Muon studies of Li + di ﬀ usion in LiFePO 4 nanoparticles of di ﬀ erent polymorphs † Royal

The lithium di ﬀ usion in nanostructured olivine LiFePO 4 has been investigated for the ﬁ rst time using muon spectroscopy ( m SR). A microwave-assisted approach has been employed for nanoparticle preparation, where the choice of solvent is shown to play an important role in determining particle morphology and crystal chemistry. Two phases have been obtained: Pnma LiFePO 4 and the high pressure Cmcm phase. The Li + di ﬀ usion behaviour is strikingly di ﬀ erent in both phases, with D Li of 6.25 (cid:1) 10 (cid:3) 10 cm 2 s (cid:3) 1 obtained for Pnma LiFePO 4 in good agreement with measurements of bulk materials. In contrast, Li + di ﬀ usion is impeded with the addition of the high pressure Cmcm phase, with a lower D Li of 3.96 (cid:1) 10 (cid:3) 10 cm 2 s (cid:3) 1 noted. We have demonstrated an e ﬃ cient microwave route to nanoparticle synthesis of positive electrode materials and we have also shown m SR measurements to be a powerful probe of Li + di ﬀ usion behaviour in nanoparticles.


A Introduction
Olivine structured Pnma LiFePO 4 has been the focus of much attention for the development of efficient positive insertion electrodes, as it presents an economical and non-toxic option for a rechargeable Li-ion battery cathode material. 1-4 LiFePO 4 exhibits a high charge density, good cyclability and is complementary to most conventional polymer electrolytes. Recently, great efforts have been made in the development of nanostructured electrodes due to potential improvements in electrochemical performance, as their small size allows for shorter diffusion pathlengths while increased surface areas improve electrode-electrolyte interactions. 5,6 Phase pure olivine materials can be obtained using conventional synthetic methods, such as solid-state ceramic routes, sol-gel routes and solvothermal methods. [7][8][9][10][11] While high temperature ceramic routes will oen yield bulk materials, the choice of solvent in solvothermal reactions can oen play a determining role in resulting particle morphology and size. One example of a class of materials nding increasing use as solvents for the preparation of electrode materials is the use of ionic liquids, where elegant control over resulting particle size and shape has recently been demonstrated for the case of the solvothermal synthesis of LiFePO 4 and LiMnPO 4 . [12][13][14] In recent years, microwave-assisted solvothermal methods have appeared as a faster, efficient approach to inorganic materials. 15 For example, LiMPO 4 (M ¼ Fe, Mn) has been prepared by using a benzyl alcohol approach aer only 3 minutes at 180 C. 16 Microwave routes to nanostructured Li 2 FeSiO 4 and Li 2 MnSiO 4 using a tetraethylene glycol solvent have also been reported, 17 while recently Nazar and co-workers have established a fast, microwave-assisted polyol route to the triplite LiFeSO 4 F phase with tetraethylene glycol. 18 Here, we report the synthesis of nanoparticulate LiFePO 4 using a microwave-assisted solvothermal route. We show how the crystal chemistry and resulting morphology can be controlled by the solvent and iron starting materials employed. We employ two methods combined with microwave heating: a polyol synthesis and an ionothermal route. We also report, for the rst time, on the diffusive nature of Li + through LiFePO 4 nanoparticles prepared in this manner using positive muon spin relaxation (mSR). The nature of Li + diffusion in LiFePO 4 continues to attract considerable attention. A number of methods already exist for the study of Li + diffusion, yet there is signicant variation between the results obtained for D Li in LiFePO 4 (ranging from $10 À7 cm 2 s À1 from Mössbauer spectroscopy 19 to $10 À14 cm 2 s À1 for galvanostatic intermittent titration techniques [GITT] 20 ). Recently, electrochemical methods employed for calculating Li + diffusion coefficients in thin lm electrodes have raised questions due to differences caused by the nature of the diffusion, the electrode surface area and the smoothness of the electrode surface. [21][22][23] Theoretical studies have found that, for LiFePO 4 ,Li + diffusion is conned to a curved 1-dimension in the [010] direction, with D Li estimates of 10 À8 cm 2 s À1 . [24][25][26] This 1-dimensional diffusion has been shown experimentally using a combination of neutron diffraction and maximum entropy methods. 