Stoichiometry matters: correlation between antisite defects, microstructure and magnetic behavior in the cathode material Li 1 − z Ni 1+ z O 2 †

As contemporary battery applications such as electric vehicles demand higher energy densities, layered LiNiO 2 (LNO) could contribute as the end-member of the LiNi 1 − x − y Co x Mn y O 2 (NCM) family with the highest extractable speci ﬁ c capacity in a practical voltage window. Achieving high capacities requires among other things a defect free crystal structure, which is not easily achieved due to the natural occurrence of Ni excess on the Li site (Ni Li ) and/or antisite defects where Ni and Li switch crystallographic sites. Here, we present a study of the evolution of point defects in a series of LNO samples varying from underlithiated to fully lithiated stoichiometry in layered Li 1 − z Ni 1+ z O 2 with − 0.05 # z # 0.35. Using the high angular resolution of synchrotron X-ray di ﬀ raction complemented with the di ﬀ erent elements contrast provided by neutron di ﬀ raction, we are able to identify two defect regimes. In the ﬁ rst regime, at the underlithiated end, both Ni Li as well as Li on the Ni site (Li Ni ) defects are present. Inhibited crystal growth during synthesis is found to coincide with the presence of these Li Ni defects for z $ 0.15. Upon decreasing z values and the vanishing of Li Ni , the primary particle size distribution as well as average re ﬁ ned crystallite size increases. Investigation of the local structure by nuclear magnetic resonance reveals the presence of a Li environment not detected by di ﬀ raction methods at low z , the Li-rich end of the sample series. Finally, magnetometry data suggest the onset of the ferrimagnetic-to-antiferromagnetic transition in LNO correlates with the elimination of Li Ni defects in the structure. The present study thus not only highlights the correlation between defect chemistry and physical properties, but also shows the relationship to crystal growth, a ﬁ eld highly relevant for industrial battery cathode materials engineering.


Introduction
Layered oxide cathode materials of the NCM family having a high Ni content have been widely adopted in applications requiring energy storage with a high energy density.To further improve gravimetric energy density, Ni-rich compositions have been developed with Ni content as high as 95%, [1][2][3] effectively approaching the LiNiO 2 (LNO) end-member.Despite being the NCM cathode active material with the highest specic capacity (z245 mA h g −1 at 4.3 V vs. Li + /Li at 25 °C), key issues remain, as LNO is challenging to synthesize, suffers from both structural and surface instabilities in the pristine and de-lithiated state, as well as crystallographic defects hindering full delithiation. 4iNiO 2 has been the subject of numerous studies regarding its synthesis, [5][6][7][8][9] crystallographic and electronic structures, [10][11][12][13][14] and electrochemical behaviour, [15][16][17][18] and the reader is directed to a recent review for a more comprehensive overview of the material. 19While current efforts yielded recipes for LNO with 1-2% of Ni 2+ on the Li site (Ni Li ), 20 the formation of defects, and thus possibility for their complete elimination, remains poorly understood in LNO.
In a recent study, the LNO formation mechanism from the mixture of the industrial relevant reactants LiOH$H 2 O + Ni(OH) 2 was elucidated by in situ diffraction. 5There, three steps were identied: (I) dehydration towards NiO + LiOH, (II) partial lithiation/oxidation of the Ni-containing phase towards cubic Ni 1−x Li x O (space group Fm 3m) up to x z 0.31 and even up to x z 0.4 during the in situ lithiation, and (III) a nal oxidation with a concomitant full lithiation towards stoichiometric LiNiO 2 .In the cubic, rock salt type phase, Ni and Li share a crystallographic site as well as an oxide anion polyhedron of the same volume.Once sufficient amounts of Ni 2+ (r = 0.69 Å) are oxidized to Ni 3+ (r = 0.56 Å), the difference of the average ionic radius of the nickel ions vs. the radius of 0.76 Å for Li + becomes too large, inducing a phase transition towards layered, rhombohedral Li 1−z Ni 1+z O 2 (space group R 3m).In ideal structure of LNO at z = 0, Ni 3+ , Li + and O occupy the 3a, 3b and 6c site, as depicted in Fig. 1a.Hence, the oxygen ions remain in a cubic close packed (ccp) array similar to the rock salt phase, while Li and Ni separate into alternating layers along the c axis of the unit cell.
In real LNO materials though, nickel oxidation and thus separation of lithium and nickel into different crystallographic sites remains incomplete, leading to structural defects.The rst such defect, excess of Ni on the Li site Ni Li , is found in many studied materials and commonly referred to as "off-stoichiometry".The defect originates from facile lithium losses during synthesis, even in samples of nearly perfect stoichiometry, and leads to a reduced, divalent oxidation state of Ni 2+ in the Li site.The additional charges in the Li layer are compensated by the formation of charge defects in the NiO 2 − layer, i.e.
As shown recently, with low temperature, ion exchange-based synthesis of LNO from NaNiO 2 at around 320 °C instead of 700 °C, Li loss can be avoided. 21The Ni Li defect is easily identied even in lab X-ray powder diffractometry due to the large additional electron density of nickel vs. lithium and thus routinely quantied in LNO studies.Another important defect, in which Ni and Li  ] 3a [O 2 ] 6c , matches the denition of an antisite defect.In general, occupancy of Li + in NiO 2 − slabs is highly unusual due to the difference in ionic radii.However, high temperatures may lead to the formation of such antisite defects, as has been reported in highly disordered Li 0.92 Ni  22 Another option to incorporate Li in the Ni site is to have a Li/Ni ratio higher than 1 and increasing the oxygen chemical potential at a lower T of around 550 °C, hence generating oxidized compounds until reaching Li 2 NiO 3 (corresponding to an extended z range from −0.33 # z # 0.0). 23A recent combined synchrotron X-ray and neutron diffraction study in isostructural NCM materials by Yin et al. 24 indicates that antisite defect concentrations increase with the volume of the transition metal oxide octahedron Ni 1−x−y Co x Mn y O 6 .There, the polyhedral volume is driven by the reduction of Ni 3+ to Ni 2+ in the presence of Mn 4+ and thus strongly dependent on the stoichiometry.While a similar mechanism could be imagined in LNO due to the Ni 2+ charge defect in the trivalent NiO 2 layer induced by the off-stoichiometry Ni Li defect, a similar correlation is not known.Moreover, the limited concentration and nature of antisite defects makes them difficult to probe with conventional characterisation techniques, for example X-ray scattering has low sensitivity for Li, or the relatively high electronic conductivity of LiNiO 2 reduces its Raman scattering efficiency. 25Researchers have hence turned to more advanced methods, including neutron scattering, 12,26 X-ray absorption spectroscopy, 27 and solid-state nuclear magnetic resonance (NMR) spectroscopy 28,29 to more precisely resolve the crystallographic, electronic, and magnetic structure of LiNiO 2 .1][32][33] Yet, to date in most of the literature models of either antisite defects or off-stoichiometry are oen chosen without a precise reasoning behind the choice of the models.Using a comprehensive suite of characterisation techniques, we aim to resolve the relationship between material stoichiometry and the presence of site defects over a wide range of compositions with nominal stoichiometry Li 1−z Ni 1+z O 2 where −0.05 # z # 0.35, and the resulting consequences for the physical properties of the materials.The site occupancy defects of Li and Ni in the structure are quantitatively determined using combined Rietveld analysis of structural models against X-ray and neutron diffraction data to characterise the bulk average structure.Complementary solid-state NMR spectroscopy provides more detailed insight into the local environments of Li in the defective structures.Finally, we correlate the observed defect chemistry to the magnetic properties and particle size, which yields insights into growth dynamics highly relevant for industrial crystal engineering.

