolyte concentration. Thus the model is limited to applications where the state of charge can be assumed to be constant or the effect of the state of charge can be neglected.

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The other commonly used model is the Thevenin battery model based on the Thevenin theorem. This model consists of a parallel circuit of capacitance (C₀) and overvoltage, resistance (R₀) is connected in series with an internal resistance (R) in series with ideal battery voltage (E₀) (Fig. 45b).^256–258 C₀ represents the capacitance of the double layer formed at the interface of the electrode and the electrolyte due to charge separation. The R₀ represents the non-linear resistance between the electrodes and the electrolyte. This model again fails to recognize that the various components considered here depend on the state of charge of the battery. The constant value assumption of the components leads to the main drawback of this model in predicting the performance of the battery. The model sometimes assumes different sets of parameters at different states of charge, but this limits the continuous battery evaluation.²⁵⁹ The model also fails to account for the faradaic processes within the battery.²⁵⁶

The Thevenin model has been expanded to account for the non-linear behavior of the parameters to develop the Dynamic Model of the battery performance.^256,257,260 The model can be represented as shown in Fig. 45c.²⁵⁶ V_b is the battery terminal voltage. The battery as a voltage source is represented by an equivalent capacitor (C_b). This helps in considering the SOC as the charge stored in the capacitor. R_p represents the small leakage current in the battery, which depends on the open circuit voltage. R_ic and R_id represent the resistance of the electrolyte and the electrodes. The values are considered to be dependent on the charge discharge process. The activation overpotential and the overpotential due to the mass transport are represented by the parallel R-C circuit. R_0c and R_0d represent the voltage drop during charging and discharging respectively while C₀ represents the capacitance due to the double layer at the interface of the electrode and the electrolyte. The values of the various elements of the circuit are considered to be a function of the open circuit voltage (OCV). Thus this model predicts the behavior of the battery with better accuracy as compared to other EECM models.

The P2D model is based on the porous electrode theory, concentrated solution theory, Ohm's law, Butler-Volmer kinetics, and charge and mass balance.^264,265 The electrodes used in the battery are porous electrodes to provide the large surface area for the electrochemical reactions. The porous electrode theory helps in modeling the actual porous electrode, which is a mixture of active material, binders, filler material, and electronic conductive coating. The porous electrode theory treats the structure of the electrode as the superposition of active material, electrolyte, and filler material. This leads to the simplification of the structure and the ability to consider the ohmic potential drop and mass transfer that occur in both series and parallel during the electrode processes across the surface.²⁶⁶ Each phase is considered to have its own volume fraction. The material balances are averaged about a volume small so that they are small with respect to the overall dimensions of the electrode but large with respect to the pore dimensions. This simplification allows one to treat the electrochemical reaction as a homogeneous term, without having to worry about the exact shape of the electrode–electrolyte interface, which can lead to heterogeneity in the electrode process.²⁶³

The electrolyte that fills the pores of the porous electrode is mostly a binary electrode with a lithium salt and organic solvent. The driving forces arising due to the chemical potential and the mass flux within this liquid phase is modeled using the concentrated solution theory.⁵³ The charge balance is applied to the charge flowing from the electrode surface to the electrolytes during the electrochemical reaction. The mass balance is applied to account for the change of the concentration within the electrolyte due to the mass transfer at the electrode-electrolyte surface.²⁶³

The potential drop in the electrode and the electrolyte is modeled using Ohm's law. The kinetics of the electrochemical processes is modeled with the Butler–Volmer equation that gives the relationship between the current density and the overpotential. The relationship depends on the exchange current density also known as the rate constant. All of these equations form a set of coupled non-linear differential equations having various dependent variables, such as the concentrations of the active material, the potential drop, and the reaction rates. Hence their solution requires a rigorous numerical treatment such as the finite-difference technique.

Fuller et al.^267,268 have laid the foundation for the mathematical model of lithium-ion batteries based on the porous electrode theory. The model was further simplified by Doyle and Newman.^269,270 The model and the equations presented here follow the work by Ramadass et al.²⁷¹ The schematic of the model is shown in Fig. 47a. The schematic shows three areas within the cell, namely the negative electrode, the separator and the positive electrode. The negative and the positive electrodes are the porous composite electrodes made of active material, binder and filler material. The potential drop across the separator is assumed to be zero and thus no current flows through the separator. For modeling purposes the cell can be considered to have two separate phases, the solid phase that represents the negative and the positive electrodes and the liquid phase that represents the electrolyte.

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The solid phase is assumed to be comprised of identical spherical particles. In the solid phase the diffusion of lithium along the radial direction is considered to be the predominant transport mode. Thus concentration of lithium needs to be calculated along the pseudo radial direction at each x interval. This gives the model its name of P2D model. In the case of the liquid phase, the concentration and the potential is assumed to vary only in x direction and it is solved for by applying the concentrated solution theory.

The overpotential in the negative and the positive electrode can be given as:

The open circuit potential (OCP) (U^θ_j) is often determined experimentally. The OCP can be a function of the state of charge of the battery. The model is setup to determine the values of the potential of each electrode (ϕ_{1, j}) and the liquid phase potential (ϕ₂).

