Muon Spin Relaxation Studies of Lithium Nitridometallate Battery

Oct 27, 2009 - School of Chemistry, University of Nottingham, University Park, Nottingham, NG7 2RD, U.K., ISIS Pulsed Muon Facility, Rutherford Applet...
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J. Phys. Chem. C 2009, 113, 20758–20763

Muon Spin Relaxation Studies of Lithium Nitridometallate Battery Materials: Muon Trapping and Lithium Ion Diffusion Andrew S. Powell,† James S. Lord,‡ Duncan H. Gregory,§ and Jeremy J. Titman*,† School of Chemistry, UniVersity of Nottingham, UniVersity Park, Nottingham, NG7 2RD, U.K., ISIS Pulsed Muon Facility, Rutherford Appleton Laboratory, Chilton, Oxfordshire OX11 0QX, U.K., and WESTChem, Department of Chemistry, UniVersity of Glasgow, Glasgow, G12 8QQ, U.K. ReceiVed: September 22, 2009; ReVised Manuscript ReceiVed: October 15, 2009

Lithium nitride has a unique layered structure and the highest reported Li+ ion conductivity for a crystalline material. The conductivity is highly anisotropic, with an intralayer contribution within the graphitic [Li2N] planes dominant at ambient temperature. In this paper transverse- and zero-field muon spin relaxation (µSR) studies on Li3N and two novel paramagnetic derivatives Li3-x-yNixN with x ) 0.36 and 0.57 are reported. These new materials have potential as anodes in rechargeable lithium batteries. The decrease in the muon depolarization rate observed above 180 K for the three materials is shown to arise from motional narrowing due to intralayer Li+ diffusion. The increase in the measured activation energy with x for Li3-x-yNixN suggests that the reduction in the layer spacing that results at high substitution levels is responsible for raising the energy barrier to Li+ jumps, despite the concomitant expansion of the [Li2N] plane. In addition, the onset of interlayer diffusion appears at lower temperatures in Ni-substituted derivatives than in the parent Li3N. The muons themselves are quasi-static, most probably located in a 4h site between the [Li2N] plane and the Li(1)/ Ni layer. This is similar to the Li+ interstitial position identified by molecular dynamics simulations as an intermediate for an exchange mechanism for interlayer diffusion. Finally, µSR gives no evidence for the formation of the muonium equivalent of the hydrogen defects thought to play an important role in intralayer diffusion in Li3N. These results demonstrate that µSR can be used to obtain diffusion coefficients and activation energies for Li+ transport even in paramagnetic materials where NMR studies are complicated by strong interactions with the electronic moments. Introduction Lithium nitride is a superionic conductor with the highest reported Li+ ion conductivity for a crystalline material.1 Its unique P6/mmm hexagonal layered structure which is shown in Figure 1 contains two Li sites: Li(2) within the graphitic [Li2N] ab planes, and Li(1) between them. Single-crystal measurements have shown that the conductivity is strongly anisotropic with σ ) 1 × 10-3 S cm-1 at 298 K perpendicular and σ ) 1 × 10-5 S cm-1 parallel to the crystallographic c axis, respectively. Low levels (1-2%) of Li(2) vacancies are thought to be responsible for the perpendicular (intralayer) contribution,2 and it was suggested3 that these are generated by the presence of hydrogen as NH2-, giving rise to Li3-xHxN. Variations in the conductivity and its activation energy were shown to be correlated with hydrogen concentration.4 Variabletemperature 7Li nuclear magnetic resonance (NMR) studies of Czochralski-grown single crystals of Li3N gave crucial insight into the diffusion mechanism. Measurements of the linewidths of the first-order quadrupolar satellites5 and of spin-lattice relaxation times confirmed the vacancy-induced perpendicular process and suggested that diffusion parallel to the c axis involves exchange of Li+ ions between the Li(2) and Li(1) sites.6 In addition, comparison of experimentally determined quadru* To whom correspondence should be addressed. E-mail: jeremy.titman@ nottingham.ac.uk. Phone: +44 115 951 3560. Fax: +44 115 951 3562. † University of Nottingham. ‡ Rutherford Appleton Laboratory. § University of Glasgow.

polar coupling constants with calculated values confirmed the ionic nature of the bonding.7 Unfortunately, the low decomposition potential8 of Li3N curtails its use in lithium secondary cells. However, interest in Li3N-based materials has been rekindled by the suggestion that Li2.6Co0.4N could be used as an improved anode material,9 in particular because of its high capacity of some 600 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 manufactured with controlled and reproducible vacancy and

Figure 1. Crystal structure of R-Li3N. The polyhedra illustrate the hexagonal bipyramidal coordination of the nitrogen atoms (blue spheres) by lithium atoms (red spheres) in the P6/mmm structure. Note the [Li2N] layers perpendicular to the crystallographic c axis which is vertical in the figure. Intralayer Li sites are designated Li(2), interlayer ones Li(1).

