Insight into Lithium Transport in Lithium Nitridometallate Battery Materials from Muon Spin Relaxation

Muon spin relaxation and powder neutron diffraction have been combined to study three lithium cobalt nitride battery materials. Neutron diffraction shows that these retain the P6/mmm space group of Li3N with Co located only on Li(1) sites. The lattice parameters vary smoothly with the degree of metal substitution, such that the [Li2N] layers expand while the layer separation contracts, as observed previously for similar series of Cuand Ni-substituted materials. However, in contrast to the latter, the Li3-x-yCoxN phases exhibit Curie-Weiss paramagnetism and this prevents the use of nuclear magnetic resonance to measure Li+ transport parameters. Therefore, muon spin relaxation has been employed here as an alternative technique to obtain quantitative information about Li+ diffusion. Muon spin relaxation shows that Li+ diffusion in Li3-xyCoxN is anisotropic with transport confined to the [Li2N] plane at low temperature and exchange between Li(1) and Li(2) sites dominant at high temperature. By a comparison with previous studies some general trends have been established across a range of Cu-, Niand Co-substituted materials. For intra-layer diffusion Ea decreases as metal substitution increases and the corresponding expansion of the layers results in a more open pathway for Li+ diffusion. However, an optimal value of x is found with a ≈ 3.69 Å after which the concomitant contraction in layer spacing reduces the polarizability of the lattice framework.


Introduction
The materials used to manufacture electrodes for lithium batteries usually contain paramagnetic transition metal centres which provide the redox mechanism associated with lithium insertion and extraction.
3][4] In µSR experiments 100% spin polarized muons are implanted into materials where they thermalize, allowing the measurement of local magnetic fields.The radioactive decay of the muons results in the emission of positrons along the spin polarization direction which are detected by a set of scintillators arranged around the sample.Hence, the histogram of the muon decay asymmetry measured in this way gives the evolution of the muon spin polarization.The spin polarization precesses in a transverse magnetic field (TF experiment geometry), and the precession spectrum is determined by the applied field and the local fields due to magnetic moments in the sample.In zero field (ZF geometry), on average only two-thirds of local fields in a powdered sample are perpendicular to the initial muon spin polarization.For a Gaussian distribution of local fields, this situation is described by the Kubo-Toyabe depolarization function. 5A longitudinal magnetic field can be applied parallel to the muon spin polarization (LF geometry) with sufficient strength to quench the interaction of the muon with local fields due to nuclear moments.This allows the electronic contribution to the muon spin relaxation to be separated for paramagnetic materials, so that Li + ion transport can be studied.In the first application of µSR to battery materials Kaiser et al. 2 detected the onset of Li + mobility in the "charged" (x = 0.2) and "empty" (x = 1.0) states of lithium manganese oxide Lix[Li0.04Mn1.96]O4for which Li substitution onto the Mn site results in improved cycling performance.More recently, both Sugiyama et al. 3 and Powell et al. 4 have used µSR for the first time to quantify Li + diffusion coefficients and activation energies, the former in lithium cobalt oxide LixCoO2 with x = 0.53 and 0.73 and the latter in Ni-substituted lithium nitride materials Li3-x-yNixN with x = 0.36 and 0.57.
In this paper we report a combined powder neutron diffraction (PND) and zero-field (ZF) µSR study on three paramagnetic lithium cobalt nitride materials with x between 0.2 and 0.6.Li2.6Co0.4Nhas been suggested as an improved anode material, 6,7 in particular because of its high capacity which can exceed 700 mA h g -1 .More recently, single crystals and bulk powders of similar ternary lithium nitridometallate phases Li3-x-yMxN (where M = Cu, Ni or Co and y represents a lithium vacancy) have been synthesized with controlled and reproducible vacancy and substitution levels. 8,9X-ray and neutron diffraction studies 10 of these materials indicate defect structures which retain the P6/mmm space group of Li3N 11 (Figure 1) with M located only on Li(1) sites and disordered Li(2) vacancies in the [Li2N] plane.The vacancy concentrations are significantly higher than in Li3N with implications for the redox chemistry and Li + conductivity which determine their use as anode materials.
Variable temperature measurements of the 7 Li NMR linewidth have illuminated some aspects of the Li + diffusion dynamics, particularly for diamagnetic Cu-substituted phases. 12However, for paramagnetic Li3-x-yCoxN, the 7 Li NMR linewidth varies with temperature (Figure S1 Supplementary Information) according to a Curie-Weiss law, indicating that any effect of dynamics is obscured by interactions with the Co electronic moments.As described above this problem can be completely circumvented by the use of µSR, since the electronic contribution to the muon spin relaxation can be measured independently via complementary LF experiments.This allows the effects of Li + dynamics on the muon depolarization to be resolved, and otherwise unobtainable diffusion coefficients and activation energies to be measured.In this paper we describe a combined µSR and neutron diffraction study of two Li3-x-yCoxN phases with the aim of understanding the links between their structure, stoichiometry and transport properties.In addition, we compare diffusion coefficients and activation energies measured by both µSR and NMR for a series of nitridometallate Li3-x-yMxN (M = Cu, Ni, Co) materials previously characterized by neutron diffraction.This allows us to draw some general conclusions about trends in these parameters with metal substitution and vacancy concentration.