Results & discussion
To better understand the consequences of Li : Ni stoichiometry for the micro-and crystal structure of LNO, a series of Li  1b.Consistent with the studies mentioned above, a clear trend is seen in the evolution of the material's microstructure/ morphology with changing nominal stoichiometry z, as shown in Fig. 2 and S1.† All the samples inherit a spherical secondary particle morphology from the Ni hydroxide precursor.However, an obvious change in the size of primary particles can be noticed among the different samples.To more accurately quantify the morphological changes, a semiautomated machine learning algorithm was used to measure the particle size distribution (PSD) from analysis of the electron microscopy images (further details are found in the Experimental section).The results are summarized in Fig. 2, including the median D eq , the 5th to 95th and 25th to 75th percentile of the PSD for each sample.The PSDs are multimodal and present some variation in their shape, which possibly originates from the counting statistics limited by the semiautomatic analysis workow.Yet, an overall trend emerges: while the median D eq stagnates between approximately 77 and 90 nm for samples with z $ 0.15, the primary particle size steadily increases for samples with z # 0.10 up to a median D eq of 308 nm.This observation indicates that the Li : Ni ratio in the precursors mixture plays a crucial role in crystal growth, with a threshold between 0.10 # z # 0.15.
In order to nd possible atomistic explanations for this observation and to quantitatively model the evolution of the crystal structure as a function of the nominal stoichiometry, synchrotron X-ray diffraction (SXRD) and neutron diffraction (ND) patterns were collected from the samples.The combination of both SXRD and ND is particularly useful for LNO and other layered cathode materials, as the high intensity and angular resolution coupled with negligible peak prole contributions of the instrument used in SXRD provides precise structural parameters.5][36] The high-quality SXRD patterns feature narrow peak shapes in the best crystallized samples, allowing for more reliable deconvolution of the contribution to peak broadening due to crystallite size.A single structural model was simultaneously rened against both synchrotron and neutron data where both diffraction data sets were available.This allows for a more meaningful determination of the cation (especially Li) distribution among the 3a and 3b sites in the layered structure.Fig. 3a and b show diffraction patterns collected from the as-synthesised LNO materials.The peak positions of the 003 and 110 reections, which depend on the c and a lattice parameter, respectively, shi towards higher 2q values with decreasing z.This indicates that increasing Li content per sum formula is accompanied by a decrease in the unit cell volume.There is also considerable peak broadening of the full-width-at-half-maximum (FWHM) observed with decreasing Li content.Patterns of samples with small Li excess feature weak peaks corresponding to a minor LiOH impurity of 0.9(3) and 1.5(3) wt% for z of −0.01 and −0.05, respectively.Such LiOH impurities have been commonly observed on the surface of Ni-rich cathode materials. 37,38As we do not observe the 200 peak at about 2q z 23.0°(l = 0.825888 Å), there is no evidence for the presence of a rock salt type side phase Ni 1−x -Li x O (x # 0.3). 39n order to quantify the trends observed in the diffraction patterns, structural models with space group R 3m were rened against the diffraction patterns using Rietveld analysis.An example of the typical quality of t by comparison of the observed vs. the calculated intensity including the difference curve is shown in Fig. 3c and d for SXRD and ND patterns of LNO with z = 0.01, and in Fig. S3 † for the complete series of pattern.The resulting structural parameters are listed in Table 1 and their evolution with varying z or rened Ni excess is visualized in Fig. 4. LNO exhibits clear trends with decreasing Ni content (decreasing z), as summarized in Fig. 4a-c 14.19515(6) Å in nearly stoichiometric LNO (z = −0.05).The unit cell volume also decreases linearly with nominal z from 104.476(9) Å 3 to 101.8037(8) Å 3 , as expected based on prior studies. 19This can be rationalized with the decreasing radii of the Ni-ions once oxidized from the di-to the trivalent state, with an accompanying reduction of the ionic radii from r(Ni 2+ ) = 0.69 Å to r(Ni 3+ ) = 0.56 Å. 40 An increase in the c/a ratio from 4.9023 at z = 0.35, near the cubic c/a limit of 2O6 z 4.8990, towards 4.9328 at z = −0.05(near stoichiometric LNO) is a common indicator for low Li/Ni site disorder, good layering and the distortion observed in the trigonal space group.
Rietveld analysis can also provide information about the materials' microstructure when instrumental and sample contributions to peak broadening are properly deconvoluted. 41,42Here, we rst characterised the instrument contribution to peak broading by measuring Na 2 Ca 3 Al 2 F 14 and performing a Rietveld analysis including a Thompson-Cox-Hastings (TCHZ) pseudo-Voigt peak shape and axial divergence.The obtained parameters for the TCHZ peak shape and axial divergence were included as xed values in subsequent renements.This approach allowed to deconvolute angle-dependent Gaussian and Lorentzian contributions to the peak shape broadening (FWHM), which were interpreted as either originating from the coherent diffracting domain size (FWHM ∼ cos(q) −1 ) and microstrain (FWHM ∼ tan(q)).We used the coherent diffracting domain size to estimate the crystallite size (D vol ), which initially remains relatively constant in the range of 70 to 75 nm for 0.15 # z # 0.35, see Fig. 5a and b.Upon z < 0.15, the defect regime changes as described in the upcoming paragraphs on site occupancies and the crystallites size grows rapidly with a higher amount of Li equivalents (decreasing z), cumulating in a size of 316 (8) nm at z = −0.05.The microstrain displays high values for high z values (Ni-rich end), which is greatly reduced once the threshold at z < 0.15 towards low z values (Li-rich regime) is reached, see Fig. 5c.These results are supported by visual observations and quantication of the primary particle size over the whole sample series via SEM.Samples in the 0.15 # z # 0.35 regime feature small, intergrown primary particles, which then grow into larger, well crystallized primary particles beyond z # 0.1, see Fig. 2.This indicates a threshold for crystal growth around z < 0.15.
For the precise determination of atomic parameters, such as site occupancies, atomic coordinates, and atomic displacement parameters (ADPs), we utilize the complementary elemental contrast of SXRD and ND.The z-coordinate of oxygen, z O , is found to increase linearly with decreasing z, see Fig.For the site occupancies of the Ni (3a), Li (3b) and O (6c) sites, different hypothesis were implemented and evaluated based on improvement of gure of merit parameters (R wp , goodness of t as gof, R Bragg ), 41 number of parameters used per renement and chemical reasoning.The free renement of the oxygen site occupancy was also tested, and was found to converge towards 1 within the renement error in all samples, suggesting the absence of any oxygen vacancies in these materials.The oxygen occupancy was thus set to 1 for all other renement models in order to reduce the number of free parameters, and the metal sites were assumed to be fully occupied.For the occupancy of the metal sites, two defect models were compared in order to introduce a Ni excess in the unit cell with increasing z.The rst model describes a fully occupied Ni site on 3a and a Ni Li defect occupancy on the Li site (the so-called off-stoichiometry).The occupancy of Li on the 3b site was modelled as Li Li = 1 − Ni Li and a shared atomic displacement parameter was used.This is the most commonly encountered model in published literature on LNO and similar compounds.In the second model, additional Ni was allowed on the Li site (Li Li = 1 − Ni Li ) as well as Li on the Ni site (Ni Ni = 1 − Li Ni ), so that the two occupancy defect parameters Ni Li and Li Ni were freely rened in parallel.In general, antisite defects appear when two different, neighboring atoms or ions exchange