10.1021/jp9091249 CCC: $40.75  2009 American Chemical Society Published on Web 10/27/2009

µSR Studies of Lithium Nitridometallate Materials substitution levels.10,11 X-ray and neutron diffraction studies of these materials indicate defect structures which retain the Li3N structure of Figure 1 with M located on Li(1) sites and disordered Li(2) vacancies in the [Li2N] plane. The vacancy concentrations are up to 50 times higher12 than in Li3N, suggesting the potential for improved Li+ transport properties. With increasing x the Li-N distance within the [Li2N] planes lengthens, although there is a concomitant reduction in the layer spacing. The former is expected to lead to a more open diffusion pathway and a consequent reduction in the activation energy for intralayer Li+ hopping, while the latter is predicted to have the opposite effect. Variable-temperature 7Li NMR measurements on very weakly paramagnetic Cu-substituted materials have illuminated some aspects of the Li+ diffusion dynamics.13,14 For example, in Li3-x-yCuxN phases with x < 0.36 the intralayer activation energy decreases as the degree of substitution increases, while the onset of interlayer exchange occurs at a significantly lower temperature than in the parent Li3N.15 It is well known that in paramagnetic battery materials, such lithium manganate spinels, the temperature variation of the 7Li NMR line width follows a Curie-Weiss law.16 This precludes detailed NMR investigations of ionic diffusion, since any motional narrowing of the 7Li resonance due to Li+ mobility will be masked by the interaction with the electronic moments. Hence, a comprehensive picture of the effect on Li+ diffusion of increased metal substitution and the associated changes in lattice parameters in the novel Li3-x-yMxN materials is not yet established. In this paper we report muon spin relaxation (µSR) studies on two Ni-substituted defect materials with x ) 0.36 and 0.57, respectively, as well as the parent compound Li3N. In µSR experiments 100% spin polarized muons are implanted into materials where they rapidly thermalize, providing a probe of local magnetic fields. The muon has a half-life of ∼2.2 µs and its radioactive decay results in the parity-violating emission of a positron along the direction of the muon spin polarization. Hence, the µSR signal which consists of a time histogram of the asymmetry in the positron distribution measured by a set of scintillation detectors arranged around the sample gives information about the evolution of the polarization. With a magnetic field oriented transverse to the muon beam direction (TF experiment geometry), the polarization precesses with a Larmor frequency determined by the sum of the applied field and the local field due to magnetic moments in the sample. The µSR signal decays due to the combined effects of the distribution of local fields and of muon dynamics. In zero field (ZF) with a powdered sample on average two-thirds of the muon polarization is perpendicular to the local field and precesses, while the remainder is parallel to the field and does not. With a Gaussian local field distribution this situation is described by the Kubo-Toyabe depolarization function17 which can be modified to take muon dynamics into account.17,18 The TF and ZF µSR experiments reported here show evidence for muon trapping, as well as motional narrowing of the local field distribution due to Li+ dynamics. In addition, a longitudinal magnetic field can be applied parallel to the beam direction (LF experiment geometry) to quench local fields due to nuclear moments in order to obtain a measurement of the electronic contribution to relaxation in paramagnetic systems. This allows diffusion coefficients and activation energies for Li+ transport to be measured, even for paramagnetic materials where the NMR studies are not informative. We note that µSR has been used previously in studies of Li+ diffusion in lithium manganate spinels,19,20 but that diffusion parameters were not measured.

J. Phys. Chem. C, Vol. 113, No. 48, 2009 20759 TABLE 1: Substitution Levels, Vacancy Concentrations, Lattice Parameters, and Magnetic Susceptibility for Li3N and Ni-Substituted Materialsa sample

Li3N (R phase)

Li3-x-yNixN x ) 0.36

Li3-x-yNixN x ) 0.57

x y a/Å c/Å χ0/emu mol-1 C/emu mol-1 K θ/K µeff per Ni/ µB

0 0 3.64551(8) 3.87281(13) 0.00182 -

0.360(1) 0.162(9) 3.70812(5) 3.7036(10) 0.00094(2) 0.075(2) -14.0(7) 1.29

0.565(2) 0.412(11) 3.73350(3) 3.61302(4) 0.00077(2) 0.063(3) -16.9(9) 0.95

a

The magnetic susceptibility is described in terms of the temperature-independent contribution, χ0, the Curie, C, and Weiss, θ, constants and the effective magnetic moment per Ni atom, µeff.