Experimental
Synthesis.Li3N was prepared as described elsewhere 13 by reaction of molten lithium-sodium alloy with dry nitrogen at 720 K for 4 days.Subsequently, excess sodium was removed by vacuum distillation at 670 -720 K for 24 hr.The product was identified as single-phase α-Li3N using powder X-ray diffraction.Li3-x-yCoxN phases with nominal x = 0.2, 0.4 and 0.6 (denoted 1 -3, respectively) were synthesized by heating a stoichiometric mixture of Li3N and cobalt powder (Goodfellows, 99.8%, 1.6 µm particle size).These were ground and pressed into a pellet which was loaded into an alumina crucible, sealed in a stainless steel reaction vessel and heated at 960 K for 6 days.Syntheses generally required repeated regrinding of the reaction mixture.All synthetic work and sample preparation was carried out in a nitrogen-filled glove box (Saffron Scientific recirculating glovebox; O2 < 1 ppm, H2O < 5 ppm).
X-ray and Neutron Diffraction.Powder X-ray diffraction (PXD) data for 1 -3 were collected at ambient temperature on a Philips XPERT θ -2θ diffractometer using Cu Kα radiation.The air-and moisture-sensitive products were sealed in custom-designed sample holders during data collection. 14Phase purity was evaluated by taking 2 hr scans over the range 5° -100° 2θ.These were cross-referenced to the ICDD PDF database via the Philips PC-IDENTIFY routine and to powder patterns generated from the Inorganic Crystal Structure Database (ICSD) using PowderCell 3. 15 Scan times of 12 hr were used to obtain data suitable for Rietveld refinements which were carried out using the General Structure Analysis System (GSAS) 16 via the EXPGUI interface. 17Initial structural models were based on α-Li3N with the inter-layer Li(1) site partially substituted by Co and fractional occupancies estimated from the nominal compositions.Lattice parameters for model structures were obtained by indexing the powder patterns using DICVOL91 18 .Time-of-flight PND data for 1 -3 were collected at 250 K using the high-intensity diffractometer POLARIS at the ISIS neutron facility in the Rutherford Appleton Laboratory.Powder samples ca.1.5 -2 g each were sealed into thin-walled vanadium cans with indium gaskets.Data were collected using three fixed detector banks at <2θ> = 35º, 90º and 145º.Rietveld refinements were performed using the structures obtained from PXD as a starting point, according to procedures outlined for Ni-substituted Li3N phases in Ref. 13 Data from all three detector banks was refined simultaneously.Note that the vanadium sample can yielded a group of reflections that were excluded from the refinements, but the excluded regions did not contain reflections arising from the compounds under study.
Magnetic Susceptibility.Magnetic susceptibility measurements were performed on a Quantum Design MPMS XL 5T SQUID magnetometer in the temperature range 2 -250 K at an applied magnetic field of 100 mT.The samples were loaded into airtight gelatine capsules.The data were corrected for the diamagnetic contributions from the gelatine containers.