their lattice sites.Thus, the amount of Li Ni matched by an equal amount of Ni Li represents antisite defects in Li 1−z Ni 1+z O 2 .Excess Ni is dened as Ni excess = Ni Li − Li Ni , which should approximately correspond to z as found by elemental analysis.In both models, Ni Li increases with increasing off-stoichiometry z, as displayed in Fig. 7a.Yet, model 1 leads to unphysically low or even negative atomic displacement parameters on the Li site, hinting at issues with Ni Li as the sole defect model.Upon inclusion of antisite defects by renement of the Li Ni occupancy on the Ni (3a) site, the R wp and R Bragg values for the data sets of z $ 0.15 decrease, indicating a better t of the model.The effect is not signicant in models with antisite defects below the limit of Li Ni z 2% (z < 0.15).This indicates that the inclusion of a single additional parameter is not responsible for the drop in R-values, but rather that there is a resolution limit to the renement despite the availability of an additional scattering contrast from the neutron data sets.To further test this hypothesis, we compared the elemental composition obtained from the two renement models with the composition obtained from chemical analysis, see Fig. 7b.A high correlation of the Ni and Li content obtained from inductively coupled plasma-optical emission spectroscopy (ICP-OES) and renement model 2 (Ni Li incl.Li Ni ) can be observed.Model 1 with only the Ni Li occupancy defect on the other hand shows highly divergent behaviour at higher z values, which is hard to reconcile with quantities of elemental amounts found in our samples.Our results regarding antisite defects, the absence of oxygen vacancies, and the renement improvement by using combined synchrotron X-ray and neutron data are aligned with a report by Yin et al. for a variety of isostructural Li 1−z Ni 1−x−y+z Co x Mn y O 2 materials, as well as with the seminal study of Pouillerie et al. 26,34 From this, we could conrm that a certain minimum amount of Ni 2+ (z $ 0.15) is needed to sufficiently enlarge the Ni layer and allow a measurable amount of Li Ni to be present.In addition to the described parameters, we also rened the atomic displacement parameters B iso , which are shown in Fig. 7c for Li, Ni and O.The values are fairly stable between B iso z 0.23 to 0.3 Å 2 for Ni and B iso z 0.77 to 0.82 Å 2 for O over the range of −0.05 # z # 0.35.The atomic displacement parameters of Li decrease with increasing z from around B iso z 0.92 Å 2 at z = −0.05towards B iso z 0.29 Å 2 in Li 0.65 Ni 1.35 O 2 (z = 0.35).This evolution is chemically intuitive, as increasing z statistically places additional, heavier Ni-ions (MW Ni = 58.693g mol −1 vs. MW Li = 6.938 g mol −1 ) on the Li site, thus leading to an average lower displacement from the site at the same temperature.Overall, the observed values are physically meaningful and close to other values obtained in similar studies utilizing combined renements against synchrotron X-ray and neutron data sets. 34,35ombining the observations from X-ray and neutron diffraction with SEM imaging points towards a correlation of Li Ni defects with inhibited crystallite and particle growth and    this case, the shrinkage of the NiO 6 polyhedral volume with increasing oxidation state would allow to indirectly quantify Li Ni .Additionally, one could rationalize the presented observations in a similar manner to the established Cabrera-Vermilyea theory on crystal growth inhibition. 44There, impurities act as stoppers by impinging step growth.Viewing the results of our studies through this lens, Li Ni defects present for z $ 0.15 act as a growth inhibitor for the NiO 2 − layer based on the ionic Li-O bond disrupting the formation of hybridized Ni-O bonds.On the other hand, one may also recognize that Li ions are likely to be the more mobile cations during the synthesis, hence samples with high z and little Li content have less ion diffusion hence less crystal growth.Either way, these ndings also point to the importance of choosing the appropriate Li/Ni ratio when tailoring the size of the particles, in particular in two-steps synthesis aiming at preparing single crystalline cathode materials. 45,46n order to probe changes to the local environment, ex situ 7 Li MAS NMR spectra of the Li 1−z Ni 1+z O 2 sample series were measured and are displayed in Fig. 8a and b.For ideal LiNiO 2 , there is only one Li + local environment, i.e.Li + is surrounded by 12 Ni 3+ (3d 7 , S = 1/2) within the two neighbouring NiO 2 − layers.
Six of them are linked to Li + via 90°oxygen bonds and the other six via 180°oxygen bonds. 47In off-stoichiometric Li Aside from the main peaks, some other, minor bands can be observed in the NMR spectra.There is also a small, broad peak observed at 450 ppm, which carries 5.6%, 3.0%, and 2.5% of the intensity of the main peak for z = −0.05,−0.01, and 0.01, respectively, before completely diminishing.There are two common, yet opposing explanations found in the literature regarding its origin.A recent study argues that Li + in the Ni layer close to Ni 4+ (3d 6 , S = 0) would produce such a shi. 23The most extreme cases were described for a system Li ordered structure with a high amount of Li + in the Ni layer, the signal could originate from a small amount of a solid solution of LiNiO 2 -Li 2 NiO 3−d with #2% Li + excess on the local scale, which would be below the resolution limit of our diffraction study.This hypothesis is further strengthened by the fact that the NMR data from LiNiO 2 prepared by low temperature ion exchange from well-ordered NaNiO 2 (no Li + in the Ni layer) does not show a peak at 450 ppm. 21The second explanation for the 450 ppm peak commonly encountered in the literature assumes the presence of a Ni 1−x Li x O, rock salt type phase with a large amount of Ni 2+ . 50If present, the prominent cubic phase reection 200 would be expected at 2q z 23.0°(e.g.Ni 0.8 Li 0.2 O) 39 at the wavelengths utilized in this study (l = 0.825888 Å).However, as no peaks are observed in that region, we exclude the presence of a rock salt type phase.The last remaining, sharp and narrow peak at 0 ppm originates from diamagnetic impurities such as LiOH, which were also found via X-ray and neutron diffraction in this and others studies. 51verall, there are three regimes which give rise to different observations via NMR: the highly off-stoichiometric Li 1−z Ni 1+z -O 2 regime (I) from z = 0.35 to 0.25, where 90°Ni-O-Li bonds dominate the signal and lead to a decreasing peak position as well as strongly increasing line width of the main NMR signal with increasing z.In the slightly off-stoichiometric Li 1−z Ni 1+z O 2 regime (II) with z reaching from 0.2 to 0.05, Li + ions within LNO are surrounded by an increasingly uniform environment with decreasing z.There, 180°Ni-O-Li bonds dominate and lead to a decrease in the peak position and a sharpening of the FWHM with lower off-stoichiometry.In the nearly stoichiometric regime (III) from z = 0.01 to −0.05, peak intensity and FWHM are at their maximum and minimum, respectively, as the environment of the Li + ions is the most homogeneous.In addition, a secondary peak arises which increases in intensity with increasing Li content.
3][54][55] Nearly stoichiometric Li 1−z Ni 1+z O 2 has been described as a glassy antiferromagnet, which features ferromagnetic intralayer coupling and weakly antiferromagnetic coupling between different NiO 2 − layers. 56With increasing offstoichiometry, Ni 2+ resides on the Li site, leading to local magnetic coupling between neighboring layers via small ferrimagnetic clusters.In order to characterise our samples, we measure the cusp in the magnetic susceptibility vs. T curve as a proximate to the magnetic ordering transition and the lowtemperature magnetization as a function of an applied magnetic eld.The magnetic transition temperature measured under zero eld cooled conditions changes with composition, ranging from 10 to 247 K in our data, very similar to the data of Barton et al. as displayed in Fig. 9. 53 In a simplied picture, it was assumed that increasing the amount of Ni Li beyond a critical threshold leads to the formation of ferrimagnetic clusters. 52rior studies hypothesized that long-range antiferromagnetic ordering in a composition of the