Experimental Section Synthesis. Li3N was prepared 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. Disordered Li3-x-yNixN phases were synthesized by heating a stoichiometric mixture of Li3N and nickel powder. These were ground and pressed into a pellet which was loaded into an aluminum crucible, sealed in a stainless steel reaction vessel and heated at 990-1020 K for 6 days. Note that syntheses generally required repeated regrinding of the reaction mixture and that all synthetic work was carried out in a nitrogen-filled glovebox. Characterization. The structure and magnetic properties of several Ni-substituted materials have been studied previously.21 Relevant parameters are reproduced in Table 1 for Li3-x-yNixN phases with x ) 0.36 and 0.57, along with values22 for the parent Li3N for comparison where appropriate. Muon Spin Relaxation Measurements. 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 with a time resolution between 0.5 and 32 ns, recording about 2.5 × 107 events per hour. Helmholtz coils are used to apply magnetic fields up to 250 mT in TF or LF experiment geometry and to compensate for the earth’s magnetic field in ZF geometry. A closed cycle helium refrigerator was used to regulate the sample temperature between 15 and 340 K and a furnace for higher temperatures. Approximately 2 g of each material under investigation was packed in a nitrogen-filled glovebox into an airtight sample holder with a titanium foil window. At ISIS we carried out µSR experiments on two Li3-x-yNixN samples with x ) 0.36 and 0.57 at temperatures between 12 and 340 K. For the parent Li3N additional measurements were made at higher temperatures to extend the range up to 700 K. TF measurements used a field of 2.4 mT and typically 5 × 106 events were recorded for each temperature studied, while ZF experiments required at least 1 × 107 for sufficient signal. The longitudinal field was scanned between 0 and 40 mT with an increment of 0.2 mT during avoided level crossing experiments on Li3N at selected temperatures. Finally, for the paramagnetic Ni-substituted materials LF measurements with fields up to 100 mT were used to quantify the electronic contribution to muon relaxation. TF µSR signals at each temperature were used to calibrate a correction factor R that accounts for the relative efficiency of the forward and backward groups of scintillation detectors. Data analysis was carried out using the WiMDA program.23

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Figure 2. Relaxation rate λ extracted from variable-temperature TF µSR measurements carried out as described in the text for Li3N (circles) and Li3-x-yNixN with x ) 0.36 (filled triangles) and 0.57 (open triangles). Note that the behavior of the Ni-substituted materials contrasts with that of Li3N at low temperatures, but all three samples show a rapid fall in λ above 190 K.

Results and Discussion Transverse Field µSR Measurements. TF µSR signals for the three materials have a initial positron count asymmetry of ∼25% and oscillate at a Larmor frequency of 0.33 MHz. This suggests that the muons implant as diamagnetic µ+ across the whole of the observed temperature range. In addition, the TF µSR signals decay in an approximately exponential fashion, behavior which has been ascribed to fluctuating Mn electronic moments in lithium manganate spinels.19 Li3N is diamagnetic, but SQUID magnetic susceptibility measurements21 show that the temperature variation of χ for the Li3-x-yNixN phases can be described by a small temperature-independent contribution χ0 characteristic of Pauli paramagnetism superimposed on a weak Curie-Weiss component. As the degree of Ni substitution increases the Weiss constant θ becomes more negative and the effective magnetic moment µeff decreases owing to the formation of 1∞[Ni-N] chains of increasing length parallel to the crystallographic c axis. LF µSR experiments indicate that a field of only 10 mT was sufficient to quench the local field due to nuclear moments in both Li3-x-yNixN phases, and the resulting µSR signals showed a small relaxing fraction with a very slow relaxation rate. Hence, the electronic contribution to the muon spin relaxation in these weakly paramagnetic materials is small enough to be neglected in the following analysis. In order to compare the samples qualitatively the TF µSR signals were fitted to a damped Larmor oscillation. The resulting relaxation rate λ is a measure of the combined effects of the local field distribution due to magnetic moments in the surroundings and of relaxation due to muon dynamics. The temperature variation of λ is plotted in Figure 2 for Li3N (circles), as well as for Li3-x-yNixN with x ) 0.36 (filled triangles) and 0.57 (open triangles). Both the Ni-substituted materials show a gradual decrease in λ at low temperatures, coupled with a more rapid fall above 180 K. For Li3N the behavior above 150 K is similar, but at low temperatures there is rapid decrease in λ up to 80 K which is reversed between 80 and 150 K. This indicates that after implantation the muons diffuse to trapping sites of low energy in the lattice. The initial fall in λ results from an increase in muon hopping as the temperature is raised, while the subsequent rise originates from an increasing proportion of trapped and therefore static muons. The contrast between Li3N and the Ni-substituted materials suggests that the muons are rapidly trapped even at the lowest temperatures in the latter case. This raises the possibility that

