Lithium-Ion Batteries

Abstract

The effort of material scientists in the discovery, understanding, and development of Li-ion batteries largely depends on the techniques available to observe the relevant processes on the appropriate time and length scales. This chapter aims at demonstrating the role and use of different neutron-scattering techniques in the progress of Li-ion battery electrode and electrolyte properties and function. The large range in time and length scales offered by neutron-scattering techniques is highlighted. This illustrates the type of information that can be obtained, including key parameters such as crystal structure, Li-ion positions, impact of nano-particle size and defects, ionic mobility, as well as the Li-ion distribution in electrodes and at electrode-electrolyte interfaces. Special attention is directed to the development of in situ neutron-scattering techniques providing insight on the function of battery materials under realistic conditions, a promising direction for future battery research.

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

1 Li-Ion Batteries for Energy Storage

Electrochemical energy storage is attractive, having very high storage efficiencies typically exceeding 90 %, as well as relatively-high energy densities. Li-ion battery technology provides the highest energy densities of commercialized battery-technologies and has found widespread use in portable electronic applications. Application of Li-ion batteries in electrical vehicles and as static storage media is emerging, however, improved performance and reduced cost, combined with safety enhancements, are required. This has initiated a worldwide research effort for Li-ion electrode and electrolyte materials that combine desirable properties such as high energy and power density, low cost, high abundance of component elements, and electrochemical stability [1–4]. In the current generation of Li-ion batteries, insertion materials that reversibly host Li in the crystal structure form the most important class of electrodes. Although the future of Li-ion batteries looks bright, it should be noted that the availability of a number of relevant transition metals and possibly Li itself is a topic of interest [2].

In a Li-ion battery two insertion-capable electrodes¹ with a difference in Li chemical potential (change in free energy upon Li addition) are in contact through an electrolyte (an ionic conductor and electronic insulator) and a separating membrane, see Fig. 7.1. The Li will flow from the insertion material in which Li has a high chemical-potential towards the electrode in which Li has a low chemical-potential. Only Li-ions can flow through the electrolyte and the charge compensation requires electrons to follow via the external circuit which can be used to power an application. By applying a higher electrical potential than the spontaneous equilibrium open circuit polarization the process can be reversed. High energy-density requires a large specific-capacity of ions in both electrodes and a large difference in chemical potential. High power (and fast insertion/extraction) requires both electrons and Li-ions to be highly mobile throughout the electrode materials and electrolyte.

Fig. 7.1

Schematic illustration of the operating principle of a Li-ion battery. Reprinted with permission from (M. Wagemaker, F.M. Mulder, Acc. Chem. Res. 46, 1206 (2013)) [37]. Copyright (2013) American Chemical Society

1.1 Demands and Challenges

The success of Li-ion batteries is based on their high volumetric and gravimetric energy-density available for storage. This has enabled the realization of small portable devices like mobile telephones and laptops. However, important demands also include material and production costs, safety, cycle life (number of charge/discharge cycles), and high (dis)charge rates. Addressing all these demands makes it very challenging to find better electrode and electrolyte materials to improve Li-ion batteries [2, 4]. To gain more insight into the challenges in battery research it is useful to express the performance-related demands in more specific material properties of the electrodes and electrolytes. With respect to the general demands of cost and safety we merely state that batteries require abundant and cheap materials that are intrinsically stable during battery operation. For more extensive literature we refer the reader to some excellent reviews [2, 4–6].

The gravimetric and volumetric energy density of a battery is CV _OCP , where C is the specific or volumetric capacity (mAhg⁻¹ or mAgcm⁻³), respectively, and V _OCP is the open circuit, or equilibrium potential of the battery. Large gravimetric energy-density is required for automotive applications, and large volumetric energy densities are essential in mobile electronic equipment. It is important to realize that the specific Li capacity of the electrode materials is not necessarily the only decisive factor, and that the actual capacity of an electrode also depends significantly on the electrode morphology [7–9]. Large gravimetric energy-density requires dense electrodes and hence low porosities. In this context nano-sizing of electrode materials, aimed at higher storage capacities and higher rates, typically carries the disadvantage of low tap densities (powder packing) leading to less dense electrodes and compromising both volumetric and gravimetric energy-density.

The power density is the product of the specific current and the voltage that the battery can deliver. The battery voltage is defined by the difference in potential between the electrodes and the current via the internal resistance of the battery. High power densities, allowing for fast (dis)charge, require low internal resistance of the battery. The various charge-transport phenomena inside a battery contribute to this internal resistance, including the electronic conductivity through the electrodes, the ionic conductivity through the electrode and electrolyte, and finally the charge transfer through the interface between the electrode and electrolyte. Generally, the Li ion and electronic conductivity through the electrodes are assumed to be rate limiting in Li-ion batteries. Note that because the electrode is porous the ionic conductivity of the electrodes includes both the transport of ions through the solid-state electrode as well as through the electrolyte dispersed in the electrode pores. The solid-state transport of ions through electrodes depends on the specific electrode host material and is typically orders of magnitude slower than in liquid electrolytes. The overall Li-ion conductivity within the electrodes also depends strongly on the electrode morphology, such as characterized by the porosity [10] and the interconnectivity of the pores [11, 12].

High energy and power density are conflicting demands, as evidenced by the impact of electrode morphology and electrode thickness on these. High porosities, such as in nanostructured electrodes, generally lead to fast ionic transport throughout the electrodes responsible for high (dis)charge rates, and hence high power densities. However, the downside of large porosities is the larger volume required to store the same amount of energy, resulting in smaller volumetric energy-density. Because in most cases either electronic or ionic conductivity through the electrodes is rate limiting [7–9], thin electrodes can be charged faster than thick electrodes. Hence, the power density of a battery can be improved by the use of thinner electrodes. However, building a battery from thin electrodes leads to a smaller amount of active electrode material per gram of battery because of the relatively larger amount of current collector, electrolyte, and packing materials.

The cycle life of batteries is determined by a combination of the chemical and physical processes that occur during (dis)charging in the electrolyte and electrodes of a battery. Generally, electrodes undergo structural changes upon Li insertion and extraction. Large volumetric changes upon Li insertion and extraction lead to mechanical failure of the electrode. The result is generally that part of the active material is electronically disconnected from the electrode and therefore inactive. Consequently, small structural changes, such as occurring in Li₄Ti₅O₁₂ spinel (where the change in the unit-cell volume, ΔV _unit-cell , ≈ 0.1 %) [13], and moderate structural changes, such as occurring in LiFePO₄ (ΔV _unit-cell  ≈ 6.5 %) [14], contribute to batteries with long cycle-life. The other extreme is the alloying reaction of Li with silicon up to the Li_4.4Si composition resulting in a volume expansion >300 %, which leads to mechanical failure of the electrodes containing relatively large silicon particles within only a few charge/discharge cycles [15]. Nevertheless, the very high capacity associated with this type of alloying reaction has motivated chemists and material scientists to develop smart strategies to maintain the mechanical coherence of these electrodes [15–17].

The second factor that is important for the cycle life, and also to safety, is the thermodynamic stability of the electrolyte with respect to the positive and the negative electrodes (Fig. 7.2). The electrodes have electrochemical potentials μ _A (anode) and μ _C (cathode) equal to their Fermi energies ε _F . If μ _A is above the lowest unoccupied molecular orbital (LUMO) of the electrolyte, the anode will reduce the electrolyte. This reduction decomposes the electrolyte unless a passivating layer, generally referred to as the solid electrolyte interface (SEI) layer, is formed. The SEI layer often forms in the first few cycles and can act to electronically insulate the anode from the electrolyte, preventing further reduction. The SEI growth tends to stop after a few cycles, resulting in stable battery performance. Similarly, if μ _C is below the highest occupied molecular orbital (HOMO) of the electrolyte, the cathode will oxidize the electrolyte unless a passivating SEI layer is formed, electronically insulating and preventing further oxidation. Therefore, not only should the electrolyte provide a wide stability window in terms of voltage, but the gap between its LUMO and HOMO must be larger than the difference between the chemical potentials of the electrodes. That is, the electrolyte voltage window should be positioned such that LUMO > μ _A and HOMO < μ _C . The large open-cell voltage (V _Cell ) of Li-ion batteries (e.g. 3.6 V) that is responsible for their high energy and power densities requires electrolyte stabilities that exceed that of water (E_LUMO−E_HOMO ≈ 1.3 V) or water-containing electrolytes, leading to the application of non-aqueous electrolytes. Such stability demands do not apply if an electronically-insulating layer is formed upon electrolyte reduction or oxidation which can passivate further reactions. An example of passivation of SEI layers is the graphite or carbon-based anodes that work at about 0.5 V below the stability of typical carbonate electrolyte solutions, and hence 0.5 V above the LUMO of the electrolyte. The first few cycles with these anodes and carbonate-based electrolyte solutions results in the reduction of the electrolyte which leads to the formation of a stable SEI layer that prevents further reduction of the electrolyte. Importantly, the SEI layer does not grow significantly in subsequent cycles. Therefore, strategic combinations of electrodes, electrolytes, and SEI layers can result in better-performing batteries.

Fig. 7.2

Schematic energy diagram of an electrolyte as well as the cathode and anode work functions, Φ_C and Φ_A, respectively (equal to the electrode electrochemical potentials, the difference of which is the open-cell voltage of the battery, V _Cell ). The difference between the LUMO and the HOMO is the stability window of the electrolyte. If the electrode electrochemical potentials fall outside this stability window the electrolyte will decompose, which SEI layer formation can passivate, leading to the kinetic stability of the electrolyte and making the light areas (lower left and upper right) accessible

Improving Li-ion batteries with respect to energy and power density, manufacturing costs, safety, and cycle life is clearly a formidable challenge. A common starting point is to lower costs and use environmentally-benign materials for both the electrodes and the electrolyte, noting that the cathode can account for as much as 40 % of the cost of the battery. The electrolyte should have high Li-ion conductivity over a practical ambient-temperature range and a large stability (potential) window allowing use of large differences in electrode potentials. The electrodes should work within the stability window of the electrolyte and allow fast (dis)charge of a large reversible capacity. This not only depends on the electrode material and composition but also on the electronic and ionic ‘wiring’ of the electrodes determined by the electrode morphology. The development of new electrode and electrolyte materials and the improvement of existing materials requires a fundamental understanding of the Li insertion and transport mechanisms that involve both structural and kinetic phenomena. Probing these is a tremendous challenge given the complexity of the system and the difficulty of probing a light element such as Li, particularly under in situ conditions.

1.2 Development Using Neutron Scattering

The work of material scientists in the discovery, understanding, and development of Li-ion batteries largely depends on the techniques available to observe the relevant processes on the appropriate time and length scales. This chapter aims at demonstrating the role and use of different neutron-scattering techniques in gaining insight into Li-ion battery electrode and electrolyte function. This is not an exhaustive review of the neutron-scattering work on Li-ion battery materials or on the materials themselves, but an attempt to demonstrate the range of possibilities of neutron scattering in Li-ion battery materials research.

The role of neutron scattering in battery research is mainly based on the sensitivity of neutrons to Li compared to X-rays and electrons. The coherent neutron-scattering cross section of Li often allows the determination of the Li positions, atomic displacement parameters (ADPs), and occupancies using diffraction where X-rays do not, making it possible to elucidate Li-ion insertion/extraction mechanisms. The relatively-large coherent neutron-scattering cross section of Li provides sufficient contrast that Li distributions can be studied using imaging and, in thin-films, reflectometry. The incoherent neutron-scattering cross section of Li allows examination of Li mobility. Measuring Li diffusion directly is difficult as Li has only a moderate incoherent neutron-scattering cross section, so each material has to be considered individually to determine if the neutron-scattering signal originates from Li. Often measuring host material dynamics, e.g. anion and hydrogen group dynamics or lattice vibrations using quasi-elastic neutron scattering (QENS) and inelastic neutron scattering (INS), can provide information on Li dynamics. The diffusion pathway can be additionally corroborated or even independently obtained using the abovementioned large coherent cross-section of Li by considering the anisotropic contribution in the displacement parameter because of the deviation from harmonicity due to thermal motion at elevated temperatures. The relatively large neutron absorption cross-section of Li enables neutron depth profiling to determine Li distributions in materials. In these neutron-based techniques used to study Li-ion battery materials, the effective cross-sections of samples under study can be tuned through the isotopic composition. Naturally occurring Li is composed of 7.5 % ⁶Li and 92.5 % ⁷Li. The larger coherent neutron-scattering cross section and lower incoherent neutron-scattering and absorption cross-section of ⁷Li make it possible to improve data quality by tuning compositionally (isotopically) samples according to the neutron investigation technique being used.

2 Electrodes

Since the commercialization of the Li-ion battery by SONY Corporation in 1991, research has focused on identifying better electrode and electrolyte materials. SONY combined LiCoO₂ as a positive electrode material with a carbonaceous material as a negative electrode, and LiPF₆ in a carbonate solution as the electrolyte. Initially, research focused on replacing the relatively expensive LiCoO₂ with other transition-metal oxides where the most important structural groups include spinel and layered transition-metal oxides. Layered Li transition-metal oxides, LiMO₂ with M = Mn, Co, and Ni, represent one of the most successful classes of positive-electrode materials. The layered topology offers easily-accessible two-dimensional ion diffusion pathways. In particular, the LiCo_1/3Ni_1/3Mn_1/3O₂ composition [18] results in high capacity, safety, and lower material costs than LiCoO₂.

An important alternative to LiCoO₂ is the spinel LiMn₂O₄ with the inexpensive and environmentally-benign Mn, which functions with the Mn^3+/4+ redox couple. LiMn₂O₄ operates at 4.1 V versus Li/Li⁺ offering excellent safety and high power due to its three-dimensional lattice, in principle allowing three-dimensional Li-ion diffusion. Substitution of Mn by M = Co, Cr, Cu, Fe, and Ni, has led to the discovery of the high-voltage spinels LiM _0.5Mn_1.5O₄ and LiMMnO₄ with potentials between 4.5 and 5 V versus Li/Li⁺ [19], exemplified by spinel LiNi_0.5Mn_1.5O₄ operating at 4.7 V versus Li/Li⁺ [20, 21]. However, Mn-based spinels have been plagued by capacity fade, generally considered to be the result of Mn dissolution into the electrolyte and Jahn-Teller distortion of Mn³⁺. Mn dissolution has been largely inhibited by substitution of dopants in the spinel structure [22].

The introduction of LiFePO₄ [14] has initiated research on polyanion-based positive electrodes with the structural formula LiM(XO)₄ (M = Fe, Mn, Co, and X = S, P, Si). The strong covalent X-O bonds result in the large polarization of oxygen ions towards the X cation, leading to larger potentials compared to oxides. Phosphates, in particular LiFePO₄, have been extensively explored because of their favourable electrode properties, reasonably high potential and capacity, stability against overcharge or discharge, and their composition of abundant, cheap, and non-toxic elements. To date, almost a thousand papers have been devoted to the understanding and improvement of conductivity in the semiconductor LiFePO₄. These have encompassed studies of surface-conductive phases [23, 24], modification of crystallite size [25], and elegant fundamental mechanistic and modelling studies [26–28]. Compared to the phosphates, the silicates (LiMSiO₄) exhibit lower electrode-potentials and electronic conductivity [29]. Other promising groups of positive-electrode materials include fluorophosphates with the A ₂ MPO₄F (A = Alkali metal) stoichiometry [29].