Conclusion
Our study maps the rhombohedral phase space of the Li-ion battery cathode active material Li 1−z Ni 1+z O 2 with −0.05 # z # 0.35 and reports the correlation of stoichiometry, observed crystal defects, particle growth and magnetic properties.The increase in crystallite size strongly correlates with an increasing LiOH : Ni(OH) 2 ratio once the off-stoichiometry parameter z is <0.15, as shown by SEM and SXRD.This suggests the presence of Li Ni defects for z $ 0.15 coincides with an inhibited growth of

Diffraction
Synchrotron XRD data were collected on the BL04-MSPD beamline at the ALBA Synchrotron, Spain. 57,58Powder patterns were collected in Debye-Scherer mode geometry using the onedimensional silicon-based position-sensitive detector MYTHEN, enabling fast data acquisition with excellent statistics and high angular resolution.Data were collected in the angular range 0.4°< 2q < 57°(Q range 0.0708-9.671Å −1 ) at a wavelength of l = 0.825888(3) Å.The wavelength was determined using a NIST Si 640c SRM.The instrumental contribution to the peak broadening was determined by measuring a crystalline Na 2 Ca 3 Al 2 F 14 :CaF 2 (NAC) sample as a line broadening reference in a 0.5 mm diameter borosilicate capillary and modelled via Thompson-Cox-Hastings pseudo-Voigt functions.An overall acquisition time of 5 minutes was used to measure each sample, which were packed in 0.5 mm diameter borosilicate glass capillaries.Neutron diffraction (ND) data were acquired on the D2B high-resolution powder diffractometer of the Institute Laue-Langevin (Grenoble, France), at a wavelength of 1.594 Å, calibrated with a Na 2 Ca 3 Al 2 F 14 reference. 59Samples were loaded into cylindrical vanadium cans of diameter 10 mm and data were collected in the 10°< 2q < 160°angular range.Rietveld renement was performed using Topas v6 (Bruker AXS).Combined renements against the X-ray and neutron data were performed for samples with z = −0.05,−0.01, 0.01, 0.05, 0.1 and 0.2, the remaining samples were investigated using synchrotron X-ray data only.The measured intensities of X-ray and neutron data were weighted according to their experimental uncertainties with 1/s(Y obs ). 2 The background was tted to the data using a Chebyshev polynomial function with 11 terms for X-ray and 7 terms for neutron data.During combined renements, the lattice parameters, size broadening and microstrain contributions were rened vs. X-ray data, while the unit cell content (atomic coordinates, SOFs and ADPs) were rened vs. X-ray and neutron data.For renements, scale factor, zero shi, crystallite size and anisotropic strain broadening parameters based on the Stephens model 60 were allowed to vary.In the structural model, the unit cell parameters, the oxygen z coordinate, site occupancy factors (SOFs) and the isotropic atomic displacement parameters B iso for each site were rened.Two site occupancy defects, Ni occupancy on the Li site and antisite defects were rened.Atoms occupying the same site were constrained to have the same B iso , and SOFs were constrained such that each site remained fully occupied.Previous studies have shown that systematic errors in renement of XRD data from layered cathode materials can be corrected by choosing specic form factors 34 or representing them as linear combinations of a charged and uncharged state. 35In our renements, we chose the form factors of Li + , Ni 2+ and O 2− in order to represent the electron density in the unit cell.
Peak shapes were modelled in a double Voigt approach including Gaussian and Lorentzian contributions.The width of the peaks in the synchrotron data evolving with 2q as cos(q) −1 were interpreted as crystallite size broadening.Crystallite size is reported as the volume-weighted average column height (D vol ) calculated via 1/integral breadth (Gaussian & Lorentzian contribution). 41Broadening contributions with Voigt components that follow a tan(q) evolution were interpreted as microstrain and analyzed via the phenomenological model described by Stephens. 60The model allows the description of anisotropic strain parameters S hkl , which are symmetry restricted and related to the variance of the spacing of lattice planes along certain hkl directions.Thus, a higher number of local defects on certain hkl lattice planes increases S hkl .Both crystallite size and microstrain broadening contributions were determined from the X-ray data during initial LeBail ts, xed and re-rened towards the end of the renement process.Critical parameters affecting the intensity apart from the choice of the structure factor are the oxygen z-coordinate (z O ), occupancy of excess Ni 2+ on the Li site Ni Li , antisite defect concentration as well as the isotropic atomic displacement parameters B iso and were rened in this order from X-ray and neutron data, where neutron data was available.Antisite defects are dened as an exchange of a pair of Li and Ni ions from their respective layers into the other layer. 24The average antisite defect occupancy was modelled by a free, parallel renement of defect occupancies of Li + on the Ni site (Li Ni ) and Ni 2+ on the Li site (Ni Li ) and evaluated by the reduction in R wp and the comparison of the overall composition to values measured in elemental analysis.