27 Activation barriers for Li + and electron mobility have also been investigated experimentally using NMR and impedance analysis. 28,29 mSR has previously been employed as a sensitive probe for magnetic ordering and also in the investigation of dynamic sample effects. 30 It has also been successfully applied to the study of Li + diffusion in a number of Li-ion battery materials including lithium metal oxides and ternary lithium nitridometallates, where the Li + diffusion perturbs the muon environment. 31-34 mSR has been shown to reliably determine D Li values for Li x CoO 2 , with values obtained close to theoretically predicted values. 32,35 Recently, the use of mSR as a probe to study Li + diffusion in olivines has also been demonstrated for bulk olivine materials, including bulk LiFePO 4 . [36][37][38] Herein, we examine the Li + diffusion in nanoparticulate Pnma LiFePO 4 and the high pressure Cmcm LiFePO 4 phase using mSR for the rst time. We observe a thermally activated Li + hopping regime for nanostructured Pnma LiFePO 4 , similar to measurements obtained for bulk samples, demonstrating the reliability of this technique for the study of Li + diffusion. We also examine muon diffusion of the Cmcm LiFePO 4 polymorph for the rst time in a mixed phase sample of Pnma LiFePO 4 / Cmcm LiFePO 4 .

B Synthesis
Powder samples of LiFePO 4 were prepared by grinding LiH 2 PO 4 (0.263 g; 2.54 mmol) and FeC 2 O 4 $2H 2 O (0.456 g; 0.254 mmol) in an agate mortar for 10 min and adding to 10 ml of either ethylene glycol (Sample LFP-EG1; Alfa Aesar, 99%) or 1-ethyl-3methyl imidazolium triuoromethanesulfonate (EMI-TFMS) (Sample LFP-IL; Solvionic, 99.5%) in 35 ml glass reaction vessels. The mixtures were stirred for 20 minutes before irradiation with microwaves in a CEM Discover SP microwave synthesiser (2.45 GHz) for 3 hours at 250 C. The products were washed with water (2 Â 20 ml), ethanol (2 Â 20 ml) and acetone (20 ml), before drying in a vacuum oven at 80 C overnight. The pale green powders were characterised by X-ray diffraction (XRD) (PANalytical X'Pert powder diffractometer) and scanning electron microscopy (SEM) (Carl Zeiss Sigma variable pressure analytical SEM). SEM samples were prepared on adhesive stubs and coated using a plasma sputter coater with a 99 : 1, Au : Pt target to avoid charging feedback. Transmission electron microscopy (TEM) was performed on a JEOL ARM instrument, operated at 200 keV. TEM samples were prepared by dispersing the sample in ethanol and dropping the suspension onto an amorphous holey carbon coated grid.

Muon spectroscopy
Spin polarised positive muons were implanted into LiFePO 4 samples, where they stop at interstitial sites and decay with a mean lifetime of 2.2 ms. Whilst implanted in the sample, the muon spin direction is affected by the local magnetic eld at the stopping site. When the muon decays into a positron and two neutrinos, the positron is preferentially emitted in the direction of the muon spin at the instant of decay. The muon spin polarisation can be followed as a function of time by measuring the asymmetry in the count rate of the decaying positrons, A(t), in two banks of detectors on opposite sides of the sample; (essentially, we monitor the muon's spin through its daughter positron).
mSR experiments were carried out at the ISIS pulsed muon and neutron source, using the EMU instrument and data were analysed using the WIMDA program. The samples were prepared by transferring the powders of LiFePO 4 (approximately 1 g) into titanium sample holders with a titanium foil window. Ti depolarises muons very weakly and so gives an easy-tosubtract background. In order to probe the lithium diffusion behaviour in two of our samples, we measured a temperature range of 100 K to 400 K at 10 K increments and at 0 G and applied longitudinal elds of 5 and 10 G. Multiple magnetic eld measurements give more reliable determinations of simultaneously tted parameters since it allows greater investigation of how the eld distribution experienced by the muon is decoupled by the eld applied parallel to the initial muon spin polarisation.