For many years graphite has been the main negative-electrode material allowing Li-ion intercalation between graphene sheets at ~0.3 V versus Li/Li⁺. The low potential results in a high battery-voltage, partly responsible for the high energy and power density of Li-ion batteries. The main disadvantage of the low voltage of a negative electrode is the restricted stability of the commercial carbonate-based electrolyte solutions at low potentials versus Li/Li⁺. Depending on the electrolyte-electrode combination a kinetically stable SEI layer can be formed. For graphite this was achieved by the addition of ethylene carbonate [30] which lead to the success of the LiCoO₂–C battery. Efforts to develop low-voltage negative electrodes with capacities that exceed that of C have concentrated on reaction types other than insertion reactions. Metals such as Si and Sn form alloys with Li in so-called conversion (or alloying) reactions [31–34]. Although the (gravimetric) capacities of these reactions can reach almost 10 times that of graphite, the volumetric energy-density is not significantly improved. Moreover, the large volume changes inherently related to this type of reaction make it a challenge to reach good cycleability. The oxide insertion hosts offer much better stability, highlighted by the Li₄Ti₅O₁₂ spinel [35] that has almost no volume change upon Li insertion. Other titanium oxides that attract considerable attention as negative electrodes are anatase, brookite, and rutile TiO₂, particularly in the nanostructured form [36, 37] and in combination with carbonaceous materials providing good with electronic-conductivity [16, 36]. The disadvantage of titanium oxides is their relatively high negative-electrode potentials, reducing the overall working voltage of the battery and thereby reducing both energy and power density. For example, titanium oxides operate at ~1.6 V versus Li/Li⁺, over four times higher in voltage than graphite. In this context, an interesting oxide exceeding the graphite capacity at similarly low potentials is the layered transition-metal oxide Li_1+xV_1−xO₂ [38].

One of the key strategies that improved electrode performance in general is the nano-sizing of the electrode crystal particles. The nano-sized electrode particles reduce both solid state (Li-ion) diffusion and electron conduction. The latter is achieved by mixing and coating with conducting phases (i.e. with carbonaceous materials). However, numerous recent observations indicate that nano-sizing electrode particles also has a large impact on electrode materials properties [39, 40] creating both opportunities and challenges for enhanced Li-ion storage. Changes in properties that are observed upon nano-sizing include smearing of the voltage profile [41–43], changing solubility limits and phase behaviour [41, 44–46], unexpected kinetics [47], and larger capacities [45, 48–51]. The downside of the large surface-area of nanostructured materials is the relative instability of nano-materials, which can promote electrode dissolution and the increased reactivity towards electrolytes at commonly used voltages, e.g. below 1 V versus Li/Li⁺, which may adversely affect performance. Another potential disadvantage is the lower packing density of electrodes, leading to lower volumetric energy-densities. Among the materials that benefit from the possibilities of nano-sizing are the relatively stable transition-metal oxides and phosphates operating well within the stability window of the electrolyte.

2.1 Crystal Structure

In Li-ion battery electrode research, neutron powder diffraction (NPD) is one of the first techniques used for structural characterization of synthesized materials, often in combination with X-ray diffraction. NPD also plays an essential role in understanding the insertion mechanisms that may induce phase transitions and/or solid-solution behaviour, both of which may depend strongly on temperature, particle size, doping, and the chemical or electrochemical conditions.

The coherent neutron-scattering cross-sections of Li is relatively greater than that obtained for many transition-elements and greater than the analogous coherent scattering cross-sections of Li for X-ray or electron scattering, making it possible to determine Li-ion positions and occupancies. Thanks to these and other advantages of NPD, the technique has played a key role in the development of the large diversity of Li-ion battery electrode materials that exist to date.

Knowledge of the Li-induced phase transitions in C is primarily based on X-ray diffraction [52]. Although the crystal stages I and II in C are proven, long standing debate exists concerning LiC₁₈ and no evidence of the higher-order lithiated stages exists based on X-ray diffraction studies. Neutron diffraction proved the existence of the LiC₁₈ stage [53] and showed deviations from the common structural picture of lithiated C, including a charge-discharge dependent structural evolution and the appearance of higher-ordered stages [54].

Neutron diffraction has been used to determine the lithiated structures of titanium oxides including Li_xTiO₂ anatase [55–57], rutile [58], brookite [59], and Li_1+xTi₂O₄ and Li_4+xTi₅O₁₂ spinel [55]. Li₄Ti₅O₁₂ spinel is a state-of-the-art Li-ion battery electrode material [35, 60–63] operating at 1.56 V versus Li and is suitable as an anode using high-voltage cathode materials. Li₄Ti₅O₁₂ can be lithiated up to the composition Li₇Ti₅O₁₂ and possibly higher, with end members having a spinel structure adopting the cubic space group Fd-3m. This material is attractive as a Li-ion insertion electrode because the ‘zero strain’ property results in excellent cycle life: upon lithiation from the initial Li₄Ti₅O₁₂ to the ‘fully-lithiated’ Li₇Ti₅O₁₂ there is almost no change in lattice parameters (0.2 %) [35, 60–65]. In the defect spinel Li₄Ti₅O₁₂ all the energetically-favourable tetrahedral 8a sites are occupied by Li. Additionally, 1/6 of the 16d sites are also randomly occupied by Li while the remaining 5/6 of the 16d sites are occupied by Ti atoms, and this can be represented as [Li₃]^8a[Li₁Ti₅]^16d[O₁₂]^32e. Lithiation leads to occupation of all the octahedral 16c sites and emptying of the tetrahedral 8a sites to reach the lithiated Li₇Ti₅O₁₂ composition, which can be represented as [Li₆]^16c[Li₁Ti₅]^16d[O₁₂]^32e.

In lithiated anatase, neutron diffraction data obtained to relatively high momentum transfers were used to resolve the split Li-ion positions within the material’s distorted oxygen octahedra [56]. In composite anatase TiO₂/Li₄Ti₅O₁₂, neutron diffraction showed that the TiO₂ phase was lithiated before Li₄Ti₅O₁₂, as expected from the lower potential of Li₄Ti₅O₁₂ versus Li/Li⁺, enabling tuned Li insertion/extraction based on the choice of voltage range [66]. The increase in curvature of the voltage profile and larger capacities for nano-sized materials appears to be a general observation for the various TiO₂ polymorphs such as the tetragonal anatase [42, 45, 48, 58, 67] and rutile [48], orthorhombic brookite [68] and monoclinic TiO₂(B) [50, 69]. The sensitivity of neutron diffraction for Li-ions has been decisive in revealing the altered thermodynamics of nano-sized titanium oxides. In anatase the Li solubility increases systematically when particle sizes are reduced leading to a phase-size diagram [45]. In addition, a second phase transition from the known Li-titanate phase towards tetragonal LiTiO₂ was discovered, which was later confirmed by neutron diffraction in anatase nano-tubes [70]. Higher Li-ion solubility was also observed in nanostructured rutile using neutron diffraction [71], suggesting similar size effects. A remarkable finding in spinel nano-sized Li₄Ti₅O₁₂ is that of increased capacity with decreasing particle size, exceeding the maximum composition observed for the micron-sized Li₇Ti₅O₁₂. Neutron diffraction proved the increase in capacity to be due to simultaneous Li occupation of both 8a and 16c sites, providing an atomic-scale explanation for the larger capacity of the nano-sized materials [43].

A very interesting negative electrode, exceeding the graphitic anode capacity, at similarly low potentials, is the layered transition-metal oxide Li_1+xV_1−xO₂ [72]. Interestingly, LiVO₂ does not allow Li insertion whereas Li_1+xV_1−xO₂ with x > 0 leads to a very low intercalation voltage close to 0.1 V with a capacity almost twice that of graphite. Neutron diffraction has shown that in Li_1.07V_0.93O₂ part of the octahedral V is replaced by Li, which allows additional Li-ions, responsible for the large capacity, to occupy the neighbouring tetrahedral sites that are energetically unfavourable in LiVO₂, and is supported by modelling studies [38].

Gummow et al. used neutron diffraction to show that the structure of the low-temperature cubic phase of LiCoO₂ is not ideally layered, and that 6 % of the Co reside in the octahedral (8a) sites of the Li layers [73, 74]. The hexagonal structure of the high-temperature phase of LiCoO₂ was also determined from neutron diffraction, illustrating that Co and Li planes alternate in the ABCABC oxygen stacking. Aiming at higher capacity cathodes, Li_1+xCoO₂ has been prepared raising the question of where the additional Li resides [75]. Combined Rietveld refinement using both X-ray and neutron diffraction data excluded both Co in the Li site and the presence of tetrahedral Li and Co [76]. Based on this, it was deduced that excess Li replaces some Co and that the charge is compensated for by O vacancies [77]. In mixed-cation layered transition-metal oxides, such as the so called ‘high capacity’ LiMn_1/3Co_1/3Ni_1/3O₂, neutron diffraction continues to be an indispensable tool for determining the cation distributions which have been shown to depend on the synthesis conditions [78–80].

Neutron diffraction has played a pivotal role in understanding the complex insertion and phase transitions in spinel transition-metal oxides. Using NPD, Fong et al. [81] described the crystal structure of Li _x Mn₂O₄ for x = 1 and 0.2 and Wills et al. [82] determined the crystal structure of LiMn₂O₄ at low temperatures as well as its magnetic properties. Neutron diffraction revealed the partial charge-ordering in spinel LiMn₂O₄ at 290 K that further hinders its use as a positive-electrode material in Li-ion batteries [83]. From neutron diffraction data, superstructure reflections were found (related to charge-ordering phenomena) at 230 K which in combination with electron diffraction patterns revealed a 3a × 3a × a super cell of the cubic room-temperature spinel representing the columnar ordering of electrons and holes [83]. Two of the five Mn sites correspond to well-defined Mn⁴⁺ and the other three sites are close to Mn³⁺ as derived from Mn–O bond length analysis. This charge ordering is accompanied by simultaneous orbital ordering due to the Jahn-Teller effect in the Mn³⁺ ions. Li-excess compounds Li_1+xMn_2−xO₄ were found to provide better cycling performance than the stoichiometric LiMn₂O₄ as they minimize the extent of the Jahn-Teller distortion during cycling (i.e. increase the overall oxidation state of Mn during cycling). In addition, Li doping at octahedral 16c sites reduces the exothermicity of the Li insertion/extraction reactions by an amount similar to that associated with the dilution of the Mn³⁺ ion [84]. Neutron diffraction by Berg et al. [85] showed that Li occupies 16c sites in Li_1.14Mn_1.86O₄ which is also accompanied by charge-compensating vacancies at Mn 16d sites. Calculations also showed that the 16d sites should be favourable for Li at low Li contents while at higher contents, the 16c and mixed 16c and 16d site occupation is likely [86]. However, a recent study by Reddy et al. [87, 88] shows that at lower Li doping regimes, x = 0.03 and 0.06, the structural model containing Li at 16c sites still results in a better fit to the neutron diffraction data than models with 16d site Li occupation. In the work by Yonemura et al. [89] samples were synthesized in controlled atmospheres which led to the realization and quantification of O-deficient LiMn₂O₄ and Li-excess (O-deficient) Li_1+x Mn_2−x O_4−y spinels. Using neutron diffraction data they determined the quantity of O, mixing of Li and Mn at the 8a and 16c sites, the interatomic bond distances, and the relationship between these crystallographic parameters.

In the high-voltage spinels, neutron diffraction enabled the transition-metal ordering in LiNi_0.5Mn_1.5O₄ that breaks the cubic Fd-3m to cubic P4₃32 symmetry to be determined and this was found to be dependent on the cooling rates used in the synthesis [90]. In X-ray diffraction data the small difference in atomic number between Mn and Ni makes it hard to quantify this ordering, whereas it is easily modelled using neutron diffraction [91, 92]. In the low-voltage plateau, using the large difference in the coherent neutron-scattering cross section of Mn and Ni, researchers determined that extensive migration of Ni and Mn was occurring in the spinel structure due to the loss of long range Ni-Mn ordering [92].

In the polyanion-based positive-electrode materials, neutron diffraction data contributes significantly in the characterization and understanding of the electrode properties. The higher potential of the Mn³⁺/Mn²⁺ redox couple has initiated the synthesis of LiMnPO₄ and LiMn_yFe_1-yPO₄ materials. Neutron diffraction data helped reveal that the reduced activity of the Mn³⁺/Mn²⁺ couple is related to the distortion of the MO₆ octahedra with M = Mn³⁺, and this distortion was found to be much larger than the change in the unit cell [93], effectively prohibiting the Mn³⁺ to Mn²⁺ transition. Neutron diffraction was also used to characterize the cation distribution in related olivine structures with other transition metals and transition-metal mixtures such as LiCo_yFe_1−yPO₄ [94], Li_xCoPO₄ [95], and V-substituted LiFePO₄ [96, 97].

For tavorite, LiFePO₄(OH), neutron diffraction showed both the Li and H to be located in two different tunnels running along the a and c-axes, the tunnels being formed by the framework of interconnected PO₄ tetrahedra [98]. Another promising class of tavorite-structured cathode materials are the fluorophosphates which exhibit good storage capacity and electrochemical and thermal stability. LiFePO₄F exhibits a complex single-phase regime followed by a two-phase plateau at 2.75 V. Neutron diffraction in combination with X-ray diffraction was used to resolve the single phase end-member Li₂FePO₄F structure showing that Li-ions occupy multiple sites in the tavorite lattice [99]. Additionally, in the pyrophosphate-based positive electrode Li_2−x MP₂O₇ (M = Fe, Co), multiple Li sites were identified using neutron diffraction [100].

In general, the combination of X-ray and neutron diffraction has become the established approach to characterizing electrode materials in great detail. The following example concerning the extensively-studied olivine LiFePO₄ demonstrates the value of neutron diffraction in revealing the impact of dopants, defects, and particle size on LiFePO₄ structure and performance, thereby providing crucial understanding for the design of future electrode materials.

In the last decade LiFePO₄ has emerged as one of the most important positive electrodes for high-power applications owing to its non-toxicity and outstanding thermal and electrochemical stability [14]. The first-order phase transition, preserving its orthorhombic Pnma symmetry, results in highly-reversible cycling at the 3.4–3.5 V versus Li/Li⁺ voltage plateau with a theoretical capacity of 170 mAhg⁻¹. The olivine structure is built of [PO₄]³⁻ tetrahedra with the divalent M ions occupying corner-shared octahedral ‘‘M2’’ sites, and the Li occupying the ‘‘M1’’ sites to form chains of edge-sharing octahedra. The magnetic structure of LiFePO₄ has been solved using neutron diffraction, with the appearance of extra reflections below the Néel temperature indicating antiferromagnetic behaviour at low temperatures for both end-members FePO₄ (Fe³⁺) and LiFePO₄ (Fe²⁺) [101].

In contrast to the well-documented two-phase nature of this system at room temperature, Delacourt et al. [102, 103] gave the first experimental evidence of a solid solution Li _x FePO₄ (0 ≤ x ≤ 1) at 450 °C, and in addition, the existence of two new metastable phases with compositions Li_0.75FePO₄ and Li_0.5FePO₄. These metastable phases pass through another metastable phase on cooling to room temperature where approximately 2 out of 3 Li-positions are occupied, again determined using neutron diffraction to be Li_~0.67FePO₄ [103]. In Li_~0.67FePO₄, the average Li–O bonds are longer than in LiFePO₄ due to the shortening of Fe–O bond lengths as shown in Fig. 7.3. It was suggested that this bond-length variation is the origin of the metastability of the intermediate phase, and thus of the two-phase mechanism between LiFePO₄ and FePO₄. Interestingly, this metastable phase appears to play a vital role in the high charge/discharge rate of the olivine material [104].