Muon Spin Relaxation. The MUSR instrument at the ISIS pulsed muon facility in the Rutherford Appleton
Laboratory was used to make µSR measurements.On the MUSR instrument there are 64 positron scintillation detectors in two circular arrays, and data acquisition occurs via 64 TDCs, recording about 2.5 x 10 7 events per hour.Helmholtz coils are used to apply magnetic fields up to 250 mT in transverse or longitudinal experiment geometry and to compensate for the earth's magnetic field in zero field.A closed cycle helium refrigerator was used to regulate the sample temperature between 15 K and 340 K, while a furnace was used to obtain higher temperatures.The µSR experiments were carried out on samples 2 and 3 at temperatures between 20 K and 540 K. Approximately 2 g of each was packed in a nitrogen-filled glove box into airtight titanium sample holders with titanium foil windows.Transverse field (TF) measurements used a field of 2.4 mT and typically 5 x 10 6 events were recorded for each temperature studied.These were used to calibrate a correction factor α which accounts for the relative efficiency of the forwards and backwards groups of scintillation detectors.In contrast zero field (ZF) experiments required at least 1 x 10 7 events for sufficient signal.Longitudinal field (LF) measurements with fields up to 100 mT were also recorded at each temperature and used to quantify the paramagnetic contribution to muon relaxation.Data analysis was carried out using the WiMDA programme. 19

