Neutron Pair Distribution Function Study of FePO4 and LiFePO4

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Cite This: Chem. Mater. XXXX, XXX, XXX−XXX

Neutron Pair Distribution Function Study of FePO4 and LiFePO4 Wojciech A. Sławiński,*,†,‡,∥ Helen Y. Playford,† Stephen Hull,† Stefan T. Norberg,‡,⊥ Sten G. Eriksson,‡ Torbjörn Gustafsson,§ Kristina Edström,§ and William R. Brant§ †

The ISIS Facility, STFC Rutherford Appleton Laboratory, Oxfordshire OX11 0QX, United Kingdom Department of Chemistry and Chemical Engineering, Chalmers University of Technology, Gothenburg SE-412 96, Sweden § Department of Chemistry, Ångström Laboratory, Box 531, Uppsala University, 751 21 Uppsala, Sweden ‡

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S Supporting Information *

ABSTRACT: Neutron powder diffraction studies of the compounds FePO4 and LiFePO4 are reported. Rietveld refinement of the diffraction data provides averaged structures for both materials that are in good agreement with the published structures. In addition, detailed investigations of the short-range ion−ion correlations within each compound have been performed using the reverse Monte Carlo (RMC) modeling of the total scattering (Bragg plus diffuse) data. Although the short-range structural information for LiFePO4 is consistent with the long-range (averaged) picture, a small, but statistically significant, proportion of the anions is displaced away from their ideal sites within the RMC configurations of FePO4. These anion displacements are discussed in terms of a small concentration of Li+/Fe2+ occupying the empty octahedral sites, probably arising from incomplete delithiation of the LiFePO4 and/or antisite (Li+−Fe2+) defects introduced during the delithiation process.

1. INTRODUCTION Lithium-ion batteries provide a higher energy density compared to other rechargeable battery systems and now dominate the market for portable power sources, with a large number of manufacturers offering a wide range of batteries to meet a diverse range of technological applications.1−15 The principal advantages of lithium-ion batteries over other battery types are their high voltage, high energy density, low selfdischarge rate, and wide temperature range of operation. Nevertheless, they suffer from a number of limitations, including the need for relatively long recharging times, degradation of the battery performance after repeated charge−discharge cycles, and potential safety issues. These issues are a direct consequence of the materials used within the current lithium-ion batteries and have motivated extensive research effort aimed at identifying and characterizing new candidate compounds. There are numerous requirements placed on the cathode material for use in a lithium-ion battery,3,7,15 including (i) a metal cation that can be easily reduced or oxidized; (ii) the ability to accommodate a high concentration of Li+ (high energy density); (iii) rapid diffusion of Li+ for fast discharge/ charge (high power density); (iv) minimal structural changes to the host lattice during Li+ insertion/extraction (maximize cyclability and battery lifetime); (v) a high chemical potential (high operating voltage); (vi) a minimal change in the chemical potential with Li+ content (roughly constant voltage during discharge); (vii) stability with the electrolyte (safety); (viii) good electronic conductivity; (ix) low density (battery weight); (x) low cost; (xi) ease of fabrication; and (xii) © XXXX American Chemical Society

minimal environmental impact. Requirement (i) essentially restricts the choice to transition metals, whereas item (ix) favors the top row of elements, of which Cr must be excluded due to the toxicity of Cr4+ compounds (item (xii)). Oxides are favored over chalcogenides and halides, because they generally offer higher chemical potentials (item (v)). Therefore, the majority of candidate cathode materials for lithium-ion batteries are oxides of the transition metals Ti, V, Mn, Fe, Co, and Ni, with specific attention focussed on the LixMO2 (M = Mn, Co, and Ni) and LixM2O4 (M = Mn) systems and their discharge