C Results and discussion
Microwave synthesis of nanoparticulate LiFePO 4 Ethylene glycol and EMI-TFMS were chosen as solvents for the preparation of LiFePO 4 nanoparticles for two reasons: (a) Choice of solvent has been previously shown to heavily inuence the resulting nanoparticle shape. 39 (b) Both solvents are high boiling point solvents (ethylene glycol boils at 196 C; EMI-TFMS has a decomposition temperature of 340 C) with dipole moments which can interact with incoming microwaves to uniformly heat reactants.
Our synthetic approach takes advantage of a solvent's ability to efficiently absorb microwave energy and convert this into heat through the dielectric heating effect. 40 A material's dielectric properties can be described by its complex relative permittivity 3 ¼ 3 1 À i3 2 , which depends on both frequency and temperature. The real part 3 1 (more precisely, the quantity 3 1 À 1) is a measure of the ability of the material to be polarized by an electric eld, and the imaginary part 3 2 is a measure of the efficiency with which the material converts electric eld energy into heat. Assuming a uniform internal electric eld of magnitude E within a sample of volume V, the time-averaged power dissipated P at some frequency f can be written as P ¼ p3 2 In order to assess the behaviour of the solvents we have employed in greater detail, we measured the microwave dielectric properties of ethylene glycol and the ionic liquid EMI-TFMS. Measurements were taken in the range 0.01 GHz to 10 GHz using a broadband coaxial probe connected to a microwave network analyser (N5232A PNA-L, Agilent Technologies). 41 All measurements were taken at a constant temperature of 27.5 C and values of complex permittivity were veried using a TM 010 microwave cavity operating at 2.45 GHz. 42 Results for the frequency dependence of the complex permittivity of both liquids are shown in Fig. 1(a) and (b). We nd that ethylene glycol behaves close to that of a classical Debye liquid 43 of static permittivity 3 s ¼ 37.8 AE 0.4 and relaxation frequency of 1.57 AE 0.01 GHz. EMI-TFMS, on the other hand, behaves as a liquid with nite electrical conductivity, whose imaginary (i.e. lossy) permittivity 3 2 exhibits the expected frequency variation below about 1 GHz of 3 2 z s/2p3 0 f f 1/f. From this, we deduce a dc electrical conductivity of s ¼ 0.96 AE 0.01 S m À1 .
Some numerical values of complex permittivity of both liquids at spot frequencies of importance for microwave heating applications (namely 915 MHz, 2.45 GHz and 5.8 GHz) are shown in Table 1. The results obtained for ethylene glycol compare well with previously reported values. 44 Note that the errors quoted in our data are systematic errors of around AE1% associated with the simple quasi-static model 41 used to model the aperture admittance of the coaxial probe to convert microwave reectance data into complex permittivity values. We nd that both solvents have large measured values of 3 2 , conrming their effectiveness as microwave absorbers. In Fig. 2 we plot the rms power dissipated P (expressed in W cm À3 of solvent) calculated for a xed internal electric eld of 10 kV m À1 ,a si s typical in a microwave heating application, using our measured complex permittivities shown in Fig. 1. We nd that that the dissipated power densities are 72 and 95 W cm À3 at 2.45 GHz for EMI-TFMS and ethylene glycol, respectively, which are sufficient to drive the high temperatures required for our reactions.