Results and Discussion
Crystal Structure.PXD data for 1 -3 yielded powder patterns (Figure S2 Supplementary Information) showing single-phase samples which were successfully indexed in the α-Li3N space group P6/mmm.No reflections for Co metal were observed for samples with x ≤ 0.7 which is the highest substitution level reported to date for the Li3-x-yCoxN series.Critical factors for obtaining high x were found to be the use of Co metal powders with particle sizes ≤ 2 µm and high reaction temperature (950 -970 K).Use of larger particle sizes limited the substitution level to x ≈ 0.5 in line with previous reports, 20,21 while reaction temperatures below 920 K produced samples with Co metal impurities.This is in contrast to the Li3-x-yNixN materials which are easily obtained as single phases across a much wider temperature range, from 820 K to 990 K. 13,22 While PXD gave an initial model, fine tuning the structure requires neutron diffraction in order to precisely locate the light Li atoms, to accurately quantify vacancy concentrations and to obtain improved thermal displacement parameters.PND refinements using lattice parameters from PXD confirmed the retention of the Li3N structure with Co occupying the inter-layer Li(1) site only.Profile plots for Rietveld refinement against PND data for a representative sample (Li3-x-yCoxN with x = 0.58, 3) are shown in the Supplementary Information (Figure S3).The resulting crystallographic parameters at 250 K are given in Table 1, and calculated inter-atomic distances and bond angles are in Table 2. Refined atomic parameters are in the Supplementary Information (Table S1).The lattice parameters vary smoothly with x in common with Cuand Ni-substituted materials, as shown in Figure 2 where results from this work have been combined with those of our previous PND studies. 10,12,13In all cases the a parameter, which depends on the Li(2) -N distance, increases with the degree of substitution, while the c parameter, which corresponds to the interlayer separation, contracts.Magnetic Susceptibility.The temperature variation for the magnetic susceptibility of all the Li3-x-yCoxN materials 1 -3 (see Supplementary Information Figure S4) follows a modified Curie-Weiss law χ = χ0 + C/(T θ) where χ0 is a temperature-independent contribution, and C and θ are the Curie and Weiss constants, respectively.Values for these, along with the effective magnetic moment µeff per Co atom, are given in Table 3.Both C and µeff depend strongly on composition, and the large values at low x are not consistent with the existence of exclusively Co(I) species with spin-only contributions (S = 1, µeff = 2.83 µB).Although an orbital contribution to the moment has been suggested, 23 the presence of higher oxidation states Co(II) or Co(III) is also possible, and this picture is supported by the significant vacancy concentration at the Li(2) site evident in the refined structural data.Note that electron energy loss spectroscopy studies of Li2.6-yCo0.4N also reveal multiple spin states for Co. 24 The magnetic properties of the Li3-x-yCoxN series contrast with those reported previously 13 for the corresponding Ni-substituted materials which show a temperature-independent χ with where Δ is the depolarization rate which is related to the second moment of the Gaussian local field distribution.However, the ZF signal in Figure 3 (open circles) never fully recovers to the value of 1/3 predicted by Eq. ( 1), so the depolarization function was modified to take account of muon dynamics which can be included by assuming a Markovian strong collision model. 5The dynamic Kubo-Toyabe function which depends on the muon hopping rate ν cannot be obtained in closed form and must be generated during fitting by a numerical inverse Laplace transform. 19The dynamic Kubo-Toyabe behaviour observed in ZF (open circles) is damped by an exponential decay in muon polarization which, as in the TF case, arises from fluctuating Co electronic moments.With a LF (filled circles) the interaction between the muon and local fields due to nuclear moments is quenched and this paramagnetic process is the only contribution to relaxation.For both materials studied a LF of 10 mT was found to be sufficient to quench the nuclear moments, and further increases did not alter the decay of the muon polarization, even at the lowest temperature studied.The time constant for paramagnetic relaxation λ was obtained by a straightforward fit of the LF µSR signal to an exponential function.Its temperature variation is shown in Figure 4 for samples 2 with x = 0.43 (red circles) and 3 with x = 0.58 (blue squares) and qualitatively follows a Curie-Weiss law as expected from magnetic susceptibility measurements (Table 3).The depolarization rate and the muon hopping rate were extracted at each temperature from the ZF µSR signal by fitting to a dynamic Kubo-Toyabe function damped by a fixed λ taken from the corresponding LF experiment.The baseline asymmetry was used as a third fitting parameter.Values of Δ extracted from the µSR data in this way are plotted in Figure 5 for 2 with x = 0.43 (red circles) and 3 with x = 0.58 (blue squares) for temperatures above 66 K.The depolarization rate is approximately constant for both materials below 190 K with Δ = 0.53 ± 0.02 µs -1 and 0.54 ± 0.02 µs -1 , respectively.The lowtemperature values for Li3-x-yCoxN are significantly higher than those for Ni-substituted materials, 4 as expected because of the replacement of 58,60 Ni with I = 0 by 59 Co with I = 7/2.Above 200 K there is a rapid fall to less than 20 % of the low-temperature Δ.The muon hopping rate ν obtained from the dynamic Kubo-Toyabe fits is plotted for temperatures above 190 K in Figure 6 for 2 with x = 0.43 (red circles) and 3 with x = 0.58.The muon hopping rate does not vary significantly with temperature in this range with ν = 0.46 ± 0.02 and 0.51 ± 0.02 µs for 2 and 3, respectively.This implies that above 190 K the muon is quasi-static with a temperature-independent mean residence time 1/ν longer than its half-life.Muon Implantation Sites.The depolarization rate can be calculated for a powder sample by summing over the dipolar interactions between the muon and each nuclear spin in the surrounding crystal lattice.Table 4 shows values of Δ for several possible muon sites calculated using the lattice parameters obtained from neutron diffraction following the procedure described by Powell et al. 12 (see the Supplementary Information for further details).Plausible choices for muon implantation include the Wyckoff 2c site which corresponds to a Li(2) vacancy in the [Li2N] ab plane and the 2d interstitial located directly above the 2c site in the Li(1)/Co plane which is the most open site in the structure.However, the experimental values of Δ for both Co-substituted materials are substantially larger than those calculated in Table 4 for either of these sites.
Significantly better agreement with experiment is obtained if the muon is displaced along the crystallographic c axis away from the 2d interstitial towards a 2c Li(2) site, and muon implantation in this Wyckoff 4h site with a displacement equal to 10% of the c lattice parameter was suggested previously for Li3- x-yNixN. 4 Interestingly, a similar interstitial location has been identified by molecular dynamics simulations 25 as an intermediate Li + site in the exchange between Li(1) and Li(2) required for inter-layer diffusion in the parent Li3N.As the degree of Co substitution increases, the calculated Δ for all sites decreases slightly, as expected, because of the replacement of 7 Li magnetic moments by 59 Co and the expansion of the [Li2N] ab plane.However, the errors on the experimental values of Δ are such that these small variations cannot be detected.Other possibilities for muon sites, such as in a Li(2) vacancy adjacent to a possible NH 2-defect or close to the N 3-ion in the [Li2N] plane, result in calculated Δ values which are much higher than those observed experimentally.
Table 4 also shows depolarization rates calculated with either the Li(2) atoms only or all the Li atoms removed from the structure.The former represent the residual contribution to the muon depolarization in the case that the intra-layer Li + jump rate substantially exceeds the low-temperature limiting value of Δ.The latter also take account of similarly rapid inter-layer Li + diffusion and are significantly higher than their counterparts in Li3-x-yNixN materials with similar x. 4 Once again, this is expected given the replacement of 58,60 Ni with I = 0 by 59 Co with I = 7/2.The calculated depolarization rates suggest that for Co-substituted materials µSR is particularly sensitive to intra-layer diffusion, since Δ decreases to approximately half its low-temperature limit with rapid Li + jumps between Li(2) sites.