Figure 3. ZF µSR signals for Li3N (a) and Ni-substituted materials with (b) x ) 0.36 and (c) 0.57 shown at selected temperatures. For Li3N the decay rate is rapid at 13 K (red circles), decreases as the temperature is raised to 82 K (black circles), and subsequently increases again by 162 K (green circles). In contrast, for the Ni-substituted materials the decay rate remains rapid between 13 (red circles) and 176 K (green circles). At high temperatures, as illustrated here by data recorded at 300 K (blue circles), the decay rate for all three materials decreases.

the muons are trapped in the Li(2) vacancies in the [Li2N] plane which occur in much higher concentrations in the Ni-substituted phases. ZF µSR Measurements. ZF µSR measurements confirm that there are significant differences between the parent Li3N and the Ni-substituted materials, especially at temperatures below 150 K. As an illustration, ZF µSR signals are shown in Figure 3 for (a) Li3N, as well as Li3-x-yNixN with (b) x ) 0.36 and (c) x ) 0.57 at representative temperatures up to 300 K. For the Ni-substituted materials the muon polarization decays rapidly in ZF at all temperatures up to 180 K, as illustrated in (b) and (c) by ZF µSR signals recorded at 13 K (red circles) and 176 K (green circles). In contrast, for Li3N the decay rate decreases as the temperature is raised to 80 K and subsequently increases between 80 and 180 K. This is evident from a comparison of the Li3N data in (a) at 13 (red circles), 82 (black circles), and 162 K (green circles). Above 180 K the decay rate for all three samples decreases as illustrated in Figure 3 by ZF µSR signals recorded at 300 K (blue circles). If the muon dynamics is negligible, the Kubo-Toyabe depolarization function17 is given by

Gz(t) )

1 1 2 + (1 - ∆2t2) exp - ∆2t2 3 3 2

(

)

(1)

where ∆ is the depolarization rate which is related to the second moment of the local field distribution. However, the ZF signals

µSR Studies of Lithium Nitridometallate Materials

Figure 4. Temperature variation of the Kubo-Toyabe depolarization rate for Li3N (circles) and for Li3-x-yNixN with x ) 0.36 (filled triangles) and 0.57 (open triangles). For all three materials ∆ is approximately constant at low temperatures, while a rapid fall is observed above 180 K. For Li3N there is a plateau between 300 and 340 K, followed by a second fall in ∆ at the highest temperatures. Note that the error bars for ∆ fall within the symbols for all points on this plot.