M4+/M3+ couples (i.e., M 4 +XooooooooYM3 + + Li+). Of these, charge

LixCoO2 has advantages in terms of its performance (items (iv), (v), and (vi)) and has been widely used since first being exploited in commercial cells by Sony in the 1990s.16 However, it does have a drawback of higher cost (item (x)).10 Compared to other transition metals, Fe-based compounds are particularly attractive owing to their relative abundance and low cost. Li+ can be readily inserted into compounds such as αFe2O3, γ-Fe2O3, Fe3O4, and LiFe5O8 (see ref 17), but charge compensation occurs via the Fe 3+ /Fe 2+ couple (i.e., discharge

Fe3 +XooooooooYFe 2 + + Li+), which generally limits the operating charge

voltage to below 3 V. The replacement of the O2− anions by XO43− polyanions is an effective route to increase the electrochemical potential associated with the Fe3+/Fe2+ Received: February 7, 2019 Revised: May 23, 2019 Published: May 24, 2019 A

DOI: 10.1021/acs.chemmater.9b00552 Chem. Mater. XXXX, XXX, XXX−XXX

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Chemistry of Materials

0.05 ≤ x ≤ 0.89.21 However, in an operating battery under nonequilibrium conditions, this behavior is also dependent on factors such as particle size, current density, local compositional variations, and surface modifications.30−34 This paper presents the first diffraction study of the two end members, FePO4 and LiFePO4, using pair distribution function (PDF) analysis to probe the nature of the short-range ion−ion correlations.

2. EXPERIMENTAL SECTION The LiFePO4 powder was prepared by the solid-state reaction of stoichiometric amounts of Li2CO3, FeC2O4·H2O, and (NH4)2HPO4 using the method described previously17 and with the materials handled, as far as possible, under an inert atmosphere. Li2CO3 isotopically enriched with 7Li to 99.950%, supplied by the Oak Ridge National Laboratory, was used to avoid the significant neutron absorption cross-section associated with the 6Li content of natural lithium.35 The FePO4 powder was formed by chemical delithiation of the LiFePO4 using Br2(l) in an acetonitrile solution under an inert atmosphere, as discussed elsewhere.17 The neutron powder diffraction studies were performed using the Polaris diffractometer at the ISIS Facility, Rutherford Appleton Laboratory, United Kingdom.36 Data were collected using the backscattering “145°” (130−160°), “90°” (85−95°), low-angle “35°” (28− 42°), and very low-angle “14°” (13−15°) detector banks over the time-of-flight ranges 2.0−19.6, 1.5−19.2, 1.0−17.8, and 1.0−10.0 ms, respectively. The powdered samples were encapsulated in cylindrical 6 mm-diameter thin-walled (40 μm thickness) vanadium cans and measured for approximately 12 h to obtain counting statistics of sufficient statistical quality to allow the analysis of the total (Bragg plus diffuse scattering components) scattering. Initial Rietveld analysis, against all four datasets, of the averaged structures using only the Bragg scattering, was performed using the GSAS software.37 For the total scattering study, the measured neutron diffraction data was corrected for the effects of background scattering from the sample environment and beam attenuation using the program Gudrun,38 which also puts the scattered intensity onto the absolute scattering cross-section scale required for subsequent modeling. The resultant normalized total scattering structure factors, F(Q), were then used to obtain the corresponding total radial distribution functions, G(r), via a Fourier transform

Figure 1. Crystal structures of (a) LiFePO4 and (b) FePO4, illustrated using PO4 tetrahedra (green) and FeO6 octahedra (blue) and showing the channels along the [010] directions occupied by Li+ (black) in the case of LiFePO4.