Site Wyckoff notation
Co-ordinates 2 x = 0.43 a. corresponds to the residual contribution to depolarization rate when the intra-layer Li + jump rate substantially exceeds the low-temperature limiting value of Δ.
b. corresponds to the residual contribution to depolarization rate when both intra-and inter-layer Li + jump rates substantially exceeds the low-temperature limiting value of Δ.
Lithium Diffusion in Li3-x-yCoxN.The significant decrease in the depolarization rate observed for both samples at temperatures above 190 K does not originate from muon dynamics, since the muon is quasi-static in this regime, as confirmed by the temperature-independent hopping rate.Instead, the reduction in Δ originates from motional narrowing of a contribution to the local field distribution at the muon due to the onset of Li + diffusion within the [Li2N] plane.At 300 K the experimental depolarization rate (Figure 5) is approximately equal to the value calculated (Table 4) with the Li(2) atoms removed from the structure, suggesting that the intra-layer Li + jump rate substantially exceeds the low-temperature limiting value of Δ by this temperature.
Similar motional narrowing for a quasi-static muon in ZF µSR has been attributed previously to Li + diffusion in lithium manganate spinels 2 , as well as for the parent Li3N and Li3-x-yNixN. 4In contrast, Sugiyama et al. 3 found an activated ν, coupled with decrease in Δ for a muon forming a hydrogen-like bond to oxygen in LixCoO2.Only the contribution which arises from dipolar interactions with 6 Li or 7 Li nuclei is narrowed by Li + diffusion.The line narrowing has been modelled in this work by 26 where τc is the mean residence time for diffusing Li + ions and Δ0 is the low-temperature limiting value of Δ.
For intra-layer diffusion Δ0 was taken as the average of all measurements below 190 K.The Li + jump rates 1/τc extracted from Eq. ( 2) in this way are in the MHz regime at room temperature, and the assumption of a simple Arrhenius law allows an activation energy to be obtained from the temperature variation.Arrhenius plots shown in Figure 7 for 2 (open red circles) and 3 (open blue squares) indicate that this model provides a good fit to the data for temperatures from the onset of motional narrowing at 190 K up to about 300 K.The resulting intra-layer Ea and intrinsic jump rates 1/τc,0 (1/τc at T = ∞) are given in Table 5.
Above 300 K the depolarization rate continues to decrease beyond the value calculated for rapid intra-layer Li + diffusion.This implies the onset of inter-layer Li + jumps at a rate sufficient to motionally narrow the residual contribution to Δ arising from dipolar interactions between the muon and Li nuclei on Li(1) sites.
Jump rates for inter-layer diffusion were obtained by setting Δ0 equal to the value calculated with the Li (2)   atoms removed from the structure (Table 4).The corresponding Arrhenius plots for 2 (filled red circles) and 3 (filled blue squares) are also shown in Figure 7, and the resulting inter-layer activation energies and intrinsic jump rates are given in Table 5.The narrow temperature range over which Δ is sensitive to interlayer diffusion and the lack of an experimental value for Δ0 these parameters prevent a more accurate determination.For 1/τc,0 the errors are so significant that only an order of magnitude is given in Table 5, but this is around 10 13 Hz as expected for a lattice vibration.Note that similar high-temperature inter-layer contributions to diffusion were not measured in µSR studies of the Ni-substituted materials 4 , since the maximum temperature in those experiments was only 350 K.
Trends in Diffusion Parameters for Li3-x-yMxN.For intra-layer diffusion the effect of metal substitution on the activation energy revealed by µSR and NMR studies can be rationalized in terms of the structural information obtained from neutron diffraction.As x increases the lattice parameter a in Li3-x-yCoxN increases and the Li -N distance within the [Li2N] planes lengthens, resulting in a more open pathway for Li + diffusion through the expanded layers and a decrease in the intra-layer Ea.However, the accompanying decrease in the lattice parameter c corresponds to an increase in the covalent character of the Li -N bond which in turn reduces the polarizability of the lattice framework and increases the energy barrier.For the two Li3-x-yCoxN materials the activation energy for intra-layer diffusion obtained with µSR increases as the degree of substitution increases, suggesting that the most important effect in this case is the reduction in the c lattice parameter.This situation is similar to that observed for two Ni-substituted materials 4,10 with x > 0.36, but in contrast to that observed for three members of the Li3-x-yCuxN series with x < 0.35. 12Figure 8 shows the variation in the inter-layer Ea with the lattice parameters a and c for Li3-x-yMxN with M = Cu, Ni, Co.The plot suggests that an optimal substitution level exists which minimizes the energy barrier for Li + hopping.
This optimum corresponds to a common value for the a parameter of around 3.69 Å, regardless of M. For this value the beneficial effect of expanding the Li -N distance within the [Li2N] layers still dominates, but any further expansion in a is accompanied by a detrimental contraction in c.In contrast to substitution level, vacancy concentration has little effect on intra-layer diffusion.The Li3-x-yCoxN materials measured here show slightly lower intrinsic jump rates than their Cu-substituted counterparts, 12 despite the vanishing vacancy concentrations of the latter.Note, however, that this is not unexpected in the light of the complex mechanisms for Li + transport in the parent Li3N suggested by molecular dynamics calculations. 25terestingly, while magnetic measurements indicate significant differences in bonding between the layers for different substituent metals, intra-layer diffusion remains essentially unaffected.For inter-layer diffusion Ea for Li3-x-yCoxN with x = 0.43 is comparable to that obtained previously 12 for the members of the Li3-x-yCuxN series.However, there is a significant rise in Ea as the substitution level increases to x = 0.58 which may reflect the increased electronic delocalization associated with inter-layer bonding as revealed by magnetic measurements.