Fig. 7.3

View of the FeO₆ and LiO₆ octahedra for a LiFePO₄, b Li_~0.67FePO₄, and c FePO₄, displaying the contraction of average Fe–O bond lengths from LiFePO₄ to FePO₄, together with the slight expansion of the M1 size (related to the average Li–O bond lengths in Li-containing phases). The models are based on combined structural refinements using neutron and X-ray diffraction data. Reprinted with permission from (C. Delacourt, J. Rodriguez-Carvajal, B. Schmitt, J.M. Tarascon, C. Masquelier, Solid State Sci. 7, 1506 (2005)) [103]. Copyright (2005) Elsevier

The room-temperature miscibility gap in Li_xFePO₄ was determined by Yamada et al. [105] using NPD. These researchers found intermediate Li-poor Li_α=0.05FePO₄ and Li-rich Li_1−β=0.89 phases, as shown in Fig. 7.4. This explains the compositional range over which the voltage is constant (plateau) and proves the presence of mixed-valence states of iron (Fe²⁺/Fe³⁺). These mixed-valence states provide ionic and electronic conductivity, an essential ingredient for the material’s application as a Li-ion battery electrode.

Fig. 7.4

Left Refinement using neutron diffraction data of Li_0.5FePO₄ resulting in solubility limits α = 0.05 and 1−β = 0.89 in the Li-poor triphylite and Li-rich heterosite phases, respectively. Right Open circuit voltage versus composition, where the vertical lines indicate the monophase/biphase boundary as determined from the Li site occupancies resulting from Rietveld refinement using neutron diffraction data. Reprinted by permission from Macmillan Publishers Ltd: (A. Yamada, H. Koizumi, S.I. Nishimura, N. Sonoyama, R. Kanno, M. Yonemura, T. Nakamura, Y. Kobayashi, Nat. Mater. 5, 357 (2006)) [105]. Copyright (2006)

An early report that led to intensive discussions suggested that the poor electronic conductivity of LiFePO₄ could be raised by 8 orders of magnitude by supervalent-cation doping, which was proposed to stabilize the minority Fe³⁺ hole carriers in the lattice [106]. It was only after detailed refinement of models against combined neutron and X-ray diffraction data that researchers were able to determine the positions and role of the dopants. In this case NPD provides contrast between Li and the dopants at the Li site (M1), and X-ray powder diffraction provides contrast between the Fe and many of the dopants at the Fe site (M2). Moreover, to determine three species (Li or Fe, dopants and vacancies) on crystallographic sites (M1 or M2) requires more than X-ray or neutron diffraction alone. The neutron diffraction pattern for one of the doped materials is shown in Fig. 7.5. Although the changes in the diffraction pattern upon doping are extremely small, the accuracy afforded by the data make it possible to conclusively locate the supervalent-cation dopants in LiFePO₄. Figure 7.6 shows that supervalent-cation doping of up to ~3 % atomic substitution can be achieved in the LiFePO₄ lattice in bulk materials prepared by a solid-state route at 600 °C. The results show that the dopant resides primarily on the M1 (Li) site and that aliovalent-dopant charge is balanced by Li vacancies, with the total charge on the Fe site being +2.000 (± 0.006), within the limit of experimental error [107]. It is thus expected that dopants may have little influence on the electronic conductivity of the material, which is confirmed by calculations [108]. Furthermore, the location of the immobile high-valent dopant within the Li channels is expected to hinder Li-ion diffusion assuming one-dimensional diffusion.

Fig. 7.5

a LiFePO₄ adopting Pnma symmetry with the split Li-ion (medium grey) position in the centre. b NPD data for LiFePO₄ and Li_0.96Zr_0.04FePO₄ (target composition) including the difference between the fits and data. The fit residuals are wR _p  = 1.7 % and R _p  = 1.9 %, as well as wR _p  = 1.7 % and R _p  = 1.8 %, respectively. c The same data as in (b) shown for a limited d-spacing range. Reprinted with permission from (M. Wagemaker, B.L. Ellis, D. Luetzenkirchen-Hecht, F.M. Mulder, L.F. Nazar, Chem. Mater. 20, 6313 (2008)) [107]. Copyright (2008) American Chemical Society

Fig. 7.6

Supervalent doping occupancies from refinements using combined X-ray and neutron diffraction data plotted versus the targeted dopant concentration. Reprinted with permission from (M. Wagemaker, B.L. Ellis, D. Luetzenkirchen-Hecht, F.M. Mulder, L.F. Nazar, Chem. Mater. 20, 6313 (2008)) [107], Copyright (2008) American Chemical Society

The one-dimensional migration channels through the LiFePO₄ olivine structure means that the electrode performance can be severely influenced by defects. In the olivine structure the most favourable defect is predicted to be the Li–Fe anti-site pair, in which a Li-ion (at the M1 site) and a Fe ion (at the M2 site) are interchanged. These defects, with concentrations up to 8 %, were first observed in LiFePO₄ synthesized at low temperatures, leading to non-thermodynamically favoured materials [109]. Small concentrations of anti-site defects, as high as 1 %, were suggested to remain even up to solid-state synthesis temperatures as high as 600 °C [110]. In addition, combined neutron and X-ray diffraction has indicated that after fast hydrothermal synthesis crystalline-defective Li_xFe_yPO₄ coexists with amorphous Li/Fe-PO₄ structures. These techniques also showed that the Fe is included in the structure more rapidly from the amorphous precursor than Li, causing defects in the structure [111]. Anti-site defects are expected to play a decisive role in the Li-ion conductivity and Gibot et al. [112], using combined neutron and X-ray diffraction data, demonstrated that large concentrations (up to 20 %) of these anti-site defects in nanoparticles suppress the first-order phase transition normally observed in LiFePO₄ leading to a single-phase room temperature reaction upon (de)lithiation. More detailed insight into the correlation between particle size and Li-ion substoichiometry was obtained by the direct synthesis of substoichiometric Li_1−yFePO₄ nano-particles [113]. Combined neutron and X-ray diffraction data of partially-delithiated substoichiometric olivines revealed segregated defect-free (where Li is extracted) and defect-ridden (where Li remains) regions, as shown in Fig. 7.7. This proved that both the anti-site defects obstruct Li⁺ diffusion, explaining the detrimental electrochemistry and that the anti-site defects form clusters.

Fig. 7.7

Interpretation of the combined neutron and X-ray diffraction results for delithiation of Li_0.90FePO₄: Composition dependence and site disorder. a Evolution of the site-defect concentration in the Li-rich and Li-poor phases as a function of delithiation. b Overall schematic illustration of the phase segregation of the Li-rich and Li-poor regions of the crystallites with regions free of Fe anti-site defects delithiating before regions containing M1 site defects. Reproduced from (S.-P. Badi, M. Wagemaker, B.L. Ellis, D.P. Singh, W.J.H. Borghols, W.H. Kan, D.H. Ryan, F.M. Mulder, L.F. Nazar, J. Mater. Chem. 21, 10085 (2011)) [113] with permission from The Royal Society of Chemistry

Further details of the anti-site clustering in LiFePO₄ were obtained using a combination of neutron diffraction with high-angle annular dark-field scanning transmission electron microscopy and ab initio calculations, indicating that they form zig-zag type clusters, completely different from the structurally equivalent LiMnPO₄ where the anti-site defects appear to be randomly distributed [114].

Another topic that has been of great interest is the impact of the particle size on the intercalation properties. When insertion electrode materials are downsized to nanometer dimensions, voltage profiles change considerably reflecting a change in thermodynamics [37, 39]. First direct evidence of modified electrochemical-structural behaviour in nano-sized insertion electrodes was provided by neutron diffraction on TiO₂ anatase, which showed large changes in Li solubility in phases and a strongly-altered phase composition and morphology [45]. Also, the solubility limits during the insertion reaction in LiFePO₄ have been under active research, mainly using neutron diffraction as a direct probe [41, 44, 102, 115–120]. This research shows narrow solid-solution domains in micron size particles at room temperature [117] and a solid solution over the entire compositional range above 520 K [102, 121]. Yamada et al. [117] suggested that the extended solid-solution composition-ranges in small particles and a systematic decrease of the miscibility gap was due to strain based on Vegard’s law [41]. Kobayashi et al. [44] isolated solid-solution phases, also supporting a size-dependent miscibility gap. Direct evidence of enhanced solubility in the end phases with decreasing primary crystallite-size was provided by a systematic neutron diffraction study of particle sizes between 22 and 130 nm [46]. The Fourier-density difference maps in Fig. 7.8 illustrate that the Li densities in the Li-poor and Li-rich phases increase and decrease respectively, with decreasing particle size. These observations could be reproduced by calculations based on a diffuse interface model [46, 122]. The diffuse interface introduces an energy penalty for a Li concentration-gradient creating a smoothly-varying Li concentration over an interface region with a width of ~10 nm, as shown in Fig. 7.9. The confinement of this interface layer in nano-sized particles moves the observed solubility away from the bulk values. Interestingly, neutron diffraction also proved that the solubility in both phases (LiFePO₄ and FePO₄) depends on the overall composition, especially in crystallites smaller than 35 nm. Furthermore, this observation could be explained quantitatively by the diffuse-interface model. By varying the overall composition the domain sizes of the coexisting phases change, in this case leading to confinement effects in the minority phase.

Fig. 7.8

The structural impact of nano-sizing illustrated by Fourier-density difference maps obtained from neutron diffraction. The maps are shown for both the Li-poor α-phase and the Li-rich β-phase in Li_0.5FePO₄ for the three different particle sizes indicated. The maps were obtained by the Fourier transform of the difference between the neutron diffraction data and the calculated diffraction pattern based on the structure with no Li present. Therefore, these density maps should show Li density. As expected for large particles, large Li density is observed in the Li-rich heterosite β-phase, and no density is observed in the Li-poor triphylite α-phase. Progressive particle-size reduction decreases observed Li density in the heterosite β and more evidently Li density increases in the triphylite α phase, indicating a reduction of the miscibility gap with decreasing particle size. Reprinted from (M. Wagemaker, D.P. Singh, W.J.H. Borghols, U. Lafont, L. Haverkate, V.K. Peterson, F.M. Mulder, J. Am. Chem. Soc. 133, 10222 (2011)) [46]

Fig. 7.9

Measured and calculated solubility limits as a function of particle size and overall composition. Left a Symbols Li occupancy for both the Li-poor triphylite α-phase Li_xαFePO₄ and the Li-rich heterosite β-phase Li_xβFePO₄ where x_α and x_β represent the average solubility limits as a function of particle size, having an overall composition Li_0.5FePO₄. V_α and V_β represent the corresponding unit-cell volumes. The size of the symbols is approximately the size of the error. Lines Calculated average compositions based on the diffuse interface model. b Calculated concentration profiles based on the diffuse interface model in the a-lattice direction for three different particle sizes at the overall composition Li_0.5FePO₄. Right Measured and calculated solubility limits as a function of overall composition. a Symbols Li occupancy derived from neutron diffraction data for both the Li-poor triphylite α-phase and the Li-rich heterosite β-phase representing the average solubility limits as a function of overall composition for different particle sizes. Lines Calculated average compositions based on the diffuse interface model. The size of the symbols is approximately the size of the error. b Calculated concentration profiles based on the diffuse interface model in the a-lattice direction for three different overall compositions all having the particle size 35 nm. Reprinted from (M. Wagemaker, D.P. Singh, W.J.H. Borghols, U. Lafont, L. Haverkate, V.K. Peterson, F.M. Mulder, J. Am. Chem. Soc. 133, 10222 (2011)) [46]

The ex situ neutron diffraction studies discussed above have contributed to our current state of understanding of electrode materials. This is in particular based on the sensitivity of neutrons for Li, the charge-carrying element in Li-ion battery electrodes. This is vital knowledge not only for the synthesis of new materials, but also for mechanistic understanding of the impact of supervalent doping, defects, composition, and particle size on the intercalation process as illustrated for olivine LiFePO₄.

2.2 Local Structure

To obtain the local structure in glassy, nano, disordered and amorphous materials, having unresolved, weak or broad signals, neutron total scattering, or/and inelastic neutron scattering (INS) or quasielastic neutron scattering (QENS) can be powerful tools. Total scattering allows extraction of the local structure in terms of interatomic distances, bond angles and coordination numbers. In this case scattering is detected over a wider Q-range and short-range interactions of a sample are probed and modelled. In addition, rotations and vibrations picked up by INS and QENS are very sensitive to local distortions and allow otherwise difficult to detect relevant species such as protons, OH, water and in rare cases Li to be studied.

The negative-anode carbon is a good example of where neutron total scattering, in conjunction with other neutron-based methods, has been able to quantify important, previously ill-defined, aspects of the material’s function [20, 123, 124], as demonstrated with a range of low-crystallinity C negative electrodes. Additionally, C-based anodes can be analysed in the lithiated and delithiated states and over the course of phase transitions. Typical neutron total-scattering data for graphite is presented as a radial distribution function (or pair distribution function) as illustrated in Fig. 7.10, and peak positions are indicative of interatomic distances. Often, neutron total scattering is combined with INS data to provide supporting information concerning the short-range order in C. For further information on total scattering the reader is directed to a review on the structure and dynamics of ionic liquids [125], and total scattering is likely to become increasingly used as the range of nano-sized active electrode materials increase.

Fig. 7.10

Radial distribution functions (RDFs) of graphite and the in-plane honeycomb structure inset. Each concentric circle in the honeycomb structure produces a peak in the RDF. Reprinted with permission from (P. Zhou, P. Papanek, R. Lee, J.E. Fischer, W.A. Kamitakahara, J. Electrochem. Soc. 144, 1744 (1997)) [124]. Copyright (1997), The Electrochemical Society

Total scattering and INS are particularly attractive for disordered C where conventional diffraction provides limited information and more generally for Li arrangements in C. Disordered C where a large amount of H is present can exhibit significant Li capacity (one ‘excess’ Li per H) and studies have investigated how Li is taken into these materials [123, 124, 126]. Studies have shown that these materials exhibit randomly-arranged graphene fragments of different sizes with edges terminated by a single H, similar to Si with H at the surface. The spectra also contain a boson peak, an indicator of disorder, and distinct similarities to polycyclic aromatic hydrocarbon (PAH) spectra exist, some of which feature two or three edge-terminating H. Additionally, comparison with PAH spectra allowed the determination of methyl groupings when higher H concentrations are used. The boson peak is at the same position in samples with different concentrations of H and changes in position and intensity with Li insertion. This shows that the Li interacts with the C environment, contrary to the idea of Li accumulation in voids. These findings agree with two models of Li insertion: One where Li resides on both sides of the graphene layers (the so-called ‘house-of-cards’ model) and the other where Li is bonded to the H-terminated C at the edge of the graphene layers (and reside in interstitial sites). INS data also illustrate that the Li–Li interlayer and intralayer interactions are comparable in strength. Computer modelling showed that there is insignificant energy difference between interstitial Li and those that are bonded to the terminal H. Other models include the formation of covalent Li₂ molecules, but no evidence was found in support of these. The key aspect in these studies is that all models satisfy the observed capacity of LiC₆. Finally, QENS [124] was used to show that Li jumps between nearest or second-nearest neighbour interstitial sites.