couple,18,19 and particular attention has focussed on the compound LiFePO4 first reported by Padhi et al.20 LiFePO4 is increasingly used in lithium battery applications, with a theoretical capacity of 170 mAh g−1 and a flat voltage curve with a plateau at around 3.5 V,20,21 though there remain some technological challenges for electric vehicle use, including the requirement for fast charging (see, for example ref 22). LiFePO4 adopts the orthorhombic olivine crystal structure (space group Pnma, a = 10.3290(3)Å, b = 6.0065(2)Å, and c = 4.6908(2)Å, Z = 417). As illustrated in Figure 1a, the crystal structure comprises of a network of FeO6 octahedra and PO4 tetrahedra, providing potential pathways for Li+ diffusion in both the [010] and [001] directions. On simple Coulombic grounds, the former should be preferred, since the Li+ passes through a sequence of sites which do not share faces with occupied polyhedra, and this has been confirmed by measurements of the ionic conductivity using single-crystal samples,23 computer simulations,24,25 electron microscopy,26 and neutron diffraction experiments.27 In its fully delithiated state, the structure of FePO4 is essentially the same (space group Pnma, a = 9.8142(2)Å, b = 5.7893(2)Å, and c = 4.7820(2)Å, Z = 417) (Figure 1b). However, rather than a solid solution of the form 3+ LixFe2+ x Fe1−xPO4 for 0 ≤ x ≤ 1, the phase diagram for the LiFePO4−FePO4 system28,29 shows that, at least under temperatures close to ambient, the insertion/extraction of Li+ largely occurs via the formation of a two-phase mixture of the two end members, i.e., (LiFe2+PO4)x + (Fe3+PO4)1−x, where the solid solution regime has been reported to extend from

G(r ) =

1 (2π )3 ρ0

∫0

∞

4πQ 2F(Q )

sin Qr dQ Qr

(1) −3

where ρ0 is the average atom number density (in atoms Å ). G(r) can also be written as a sum of the individual partial radial distribution functions, gij(r), weighted by the concentrations of the two species, ci and cj, and their neutron scattering lengths, bi and bj, so that Ns

G(r ) =

Ns

∑ ∑ cicjbibj{gij(r) − 1} i=1 j=1

(2)

where Ns is the number of ionic species (i.e., four in the case of LiFePO4 and three in the case of FePO4). The partial radial distribution functions are given by gij(r ) =

1 nij(r ) 4πr 2dr ρj

(3)

where nij(r) is the number of particles of type j located at a distance between r and r + dr from a particle of type i and ρj is the number density of particles of type j, given by ρj = cjρ0 (for further details, see ref 39). The analysis of the total neutron scattering data was performed using the RMCProfile6 software,40 which uses the reverse Monte Carlo (RMC) method.41 Each RMC simulation used a configuration box of 9 × 14 × 17 unit cells, i.e., containing a total of 59976 atoms and 51408 atoms in the cases of LiFePO4 and FePO4, respectively. B


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Table 1. Summary of the Results of the Least-Squares Rietveld Refinement of the Neutron Powder Diffraction Data for LiFePO4 and FePO4, Presenting the Lattice Parameters, Positional Parameters, and Quality-of-Fit Parametersa LiFePO4 space group lattice parameters

unit cell volume Li in 4(a); 0, 0, 0, etc. Fe in 4(c); xFe, 1/4, zFe, etc. P in 4(c); xP, 1/4, zP, etc. O1 in 4(c); xO1, 1/4, zO1, etc. O2 in 4(c); xO2, 1/4, zO2, etc. O3 in 8(d); xO3, yO3, zO3, etc.

overall goodness-of-fit total number of data points total number of variables profile R-factors

weighted profile R-factors

FePO4

Pnma (#62) a = 10.32731(5)Å b = 6.00707(3)Å c = 4.69175(2)Å V = 291.062(2)Å3 Positional Parameters

Pnma (#62) a = 9.81251(5)Å b = 5.78751(3)Å c = 4.78183(2)Å V = 271.560(2)Å3

xFe = 0.28218(2) zFe = 0.97473(4) xP = 0.09482(3) zP = 0.41824(6) xO1 = 0.09695(3) zO1 = 0.74267(4) xO2 = 0.45714(3) zO2 = 0.20568(7) xO3 = 0.16550(2) yO3 = 0.04682(3) zO3 = 0.28506(4) Quality-of-Fit Parameters χ2 = 8.27 Nd = 17458 Nv = 112 Rp = 2.74% (v. low angle) Rp = 2.54% (low angle) Rp = 2.57% (90° detectors) Rp = 2.51% (backscatt.) Rwp = 3.63% (v. low angle) Rwp = 2.72% (low angle) Rwp = 2.01% (90° detectors) Rwp = 1.40% (backscatt.)