Elemental analysis
The Li, Ni, and O content of the samples was determined via inductively coupled plasma-optical emission spectroscopy (ICP-OES) using a Thermo Fischer Scientic iCAP 7600 DUO.The mass fraction was determined from three independent measurements.About 10 mg of the samples was dissolved in 6 mL of hydrochloric acid and 2 mL of nitric acid at 353 K for 4 h in a graphite oven.The digestions were diluted, and analysis of the elements was accomplished with four different calibration solutions and an internal standard (Sc).The range of the calibration solutions did not exceed a decade.Two or three wavelengths of elements were used for calculation.The O content was analyzed by carrier gas hot extraction (CGHE) using a commercial oxygen/nitrogen analyser TC600 (LECO).The O concentration was calibrated with the certied standard KED 1025, a steel powder from ALPHA.The standards and samples were weighed with a mass in the range from 1-2 mg together with 5 mg of graphite in Sn crucibles (9-10 mm) and wrapped.Together with a Sn pellet, the wrapped samples were put into a Ni crucible and loaded in an outgassed (6300 W) doublegraphite crucible.The measurements took place at 5800 W. The evolving gases, CO 2 and CO, were swept out by He as inert carrier gas and measured by infrared detectors.
Nuclear magnetic resonance 7 Li magic-angle spinning (MAS) NMR experiments were conducted on a Bruker Avance 200 MHz spectrometer at a magnetic eld of 4.7 T. Spectra were acquired at a Larmor frequency of 77.8 MHz with 1.3 mm rotors and spinning at 55 kHz.A rotorsynchronized Hahn-echo pulse sequence (90°-s-180°-s-acquisition) was used with a 90°pulse length of 0.85 ms and a recycle delay of 1 s.The 7 Li NMR shis were referenced using an aqueous 1 M LiCl solution (0 ppm).All spectra were normalized with respect to sample mass and the number of scans.