in Figure 3 never recover to the value of 1/3 predicted by eq 1 and, as described above, the exponential relaxation observed in TF µSR is evidence of muon diffusion. Hence, the depolarization function was modified to take account of muon dynamics which can be included by assuming a Markovian strong collision model.17,18 The dynamic Kubo-Toyabe function, which depends on the muon hopping rate, ν, in addition to ∆, cannot be obtained in closed form and must be generated during fitting by a numerical inverse Laplace transform. The effect of increasing ν on the shape of the Kubo-Toyabe function is illustrated in the Supporting Information (Figure S1). Values of the depolarization rate were obtained by fitting the ZF µSR signals to a dynamic Kubo-Toyabe function with the hopping rate and the baseline asymmetry as additional variable parameters. The results are plotted in Figure 4 for Li3N (circles) above 150 K and for Li3-x-yNixN with x ) 0.36 (filled triangles) and 0.57 (open triangles) across the whole temperature range. For the latter the depolarization rate is approximately constant below 170 K at 0.42 ( 0.02 and 0.40 ( 0.01 µs-1 with x ) 0.36 and 0.57, respectively. ∆ takes a similar constant value for Li3N at 0.39 ( 0.01 µs-1 between 150 and 190 K. At temperatures above 190 K there is a rapid fall for all three materials, during which ∆ is decreased by over 50%. For Li3N there is a plateau between 300 and 340 K, followed by a second steeper fall at the highest temperatures. The parabolic shape observed for the µSR signals in Figure 3 at short times suggests qualitatively that the muon is quasistatic, such that its lifetime is shorter than the mean residence time 1/ν. Quantitatively, the hopping rates obtained from the dynamic Kubo-Toyabe fits for the Ni-substituted materials are approximately constant for all temperatures at 0.42 ( 0.03 and 0.43 ( 0.06 µs-1 with x ) 0.36 and 0.57, respectively. For Li3N ν is constant at 0.43 ( 0.04 µs-1 in a restricted range between 160 and 280 K, while at low temperatures it fluctuates erratically, suggesting that a single dynamic Kubo-Toyabe depolarization function is not sufficient to model the Li3N ZF µSR signals in this regime. This is consistent with the TF µSR results described above which indicate that for Li3N there is significant muon hopping at low temperatures, with the muon diffusing rapidly to trapping sites at higher temperatures. The variation of ν with temperature for the three samples is shown in the Supporting Information (Figure S2). As mentioned above, LF µSR experiments allowed the small electronic contribution to muon relaxation to be separately quantified. Avoided Level-crossing Experiments. The magnitude of the longitudinal field can be varied to probe resonances due to

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Figure 5. Muon relaxation rate, λ′, obtained as described in the text during avoided level-crossing experiments for Li3N at 160 K with the longitudinal field B varied between 0 and 15 mT.

avoided level crossings between muon Zeeman transitions and quadrupolar splittings of neighboring nuclei. Figure 5 shows the result of an avoided level-crossing experiment for Li3N which involved scanning the longitudinal field between 0 and 15 mT at 160 K. The relaxation rate λ′ was obtained by fitting the LF µSR signals to eq 1 modified by the addition of a Lorentzian decay function. Note that λ′ shows a broad peak between 0.8 and 2.4 mT, where the muon Zeeman frequency matches the Li(2) and Li(1) nuclear quadrupole transitions which are expected at 143 kHz (corresponding to a field of 1.06 mT) and 291 kHz (or 2.15 mT), respectively, from values of the quadrupolar coupling constant obtained from 7Li NMR.7 Muon Implantation Sites. Values of the depolarization rate can be evaluated for a powder sample by summing over the dipolar interactions between the muon and each nuclear spin, j, in the surrounding crystal lattice according to

( )

∆2 ) κI(I + 1)

µ0 2 2 2 2 p γµγn 4π

∑ 1/rj6

(2)

j

where the prefactor, κ, is 2/3 for the spin-1/2 case where the quadrupolar interaction is zero. For quadrupolar spins the nuclear moments precess about the electric field gradient (EFG) vector which extends radially from the muon. Since the local field arises only from the projection onto the EFG axis, this overestimates the contribution to ∆ from nuclei with I > 1/2. If the quadrupolar interaction dominates then κ is 4/9 for integer spins and 8/15 for half-integer spins with I ) 3/2.24 Values of ∆ for several possible muon sites calculated from eq 2 using lattice parameters obtained from neutron diffraction21,22 are given in Table 2. For the disordered Ni-substituted materials, an average value is given in which each local muon environment was weighted according to the Li occupancies given in Table 1. No correlation was assumed between the positions of the Ni atoms in the Li(1) plane and the Li(2) vacancies. 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)/Ni plane which is the most open site in the Li3N structure. As x increases in Li3-x-yNixN, the calculated ∆ decreases, as expected, because of the replacement of Li magnetic moments by Ni and the expansion of the [Li2N] ab plane. This trend is confirmed experimentally for the Ni-substituted materials which have an average low-temperature ∆ equal to 0.42 and 0.40 µs-1 with x ) 0.36 and 0.57, respectively. However, the experimental values are substantially larger than those calculated in Table 2 for the 2c Li(2) site, suggesting that the muon is trapped in some alternative site.