In a typical synthesis, stoichiometric amounts of iron precursor and LiH 2 PO 4 were mixed with 10 ml solvent for 20 min at 30 C before a heat treatment in the microwave chamber at 250 C for 3 hours. The results from three experiments are presented here: (1) LFP_EG1 from iron oxalate dihydrate, LiH 2 PO 4 and ethylene glycol solvent, (2) LFP_EG2 from iron acetylacetonate, LiH 2 PO 4 and ethylene glycol (note, temperature is 220 C here) and (3) LFP_IL from iron oxalate dihydrate, LiH 2 PO 4 and ionic liquid EMI-TFMS solvent.
XRD patterns collected for each dried powder sample are shown in Fig. 3. For sample LFP1_EG with iron oxalate as a starting material and ethylene glycol as a solvent, a two-phase system is found with the pattern plotted in Fig. 3(a) matched to Pnma LiFePO 4 and a high pressure LiFePO 4 phase which crystallizes in the Cmcm space group. Heating this sample in a tube furnace under Ar at 600 C for one hour completely transforms the high pressure phase to Pnma LiFePO 4 . This high pressure Cmcm phase has been realised before by García-Moreno and coworkers at high pressures (tens of kbar) and temperatures (hundreds of degrees). 45 Very recently Niederberger and coworkers have observed this phase at much lower reaction temperatures and times (195 C, 3 min) for a nonaqueous microwave synthesis, whereby a change in the benzyl alcohol-2pyrrolidinone solvent ratio can be used to tailor the phase obtained. 46 In our experiments, the solvent volume is held Fig. 1 (a) Experimental data for the real part 3 1 of the complex permittivity 3 measured as a function of frequency for the polar liquid ethylene glycol (EG) and the ionic liquid EMI-TFMS. (b) The same plot, only this time for the imaginary part 3 2 . No errors bars are shown but all data are subject to a systematic error of AE1% imposed by the aperture module of the coaxial probe used to extract the permittivity data. 41 Table 1 Numerical values for the real part 3 1 and imaginary part 3 2 of the complex relative permittivity 3 for the two solvents used in the microwave reactions, measured at 27.5 constant while the solvent itself is changed. Using a controlled synthesis, we can monitor the vessel pressure during synthesis. For the LFP_EG1 reaction, the observed pressure is approximately 5.86 bar once the reaction temperature of 250 Ci s reached. This build-up of pressure is due to the removal of the waters of crystallisation from the iron starting material, which occurs between 170 C and 230 C. 47 We believe it is this change in pressure which drives the formation of the high pressure phase in the ethylene glycol reaction. By employing Fe(acac) 3 which has no water of crystallisation instead of Fe(C 2 O 4 )$2H 2 O, we can obtain pure, single phase Pnma LiFePO 4 at 220 C using an ethylene glycol solvent. The X-ray pattern of this sample, LFP_EG2, was t by Rietveld prole analysis to the orthorhombic Pnma LiFePO 4 structure and is shown in Fig. 4(a). The solubility of starting materials is also different, with Fe(acac) 3 more soluble in ethylene glycol than the oxalate salt, as observed by the deep red colour of the solution prior to microwave treatment. The nature of the solvent is also of great importance in determining what phase is obtained, as demonstrated by the ionic liquid sample, LFP_IL. Using Fe(C 2 O 4 )$2H 2 O as a starting material and EMI-TFMS as solvent, which has a greater dissipated power density than ethylene glycol, single phase Pnma LiFePO 4 is obtained aer 3 hours [ Fig. 4(b)]. We have also studied the effect of reaction temperature on the phase obtained. For increasing reaction temperatures using ethylene glycol as a solvent and an iron oxalate starting material, we observe a two phase product made up of aand b-LiFePO 4 even up to reaction temperatures of 300 C (see XRD patterns in ESI, Fig. S1a †). In the case of EMI-TFMS as a solvent, we do not see the formation of the b-LiFePO 4 phase and only obtain a-LiFePO 4 at temperatures above 250 C (see XRD patterns in ESI, Fig. S1b †). We are currently investigating the use of several commercial and tailored precursors to examine the effect of starting material and solvent on crystal chemistry in greater detail. SEM images taken of dried powders of LFP_EG1 and LFP_IL reveal a dependence of particle morphology on the choice of solvent. In the case of LFP_EG1, large platelets are noted, with a typical platelet diameter of 6 mm. The thickness of these platelets is of the order of 20 nm and they appear as clusters of stacked particles as shown in Fig. 5(a). A dramatic difference is   2 The rms dissipated power density P (expressed in W cm À3 ), calculated from the permittivity data of Fig. 1 for a uniform internal electric field of magnitude 10 kV m À1 , plotted as a function of frequency.