Electron microscopy
The morphology of the samples was investigated utilizing a Merlin thermal eld emission scanning electron microscope (FESEM, Carl Zeiss).Prior to the measurements, samples were glued onto conductive carbon pads and coated with an approximately 5 nm layer of Au 0.8 Pd 0.2 using an EM ACE 600 coater (Leica).Images were segmented using the trainable WEKA segmentation algorithm in order to count the number of particles and measure their areas using Image2 (Fiji). 61,62Each segmentation was visually crosschecked in order to avoid counting artefacts.In this manner, at least three secondary particles and approximately 380 to 530 individual primary particles were characterized for good counting statistics.Pixelcount areas were transformed into physical units via magnication based calibration factors from the image metadata.Only particles of an area of at least 500 nm 2 and a circularity (dened as 4pA/[perimeter] 2 ) of $0.5 were used for counting statistics, similarly to a procedure described in the literature. 20The areas A of the particles with a circularity $0.5 were transformed into an equivalent diameter D eq of a circle of the same area using the formula D eq ¼ 2 ffiffiffiffiffiffiffiffi ffi A=p p .X-ray absorption spectroscopy X-ray absorption spectroscopy (XAS) was performed at the XAS beamline of the KIT synchrotron in transmission mode with the IC Spec ionisation chamber.The measurements were undertaken inside a vacuum chamber to avoid contact with air/ moisture and to maximize the signal-to-noise ratio.The samples were transferred with a sample transfer system.The position of the absorption edge was determined via the maximum in the rst derivative.