Related work investigated the entropy of intercalation into C [127]. This study shows how the sign of entropy changes from low Li concentrations on initial charge (x < 0.2 in Li _x C₆) to higher concentrations (x > 0.2) indicating that multiple processes are occurring and that one of these is vibrational in origin. In graphite the entropy remains negative, but reduces in magnitude as lithiation progresses. Similar entropy information from INS data during lithiation of LiCoO₂ cathodes has also been reported [128].

Cathode materials pertinent to Li-ion batteries based on olivine LiMPO₄ have also been probed with INS, but for magnetic properties (low temperature) rather than Li-ion diffusion or lattice dynamic studies. Studies of LiFePO₄ [129], LiNi_1−x–Fe_xPO₄ [130], and LiMnPO₄ [131], show spin-wave dispersions and allow characterisation of magnetic-exchange interactions. Further INS work was motivated by the need to understand the electronic conductivity in LiFePO₄ and probed the thermodynamics and vibrational entropy of the phase transition in Li_0.6FePO₄ [121]. The oxidation state of Fe influences its neighbouring O atoms and the polyhedral distortions can characterize the motion of carrier hopping between Fe sites, which results in relaxations or displacements that can in turn be considered as the sum of longitudinal phonons. Similarly, occupation or vacancy of Li can result in distortions of atom positions and are expected to alter the frequency of phonons, in particular longitudinal optical phonons.

The phase evolution of Li_0.6FePO₄ as a function of temperature, via a two-phase transition to a disordered solid-solution transition at 200 °C [121], can shed light on the reaction mechanism during charge/discharge of this cathode. This is particularly pertinent as the two-phase or solid-solution mechanism of LiFePO₄ is a topical issue as discussed above. The difference in two-phase and solid-solution LiFePO₄ optical modes above 100 meV (higher energies) was found, with broadening evident for the solid-solution sample. The low-energy region features mostly acoustic lattice modes, translations and librations of PO₄ and translations of Fe. By comparison with infrared (IR) and Raman data, it was found that the PO₄ stretching vibrations are damped in the solid-solution sample. The difference in INS data of solid-solution and two-phase samples at higher energy mostly involve optical modes that can arise from motion of Li-ions, charge hopping between Fe-ions, and heterogeneities. The entropy was found to be larger in the solid-solution phase in conjunction with the subtle differences in the dynamics due to different optical modes. The similarity in two-phase and solid-solution phonon density of states (Fig. 7.11) agrees with the ease with which LiFePO₄ seems to undergo either transition, and the difficulty in pinning down the experimental evidence related to the reaction-mechanism evolution.

Fig. 7.11

The phonon density-of-states of Li_0.6FePO₄ at 180 °C (solid) and 200 °C (dashed). Reprinted with permission from (R. Stevens, J.L. Dodd, M.G. Kresch, R. Yazami, B. Fultz, B. Ellis, L.F. Nazar, J. Phys. Chem. B 110, 22732 (2006)) [121]. Copyright (2006), American Chemical Society

Arguably the most studied materials using INS are manganese oxides and lithiated manganese oxides, predominantly due to the ease of using H as a probe for Li. These compounds are used for both primary and Li-ion batteries and ion-exchange methods have been used to show where Li may reside in these compounds. Although indirect, this information can provide further answers to some of the problems in this field of research. Attempts are also being made to use INS to provide comparisons between H and Li where H is used as a calibrated probe for Li [132].

One approach is to replace structural or surface water present on manganese oxides with protons, which can in turn be exchanged for Li to see how Li might displace water in these compounds. This was undertaken for spinel Li_1.33−x/3Co _x Mn_1.67−2x/3O₄ [133] which shows, as is the case in many compounds of this family, that protons are inserted as hydroxyl groups giving a strong incoherent INS signal. The hydroxyl groups are located on the O atoms neighbouring the vacant 16d sites and aligned with the 8a sites in the spinel structure. Conversely, studies on undoped spinels have shown that the Li extraction from the 16d sites allows the insertion of protons. The main features of the INS spectra are strong γ(OH) modes, a highly ordered proton site, a shoulder and smaller features between 300–700 cm⁻¹ showing riding of protons on the oxide lattice and some librational water modes. The hydroxyl groups have characteristic signals around 908 cm⁻¹ and their orientations are also determined using INS [134–137] of spinel-derivative compounds. Interestingly, IR data shows features between 950 and 1300 cm⁻¹ which were considered to arise from protons, but the absence of these features at corresponding frequencies in the INS data indicate a manganese oxide lattice origin. Notable discoveries of this and related studies include the finding that in undoped spinels 40 % of protons cannot be exchanged and form disordered water, the chemical re-insertion of Li in Li-rich spinel Li_1.6Mn_1.6O₄ removes most of the hydroxyl groups [137], that generally the reversible Li amount is 50 % in both undoped and doped spinels, and that fewer protons are re-exchanged as the Co concentration increases. The latter is an interesting way to tune the Li-proton exchange capacity of these materials.

Figure 7.12 shows the INS data from a series of Li-rich Li_1.6Mn_1.6O₄ spinels formed through various methods. The pure sample (bottom of Fig. 7.12) shows some evidence of protons, OH and water, whilst the acid-treated version, where acid results in H–Li exchange, shows strong characteristic peaks for protons and γ(OH) groups. Finally, the acid-treated sample undergoes a chemical Li re-insertion step and results in the loss of the proton and OH signatures. However, the re-inserted material does not replicate the pure sample suggesting some protons remain as structural water and hydroxyl groups [137]. Relative comparisons of the INS intensity can be made between the acid-treated and re-inserted samples, with the 909 cm⁻¹ peak showing a larger drop in intensity compared to the 1,087 cm⁻¹ peak, which is attributed to an H site being easier to depopulate. A comparison of INS data for two Li-rich variants, Li_1.33Mn_1.67O₄ and Li_1.6Mn_1.6O₄, shows that the proton stability is higher in Li_1.6Mn_1.6O₄ than in Li_1.33Mn_1.67O₄. This suggests the reason that Li_1.6Mn_1.6O₄ has a larger Li-ion exchange capacity than Li_1.33Mn_1.67O₄ concerns the stability of the inserted species (or more specifically the stabilized proton sites).

Fig. 7.12

INS spectra of as-synthesized Li_1.6Mn_1.6O₄ (p), acid-washed (d), and Li chemically re-inserted (r) samples. Reprinted with permission from (M.J. Ariza, D.J. Jones, J. Roziere, R. Chitrakar, K. Ooi, Chem. Mater. 18, 1885 (2006)) [137]. Copyright (2006) American Chemical Society

Studies of λ-MnO₂ [135] illustrate subtle differences in INS spectra depending on synthesis precursors, noting that precursors and conditions are both important. This work again highlights the need to focus on the protons (often disordered). A related study investigated proton-exchanged spinels that form λ-MnO₂ showing that the proton diffusion was dependent on octahedral Mn vacancies [136]. In this study, certain features in the INS spectrum were found to disappear in the highly crystalline sample, suggesting that motion can be perturbed with crystallinity. Researchers have also looked at the proton and water environments in bare and lithiated MnO₂ [132] to demonstrate how lithiation influences the proton and water motions, which can then be used to extract information on lithiation processes. Using neutron total scattering from oxidized and lithiated versions of λ-MnO₂ researchers derived models for oxidation and lithiation [138].

Further work on the spinel LiMn₂O₄ system investigated the cubic to orthorhombic phase transition near room temperature, which is associated with Mn³⁺/Mn⁴⁺ charge ordering [139]. Excess Li was introduced at the 16c site to study why the phase transition is suppressed in this situation. QENS was used here, where data were found to be dominated by magnetic contributions rather than that from Li hopping, with the slight narrowing of the elastic line near room temperature leading to the preliminary conclusion that electrons are localized on the Mn. A dynamic transition in Li-rich compounds seems to coincide with the structural transition in the parent. The magnetic properties of Li_0.96Mn₂O₄ were explored in a related INS study [140] showing that two short-range magnetic transitions are present and related to spin ordering of Mn³⁺ and Mn⁴⁺.

3 Lithium Diffusion

A critical property of electrode materials is the ability to conduct Li through the host lattice. Li-ion mobility can be directly probed with INS and QENS, however only a few neutron studies report the direct measurement of Li dynamics mostly due to its moderate incoherent neutron-scattering cross section. Typically, each material has to be considered in order to determine whether the signal originates from Li, magnetism or other atoms. Usually, the hopping diffusion in Li-ion insertion electrodes is relatively slow compared to the timescale of INS and QENS in which case the local mobility is observed. As a consequence few studies exist that probe the Li motion directly. A different approach is to probe the Li diffusion in electrode materials with diffraction. Both the anisotropic contribution in the Debye-Waller factor and the deviation from harmonicity due to thermal motions at elevated temperatures can indicate the directionality of Li motion, which in turn may allow the identification of diffusion pathways. Both are illustrated here: anisotropy in the ADPs in combination with a maximum-entropy method (MEM) was used to identify the Li-ion trajectory in the positive-electrode material LiFePO₄, and anharmonicity of the ADPs revealed the Li-ion trajectory in the negative electrode material Li₄Ti₅O₁₂.

Li₁₂C₆₀ fulleride is a good example where Li diffusion was studied using QENS and INS, quantifying the diffusional motion of Li-ions across a phase transition proposing a localized jump-diffusion model in the octahedral voids of the Li₁₂C₆₀ structure. This accounts for the changes in the vibrational density of states near the phase transition and results in a model of the dynamical behaviour [141]. Another QENS study revealed the diffusion coefficient of Li in a highly-oriented pyrolytic graphite electrode at high temperatures, deriving an activation energy of 0.35 eV [142]. Interestingly, the diffusion coefficient obtained is similar to that obtained using electrochemical methods despite the diffusion lengths measured by the two techniques differing by a factor of 15,000. Li diffusion is more frequently determined indirectly using neutrons, and an example of this is the studies of anion dynamics to shed light on Li diffusion. Li-containing metal hydride systems have been investigated, such as in LiBH₄ and LiAlH₄, where translational modes of Li are linked with BH₄ in the high-temperature form of LiBH₄ [143]. Additionally, the disappearance of Li-containing lattice vibrations near phase transitions in these compounds is thought to be associated with the delocalisation of Li that enhances diffusivity. In this way, hydrogen-containing group dynamics can provide information on Li dynamics.

One QENS study describes alkali-ion diffusion (including for Li) in alkali-containing silicate melts [144], of interest for cathode materials based on silicates. This study used the decoupling of the incoherent (below 60 ps) and coherent neutron-scattering as a signature for Li-ion diffusion along channels in the immobile Si–O network. The relaxation times for Li were a factor of two smaller than for Na, indicating that Li-ion diffusivity is a factor of two larger, in agreement with conductivity data. QENS experiments have also been performed on single crystals of ⁷Li₂MnCl₄ (an inverse spinel-type structure), revealing a lack of anisotropy in the local Li motion [145]. Li-ions at 8a tetrahedral sites were shown to visit neighbouring 16c interstitial sites and jump back, but longer-range translational motion was outside the timescale used for the measurement.

Significant insight into Li diffusion can be gained from diffraction. Diffusion pathways can be identified by the anisotropy in ADPs in combination with MEMs. The exceptionally high discharge rate [47] observed in LiFePO₄ indicates that ionic mobility in the LiFePO₄ matrix is unusually fast. This has raised the question of how this is possible by the small polarons that are strongly localized at Fe sites in phase-separated LiFePO₄ and FePO₄ [146]. Morgan et al. [27] used the nudged elastic band method in calculations that show high Li ion mobility occurs in tunnels along the [010] direction, but reveal that hopping between tunnels is unlikely, confirmed by calculations of Islam et al. [108]. Fast one-dimensional conduction along the b-axis in the LiFePO₄ Pnma structure was predicted by atomistic modelling [27, 108] and the first experimental proof of the diffusion trajectory came from Nishimura et al. [147] using NPD in combination with the MEM. To enhance the sensitivity towards Li ⁷LiFePO₄ was prepared using ⁷Li-enriched Li₂CO₃ as the raw material. In this study the ADPs readily show the direction of the Li-trajectory towards adjacent Li-sites, with green ellipsoids in Fig. 7.13 representing the refined Li vibration (displacement parameters) and indicating preferred diffusion towards the face-shared vacant tetrahedra. This suggests a curved trajectory in the [010] direction, consistent with atomic modelling [27, 39].

Fig. 7.13

Left Neutron diffraction patterns and Rietveld refinement profile of a room temperature and b 620 K Li_0.6FePO₄. The specific points of measured composition and temperature are given in the inset phase diagram reported by Delacourt et al. [102] and Dodd et al. [120] Right Anisotropic harmonic Li vibration in LiFePO₄ shown as green ADPs and the expected diffusion path indicated by the dashed lines. The ellipsoids were refined by Rietveld/MEM analysis of room-temperature NPD data. Reprinted by permission from (S. Nishimura, G. Kobayashi, K. Ohoyama, R. Kanno, M. Yashima, A. Yamada, Nat. Mater. 7, 707 (2008)) [147]. Copyright (2008)

To relate further the vibrational motions with diffusion, the material with the overall composition Li_0.6FePO₄ was heated to approximately 620 K. In this composition Li_0.6FePO₄ forms a solid solution at a relatively low temperature, ~500 K, due to the unusual eutectoid as shown in the phase diagram in Fig. 7.13. This is confirmed as single phase by neutron diffraction. Thereby a large number of Li defects are introduced, that in combination with the higher thermal energy, enhances Li motion. Note that the Li trajectory in the solid solution should represent both end members because the crystal symmetry does not change upon heating and Li insertion. In the refinement of the Li_0.6FePO₄ structure no reliable solution using harmonically-vibrating Li could be found. To evaluate the dynamic disorder of the Li the MEM was used to estimate the nuclear-density distribution from neutron diffraction. By considering the entropy the most probable distributions of nuclear species can be evaluated, making it possible to evaluate not only the missing and overlapping reflections, but also the more complicated nuclear densities. This approach applied to neutron diffraction data of Li_0.6FePO₄ at 620 K leads to the three-dimensional nuclear distribution of Li (Fig. 7.13). The observed diffusion along the [010] direction is consistent with the shape of the anisotropic thermal motions shown in Fig. 7.13 and atomistic modelling [27, 39]. Note that the Fe, P, and O atoms remain at their normal positions. The data show that the Li-ions move from one octahedral 4a site to the next via the intermediate tetrahedral vacant site. Along this trajectory the sites do not face-share with other occupied polyhedra. This is in contrast to, for instance, diffusion along the [001] direction where the intermediate octahedral position shares two faces with PO₄ tetrahedra which will lead to higher activation energies.

Laumann et al. [148] investigated Li migration in commercial spinel Li₄Ti₅O₁₂ using variable-temperature neutron diffraction. At 900 °C a marked deviation is observed in the linear dependence of the cell volume, O position, and anisotropic displacement parameters. Refinement of the Li occupancies resulted in almost complete 8a site occupation below 900 °C. However, at 900 °C a Li deficiency of approximately 14 % was observed, which was interpreted as the result of anharmonic motions and migration of the Li-ions. Therefore, in the fitting procedure one isotropic anharmonic ADP was refined. Examination of the nuclear density revealed negative scattering-length density peaks next to the 16c site. In this way Li-ion occupancy at the 32e site was discovered and subsequent refinement of Li at the 32e sites results in the probability density shown in Fig. 7.14. This makes it possible to formulate the diffusion pathway. Rather than occupying the 16c as an intermediate site between two 8a sites, which introduces an unacceptably long Li–O bond, Li passes from the 8a site through the face of the surrounding O tetrahedron to the nearby 32e site. This is followed by switching to the adjacent 32e site where it is bonded to another O atom, and from where it can hop to the next tetrahedral 8a position. Effectively, this mechanism results in a number of short jumps along the [111] direction between adjacent 8a sites. The energy barriers can be approximated by assuming Boltzmann statistics for single-particle motion resulting in the one-particle potential shown in Fig. 7.14. These findings are consistent with nuclear magnetic resonance measurements indicating that the 16c site forms the saddle point of the barrier between two 8a sites [149]. In this way NPD is able to reveal the details of the three-dimensional long-range diffusion pathway in spinel Li₄Ti₅O₁₂.