noted for the LFP_IL sample, where more nanoparticulate material, which oen adopts geometric forms, is found to form under the same reaction conditions. The typical particle size in this case is 200 nm and in some cases the particles appear faceted [ Fig. 5(b)]. High resolution TEM images conrm the highly crystalline nature of the LFP_IL sample [ Fig. 5(d)], with lattice spacings consistent with Pnma LiFePO 4 . Larger, sheetlike particles are again observed for the LFP_EG1 sample [ Fig. 5(c)].
mSR studies of Li + diffusion in nanoparticulate LiFePO 4 In terms of structure, the Pnma LiFePO 4 phase is characterised by open channels running in the b-direction through which Li + ions can diffuse during electrochemical cycling, as shown in Fig. 3(c). The structure of the Cmcm phase, shown in Fig. 3(b), is made up of rows of edge-sharing octahedral along the c axis, with PO 4 and LiO 4 tetrahedra running in the a direction. 45 As demonstrated previously, the major structural difference between these polymorphs is in the Li-Li distances, with the high pressure phase increasing to a point at which the lithium hopping mechanism is no longer viable. 46 The electrochemical properties of this phase have been investigated and it has been shown to be electrochemically inactive, with theoretical predictions in agreement with experiment. 45,46 In order to probe the Li + diffusion in the pure Pnma and Cmcm-containing nanosized LiFePO 4 samples prepared here, we recorded mSR data at zero eld (ZF) and applied longitudinal elds (LF) of 5 G and 10 G. The typical raw data obtained for the LFP_IL sample, recorded at 300 K, are shown in Fig. 6. The initial positron asymmetry, regardless of applied eld, is approximately 17%. These measurements, which are taken above the antiferromagnetic ordering at T N (LFP_IL, 51 K; LFP_EG, 49 K), contain a fast initial relaxation likely due to interactions with the paramagnetic iron moments and a slow relaxation from interactions with nuclear magnetic elds from 7 Li, 6 Li and 31 P. By applying a longitudinal eld parallel to the   direction of the beam, any interactions between the muon and the local nuclear magnetic eld distribution that it probes can be eliminated. Fig. 6 demonstrates this decoupling, where it can be seen that the application of progressively larger LF (from 5 G to 10 G) reduces this slower relaxation rate. Similar observations have been reported for bulk LiFePO 4 . [36][37][38] In order to probe the Li + diffusion dynamics in our samples, data were collected over a temperature range of 100 K to 400 K at ZF and LF of 5 G and 10 G. All data were t using three parameters: a combination of an exponentially relaxing signal to account for the initial fast relaxation from the iron magnetic moments, a baseline asymmetry and an exponentially relaxing dynamic Kubo-Toyabe function, 30 which has been modied to account for uctuations due to muon or lithium diffusion and can be employed for an assumed Gaussian distribution of local elds. 48 From these ts, we can extract parameters which provide us with insight into the Li + diffusion mechanism in our materials. In Fig. 7 and 8, we show the values of n, the eld uctuation rate, and D, the local eld distribution at the muon stopping site, for data collected over the full temperature range. Data extracted for the single phase LiFePO 4 sample LFP_IL are shown in Fig. 7. The values obtained for D are very similar to those observed for bulk LiFePO 4 samples reported previously, i.e. a low temperature plateau followed by a smooth decrease to higher temperatures [ Fig. 7(b)]. In the case of the uctuation rate, n, we again observe similar behaviour as seen for bulk LiFePO 4 . From 160 K, we see a steady increase until 230 K aer which there is a sharp drop. The observed decrease in n above 240 K likely results from the Li + diffusion being too fast for m + SR. 38 To evaluate the diffusion coefficient for Li + , we consider only jumps of Li + to interstitial sites and we take the primary hopping axis to be in the b-direction. The distance travelled for each hop will be therefore b/2, giving an estimation of the Li + diffusion coefficient, D Li , from b 2 n/4. For the LFP_IL sample, we can extrapolate ts of D Li versus 1/T to obtain a Li + diffusion coefficient at 300 K of 6.25 Â 10 À10 cm 2 s À1 . This is in close agreement to bulk sample measurements. 