Conclusion
PND shows that the three lithium cobalt nitride materials studied here retain the P6/mmm space group of Li3N with Co located only on Li(1) sites.The lattice parameters a and c vary smoothly with x in a similar fashion to similar series of Cu-and Ni-substituted materials. 12,13In contrast to the latter, the Li3-x-yCoxN phases exhibit Curie-Weiss paramagnetism which precludes the use of NMR to gain atomic-level insight into Li + transport.However, the results described here demonstrate that µSR can be employed as an alternative technique to study these paramagnetic materials, and that quantitative information about Li + diffusion can be obtained.Insight gained from µSR measurements shows that Li + diffusion is anisotropic in a similar fashion to that detected in Li3N and in Li3-xCuxN by NMR 12,26 with transport confined to the [Li2N] plane at low temperature and exchange between Li(1) and Li(2) sites dominant at high temperature.In conjunction with previous NMR, µSR and PND studies 4,12,13 the new data for Li3-x-yCoxN allow some general trends to be established across a range of Li3-x-yMxN materials.For intra-layer diffusion Ea initially decreases with x as the corresponding expansion in a results in a more open pathway for Li + diffusion through the layers.However, an optimal value of x is reached with a ≈ 3.69 Å after which the concomitant contraction in c reduces the polarizability of the lattice framework.By contrast, considering all the Li3-x-yMxN materials together, there appears to be no correlation between intra-layer diffusion and vacancy concentration.