Fig. 7.14

Left: Probability density function derived from the anharmonic ADPs at 900 °C in the (xxz) plane through 8a and 16c sites. The shortest bond distances between Li (white at 8a and grey at 32e) and O (black at 32e) are indicated. Long dashed lines indicate zero densities and short dashed lines negative densities. Right: One-particle potential of Li at 900 °C in the (xxz) plane through 8a, 32e, and 16c sites (the same section as that in the left figure). Contour lines are in steps of 100 meV. The dotted line shows the linear section along the [111] direction. Reprinted with permission from (A. Laumann, H. Boysen, M. Bremholm, K.T. Fehr, M. Hoelzel, M. Holzapfel, Chem. Mater. 23, 2753 (2011)) [148]. Copyright (2011) American Chemical Society

4 Electrolytes

Commercial electrolytes typically contain a Li salt dissolved in an organic solvent and are often composed of two components: one for the dissolution of the salt and another that assists in the formation of a protective layer on the anode to prevent continuous electrolyte-reduction and self-discharge, e.g. ethylene carbonate. These electrolyte systems, being non-aqueous and highly air-sensitive, tend to be flammable and can turn from liquid to gas at elevated temperatures (Fig. 7.15). The electrolyte also determines the cathode and anode materials that can be used by limiting the applicable voltage range which is associated with the HOMO of the cathode and LUMO of the anode [4]. The key factors that determine a good electrolyte are ionic conductivity, flammability and chemical stability, and applicable voltage windows.

Fig. 7.15

An example of a LiFePO₄∥graphite battery containing 1:1 mol. % ethylene carbonate:dimethyl carbonate heated to 90°C where the dimethyl carbonate (organic solvent) has boiled, expanding the casing of the battery

To overcome the safety and long-term reliability issues of using organic electrolytes, research has been directed to aqueous electrolyte systems with Li salts. Unfortunately, voltage limitations have hampered significant development of aqueous electrolytes, but these safe electrolyte-systems have found niche use in medical applications. In addition to aqueous electrolytes, liquid electrolytes based on ionic liquids have attracted significant attention.

Apart from electrolytes in the liquid state, semi-solid or solid-state electrolytes such as gel and solid polymer electrolytes continue to be a preferred option in overcoming safety and leakage issues. Neutron scattering work has been undertaken on ceramic and glass-ceramic solid state Li-ion conducting electrolytes. Some of these electrolytes feature Li-ion conductivities that can be as good as commercial organic electrolytes as elegantly demonstrated for Li₁₀GeP₂S₁₂ [150]. This is the first solid-state electrolyte that shows conductivity that matches that of commercially-available liquid electrolytes (Fig. 7.16).

Fig. 7.16

A collection of conductivity data of pertinent electrolytes used for commercial and research-scale Li-ion batteries. Reprinted with permission from (N. Kamaya, K. Homma, Y. Yamakawa, M. Hirayama, R. Kanno, M. Yonemura, T. Kamiyama, Y. Kato, S. Hama, K. Kawamoto, A. Mitsui, Nat. Mater. 10, 682 (2011)) [150]. Nature Publishing Group

4.1 Structure

Detailed structural analysis has been undertaken with the use of neutron diffraction on a variety of Li ionic conductors as demonstrated by studies of Li argyrodites. Using a combination of simulations and structural refinements against X-ray and NPD data, the structure of the Li-ion conducting argyrodites, Li₆PS₅ X where X = Cl, Br, and I, were determined [151]. The Li content and location, along with the mixed occupancies of the X and Li or X and S sites was modelled. For X = Cl and Br, Cl or Br was found on two S sites, whilst I was found on an independent wholly I-containing site. For X = Cl only one Li site was found, while for X = Br and I two Li sites were revealed with a distribution of Li that differs depending on X. This highlighted that the halide plays a critical role in the distribution of atoms, including the location and occupancy of Li. Ionic conductivity was found to be highest for the X = Br samples, suggesting the influence Br has on the atomic distribution to be favourable for this property [151].

These materials were also investigated using variable-temperature neutron diffraction, where the starting reagents were reacted under similar conditions to those used in the laboratory synthesis. This was to determine the optimal reaction temperatures and conditions for favourable properties and whether any intermediate highly-conducting phases were present. The notion was to explore whether synthesis temperatures could be lowered, potentially reducing manufacturing costs, or whether intermediate phases were able to provide superior ionic-conduction properties. Analysis of neutron diffraction data showed that argyrodite formation begins at relatively low temperatures around 100 °C, well below the reported synthesis temperature of 550 °C, but at temperatures around 550 °C the reagents become amorphous or nano-crystalline with all reflections from the sample disappear (Fig. 7.17). Notably, on cooling the desired phase re-condenses and on inspection it is found that the anion ordering, leading to the most conductive phase, is actually found in the re-condensed phase rather than the initially-formed phase [152]. These types of systematic studies on bulk formation shed light on which phases and synthetic routines may provide the best ionic conduction.

Fig. 7.17

Collated NPD patterns of a heating and cooling sequence applied to Li₆PS₅Br. Although an argyrodite phase forms at relatively low temperatures, it is found to be less conducting than the phase formed after the loss of long-range order

Structurally disordered solid-state electrolytes have been investigated using INS. Work [153] exploring low-energy vibrational dynamics of the ¹¹B₂O₃–⁷Li₂O system showed a boson peak between 2 and 10 meV. It was found that with increasing Li content the intensity and position of the boson peak changed, suggesting the presence of intermediate glass structures. More importantly, this information can be used to generate a master curve, which suggests a universal distribution of vibrational density-of-states that is composition independent, even though the structure changes markedly. Furthermore, increasing the Li content in these glasses results in chemical structure-induced densification, as fewer low-density B-containing groups are found. It is argued that the densification may arise from the same microscopic origin as the boson peak.

4.2 Lithium Diffusion

Perovskite structures (ABO₃, where A and B are different-sized cations) have good ionic conductivities, with La_0.5Li_0.5TiO₃ showing the highest conductivity of these compounds. Nuclear-density maps derived from neutron diffraction data were used to illustrate the disordered nature of Li in these systems at high temperatures. Neutron diffraction data were also used to show the migration pathway of 2c-4f-2c or 2c-2d-2c [154, 155] (Fig. 7.18), with data at lower temperatures showing Li localized at the 2c site. Other work detailed descriptions of TiO₆ tilting, La and vacancy ordering, and localization of Li. This was achieved using low-temperature data collection on ⁷Li-enriched samples in addition to different heat treatments to determine the origin of the high conductivity in these materials [156]. Notably, it was shown that quenched samples in the Li-poor La_0.18Li_0.61TiO₃ stabilize into a structure featuring three-dimensional Li pathways. In contrast, slow-cooled samples only feature two-dimensional pathways and the Li-ions feature unusual four-fold coordination environments. The best conduction is found in samples with vacant A-sites nearby [156]. The crystallographic nature of Li and its conduction pathways are critical in assessing the origin of the high ionic-conductivities found in these compounds, and how to modify the crystal-chemistry to improve it.

Fig. 7.18

Nuclear-density distribution on the (002) plane of La_0.62Li_0.16TiO₃ at room temperature. Negative amplitudes indicate Li diffusion paths with dark ovals showing maximum scattering amplitude and blue minimum amplitude. Reprinted with permission (M. Yashima, M. Itoh, Y. Inaguma, Y. Morii, J. Am. Chem. Soc. 127, 3491 (2005)) [155]. Copyright 2005 American Chemical Society

Spinels can also have three-dimensional Li diffusion pathways. Recent neutron diffraction work on complex ordered spinels Li₂(Ni/Zn)Ge₃O₈ [157] shows that the Ni and Zn compounds have different Li-ion conduction pathways. The Ni-case shows 8c-12d-8c hopping with concerted harmonic displacements of O, whilst the Zn-case shows a complex 4b-24e-4a-24e-4b pathway. The Zn-case features smaller windows through which Li can pass and this is in part responsible for the lower ionic conduction. The strategy used by the authors involved refining the room and high-temperature structure. In the highest-temperature case the Li anisotropic displacement parameters were kept small and nuclear density maps revealed new Li sites. This process was continued with intermediate temperatures and the number of Li-sites compared to total Li content and thereby showed the pathways for Li conduction [157].

Neutron radiography can also be used to track macroscopic Li diffusion in battery materials. Early work on Li_1.33Ti_1.67O₄ prepared using pure ⁷Li and natural Li illustrated and quantified Li-transport [158]. The experimental setup placed two materials, the pure ⁷Li-containing material and the natural Li-containing material in contact with each other. Electrodes were applied to the non-adjacent sides and a field applied during heating. Standard samples with controlled ⁷Li/⁶Li contents were also measured to quantify Li content. Figure 7.19 illustrates the experimental setup and some of the results showing how ⁷Li moves from the labelled ‘smpB’ to ‘smpA’. Note that the ⁷Li near the anode is consumed, as no white regions are left.

Fig. 7.19

Left The experimental setup for the electrolysis experiment. Right Neutron radiography image obtained after charge transfer at 200 °C. Reprinted with permission from (M. Kamata, T. Esaka, S. Fujine, K. Yoneda, K. Kanda, Nucl. Instr. Meth. Phys. Res. A 377, 161 (1996)) [158]. Elsevier

An elegant example of neutron imaging to study Li diffusion is given for the lithium zinc germanium oxide as shown in Fig. 7.20. This material is often referred to as a Li super ionic conductor, abbreviated to LISICON. In Fig. 7.20 standard samples with known ⁶Li/⁷Li ratios are shown and regions with more ⁶Li are represented by a lighter colour [159]. The work shows how annealing temperatures influence Li-ion diffusion through the sample. Further studies compared the Li_3.5Zn_0.25GeO₄ material with the analogue Li_3.Zn_0.5GeO₄ and found that ionic-conductivity differences were due to high ion-mobility rather than differences in diffusion paths [160]. The authors obtained tracer diffusion coefficients using neutron radiography data, similar to the work determining the tracer diffusion coefficients in Li_1.33Ti_1.67O₄ [161].

Fig. 7.20

Left Neutron radiography images of standard samples varying the Li isotope ratio from ^NLi (natural ratio ⁶Li/⁷Li) to ⁷Li, a whiter image representing a higher ^NLi concentration. Right Annealed samples show increased mixing of ^NLi and ⁶Li species when the annealing time increases illustrating the diffusion of Li in these super ionic conductors. Reprinted with permission from (T. Esaka, Ionics 10, 358 (2004)) [159]. Springer

QENS and INS have been used to study diffusion in electrolyte systems. The relationship between ion transport and polymer relaxation in polymer/Li salt systems are considered to be bi-phasic at room temperature [162]. Ionic conduction occurs predominantly in the fluid-like amorphous regions as compared to the crystalline salt-rich regions. The mechanism for conduction is not completely understood. One theory is that Li ions coordinated to O on the polymer move by hopping between the O and the formation and disruption of these coordination bonds influences the local chain structure. Researchers investigated polyethylene oxide (PEO) in two different electrolytes, LiClO₄ and LiTFSI (where TFSI = N(SO₂CF₃)₂). Each of these electrolytes has salient features that make them good for battery applications. Considering the Li-ion diffusion constant and distance between neighbouring O atoms, the jump time is on the order of nanoseconds (ns). To probe the relaxation and dynamics of the polymer chain in the ns timescale QENS was used. The signal from Li is still insignificant compared to the H atoms in the polymer that make up the largest signal in QENS data. Two processes are found in both electrolytes, a fast process characteristic of rotational dynamics often related to relaxation in polymers, and a not previously-observed slower process showing more translational character. However, in the PEO and LiTFSI electrolyte two fast processes were found (see Fig. 7.21). The fast processes can be related to the fluctuations of the polymer chain segments as Li–O inter and intra-chain coordination bonds form and break during transport, associated with a rapid rotation of the polymer. This can also be visualized as a positive charge approaching and leaving, resulting in rotation of a polymeric region. The slower process appears to arise from translations of polymeric chain segments, however, these seem likely to be static on the timescale window used in this study. Overall these findings show two to three kinds of motions in the polymers with ion transport and that the O of the Li–O plays a large role in controlling the Li dynamics.

Fig. 7.21

Detail of the fast (B) and slow (A) processes in the PEO and LiTFSI electrolyte. Reprinted (adapted) with permission from (G. Mao, R.F. Perea, W.S. Howells, D.L. Price, M.-L. Saboungi, Nature 405, 163 (2000)) [162]. Nature Publishing Group

A second study used QENS to investigate complex polymer-gel electrolytes in which conventional carbonate-based electrolytes were dispersed [163]. There were conflicting ideas in the literature from other techniques that probe different time and length scales. To probe solvent (carbonate) dynamics on an intermediate time and length scale, QENS was used. In order to model the system, a weak solvent and polymer interaction had to occur, which is consistent with better ionic conduction. Stronger interactions would require more complex modelling. The undeuterated carbonates were used as a probe for the deuterated polymer-gel matrix, so that the signal was dominated by the incoherent neutron-scattering from protons in the solvent. The carbonate solution used two carbonates that differed by a methyl group. A model of the Li and carbonate arrangement of the electrolyte was generated using predictions from molecular-dynamics simulations. The interest lay not in the solvent but the complex polymer-gel matrix that was revealed using the carbonate solvent as the probe. Again, two solvent (carbonate) relaxation times were found: A faster rotational relaxation-time on the order of 100 μeV and a slower translational-diffusion signature on the order of 10 μeV. The translational diffusion was similar to that expected in a liquid electrolyte, but the characteristic distance of this process was 5 Å due to the constraints applied by the polymer matrix. This constraint also acts to lower the ionic conductivity relative to a liquid. The constraint is evidenced by a narrowing of the QENS signal at low Q, where without the constraint there should be no Q-dependence in the signal width. The rotational component shows changes in intensity as a function of Q with almost no change in width. The solvent molecules are likely to exhibit both rotational and translational motion simultaneously, so the scattering function is a frequency convolution, which also implies that the rotational peak width/intensity as a function of Q will influence the translational peak width/intensity and vice versa. Fortunately, these processes are well separated in time allowing further assumptions to be made in the model. The model considered how many protons contribute to the signal and what fraction of the protons will take part in the two processes, considered either static or undergoing both process. The possibility of a proton undergoing one process and not the other was excluded. Static protons would be close to the matrix while the free protons further away. Models were designed for the most likely scenario, e.g. uniaxial rotation of the free protons, translational diffusion of the solvent via a microscopic jump-model accounting for the constraint of the polymer matrix by random jump-diffusion between parallel impermeable walls, and longer-range ‘free’ diffusion. The researchers noted the complexity in deriving an initial model and considered only the main dynamical process (noting also that other processes may occur). However, the insight gained in this study is important to understanding the behaviour of electrolytes in matrices. For example, this study found that the proportion of static protons, which are indicative of a less-mobile solvent, ranges from 8 % at 373 K to 35 % at 253 K [163], which is consistent with the difference between electrolyte liquid solution and polymer matrix systems.