Fig. 1
Fig. 1 (a) Illustration of the LiNiO 2 crystal structure projected along the [001] vector.The illustration highlights the types of defects which may be present in the structure.S and I represent the height of the slab and interlayer distances, respectively.(b) Ternary pseudo-phase diagram of NiO-NiO 2 -Li 2 NiO 2 , as a snippet from the general Ni-O-Li phase space including formal Ni oxidation state; white dots indicate the layered Li 1−z -Ni 1+z O 2 compositions synthesised in this study.

Fig. 2
Fig. 2 Violin plot of the samples' primary particles size distribution as obtained via SEM.

Fig. 3
Fig. 3 Stacked plots of (a) SXRD patterns and (b) ND patterns collected from the as-synthesised materials.Example of simultaneous Rietveld refinements of LNO with z = 0.01 to (c) SXRD and (d) ND data.
6a.In combination with the evolution of the lattice parameters, the change of z O affects the commonly used derived descriptors of the NiO 2 − layer height (S) and interlayer height (I), which are visualized in Fig. 1a, the bond distances d(Li-O) and d(Ni-O) as well as the volumes of the LiO 6 and NiO 6 polyhedra.The height of the NiO 2 − layer is dened as S = (2/3 − 2z O )c and decreases by about 0.1 Å from 2.22 Å for the sample Li 0.65 Ni 1.35 O 2 (z = 0.35) to 2.12 Å in nearly stoichiometric LNO (z = −0.05).For the same sample range, the interlayer space I = (c/3 − S) accordingly increases from 2.54 to 2.62 Å.The descriptor S is highly correlated to the bond distance d(Ni-O) and the polyhedral volume

Fig. 4
Fig. 4 Refined structural parameters of the off-stoichiometric LNO series with (a) a and c lattice parameters (empty and full symbols, respectively), (b) c/a ratio versus the refined Ni excess and (c) unit cell volume vs. z and refined Ni excess.If error bars not visible, they are smaller than the data symbol.

Fig. 6
Fig. 6 Refined structural parameters as a function of nominal z: (a) refined fractional atomic coordinate z of the oxygen site, (b) volume of LiO 6 and NiO 6 polyhedron and (c) height of interlayer space and NiO 2 −

Fig. 5 Fig. 7
Fig. 5 (a) Crystallite size D vol in dependence of the off-stoichiometry parameter z, with the dashed line indicating a change in the defect regime as shown in Fig. 7a.(b) Comparison of the crystallite size D vol from PXRD vs. the mean equivalent diameter D eq previously determined by SEM and (c) the S 400 and S 004 microstrain parameters from the Stephens model vs. z.If error bars not visible, they are smaller than the data symbol.
1−z Ni 1+z O 2 , Ni 2+ also resides on the Li site, leading to potentially more than 12 Ni surrounding a Li + ion and an increased number of 90°Ni-O-Li bonds.Changing the oxidation state from Ni 3+ to Ni 2+ (3d 8 , S = 1; increasing z) creates different, statistically distributed local environments, which leads to Ni-O-Li bond angle dependent peak shi and broadening of the signal.The hyperne shis and thus peak position are sensitive to the Ni-O-Li bond angle and Ni oxidation state.The values for the shi contributions were determined for the model compound LiNi 0.02 Co 0.96 Mn 0.02 O 2 with highly diluted Ni and Mn ions by Zeng et al. 48and are useful to explain trends in Ni-rich NCM compositions, as observed by Märker et al. for LiNi 0.8 Co 0.1 -Mn 0.1 O 2 . 49When one Ni 3+ at 180°Ni-O-Li bond (+110 ppm) is replaced by one Ni 2+ (+170 ppm), the original signal will move to higher ppm positions by 60 ppm.In the 90°Ni-O-Li bond, reducing Ni 3+ (−15 ppm) to Ni 2+ (−30 ppm) only provides a minor contribution of −15 ppm to the peak shis.In our sample series, corresponding shis in the peak positions can be observed.From −0.05 # z # 0.20, the peaks shi towards higher ppm values, as 180°Ni-O-Li bonds dominate.As more and more Ni 2+ resides in the Li + layer, Li + should be inuenced by Ni-O-Li 90°bonds with increasing Ni Li .This hypothesis could explain the strong decrease in the ppm values for samples in the range of 0.25 # z # 0.35.In addition to changes in the peak position, there is a correlation of the peaks' FWHM and the stoichiometry of the samples.Different ratios of Ni : Li on the local scale give rise to various possible environments.The FWHM is expected to be narrow for a uniform environment, which in the present case is a single Li + ion surrounded by 12 Ni 3+ .Once samples are less stoichiometric (increasing z), there is a statistical distribution of signals arising from Li + ions from the various sites and environments.With an increasing z, the distribution becomes broader, leading to a massive increase in FWHM.This is what we observe in our samples, where the broadest peaks observed for 0.25 # z # 0.35 cover the range of approximately 2000 to −1000 ppm.
Fig.8(a)7 Li MAS NMR spectra of Li 1−z Ni 1+z O 2 (−0.05 # z # 0.35) sample series with an inset showing the evolution of the NMR shift vs. z nominal .The intensities are normalized with respect to the sample mass and the number of scans.(b) Enhanced view of the spectra of Li 1−z Ni 1+z O 2 for 0.1 # z # 0.35.
[Li x Ni 1−x ] Li [Ni] Ni O 2 type is superseded by short-range, strongly ferrimagnetic behavior in disordered [Li x/2 Ni (1−x)/2 ] Li [Li x/2 Ni (1−x)/2 ] Ni O 2 at 0.1 # z # 0.15 (ref.53) based on the change in the remanent magnetization M R .We investigated the low-temperature magnetization behavior at 2 K between −7 T # m 0 H # 7 T and observe hysteresis loops, indicating the behavior suggested by Barton et al.The resulting data are presented as an inset in Fig. 9, with the raw data hysteresis loops displayed in the ESI Fig. S4 and S5.† In our samples, a similar correlation between composition, remanent magnetization and magnetic transition temperature has been observed.The high angular resolution X-ray and neutron diffraction data indicates that the bulk presence of Ni Li as well as antisite defects $2% coincides with the transition to a strongly ferrimagnetic coupled material as postulated by B. T. Barton et al. 53 The stoichiometry dependent peak in the remanent magnetization also matches the maximum of the predicted magnetization per ion found by J. B. Goodenough et al. at x z 0.43 for Li x Ni 1−2x 2+ Ni x 3+ O (z z 0.14 in Li 0.86 Ni 1.14 O 2 ). 55Thus, our diffraction results hint at a possible mechanistic explanation and map the border for the transition of the bulk structure: the ordered regime exists until z $ 0.15 (x # (1 − z)/2 z 0.425).Aerwards, the Li incorporates into the Ni layer, which possibly separates the ferrimagnetic clusters.The presented data points towards a possible starting point of future studies for enhancing the understanding of Li 1−z Ni 1+z O 2 fundamental magnetic properties.