xFe = 0.27442(2) zFe = 0.95041(3) xP = 0.09298(3) zP = 0.39754(5) xO1 = 0.11944(2) zO1 = 0.70862(4) xO2 = 0.44194(2) zO2 = 0.16051(5) xO3 = 0.16770(2) yO3 = 0.04443(3) zO3 = 0.24951(4) χ2 = 5.23 Nd = 17468 Nv = 106 Rp = 2.03% (v. low angle) Rp = 1.94% (low angle) Rp = 1.93% (90° detectors) Rp = 1.72% (backscatt.) Rwp = 2.62% (v. low angle) Rwp = 1.84% (low angle) Rwp = 1.39% (90° detectors) Rwp = 1.07% (backscatt.)

a

The anisotropic thermal vibration parameters and derived bond lengths are listed in Tables 2 and 3, respectively. The derived bond angles are given in Table S1 in the Supporting Information supporting this manuscript. The RMC simulations were fitted using the reciprocal space data, F(Q), and the real space data, G(r), plus the Bragg profile data, which ensures that the model is consistent with the average structure. The former is broadened by convolution with a box function to reflect the finite size of the simulation box, where

Fbox(Q ) =

1 π

common O3 vertices in the (011) plane. By contrast, the LiO6 octahedra (LiO12O22O32 units) share common (O1O2) edges to form chains in the [010] direction. Each FeO6 octahedron has common (O1O2) edges with two LiO6 octahedra, whereas each PO4 tetrahedron shares one (O3O3) edge with an FeO6 octahedron and two (O2O3) edges with LiO6 octahedra. The crystal structure of FePO4 is essentially the same as that of LiFePO4 but with the LiO6 octahedra unoccupied. 3.1. Rietveld Refinements. The initial Rietveld refinements of the neutron powder diffraction data collected from the LiFePO4 and FePO4 used the data collected in all four detector banks and varied the lattice parameters, atomic positional parameters, and isotropic thermal vibration parameters. Additional fitted parameters comprised a scale factor, absorption correction factor, peak width parameters describing Gaussian and Lorentzian contributions to the Bragg profile and the coefficients of a 10th order shifted Chebyshev polynomial function to describe the background scattering. This procedure provided a good fit to the experimental data, with goodness-offit χ2 values of 11.46 and 7.94 for LiFePO4 and FePO4, respectively. However, slight discrepancies between the intensities of some of the Bragg peaks remained and, as some of the isotropic thermal vibration parameters showed larger values that was expected for a typical oxide measured under ambient conditions, the thermal vibration parameters were allowed to vary anisotropically. This resulted in a

∞

∫−∞ Fexpt(Q ′) sin LQ(Q−−QQ′ ′)/2 dQ ′

(4)

L is the smallest dimension of the RMC configuration and, as such, defines the upper limit of G(r) to be L/2 (∼40 Å). To improve the statistical significance of the results, 100 simulations were performed starting from the fitted configuration but using a different seed for the random number generator to produce distinct ionic arrangements (but with comparable goodness-of-fit values).

3. RESULTS Prior to presenting the experimental results obtained from the analysis of the neutron powder diffraction data, it is instructive to describe the orthorhombic olivine structure of LiFePO4 in more detail. The oxygen sublattice is formed by three crystallographically distinct anion sites (O1 and O2 in 4(c) sites and O3 in the 8(d) general positions of the space group Pnma) and generate a slightly distorted hexagonal close-packed arrangement. The P5+ reside in 4(c) sites and fill tetrahedral cavities, whereas the Li+ and Fe2+ both occupy 4(c) positions and are surrounded by an octahedron of anions. The FeO6 octahedra are formally FeO1O2O34 units and are linked via C


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Chemistry of Materials Table 2. Anisotropic Thermal Vibration Parameters of LiFePO4 and FePO4, Obtained by the Least-Squares Rietveld Refinement of the Neutron Powder Diffraction Data LiFePO4 Li