Li-based glasses and glass ceramics have been used as solid-state electrolytes in all solid-state Li-ion batteries. The key limitation in the commercialization of these materials is the low ionic-conductivity under ambient conditions (with minimal electronic-conductivity) and the microstructural aspects associated with solid interfaces and contacts. The first QENS work on solid-state Li-ion conductors was a polarised experiment that determined Li diffusion in single crystal of ⁷Li₂S at elevated temperatures [164]. The polarisation allowed the separation of incoherent and coherent neutron-scattering contributions. High temperatures were required as these phases show higher ionic conduction in these regimes, and fortunately adopt cubic symmetry, simplifying the modelling. Coherent neutron scattering showed minimal changes with temperature, whilst the incoherent neutron scattering changed markedly, which is predominantly from Li. The work shows that an inter-site jump model fits the QENS data, and this corresponds to Li-ions hopping to neighbouring cation sites. More complex models also fit the collected data, but further data are required to verify them, with the diffusion coefficient obtained from the simpler model matching that expected from other analysis techniques.

A related study [165] explored the ¹¹B₂O₃–Li₂O–LiBr system showing four superimposed oscillating ionic units. It revealed further information such as activation energies for two well-resolved processes: translational jump-diffusion and a localized reorientation motion of ions. The fact that each motion cannot be represented as a fraction but are superimposed dramatically influences the ease of modelling. There was no evidence of Li hopping. Figure 7.22 (left) shows the experimental spectrum and Fig. 7.22 (right) shows the model with the four units used in the modelling. Although it may seem that the choice of four units and their behaviour is arbitrary, comparison with Raman and IR data illustrates that the four units are likely to be Br, BO₃/BO₄, Li, and O. The researchers concluded that the conductivity is due to both jump and reorientation motions [165].

Fig. 7.22

Left Experimental frequency spectrum of B₂O₃·0.56Li₂O·0.45LiBr at 573 K and Right superposition of the contribution of the four oscillators used in the model. Reprinted (adapted) with permission from (C. Cramer, K. Funke, C. Vortkamp-Ruckert, A.J. Dianoux, Phys. A 191, 358 (1992)) [165]. Elsevier

In most of the solid-state electrolyte cases, the basic system is Li₂O, which crystallizes with a fluorite arrangement, where phonon-dispersion curves have been measured as a function of temperature and show a sharp decrease approaching the fast-ion conducting phase [166]. Although this material was studied for fusion-reactor applications, it forms the basis of many Li-ion conducting glasses. Li self-diffusion was identified in incoherent QENS and tracer techniques (see references in [166]). Coherent INS data was used to elucidate properties that can be related to those measured physically such as elasticity, which show anomalies near the onset of fast-ion conduction in these compounds. Therefore, a direct relation to dynamics and physical properties could be made. An interesting extension of this work was the study of Li₂O crystals with metallic Li colloids [167] which form after irradiation.

A related QENS study investigated the Li-ion conductor LiI, made in a composite form with mesoporous Al₂O₃ [168]. These materials have potential applications in the nuclear industry but can also be applied as solid-state electrolytes. Notably the activation energies for Li migration derived from QENS were smaller (by a factor of approximately 2) than that determined from electrical conductivity and pulsed-field gradient nuclear-magnetic resonance measurements. This observation was attributed to the migration mechanism in mesoporous structures and possible conductivity enhancement in confined spaces by the increased presence of interfaces in the mesoporous environment. This study highlights the importance of using a reliable model for QENS that is developed specifically for the material under study.

5 Interfaces

Acquiring a comprehensive understanding of interfacial reactions in batteries is essential for the design of new materials [4]. However, due to the difficulty in probing the interfaces, relatively little is known about the relevant processes. What is known is that the stability of electrolytes at the electrode interface plays a key role in determining the cycle life and safety of batteries. The most studied interface is between the carbon negative electrode and carbonate organic electrolytes. The instability of carbonate electrolytes with respect to the carbon chemical-potential results in deposition of the electrolyte Li-containing inorganic and organic decomposition products on the electrode surface, otherwise known as the SEI layer. This reduces the amount of active Li available to the cell and degrades the electrolyte. Typically electrolytes contain two components, one for the Li-salt dissolution, and one that assists in the formation of a protective layer on the anode preventing continuous electrolyte-reduction and self-discharge, e.g. ethylene carbonate. This requires the formation of a stable SEI film showing good ionic-conductivity and poor electronic-conductivity. In this way the SEI can passivate against further electrolyte decomposition without severely influencing battery performance. The SEI formation and maintenance during further cycling is expected to play an essential role in the cycle life and stability of batteries, however, the growth mechanism under variable battery-conditions is largely unexplored. In addition, the charge-transfer reaction at the interface, most likely influenced by the SEI development [169], is an essential parameter that in many cases limits the power of batteries. Also, interfaces within the electrode material can establish upon phase transitions during (de)lithiation. From an applications point of view these transitions have the favourable property of being associated with a constant potential that is independent of the composition, but the disadvantage of being associated with volumetric changes that may restrict the cycle life. Probing such interfaces under in situ conditions is possible using neutron reflectometry.

One of the first reported neutron-reflectometry studies on a Li-ion battery system determined the Li insertion and extraction mechanism in thin film anatase TiO₂, a negative electrode material operating around 1.7 V versus Li/Li⁺. Lithiation of the tetragonal anatase TiO₂ leads, via a first-order phase transition, to the orthorhombic Li_0.5TiO₂ Li-titanate phase. The aim of the neutron-reflectometry study was to discover the phase-evolution scheme in this electrode material, which is of more general value for electrode materials undergoing first-order phase transitions. Previous studies suggested the establishment and movement of a diffusion-controlled phase boundary, parallel to the electrode surface, between the Li-rich Li-titanate and the Li-poor anatase phase [170]. This is in contrast to, for instance, a percolation scheme where the Li-titanate phase would penetrate the original anatase layer only at certain regions of the thin film. Further intercalation would increase both the perpendicular and the lateral dimension of these percolation paths, eventually leading to a homogeneously-intercalated film. Van de Krol et al. suggested a specific scheme in order to explain the more facile Li-ion extraction rate compared to the insertion rate [170]. Based on the assumed faster Li-diffusion in the Li-anatase phase [171] one might expect fast depletion of Li in the near-surface region of the Li-titanate phase containing electrode, which is in contact with the electrolyte. As a result, during Li extraction, the Li-anatase phase starts to grow at the electrolyte surface into the layer at the expense of the Li-titanate phase.

The contrast difference between the Li_0.5TiO₂ Li-titanate phase and the TiO₂ anatase phase for neutrons should make it possible for neutron reflectometry to determine the phase-evolution scheme both during Li insertion and extraction. An approximately 25 nm smooth anatase TiO₂ electrode was deposited on a thin ~20 nm Au current collector on a 10 mm thick single-crystal quartz block that served as the medium for the incoming and reflected neutron beam. The latter is practically transparent to thermal neutrons allowing approximately 70 % transmission over 10 cm path length. The TiO₂ electrode is exposed to a 1 M solution of LiClO₄ in propylene carbonate electrolyte using Li metal both as counter and as reference electrode. Li was galvanostatically inserted in two steps and extracted in two steps using 10 mA (C/5) in the same voltage window. Neutron-reflection experiments were performed after each step when a constant equilibrium-potential was achieved. The results, including the fit and the associated scattering-length density (SLD) profiles are shown in Fig. 7.23. The profound change observed in the neutron reflection from the virgin state and the state after the electrochemistry can be explained by the formation of a SEI layer on the TiO₂ surface.

Fig. 7.23

Left Neutron reflectometry results measured at different stages in the intercalation cycle, including the best fit that corresponds to the model described in the text. a Virgin state, before any electrochemistry is performed, b approximately half-way in the intercalation, c fully intercalated state, d approximately half way in the de-intercalation, and e empty state after the de-intercalation. Right SLD profiles (a–e) as in the left figure corresponding to the fits of the neutron reflectivity data also shown left. “Qz” refers to the quartz which is the incoming and outgoing medium for the neutrons, “El” refers to the electrolyte, 1 M LiClO₄ in propylene carbonate. Reprinted with permission from (M. Wagemaker, R. van de Krol, A.A. van Well, Phys. B. 336, 124 (2003)) [220]. Elsevier

For the half lithiated state the best fit of the neutron reflection data was achieved by assuming a Li-rich Li-titanate phase (Li_0.5TiO₂) in contact with the electrolyte. As a result of the negative coherent neutron-scattering length of Li the SLD of lithiated TiO₂ being is smaller than that of pure TiO₂. Neutron reflectometry proved the establishment of a phase boundary parallel to the electrode surface rather than a percolation model, which would lead to a homogeneous change of the SLD. The fully-lithiated state was fitted with a single electrode layer with the SLD corresponding to the composition Li_0.52TiO₂. The neutron reflection data after half delithiation indicated that the phase front moves back via the way in which it came, with the Li-titanate phase being in contact with the electrolyte. This is in contrast to the expected Li depletion during extraction, which should lead to TiO₂ formation at the electrolyte interface. This symmetric phase-front movement does not immediately explain the difference in insertion and extraction rate. However, nuclear magnetic resonance experiments show the diffusion over the phase boundary to be the rate-limiting step [172, 173], giving a rationale for the more sluggish lithiation of TiO₂, which as opposed to delithiation, requires diffusion over the phase boundary.

Information related to the structure and composition of the SEI layers is mostly based on ex situ spectroscopic and microscopic studies [174, 175], but because of the reactive and delicate nature of these layers, in situ analysis is essential to improve our understanding. Being relatively sensitive to the light organic and inorganic species present in the SEI and to the surface layers ranging from a few to hundreds of nanometers, neutron reflectometry is an exceptionally suitable technique for in situ studies of the growth, composition, and the structure of the SEI.

Owejan et al. [176] used neutron reflectometry to study the formation and structure of the SEI layer in a Li battery. A requirement for neutron reflectometry is a flat and smooth surface as it probes the average in-plane SLD profile. A Li half-cell was configured with Cu as the ‘counter’ electrode to prevent Li reaction with the electrode, so that all electrochemical charge can be attributed to decomposition of the electrolyte and SEI layer formation. The use of a non-intercalating electrode, such as Cu, as model electrode for electrolyte decomposition appears to be justified by the similarity of the SEI layers formed by C materials at low potentials in Li-salt containing electrolytes [46, 47]. Additionally, the thermodynamics of electrolyte reduction appear to be governed by the cation that is used in the electrolyte [43]. The scattering contrast of the electrolyte was increased by preparation of a 1 M LiPF₆ solution in a 1:2 (v/v) ratio of deuterated ethylene carbonate and isotopically-normal diethyl carbonate. The deuterated ethylene carbonate also offers the opportunity to identify the possible preferential decomposition of cyclic (ethylene) over acyclic (diethyl) carbonates. By deuterating selected components in the electrolyte solution researchers can access which component contributes or forms the SEI layer.

In Fig. 7.24 the neutron reflectivity versus Q is shown for the pristine Cu electrode immersed in the electrolyte at the open-cell potential. This electrode underwent 10 cyclic voltammogram sweeps between 0.05 and 3 V at a 10 mVs⁻¹ rate, followed by holding the potential at 0.25 V versus Li/Li⁺ (potentiostatic reducing conditions). A clear difference between the peak amplitudes and oscillations (positions) in the reflectivity of the fresh and electrochemically-cycled electrode is observed. Initially, at the Cu-electrolyte interface, copper carbonate/hydroxide ligand-containing layers appear to be present which are removed after the cyclic voltammetry. Interestingly, after 10 cyclic voltammetry sweeps and the potential-hold step under reducing conditions, a 4.0 nm thick SEI layer at the interface had developed with a SLD much lower than that of the electrolyte. A further 10 additional cyclic voltammetry sweeps led to only a small growth of the SEI layer. For completeness, the authors then took a number of data sets at different potentials by slowly ramping the potential at 10 mVs⁻¹ to the next potential value and holding the potential during neutron reflectometry data collection. The results are summarized in Fig. 7.25. During the first two points d and e, using an oxidation current, a small decrease in the SEI layer thickness was observed and the SLD suggests a shrinking of the SEI layer due to solubility of SEI components. However, at the next point, holding at a reducing current the SEI layer grows significantly up to 8.9 nm. Most of the neutron reflection measurements indicate rather homogeneous SLD profiles with little roughness, in contrast to proposed structures in literature. After point f even the lowest potentials do not lead to further SEI layer growth, illustrating the passivating nature of the SEI layer. The systematic decrease of the SLD at lower potentials indicates that the SEI is increasingly composed of low SLD elements, which indicate Li-rich molecules.

Fig. 7.24

Neutron reflectivity versus Q shown for the sample at the open-cell voltage (OCV) and after 10 cyclic voltammetry cycles during a hold at 250 mV. The solid lines are the best fit to the two data sets. Inset SLD of Si, Cu, and Ti are indicated and electrolyte, SEI and TiSi_x layers are identified. For both parts, the darker and lighter shaded regions are the 68 and 95 % confidence intervals, respectively. Reprinted with permission from (J.E. Owejan, J.P. Owejan, S.C. DeCaluwe, J.A. Dura, Chem. Mater. 24, 2133 (2012)) [176]. Copyright (2012) American Chemical Society

Fig. 7.25

Left Cyclic voltammograms for selected scans. The points b-i denote the location of potentiostatic holds. Right Selected fitting parameters for test points. For reference, the hold potential versus Li is also shown. The dashed lines are the total thickness and SLD from composition modelling, matching well with measured values. Reprinted with permission from (J.E. Owejan, J.P. Owejan, S.C. DeCaluwe, J.A. Dura, Chem. Mater. 24, 2133 (2012)) [176]. Copyright (2012) American Chemical Society

Further insight into the composition of the SEI layer was obtained by combining X-ray photoelectron spectroscopy-derived compositions with the neutron reflectometry results for the SEI layer. This indicated an increase in LiOH and LiF molecules, and the decrease of lithium alkyl carbonates at the lower reducing-potentials. This study demonstrated the advantage of neutron reflectometry in giving direct insight into the growth and composition of the SEI layer and its relationship to the electrochemical conditions.

6 Battery Function

The progress of Li-ion batteries is severely hindered by the complexity of the chemical and physical processes and most importantly, the difficulty of observing these processes in situ during operation. Direct observation of Li ions in a battery in a non-destructive way is not possible by any conventional material analysis technique. The consequence is that a large number of practical and fundamental questions remain including: how do Li-ion battery degradation mechanisms depend on battery conditions? How do the structural changes and electrochemical processes depend on the (dis)charge rate, and what actually determines the (dis)charge rate? An understanding of the interplay between structure, electrochemistry, and reaction mechanisms is required for battery design.

To answer these questions we require time-resolved and non-destructive structural information including Li-ion positions and the Li distribution under operando conditions. These possibilities are offered by in situ neutron techniques that have been realized by the recent developments in neutron sources, detectors, and analysis methods. In situ neutron diffraction enables researchers to follow the structural changes and Li-positions upon all possible electrochemical manipulations in both the positive and negative electrodes. In situ neutron depth profiling determines Li-ion concentrations with high resolution in flat electrodes giving direct insight into the cylindrical batteries. Finally in situ neutron imaging allows a full three-dimensional picture of Li distribution in the battery to be determined. Recent advances in these three techniques will be discussed, including one of the major challenges, the cell design.