Figure 1 .
Figure 1.(Colour) Crystal structure of α-Li3N. 2 The (blue) polyhedra illustrate the hexagonal bipyramidal co-ordination of the nitrogen atoms (small blue spheres) by lithium atoms (large red spheres) in the P6/mmm structure.Note the [Li2N] layers perpendicular to the crystallographic c axis.Intra-layer Li sites are designated Li(2), inter-layer ones Li(1).

Figure 2 .
Figure 2. (Colour) Lattice parameters a (open symbols) and c (filled symbols) measured by neutron diffraction for Li3-x-yMxN as a function of x for M = Co (blue circles), Ni (green triangles) and Cu (red squares), as well as for Li3N (black stars).Lines are drawn to guide the eye.Additional data was taken from Refs. 10 , 12 and 13 .

Table 3 .
only a small Curie-Weiss contribution below 20 K.This indicates a change from Pauli paramagnetism with substantial electron delocalization to Curie-Weiss behaviour with more isolated transition metal centres on replacement of Ni by Co.For both series, however, µeff decreases as x increases, becoming smaller than the relevant spin-only value at x ≈ 0.5 for Co, suggesting progressive delocalization as the substitution level increases.Sample, composition 1, x = 0.20 2, x = 0.43 3, x = 0.58 χ0 / emu mol -Magnetic susceptibility a of Li3-x-yCoxN materials 1 -3.a.The temperature variation of χ is described in terms of a modified Curie-Weiss law χ = χ0 + C/(Tθ) where the terms are defined in the text.TF µSR Experiments.All TF µSR signals gave an initial positron count asymmetry of approximately 25% and showed a Larmor oscillation at a frequency of 0.33 MHz.This indicates that the muons implant into both samples (2 and 3) as diamagnetic µ + across the whole of the temperature range studied.In addition to a Gaussian envelope due to the local nuclear field distribution, the TF µSR signals decayed exponentially as a result of the fluctuating Co electronic moments.This behaviour has been observed previously for lithium manganate spinels. 2 ZF and LF µSR Experiments.Figure 3 shows µSR signals for the Li3-x-yCoxN material with x = 0.58 (3) recorded at 20 K in ZF (open circles) and 100 G LF (closed circles).As with TF experiments the initial positron asymmetry was approximately 25 % across the whole temperature range, confirming that muons implant as diamagnetic µ + .The total relaxing fraction measured from the ZF µSR signals was only about 50%, since a proportion of the muons are stopped in the sample holder where they do not relax.The static Kubo-Toyabe function 5 is given by

Figure 3 .
Figure 3. (Colour) Typical ZF µSR signal (open circles) obtained from Li3-x-yCoxN materials, in this case sample 3 with x = 0.58 recorded at 20 K. Also LF µSR signals (filled circles) recorded with a longitudinal magnetic field of 10 mT.Error bars increase with time due to the radioactive decay of the muons and have been omitted for clarity.

Figure 4 .
Figure 4. (Colour) Relaxation rate λ extracted from variable-temperature LF µSR measurements carried out as described in the text for Li3-x-yCoxN with x = 0.43 (2, red circles) and 0.58 (3, blue squares).Error bars are within the symbols at temperatures above 150 K.

Figure 5 .
Figure 5. (Colour) Kubo-Toyabe depolarization rate for Li3-x-yCoxN materials with x = 0.43 (2, red circles) and 0.58 (3, blue squares).Note that the error on Δ ranges from ±0.005 to ±0.014 and that the error bars are therefore inside the symbols for all temperatures.

Figure 8 .
Figure 8. (Colour) Activation energy for intra-layer diffusion in Li3-x-yMxN for M = Co (blue circles, this work), Ni (green triangles) 4 and Cu (red squares) 12 as a function of lattice parameters a (top) and c (bottom), as well as for Li3N (black star).

Table 1 .
Crystallographic parameters obtained from Rietveld refinements against powder diffraction data