Fig. 9
Fig.9Evolution of the magnetic ordering temperature determined from the maxima in ZFC curves and data from P. T. Barton et al.,53 including the remanent magnetization M R vs. composition as an inset.
DC magnetometry was measured using a Physical Property Measurement System (PPMS) DynaCool from Quantum Design equipped with a vibrating sample magnetometry (VSM) option.LNO powder was lled into polypropylene sample capsules (Quantum Design QDS-4096-388) in an Ar-lled glove box and transferred to the device.Zero-eld cooled (ZFC) and eldcooled (FC) magnetization vs. temperature was measured at a magnetic eld of 500 Oe from 2 to 390 K in temperature settle mode from 2 to 25 K and in sweep mode with 2 K min −1 from 25 to 390 K.The signal was averaged over 10 seconds for each measurement.Magnetization vs. eld scans with maximum eld of m 0 H = ±7 T were measured at 2 K by rst cooling the sample to 2 K in zero eld before measuring a full loop (4 quadrants) starting at 7 T.For samples with z = −0.05 and −0.01, which included small amounts of diamagnetic impurity phases, only the LNO phase has been considered for data evaluation.Diamagnetic corrections were applied to all data, with −7.71 × 10 −9 emu Oe −1 for the sample capsule and values for the atomic electronic closed shells by the incremental method as described by Lueken.63 1.08 O 2 h (Li 0.74 Ni 0.26 ) 3a [Ni 0.82 Li 0.18 ] 3b O 2 single crystals prepared at 900 °C.
1−z -Ni 1+z O 2 samples with a nominal stoichiometry in the range of −0.05 # z # 0.35 were prepared via solid-state synthesis from commercially relevant hydroxide precursors LiOH$H 2 O and Ni(OH) 2 , see white dots in the ternary pseudo-phase diagram in Fig.
NiO 6 , while I shows a weaker correlation to d(Li-O) and the polyhedral volume LiO 6 , as can be seen in Fig.6b, cand Table 2.In general, the LiO 6 polyhedral volume and Li-O distance barely change, while the NiO 6 polyhedral volume and Ni-O distance strongly decrease, with d(Ni-O) starting at values close to NiO (d z 2.09 Å (ref.43)) and converging towards 1.97 Å with decreasing off-stoichiometry z due to the increasing average Ni oxidation state in nearly stoichiometric LNO.The trend in Ni oxidation state was detected via X-ray absorption spectroscopy on the Ni K edge (Fig. S4 †), showing a successive oxidation of Ni with decreasing z in Li 1−z Ni 1+z O 2 .

Table 1
Refined structural parameters of the off-stoichiometric LNO samples

Table 2
Calculated bond lengths, polyhedral volumes, refined site occupancy factors (SOF) and atomic displacement parameters (B iso ) of the off-stoichiometric LNO samples