6.1 In Situ Neutron Powder Diffraction

Historically, in situ NPD has seen comparatively fewer applications to Li-ion battery research relative to in situ X-ray or synchrotron diffraction (see Ref. Brant et al. [177] for further details regarding in situ X-ray-based studies). This is due to a variety of factors, including the inherent complexities of the measurement technique, sample requirements, and the number of neutron diffractometers available for such experiments. However, in recent years neutron diffractometers and research trends have overcome the perceived difficulty of such complex experiments.

Unlike conventional neutron measurements where, in most cases, only the material under study is in the beam, with in situ methods, everything comprising the device can be in the beam, and thus contribute to the observed signal. For diffraction, H can be particularly problematic in the analysis of batteries [178] as the separator (e.g. polyethylene), electrolyte solutions, and the binder are often H-rich. Adding further to the background signal is the liquid or paste-like electrolyte. Therefore, attention has been devoted to custom-made cells for in situ neutron diffraction studies.

Commercial batteries are often produced with minimal quantities of electrolyte to maximise lifetime and avoid the issue of electrolyte leakage. Additionally, the electrodes are often coated on both sides of current collectors, and the overall of quantity of electrodes is significantly larger than that achieved in custom-made batteries. Furthermore, these batteries can be cycled at relatively high rates and are used in “real-world” applications. These considerations can outweigh the detrimental contribution to the background that H-containing components make and yield significant information on the evolution of electrode structure.

As the challenges in battery design and construction are investigated, we also look toward the best instruments for this task by considering the neutron flux, detector, and acquisition time.

6.2 Commercial Batteries

In situ neutron diffraction on commercial batteries has been used to provide structural information of electrodes at various states of charge [179, 180], under overcharge (or overdischarge) conditions [181], with fresh and fatigued or used batteries [182, 183], and at different temperatures and electrochemical conditions (applied currents) [180, 183–187]. In situ NPD allows structural snapshots of electrodes within a battery to be obtained, and depending on the diffractometer, these snapshots can be extremely fast such that the time-resolved structural evolution can be captured. Notably, new aspects of the graphitic anode and LiCoO₂ cathode that were commercialised in the 1990s are being discovered with this probe. Such insights include the existence of a small quantity of a spinel phase in the previously-thought layered LiCoO₂ cathode, an apparent lack of staged Li insertion into graphite to form LiC₁₂ with low current rates [180], and the transformation of the graphite anode to a wholly LiC₆ anode with voltages around 4.5 V—above and beyond the recommend limits applied by manufacturers [181]. Figure 7.26 shows LiCoO₂ and Li _x C₆ reflections and their evolution as a function of time. Structural changes are a function of the applied charge/discharge rates, with faster structural evolution occurring at higher rates. Importantly, higher rates produce a lower capacity which is directly related to a lower quantity of the LiC₆ (charged anode phase) being formed.

Fig. 7.26

Left In situ NPD data collected in consecutive 5-minute intervals. The red regions represent significant intensity, while the yellow/green regions are the background. Reflections arising from the Li _x CoO₂ cathode and Li _x C₆ anode are labelled. Right The integrated intensity of the LiC₆ anode reflection (top) corresponding to the line marked on the figure left. As the current is increased the integrated intensity drops, indicating a smaller quantity of LiC₆ forming. The composition of the anode displayed as individual neutron diffraction patterns during the high current experiment (bottom). Reprinted (adapted) from (L. Cai, K. An, Z. Feng, C. Liang, S.J. Harris, J. Power Sources 236, 163 (2013)) [183]

This information explains the processes in electrodes that are well known and in situ neutron diffraction can be used to explore a wide variety of battery-function parameters ranging from current, voltage, and lifetime. Kinetic processes in batteries can be probed with time-resolved data, where rates of structural changes are determined for electrode materials and related to the applied current. In most cases [184, 188, 189] the rate of structural change is directly proportional to the applied current. The rate of lattice expansion and contraction can be used to determine the viability of electrode materials for higher power applications. However, the relationship between kinetic structural parameters and the electrochemical capabilities of the battery are yet to be explored in detail. This is an active research area that may yield valuable information with more advanced experiments.

6.3 Custom-Made Batteries

Maximising the signal from materials of interest and maintaining acceptable electrochemical performance has been the overriding factor in designing neutron-friendly batteries. Initial designs were plagued by the need for large quantities of electrode materials and the associated requirement to use low current to ensure the reaction of the bulk of the electrode, for example studies of LiMn₂O₄ electrodes used 5 g of material as shown in Fig. 7.27 (left) [190, 191]. This design has evolved to designs shown in Fig. 7.27 (right) [178] which increasingly resemble their commercial equivalents, allowing high current to be used and a more direct comparison with commercial performance. For most of these examples the polyethylene separator is replaced with a separator containing a smaller amount of H, e.g. polyvinylidene difluoride, and the electrolyte solution is replaced with deuterated equivalents. By using the design in Fig. 7.27 it was possible to show the loss of long-range order of the MoS₂ anode during its first discharge [178], the composite nature of the TiO₂/Li₄Ti₅O₁₂ anode [192], relaxation phenomena in LiCo_0.16Mn_1.84O₄ cathodes [193], evolution of LiMn₂O₄ structure [190, 191], and the reaction mechanism evolution of LiFePO₄ [188, 194].

Fig. 7.27

Left One of the first batteries developed for in situ neutron diffraction, where A are brass plugs, B is a Pyrex® tube lined with Li foil, C is the separator soaked in H-containing electrolyte, D is the stainless-steel current collector, and E is the active material mixed with C black and binder. Right A more recent in situ neutron diffraction battery design with components as labelled. Reprinted (adapted) from (N. Sharma, G. Du, A.J. Studer, Z. Guo, V.K. Peterson, Solid State Ionics 199–200, 37 (2011)) [178]

Alternate designs have been developed for in situ neutron diffraction experiments and these include coin-type cells [195–197] which still feature relatively-thick electrodes but have been used to successfully investigate Li₄Ti₅O₁₂, graphite, and LiFePO₄. Similarly, pouch-type cells with alternate layers of cathode and anode-coated current collectors are applicable for investigating full cells, as opposed to the use of Li metal in the majority of the previous examples. Studies have been conducted on Li[Ni_1/3Mn_1/3Co_1/3]O₂∥graphite, Li[Li_0.2Ni_0.18Mn_0.53Co_0.1]O₂∥graphite [198], and LiNi_0.5Mn_1.5O₄∥Li₄Ti₅O₁₂ [199] full cells.

The motivation for designing these neutron-friendly cells is that any electrode material can be tested in situ in a real cell. Effectively, some of these designs can be manufactured using relatively-small electrode sizes (0.5–1 g) allowing a variety of materials to be investigated, and the interplay between structure, electrochemistry, and reaction mechanism can be elucidated. This information can then be used to direct the choice of future electrode-materials.

Some of these cells have been used to extract time-dependent information which reveals the rate of reactions as a function current applied, relating structural perturbations to electrochemical factors [188, 193]. Of particular note has been the study of the reaction mechanism of LiFePO₄ [188]. The evolution of LiFePO₄, either by a single-phase solid-solution reaction, or a two-phase reaction, during charge/discharge has been extensively discussed in the literature (see [188] ). Some parameters that lead to a particular type of reaction mechanism being favoured have been detailed. However, there was a lack of time-resolved information concerning bulk-electrode behaviour in a commercially-equivalent cell to definitively establish the working mechanism of LiFePO₄. Time-resolved in situ NPD data showed the evolution of the reaction mechanism of LiFePO₄ during charge/discharge processes. This is significant because the experiment probed the material under real working-conditions at the bulk-electrode scale. It should be noted that the LiFePO₄ sample used was expected to have only two-phase behaviour, and this work revealed a solid-solution reaction mechanism region during charge/discharge which is followed by a two-phase reaction mechanism. Moreover, the transition between the ‘competing’ reaction mechanisms was identified and characterized to be a gradual transition with solid-solution reactions persisting into the two-phase reaction region, rather than an abrupt transition. Figure 7.28 details this evolution and the co-existing reaction mechanism region.

Fig. 7.28

In situ NPD data of the Li∥LiFePO₄ battery (top) with scaled intensity highlighting the LiFePO₄ and FePO₄ 221 and 202 reflections. Bottom The applied current is the red line and the measured voltage is the black line. Parameters derived from the neutron data are shown including the phase fraction of LiFePO₄ (green crosses), the phase fraction of FePO₄ (black crosses), and the lattice parameters, where a is black, b is red, and c is blue. The lattice parameters for LiFePO₄ are solid symbols and those for FePO₄ are open symbols. Vertical black lines represent the onset of the solid-solution reaction and vertical purple lines indicate the chronological transition from a composition that is predominantly Li_1−y FePO₄ to predominantly Li _x FePO₄, where x ≈ 0.03 and y ≈ 0.04. Shaded regions indicate the coexistence of solid solution and two-phase reactions. Reprinted from (N. Sharma, X. Guo, G. Du, Z. Guo, J. Wang, Z. Wang, V.K. Peterson, J. Am. Chem. Soc. 134, 7867 (2012)) [188]

Therefore, in situ NPD not only provides information on the evolution of electrode structure, but also on the evolution of the (de)lithiation reaction mechanisms of the electrode. This information can be time-dependent and as a function of the electrochemical process, and can be used to design alternative electrodes that avoid, or undergo, certain reaction mechanisms to enhance battery performance.

6.4 Kinetics of Lithium Distribution

Ultimately, the goal of in situ neutron diffraction is to track the Li content and location in crystalline electrode materials as a function of charge and discharge. This is a difficult task, that until recently was only demonstrated at limited battery states of charge [191] with long collection times and effectively under equilibrium conditions. Other studies have inferred Li content via electrochemical approximations (amount of charge transferred) and the evolution of reflection intensities [196]. If the Li composition of an electrode can be reliably determined as a function of discharge/charge this would give a direct measure of the capacity of the battery, or more accurately, the capacity of the battery that is stored in the crystalline component of the electrode.

Recently, the ability to track the Li location and content as a function of time (and charge/discharge) has been demonstrated using commercial Li_1+yMn₂O₄ cathodes [189]. Arguably, this represents the most Li-centric view of a Li-ion battery during operation. The Li evolution is found to differ at a structural level during charge/discharge (Fig. 7.29) accounting for the ease of discharging these types of cathodes, relative to charging. Additionally, the Li evolution is shown to progress from one to two crystallographic sites during the charge/discharge processes. The lattice parameter follows a linear relationship with Li content during single Li site processes (Vegard’s law) and during processes involving two Li sites the relationship between the lattice parameter and the Li occupancy and site is a linear combination of the individual single site processes (Fig. 7.30). This work provided unparalleled insight into the function of the cathode and is used to understand the origins of how the electrode functions. Further studies on structural permutations may provide insight on how these electrodes can be improved from the perspective of the Li.

Fig. 7.29

a The evolution of Li at the 8a (black) and 16c sites and in a formula unit of Li_1+y Mn₂O₄ (lower plot) during charge/discharge. The discharge process shows an increase in Li content, whilst charge shows a decrease. b A representation of the sites described in (a) for Li_1+yMn₂O₄. Reprinted from (N. Sharma, D. Yu, Y. Zhu, Y. Wu, V.K. Peterson, Chem. Mater. 25, 754 (2013)) [189]

Fig. 7.30

The relationship between Li site occupancies and the lattice parameters of Li_1+yMn₂O₄. Single-site regions are shown in black and red and mixed-site regions are in blue and purple. Reprinted from (N. Sharma, D. Yu, Y. Zhu, Y. Wu, V.K. Peterson, Chem. Mater. 25, 754 (2013)) [189]

LiNi_0.5Mn_1.5O₄ is attracting significant attention for cathode applications due to the high-voltage redox couple during battery function, and Li₄Ti₅O₁₂ is attracting attention for anode applications due its small volume change during Li insertion and extraction. By specifically constructing a neutron-friendly cell made of this electrode-combination it was possible to study the structural evolution of these materials using time-resolved in situ neutron diffraction [199]. This highlights another advantage of using custom-made cells for in situ neutron diffraction experiments, where research is not limited to commercially-available materials. In this case, it was possible to determine the evolution of Li occupation in the cathode and indirectly infer the Li occupation in the anode (Fig. 7.31) in addition to determining the reaction mechanism evolution for the electrodes. It was found that a solid-solution reaction occurred at the cathode with the Ni²⁺/Ni³⁺ redox couple at ~3.1 V and a two-phase reaction with the Ni³⁺/Ni⁴⁺ redox couple at ~3.2 V. Thus, the extraction of Li from the cathode and insertion of Li into the anode during charge was directly determined, again in real-time. This opens up a way to evaluate a range of materials used as electrodes in Li-ion batteries, where how Li is extracted and inserted while a battery functions can be determined.

Fig. 7.31

Top Changes in the Li occupation and O positional parameter extracted from in situ neutron diffraction data of the LiNi_0.5Mn_1.5O₄ cathode. The battery operation is shown by the potential curve in black. Bottom: Simulated patterns of the Li_4+yTi₅O₁₂ anode slightly offset in Q to show the differences in reflection intensity. The inset shows the evolution of the Li_4+yTi₅O₁₂ 222 reflection which coincides with the expected variation with (de)lithiation from simulations. Reprinted from (W.K. Pang, N. Sharma, V.K. Peterson, J.-J. Shiu, S.H. Wu, J. Power Sources 246, 464–472 (2014)) [199]

6.5 Neutron Depth Profiling

A unique method to “see” Li-ion concentration profiles is provided by neutron depth profiling (NDP), Fig. 7.32. Previously it has been shown that NDP is capable of determining Li concentration gradients in optical waveguides [200], electrochromic devices [201], and under ex situ conditions in thin film battery electrodes and electrolytes [202]. NDP uses a neutron-capture reaction for ⁶Li resulting in:

Fig. 7.32

Schematic principle of NDP applied to Li-ion battery systems

$$^{ 6} {\text{Li}} + {\text{n}}_{\text{thermal}} \to ^{ 4} {\text{He }}\left( { 2.0 6 \,{\text{MeV}}} \right) + ^{ 3} {\text{H}}\left( { 2. 7 3\,{\text{MeV}}} \right)$$

(7.1)

The kinetic energy of the products due to ΔE = Δmc ², where E is the energy, m is the rest mass of the particles and c is the speed of light, is distributed over the tritium (³H) and the alpha particle (⁴He), while the incoming thermal energy of the neutron at ~25 meV, is negligible. Due to the small particle flux and the inherently-low interaction of neutrons with matter, NDP is a totally non-destructive technique. When such a capture reaction takes place in a Li-ion battery electrode, the particles produced (⁴He and ³H) lose part of their kinetic energy due to the scattering by the electrode material, referred to as stopping power. The stopping power is directly related to the composition and density of the electrode and hence is a known quantity. Therefore, by measuring the energy of the ⁴He and ³H ions when they exit from the electrode, the depth of the capture reaction can be reconstructed. Typically, the spatial resolution of NDP for well-defined homogeneous layers is on the order of tens of nano-meters, Currently, the main restrictions of the NDP technique is the maximum depth that can be probed and the time resolution which, depending on the material investigated and the in situ cell design, are approximately 5–50 microns and 10–20 min, respectively. Ideal solid-state batteries can be designed with high spatial homogeneity for initial experiments, before proceeding to more complicated systems.