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TABLE 2: Calculated Values of the Kubo-Toyabe Depolarization Rate for Li3 and Ni-Substituted Materialsa Li3N

Li3-x-yNixN x ) 0.36

Li3-x-yNixN x ) 0.57

(1/3, 2/3, 0) (1/3, 2/3, 1/2) (1/3, 2/3, z) with z ) 2/5

0.30 0.39 0.47

0.27 0.37 0.45

0.21 0.33 0.40

2c 2d 4h

(1/3, 2/3, 0) (1/3,2/3, 1/2) (1/3,2/3, z) with z ) 2/5

0.15 0.25 0.25

0.12 0.20 0.19

0.11 0.15 0.15

2c 2d 4h

(1/3, 2/3, 0) (1/3, 2/3, 1/2) (1/3, 2/3, z) with z ) 2/5

0.034 0.020 0.020

0.033 0.020 0.021

0.031 0.020 0.021

site

Wyckoff

All Atoms Present Li(2) vacancy in [Li2N] ab plane interstitial site in Li(1)/Ni plane interstitial with z displacement

2c 2d 4h

Li(2) Removed Li(2) vacancy in [Li2N] ab plane interstitial site Li(1)/Ni plane interstitial with z displacement Li(1) and Li(2) Removed Li(2) vacancy in [Li2N] ab plane interstitial site Li(1)/Ni plane interstitial with z displacement

coordinates

a Values calculated with Li(2) removed were used to estimate the residual contribution to ∆ after motional narrowing due to intra-layer diffusion in the [Li2N] plane, those with both Li(1) and Li(2) removed give the residual contribution after the onset of inter-layer diffusion.

For Li3N the 2d interstitial site gives a much better match to the experimental value for Li3N of 0.39 µs-1 observed between 150 and 190 K. Implantation at this location is consistent with the observation of avoided level-crossings in Li3N with the Li nuclear quadrupole transitions as shown in Figure 5. This is because a muon implanted in this site is surrounded by five nearest neighbors Li atoms (two Li(2) at 1.9374 Å and three Li(1) at 2.1061 Å). Furthermore, this location is consistent with the increased ease of muon trapping observed for Ni-substituted materials, since these have reduced layer spacings which increases the energy barrier for muon hopping between 2d sites. However, the agreement with experiment is less good for the Ni-substituted materials and, in the light of this, ∆ was also calculated for a 4h site. This involves a displacement along the c axis away from the 2d interstitial toward an occupied 2c Li(2) site below. Since the muon moves closer to the Li(2) atom in this situation, the calculated ∆ increases even for a small displacement. Table 2 shows the values which result from a displacement equal to 10% of the c lattice parameter, and the agreement with experiment for the Ni-substituted is significantly improved. Note that as the Ni-substitution level increases the displacement becomes more favorable, since the µ+ moves toward a Li(2) vacancy. Interestingly, a similar interstitial location has been identified by molecular dynamics simulations25 as an intermediate in the exchange between Li(1) and Li(2) required for interlayer diffusion in Li3N. Other possibilities for muon sites, such as in a Li(2) vacancy adjacent to a possible NH2- defect or close to the N3- ion in the [Li2N] plane, result in calculated ∆ values which are much higher than those observed experimentally. Together with the absence of an avoided level-crossing with the N nuclear quadrupole transitions, expected at 379.1 kHz or a field of 2.80 mT, this suggests that a NMu2- species is not formed. This result is surprising, since the hydrogen equivalent NH2- is thought to play an important role in intralayer diffusion in Li3N. Lithium Diffusion. The significant decrease in the depolarization rate observed for all three 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 temperatureindependent hopping rate. Instead, the reduction in ∆ originates from motional narrowing of a contribution to the local field distribution at the muon due to the onset of Li+ diffusion with the [Li2N] plane. Similar motional narrowing has been observed previously in ZF µSR measurements of lithium manganate spinels.19,20 Note that the onset temperature in the present case is higher than the 140 K observed for the same Li+ diffusion process in variable-temperature 7Li NMR studies. However, this is expected, since ∆ is an order of magnitude larger than the

NMR line width, so that the Li+ diffusion must be faster to cause an averaging effect. Only the contribution ∆′, which arises from dipolar interactions with 6Li or 7Li nuclei in Li(2) sites is narrowed by intralayer diffusion in the ab [Li2N] plane. The narrowing of ∆′ by Li+ diffusion has been modeled in this work by the BPP equation5