36,37 To determine the activation energy, we plot an Arrhenius t to n over the thermally activated region to give an estimated E a of 58 meV for the LFP_IL sample. This value is close to the bulk reported value from Baker et al. who employed a Keren tting function to data and obtained an E a value of 60 meV. 36 For bulk LiFePO 4 prepared by ceramic methods and using similar Kubo-Toyabe tting methods, Sugiyama et al. have found E a values close to 100 meV. 37,38 The similarities in values obtained demonstrate the robustness of this method for determining Li + diffusion behaviour.
In the case of the LFP_EG1 sample (Fig. 8), we initially observe similar behaviour to the LFP_IL case, albeit with smaller D and n values. An increase in n is noted with increasing temperature, but now a decrease aer 230 K is not seen. Instead, a steady increase is observed over the remaining temperature range. Given that this is a two phase system comprising Pnma and Cmcm LiFePO 4 , it is reasonable to assume that the initial increase up to 230 K is due to Li + diffusion, similar to the case of the LFP_IL sample and previous observations for bulk samples. Previous reports on the high pressure Cmcm phase have shown that this phase is inactive electrochemically, with DFT simulations establishing the poor Li + mobility, with no hopping observed for the ions which rattle in voids. 46 From Rietveld Fig. 7 Temperature dependence of (a) fluctuation rate (n) and (b) field distribution width (D) parameters derived from fitting mSR data to a dynamic Kubo-Toyabe function for the LFP_IL sample, measured from 100 K to 400 K. Fig. 8 Temperature dependence of (a) fluctuation rate (n) and (b) field distribution width (D) parameters derived from fitting mSR data to a dynamic Kubo-Toyabe function for the LFP_EG1 sample, measured from 100 K to 400 K. renement of our XRD pattern, the phase fraction of the sample is Pnma : Cmcm 80 : 20. Our experiments are in agreement with previous observations for the Cmcm phase, with a lower D Li value of 3.96 Â 10 À10 cm 2 s À1 obtained for the LFP_EG1 sample (E act ¼ 46 meV). We can therefore rationalise our n observations as follows for the LFP_EG1 sample. We continue to observe an increase in n due to diffusion in the Pnma phase, which is present in excess. However, the presence of the Cmcm phase acts to limit the supply of Li + ions which can diffuse. This impedes the lithium diffusion and results in a lower D Li value.

D Conclusions
We have shown that a microwave-assisted synthetic approach for the preparation of LiFePO 4 can allow for different particle morphologies, including crystalline nanoparticles and platelets, and different phases (a-and b-LiFePO 4 ) to be obtained in gramscale quantities and short reaction times. The microwave dielectric measurements of ethylene glycol and EMI-TFMS reveal these as excellent microwave absorbers to generate the temperatures required for our reactions to proceed. mSR has also proved a powerful tool to examine the Li + diffusion in these nanomaterials, with nanocrystalline Pnma LiFePO 4 exhibiting similar diffusion coefficients to bulk LiFePO 4 . mSR has also revealed that the presence of the Cmcm phase impedes Li + mobility and leads to a decrease in Li + diffusion. In future, our investigations include varying the experimental conditions to allow for further tuning of the crystal chemistry and morphology, together with additional mSR experiments on mixed metal phosphates.