NPD has only been applied occasionally to Li-ion battery research, however, in these ex situ studies [202–205] NDP is very powerful in identifying Li-ion transport and aging mechanisms. The possibilities of NDP in Li-ion battery research is demonstrated with the first in situ study on thin film solid-state batteries probing the kinetic processes in these Li-ion batteries.

Oudenhoven et al. brought NDP one step further, demonstrating that Li depth profiles can be measured in situ in an all solid-state micro battery system during (dis)charging [206]. The Li-ion distribution was studied in a thin film solid state battery stack containing a monocrystalline Si substrate with a 200 nm Pt current collector, 500 nm LiCoO₂ positive electrode, 1.5 μm N-doped Li₃PO₄ (LiPON) electrolyte, and a 150 nm Cu top current-collector. The basic setup of the experiment is shown in Fig. 7.33. By subtracting the NDP spectrum of the as-prepared electrode from the charged and discharged spectra, the changes in Li-distributions can be observed directly, see Fig. 7.33. Upon charging, Li in the positive LiCoO₂ electrode is depleted and increased at the negative Cu current collector.

Fig. 7.33

Left Schematic representation of the NDP set-up. The inset below shows the orientation of the battery inside the NDP measurement chamber. Right a Overview of the NDP spectrum of the as-deposited battery and the battery after the first charge and discharge. An offset is applied to distinguish the various spectra. Based on the ⁴He and ³H reference energies (indicated by the dashed lines) the packaging/top current collector, the anode, the electrolyte and the cathode can be clearly distinguished. b When the spectrum of the as-deposited state is subtracted from the spectra of the charged and discharged states, the amount of Li moved during use of the battery can straightforwardly be determined. Reprinted with permission from (J.F.M. Oudenhoven, F. Labohm, M. Mulder, R.A.H. Niessen, F.M. Mulder, P.H.L. Notten, Adv. Mater. 23, 4103 (2011)) [221]. Wiley

The development of large concentration-gradients in both the LiCoO₂ electrode and the LiPON solid electrolyte, Fig. 7.34, reveals that in this system ionic transport in both electrolyte and electrode limit the overall charge-rate. The cathode was enriched with ⁶Li to highlight the redistribution of ⁶Li and the natural abundance of ^6,7Li in the electrolyte during time-dependent experiments. In this case, the NDP intensity increases by approximately a factor of 13. Apart from being able to observe where ⁶Li is going, the expected diffusive equilibration of the ⁶Li concentration within the electrolyte was observed during a 2 h equilibration period. Interestingly, the enriched Li remains in the LiCoO₂ electrode, even though the exchange current that establishes the dynamic equilibrium would be expected to redistribute the ⁶Li equally throughout the LiCoO₂ electrode and the LiPON electrolyte. The absence of vacancies at the initial stage probably makes the exchange-current extremely small. As the battery is charged at 0.5 °C, this results in a large decrease in the Li-ion signal of the LiCoO₂ electrode, as shown in Fig. 7.34.

Fig. 7.34

First in situ NDP spectra representing the Li concentration depth profiles of a battery during operation. a Enriched ⁶LiCoO₂ cathode and naturally abundant ^6,7LiPON electrolyte during several stages of the charging process showing the removal of ⁶Li from the electrode and large ⁶Li concentration-gradients in both electrode and electrolyte. b Equilibration in the charged state after 0.1 and 2 h showing the disappearance of the ⁶Li concentration-gradient in the LiPON electrolyte and remaining concentration gradients in the cathode indicating two-phase separation into a Li rich and Li poor phase. Since in the cathode area the red curve is higher than the blue, some equilibration takes place between cathode and electrode. Reprinted with permission from (J.F.M. Oudenhoven, F. Labohm, M. Mulder, R.A.H. Niessen, F.M. Mulder, P.H.L. Notten, Adv. Mater. 23, 4103 (2011)) [221]. Wiley

The stronger decrease in Li-ion signal near the interface with the electrolyte suggests an inhomogeneous Li-ion distribution in the electrode. Although this may be the case, a redistribution of the ⁶Li ions due to exchange with the electrolyte will lead to a lower Li-ion signal in the electrode. That this is indeed part of the explanation is clear from the almost 70 % decrease in Li-ion signal. This decrease is more than would be expected under the mild electrochemical conditions that should lead to Li_0.5–CoO₂, and hence at most a factor of two decrease in the Li-ion signal is to be expected. However, the inhomogeneous signal from the electrode indicated that the exchange does not reach the back part of the electrode that is closest to the current collector. The inhomogeneous distribution of the Li-ion signal originating from the electrolyte indicates the presence of an inhomogeneous ⁶Li and Li-ion distribution. The evolution of this non-equilibrium situation was investigated by relaxing the system after charging during a period of 2 h and taking NDP spectra, shown in Fig. 7.34. After 2 h the ⁶Li gradient almost vanishes in the electrolyte, whereas it remains in the LiCoO₂ electrode. Clearly, Li-ions are much more mobile in the electrolyte compared to in the electrode. The work of Oudenhoven et al. shows for the first time that the evolution of the Li distribution and gradient under dynamic conditions can be studied.

6.6 Neutron Imaging

Neutron imaging (radiography) is becoming increasingly important in the study of Li-ion batteries as the spatial and temporal resolution of the detectors continually improve, and more advanced computational methods allow tomographic and/or three-dimensional rendering [207]. Neutron radiography (NR) is used to show macroscopic information concerning the Li distribution within a Li-ion battery, and in some cases while a process is occurring or at different states-of-charge [208]. Additionally, the H distribution in the electrolyte can be probed [209]. Examples of such studies include the Li distribution at the charged state versus the discharged state, during high-temperature battery operation, during fast charge/discharge cycling, and during overcharging [207, 208, 210, 211].

Neutron imaging has also been used to study alkaline [212, 213] and Li-air batteries [214]. The future for neutron radiography relies on new instruments with improved spatial resolution, but also temporal resolution to allow time-resolved in situ experiments. Another method under considerable investigation is the combination of diffraction and imaging, which requires the definition of a gauge volume which is imaged and from which diffraction data can also be collected. This has been demonstrated for physically-larger batteries such as Na metal halide batteries, which usually have larger electrodes [215]. However, to be pertinent for Li-ion battery research, the gauge volume has to be reduced to become comparable to the thickness of electrode layers.

Early work on imaging Li-ion batteries explored the different types of battery construction, e.g. coin, prismatic, and cylindrical cells, and the distribution of Li at various battery states or during charge/discharge [216]. Figure 7.35 (left) shows images of a coin cell (CR1220 from Panasonic) from the charged to the discharged state, where lighter (white) regions at the charged state correspond to the Li anode (Li metal) and electrolyte (arrow). Over the course of discharge the Li-ions move towards the cathode (MnO₂) resulting in an even distribution of white regions. The authors comment that if standard components and standardised cells are constructed then a more quantitative description of the Li distribution can be made. They also explored charging rates and other constructions, some of which had further experimental difficulties due to the internal structure of the batteries and the need to account for absorption by various layers. An example of the same electrode chemistry in the cylindrical case (CR1/3–1H) is shown in Fig. 7.35 (right) before and after discharge [158] showing similar Li distributions at the charged and discharged states.

Fig. 7.35

Neutron imaging studies of coin (left) and cylindrical (right) cells. The dark images correspond to images at different states of battery charge, with white regions representing high Li concentration. The graphs below the images show the integrated intensity highlighting the evolution of the Li distribution. The cylindrical battery construction is also shown (right). a Variation of neutron radiography images of CR 1220 with discharge. b The NR images of CR1/3-1H before and after discharge. Reprinted (adapted) with permission from (M. Kamata, T. Esaka, S. Fujine, K. Yoneda, K. Kanda, Nucl. Instr. Meth. Phys. Res. A 377, 161 (1996)) [158] and (M. Kamata, T. Esaka, S. Fujine, K. Yoneda, K. Kanda, J. Power Sources 68, 459 (1997)) [216]. Elsevier

In commercial batteries overcharging can be a potentially-devastating failure mechanism, and imaging studies on commercial graphite//LiNi_0.8Co_0.15Al_0.05O₂ (NCA) batteries show what is deposited on the graphite anode during overcharge [208]. By performing an in situ measurement the deposition of a material on the graphite anode was studied (Fig. 7.36) and later determined to be Li. In addition, the authors were able to characterize ‘where’ the Li deposits during battery processes. Another work explored ‘fresh’ and ‘fatigued’ batteries, where batteries that had been cycled 200 times. The 18650 cylindrical batteries showed no differences at the macroscopic level in the neutron images of between fatigued and fresh batteries [182], even though neutron diffraction data indicated less Li insertion in fatigued graphite.

Fig. 7.36

Neutron image from a coin cell at 4.8 V with the black region showing the anode. Other shaded regions represent regions of high neutron-attenuation (likely to be Li-containing). Reprinted (adapted) with permission from (A. Same, V. Battaglia, H.-Y. Tang, J.W. Park, J. Appl. Electrochem. 42, 1 (2012)) [208]. Springer

Another study illustrated that a 14 μm spatial resolution is attainable for battery samples using neutron imaging [210]. This work used a purpose-built graphite-containing cell to quantify Li content during charge/discharge and the residual Li content after each cycle, showing quantification over several cycles (e.g. capacity loss). Figure 7.37 shows the evolution of Li content and its distribution in graphite during the first discharge. The Li distribution was compared during cycling and between cycles. A slight difference in Li content between the separator and current collector was found. Further work investigated LiFePO₄∥graphite pouch-cells and revealed Li concentration gradients across electrodes and in their bent regions [211]. Figure 7.38 shows the distribution of Li in the layers of the pouch cell at various states-of-charge. The authors used the Beer-Lambert law to correlate colour gradients, shown in Fig. 7.38, to the Li concentration. One advantage of using a pouch cell is that one image contains many layers, so an increase in electrode thickness can be seen in multiple layers verifying the result (as can Li concentration gradients). Clearly, this information can direct the development of better performing electrodes.

Fig. 7.37

Li distribution in a graphite electrode during first discharge a showing the geometry of the experiment, b time-resolved radiographs and parameters and c the potential profile. Reprinted (adapted) with permission from (J.P. Owejana, J.J. Gagliardo, S.J. Harris, H. Wang, D.S. Hussey, D.L. Jacobson, Electrochim. Acta 66, 94 (2012)) [210]. Elsevier

Fig. 7.38

Images from a LiFePO₄∥graphite pouch cell during charge/discharge. Reprinted with permission from (J.B. Siegel, X. Lin, A.G. Stefanopoulou, D.S. Hussey, D.L. Jacobson, D. Gorsich, J. Electrochem. Soc. 159, A523 (2011)) [211], Copyright (2011). The Electrochemical Society

More recent work used cold neutrons rather than thermal neutrons, harnessing the stronger interaction of colder neutrons with matter, to visualize Li-ion distributions in Li–I batteries used in pacemakers [217]. This work also used three-dimensional imaging (tomography) and discussed methods to improve the signal-to-noise ratio in the images. The authors collected 50 images at 0.3 s for each angular step (rotation) of 0.91° which were then used to construct the three-dimemsional image. Figure 7.39 is an example of a cross section of a neutron tomography image of the fresh battery (left) and after a certain period of discharge (right). The battery is made of plates of Li and I. An unexpected change in the Li distribution (white) was observed in this study, where the smooth distribution became highly irregular. The irregularity of the Li distribution after discharge is extracted in the three-dimensional image shown in Fig. 7.39, where the Li formations are clearly seen.

Fig. 7.39

Left Cross-sections of a tomography image before (left-most) and after discharge. High neutron-attenuation regions are white. Right A three-dimensional rendering with only the Li contributions (other components removed due to the large contrast available). Reprinted (adapted) with permission from (N. Kardjilov, A. Hilger, I. Manke, M. Strobl, W. Treimera, J. Banhart, Nucl. Instr. Meth. Phys. Res. A 542, 16 (2005)) [217]. Elsevier

Further experimentation was undertaken on a Li-ion polymer battery using monochromatic imaging with cold neutrons, specifically targeting the anode and the processes that occur within it [218]. The LiC₆ compound, but no evidence of the staging phenomenon often observed in LixC₆ anodes was seen. This work was the first real-time in situ imaging of a commercial Li-ion battery, with some results shown in Fig. 7.40.

Fig. 7.40

Left Selected attenuations (corresponding to LiC₆) at different wavelengths plotted as a function of charge. The 3.6 Å attenuation seems to show the largest response to the formation of LiC₆. Right Real-time tomography of a commercial Li-ion battery. Reprinted (adapted) with permission from (L.G. Butler, B. Schillinger, K. Ham, T.A. Dobbins, P. Liu, J.J. Vajo, Nucl. Instr. Meth. Phys. Res. A 651, 320 (2011)) [218]. Elsevier

A subset of radiography research using commercial batteries, and in some cases custom-made batteries, is the study of gas evolution [209]. One in situ study showed how excess electrolyte present in batteries is consumed in the first charge-cycle, resulting in the formation of the SEI layer and some volume expansion. Additionally, gases were found to be evolved during the first charge. Figure 7.41 shows the consumption of excess electrolyte in these cells. The authors were also able to approximate the amount of expansion and contraction of the electrodes indirectly.

Fig. 7.41

Neutron radiography image of a fresh Li-ion battery (left) and a battery cycled 70 times (right). The arrow indicates the excess electrolyte level. Reprinted (adapted) with permission from (M. Lanz, E. Lehmann, R. Imhof, I. Exnar, P. Novak, J. Power Sources 101, 177 (2001)) [209]. Elsevier

In situ neutron radiography has been extensively used to study the interface between graphite and a range of gel-based electrolytes [219]. By using this technique, the generation of gas bubbles in the first charge can be visualized and quantified. This information allows the best electrolyte to be proposed, noting that the generation of gas bubbles, particularly on graphite surfaces, leads to performance degradation. This measurement also provided information on the spatial distribution and kinetic evolution of gas bubbles, as well as the electrolyte displacement and volume expansion in graphite. In order to undertake these measurements, specialised cells were developed. A neutron image of the cell is shown in Fig. 7.42. For the in situ experiment the exposure time for each image was 20 s and an image was recorded every 2 min. Figure 7.42 shows how channels of gases are formed seemingly-randomly in the cell and their evolution at different times. It was found that LiC₆ is formed only where gas emission is absent, illustrating some heterogeneities in the charge distribution and electrode composition. The gel-based electrolytes tested in this study show less gas evolution (3 %) compared to liquid-based electrolytes (60 %) and this was related to the smaller amount of gas evolution during the first cycle.

Fig. 7.42

Left A neutron radiography image of the test cell prior to electrochemical cycling. Right Images at progressive states of cycling from (a) to (d). Reprinted (adapted) with permission from (D. Goers, M. Holzapfel, W. Scheifele, E. Lehmann, P. Vontobel, P. Novak, J. Power Sources 130, 221 (2004)) [219]. Elsevier

7 Perspectives

This chapter has aimed at demonstrating how neutron-scattering methods allow researchers to elucidate crucial structural and kinetic properties of electrodes, electrolytes, and complete batteries. Neutron-scattering techniques play a key role in the development of new materials by relating structure to functional properties. Future battery research and development will in particular profit from the advances in in situ neutron-scattering techniques, probing complete battery systems. This gives the opportunity to relate battery performance to material and electrode structural, morphological, and dynamic properties under non-equilibrium and ageing conditions, which is vital information for the design of future batteries.