2 ∆′(T)2 ) (∆0)2 tan-1(∆′(T)πτ(T)) π

(3)

where 1/τ is the mean jump rate for diffusing Li+ ions and ∆0 is the low-temperature limiting value of ∆′. The residual contribution to ∆ is due to dipolar interactions with 14N nuclei and 6Li and 7Li nuclei in Li(1) sites only. Values of the residual ∆ can be calculated using eq 2 with all 6Li and 7Li nuclei in Li(2) sites removed, and these decrease with increasing x, as shown in Table 2. A value of 0.25 µs-1 is obtained for Li3N with the muon implanted in either a 2d or 4h site. This is in reasonable agreement with the plateau at 0.20 µs-1 observed experimentally for Li3N between 300 and 340 K. For the analysis the limiting ∆0 was obtained by subtracting the calculated residual ∆ from the average of the total experimental ∆ measured at temperatures below the onset of motional narrowing. The Li+ jump rates 1/τ extracted from eq 3 are in the MHz regime at room temperature for all three samples. The assumption of a simple Arrhenius law allows the activation energy Ea and the prefactor 1/τ0 to be extracted from the temperature variation. Note that 1/τ0 corresponds to the jump rate at infinite temperature. Arrhenius plots for all three samples shown in Figure 6 indicate that this model provides a good fit to the data for temperatures from the onset of motional narrowing up to about 300 K. The activation energies and Arrhenius prefactors for the intralayer diffusion extracted in this way are given in Table 3. For diamagnetic Li3N the agreement between the Ea obtained in this work and the value of 0.121 eV from previous 7Li NMR line width studies14 on a similar sample is very good. For the two Li3-x-yNixN materials the activation energy obtained with µSR increases as the degree of substitution increases, suggesting that the most important effect is the reduction in the c lattice parameter. This leads to an increase in the covalent character of the Li-N bond which reduces the polarizability of the lattice framework and raises the energy barrier for Li+ hopping. For these materials the concomitant increase in the a lattice parameter which results in more open diffusion pathways within

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Figure 6. Arrhenius plots of Li+ jump rates measured from ZF µSR experiments for Li3N (open circles) and Li3-x-yNixN materials with x ) 0.36 (filled triangles) and 0.57 (open triangles), together with the fits (lines) used to extract the activation energy for Li+ diffusion.

TABLE 3: Arrhenius Parameters and Diffusion Coefficients for Li3N and Ni-Substituted Materials sample

Li3N

Li3-x-yNixN x ) 0.36

Li3-x-yNixN x ) 0.57

Ea/eV (1/τ0)/s-1 D(298 K)/m2s-1

0.119 1.67 × 108 1.79 × 10-14

0.069 2.93 × 107 2.29 × 10-14

0.103 1.09 × 108 2.29 × 10-14

the expanded [Li2N] layers apparently has a weaker influence on Ea. As mentioned about, this situation is in contrast to that observed for Li3-x-yCuxN with x < 0.36.15 Values of the diffusion coefficient D can be obtained from the jump rate by the Einstein-Smoluchowski relation

D)

d2f gτ

(4)

where d is the distance between adjacent Li(2) sites, the correlation factor, f, is assumed to be 1 for simplicity, and g is 4 for planar diffusion within the [Li2N] layers. Above 300 K interlayer diffusion can no longer be excluded, since this process starts to affect the 7Li NMR spectrum of Li3N at 280 K. Interlayer diffusion involves the Li(1) site in addition to Li(2) and is therefore expected to result in the motional narrowing of a further contribution to ∆. This is visible in Figure 4 for Li3N (circles) above 340 K, and the fall to 0.05 µs-1 is in agreement with the value calculated using eq 2 with all Li removed. Experiments were not carried out on the Ni-substituted materials above 340 K, but by this temperature ∆ for both the Li3-x-yNixN phases has already fallen well below the value calculated for intralayer diffusion with Li(2) removed. This indicates that the onset of interlayer diffusion occurs at a lower temperature in these materials than in the parent Li3N. Conclusion This paper demonstrates that µSR can be used to obtain quantitative information about Li+ transport in lithium battery materials. The rapid decrease in the Kubo-Toyabe depolarization rate observed above 180 K in ZF µSR experiments on Li3N and its Ni-substituted derivatives arises from motional narrowing due to Li+ diffusion in the [Li2N] plane. This allows diffusion coefficients and activation energies to be obtained, even for paramagnetic materials where NMR analysis is complicated by electronic contributions to the relaxation. For diamagnetic Li3N

