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 LixTiO2 anatase [55-57], rutile [58], brookite [59], and Li1+xTi2O4 and Li4+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 Li1+xV1-xO2 [72]. Interestingly, LiVO2 does not allow Li insertion whereas Li1+xV1-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 Li1 .07V0. 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, Li1+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’ LiMn1/3Co1/3Ni1/3O2, 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 LixMn2O4 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 x 3a x 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 Li1+xMn2-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 Li114Mn186O4 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) Lij+xMn2-xO4-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 LiNi0.5Mn15O4 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 LiMnyFe1-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 LiCoyFe1-yPO4 [94], LixCoPO4 [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 Li2-xMP2O7 (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 Neel 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 LixFePO4 (0 < x < 1) at 450 °C, and in addition, the existence of two new metastable phases with compositions Li0.75FePO4 and Li0.5FePO4. 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*067FePO4 [103]. In Li*067FePO4, 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].

The room-temperature miscibility gap in LixFePO4 was determined by Yamada et al. [105] using NPD. These researchers found intermediate Li-poor Lia=0 05FePO4 and Li-rich Li1—p=089 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.

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

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 Li0.96Zr0.04FePO4 (target composition) including the difference between the fits and data. The fit residuals are wRp = 1.7 % and Rp = 1.9 %, as well as wRp = 1.7 % and Rp = 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

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 orFe, 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.

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 LixFeyPO4 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 Li1-yFePO4 nano­particles [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.

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.

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.

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 а-phase LixaFePO4 and the Li-rich heterosite р-phase LixpFePO4 where xa and xp represent the average solubility limits as a function of particle size, having an overall composition Li05FePO4. Va and Vp 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 а-lattice direction for three different particle sizes at the overall composition Li05FePO4. 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 а-phase and the Li-rich heterosite p-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 а-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]