In the case of the electronically conducting solid phase, as per the current conservation and Ohm's law, the potential distribution is given by,

Further the lithium concentration within the solid phase is given by,

Finally, the Butler-Volmer equation governs the kinetics of the electrochemical reactions and carries the overpotential term.

In the case of the liquid, the potential distribution is given by,

Finally, the mass transport through the liquid phase is governed by,

As stated earlier, and evident through the governing equations, the model involves two different length scales, the thickness of the cell (L) that is several order of magnitude higher than radius of the particle (Rj). Adanuvor et al.,²⁷² Verbrugge,²⁷³ and Verbrugge and Koch²⁷⁴ have suggested methods to avoid instabilities arising due to these two distinct length scales. Ramadass et al.²⁷¹ scales the radial coordinate as follows,

Haran et al.²⁷⁵ presented a simpler representation of the electrode. This was first presented for the metal hydride system and later extended to the lithium ion system.^81,276 In this model, each electrode is represented by a single spherical particle. This approach is popularly referred to as the single particle (SP) model. The simplified single particle model is orders of magnitude faster, however it does not account for all the physical processes. For example, the solution phase diffusion limitations are ignored, and thus the validity of the model is limited. In this model the overall framework of the PE model is maintained but instead of considering individual particles, each electrode is represented by a single spherical particle whose area is equivalent to that of the active area of the solid phase in the porous electrode. A schematic of this model is provided in Fig. 47b. This model assumes that the limitations posed by the solution phase of the cell are negligible. Hence, the solution phase is not considered while developing the model equations and so ϕ₂ is set to zero in the above equations.

Based on this simplification the electrode potential is a function of only the overpotential and the OCP as follows,

The Butler-Volmer kinetics is then given by,

Wang et al.,⁷² based on their extensive accelerated aging studies of large format cells, developed an empirical model. They have shown that the cells used at high temperatures and high discharge rates have short cycle life. It was observed that the capacity loss is strongly affected by cycling time and cell temperature, while the effect of DOD is negligible at low C-rates such as C/2. Using a curve-fitting technique, they demonstrated that capacity fade followed a power law relationship with charge throughput between 15°C and 60°C. The model parameters varied depending on the C-rate. Instead of having different model parameters for the different C-rates, they simultaneously fitted the experimental data for all C-rates and found the optimal values of the pre-exponent factor, B for each C-rate by minimizing the error (difference between measured value and the model value). The following is the model they have proposed for the capacity fade

where Q_loss is the percent of the capacity loss and A_h is the total Ah-throughput which is directly proportional to the cycling time at the given C-rate. The values of B are obtained by curve fitting the data from several cells at different C-rates. The values of B are 31630 (C/2), 21681 (2C), 12934 (6C), and 15512 (10C). For all C-rates, the model equations indicated that the power law factors were valued very close to 0.5. The square-root of time dependence was considered to be consistent with the aging mechanisms that involve diffusion and parasitic reactions leading to loss of active lithium.

The most prominent aging effect modeled for the lithium ion batteries is the SEI formation. This is modeled as a potential drop across the SEI layer formed on the anode surface due to the side reaction. Darling and Newman²⁷⁷ included a side reaction that occurs in a propylene carbonate (PC)/Li_yMn₂O₄ system in which they were able to predict the importance of the state of charge and self-discharge of the battery with cycling. Later Arora et al.⁷⁵ simulated the phenomenon of capacity fade by considering the lithium deposition as a side reaction during over-charge conditions and extended this concept to the increase in the thickness of the surface film with cycling. Here we discuss the model by Ramadass et al.²⁷¹ in which the potential drop across the film was expressed as a function of the film thickness, which varied with time in accordance with Faraday's law, as shown in the Eq. 8.11.

The loss of active material due to the side reaction and the resultant additional drop in the anodic overpotential were used to account for the capacity fade in the cell as given by Eq. 8.12.

Thus the potential of the negative electrode is given by,

Figure 48a shows the results of this model for different number of cycles. As can be seen, the capacity of the cell faded after a number of cycles.

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Sikha et al.²⁷⁸ have modeled the effect of the porosity change of the negative electrode on the capacity fade of the battery. They have assumed that during the operation of the battery, due to the side reaction and its products, plugging of pores in the negative electrode occurs. This leads to a change in the surface area of the active material and a loss of active material due to the side reaction. They have tried to overcome the use of any empirical relationship to examine the effect of the side reaction and the porosity change on the capacity fade of the battery. Their model is based on the model developed by Evans et al.²⁷⁹ for the lithium/thionyl chloride primary cell.

The governing equation for the porosity effect is the overall material balance in the matrix phase is,

Here a_j, the surface area to volume ratios is given by,

The results of the model are shown in Fig. 48b. The capacity is seen dropping after each cycle due to change in the porosity.

Nagpure et al.⁶⁷ have observed coarsening of the cathode nanoparticles during aging of the batteries. Tang et al.²⁸⁰ have modeled the effect of particle size in nanoscale olivines. This effect can also be modeled into the basic model discussed above. Figure 48c shows the effect of the change in particle size on the performance of the batteries. These results were obtained by using the BAND subroutine.^267,268,281 The change in the particle size affects the diffusion rates and leads to a change in the power rating of the cell. As seen in the Fig. 48c the resistance of the batteries changes which increased the particle size. This affects the power rating of the battery.