the diffusion parameters are in good agreement with the results of previous 7Li NMR studies.14 The increase in the measured Ea with x for Li3-x-yNixN suggests that the reduction in the layer spacing that results at high substitution levels is responsible for raising the energy barrier to Li+ jumps, despite the concomitant expansion of the [Li2N] plane. In addition, the onset of interlayer diffusion appears at lower temperatures in Ni-substituted derivatives than in the parent Li3N. The muons themselves are quasi-static, most probably located in a 4h site between the [Li2N] plane and the Li(1)/Ni layer. This is similar to the Li+ interstitial position identified by molecular dynamics simulations as an intermediate for an exchange mechanism for interlayer diffusion. Finally, µSR gives no evidence for the formation of the muonium equivalent of the hydrogen defects thought to play an important role in intralayer diffusion in Li3N. Acknowledgment. Experiments at the ISIS Pulsed Neutron and Muon Source were supported by a beamtime allocation from the Science and Technology Facilities Council. A.S.P. thanks the Engineering and Physical Sciences Council for a PhD studentship. Supporting Information Available: Figures showing the variation of the dynamic Kubo-Toyabe function with the muon hopping rate and the values of the hopping rate extracted for the three materials from ZF µSR signals. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) von Alpen, U. J. Solid State Chem. 1979, 29, 379. (2) Schulz, H.; Thiemann, K. H. Acta Crystallogr. A 1979, 35, 309. (3) Wahl, J. Solid State Commun. 1979, 29, 485. (4) Lapp, T.; Skaarup, S. Solid State Ionics 1983, 11, 97. (5) Messer, R.; Birli, H.; Differt, K. J. Phys. C 1981, 14, 2731. (6) Brinkmann, D.; Mali, M.; Roos, J.; Messer, R.; Birli, H. Phys. ReV B 1982, 26, 4810. (7) Differt, K.; Messer, R. J. Phys. C 1980, 13, 717. (8) Rabenau, A. Solid State Ionics 1982, 6, 277. (9) Shodai, T.; Okada, S.; Tobishima, S.; Yamaki, J. Solid State Ionics 1996, 86-88, 785. (10) Gregory, D. H.; O’Meara, P. M.; Gordon, A. G.; Siddons, D. J.; Blake, A. J.; Barker, M. G.; Hamor, T. A.; Edwards, P. P. J. Alloys Comp. 2001, 237, 317. (11) Gordon, A. G.; Gregory, D. H.; Blake, A. J.; Weston, D. P.; Jones, M. O. Int. J. Inorg. Mater. 2001, 3, 973. (12) Gregory, D. H.; O’Meara, P. M.; Gordon, A. G.; Hodges, J. P.; Short, S.; Jorgensen, J. D. Chem. Mater. 2002, 14, 2063. (13) Stoeva, Z.; Gomez, R.; Gordon, A. G.; Allan, M.; Gregory, D. H.; Hix, G.; Titman, J. J. J. Am. Chem. Soc. 2004, 126, 4066. (14) Stoeva, Z.; Gomez, R.; Gregory, D. H.; Hix, G.; Titman, J. J. Dalton Trans. 2004, 3093. (15) Powell, A. S.; Gregory, D. H.; Titman, J. J. In preparation. (16) Gee, B.; Horne, C.; Cairns, E.; Reimer, J. J. Phys. Chem. B 1998, 102, 10142. (17) Hayano, R. S.; Uemura, Y. J.; Imazato, J.; Nishida, N.; Yamazaki, T.; Kubo, R. Phys. ReV. B 1979, 20, 850. (18) Kejr, K. W.; Honig, G.; Richter, D. Z. Phys. B 1978, 32, 49. (19) Kaiser, C. T.; Verhoeven, V. W. J.; Gubbens, P. C. M.; Mulder, F. M.; De Scheper, I.; Yaouanc, A.; Dalmas de Re´ortier, P.; Cottrell, S. P.; Kelder, E. M.; Schoonman, J. Phys,. ReV. B 2000, 62, 9236. (20) Ariza, M. J.; Jones, D. J.; Rozie`re, J.; Lord, J. S.; Ravot, D. J. Phys. Chem. B 2003, 107, 6003. (21) Stoeva, Z.; Smith, R. I.; Gregory, D. H. Chem. Mater. 2006, 18, 313. (22) Huq, A.; Richardson, J. W.; Maxey, E. R.; Chandra, D.; Chien, W. J. Alloys Cmpds. 2007, 436, 256. (23) Pratt, F. L. Physica B 2000, 28, 9–290, 710. (24) Schenk, A. Muon Spin Rotation Spectroscopy; Adam Hilger Ltd: Bristol, UK, 1984. (25) Wolf, M. L.; Catlow, C. R. A. J. Phys. C 1984, 17, 6635.

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