Fe

P

O1

O2

O3

thermal parameters u11,Li = 0.0125(4)Å2 u22,Li = 0.0076(4)Å2 u33,Li = 0.0080(4)Å2 u12,Li = −0.0011(3)Å2 u13,Li = −0.0016(4)Å2 u23,Li = −0.045(3)Å2 u11,Fe = 0.00462(7)Å2 u22,Fe = 0.00495(8)Å2 u33,Fe = 0.00662(8)Å2 u13,Fe = 0.00067(6)Å2 u11,P = 0.00432(12)Å2 u22,P = 0.00456(11)Å2 u33,P = 0.00316(12)Å2 u13,P = 0.00012(10)Å2 u11,O1 = 0.00946(12)Å2 u22,O1 = 0.00927(13)Å2 u33,O1 = 0.00345(13)Å2 u13,O1 = −0.00073(11)Å2 u11,O2 = 0.00480(11)Å2 u22,O2 = 0.01032(12)Å2 u33,O2 = 0.00661(14)Å2 u13,O2 = −0.00016(10)Å2 u11,O3 = 0.00914(9)Å2 u22,O3 = 0.00516(8)Å2 u33,O3 = 0.00674(9)Å2 u12,O3 = 0.00241(7)Å2 u13,O3 = 0.00159(7)Å2 u23,O3 = 0.00042(6)Å2

FePO4

u11,Fe = 0.00403(6)Å2 u22,Fe = 0.00419(6)Å2 u33,Fe = 0.00377(6)Å2 u13,Fe = −0.00005(5)Å2 u11,P = 0.00424(10)Å2 u22,P = 0.00490(9)Å2 u33,P = 0.00277(11)Å2 u13,P = −0.00018(7)Å2 u11,O1 = 0.00620(10)Å2 u22,O1 = 0.00952(11)Å2 u33,O1 = 0.00439(12)Å2 u13,O1 = −0.00083(7)Å2 u11,O2 = 0.00335(9)Å2 u22,O2 = 0.01028(11)Å2 u33,O2 = 0.00739(1)Å2 u13,O2 = −0.00002(7)Å2 u11,O3 = 0.00769(7)Å2 u22,O3 = 0.00469(6)Å2 u33,O3 = 0.00564(6)Å2 u12,O3 = 0.00175(6)Å2 u13,O3 = 0.00135(6)Å2 u23,O3 = 0.00031(5)Å2

Figure 2. Least-squares fits to the powder diffraction data collected at ambient temperature from the (a) FePO4 and (b) LiFePO4 samples at back-scattering angles. The dots represent the measured data points and the solid line is the final calculated profile. The lower trace shows the difference (measured minus calculated) and the row of tick marks across the top denotes the positions of the Bragg reflections allowed in the Pnma symmetry.

significant decrease in the χ2 values (to 8.27 and 5.223), and a summary of the Rietveld refinements is shown in Table 1, with the anisotropic thermal vibration parameters listed in Table 2. Subsequent attempts to further improve the quality of the fit by, for example, allowing some swapping of Li and Fe within LiFePO4 or including a small fraction of Li on the empty octahedral sites within FePO4, did not produce a statistically significant reduction in χ2 value. The latter is consistent with the absence of any noticeable scattering density in those sites within difference Fourier maps. Both samples (FePO4 and LiFePO4) are phase pure, and not more than 0.2 wt % of any impurity phase could be observed by Bragg diffraction. Also, any attempts using a mixed phase did not improve the PDF refinement by using the small box modeling program PDFgui (see the Supporting Information for details). Figure 2 illustrates the quality of the least-squares refinement for the highest resolution neutron powder diffraction data, collected using the back-scattering detector bank, whereas corresponding figures for the other three detector banks are provided as Figures S1−S3 in the Supporting Information supporting this manuscript. 3.2. RMCProfile Modeling. The results from average structure refinements of the neutron powder diffraction data from LiFePO4 and FePO4 shown in Table 1 have been used to generate approximately cubic supercells comprising 9 × 14 × 17 unit cells. These form the starting model for the analysis of the total (Bragg plus diffuse) scattering data using the

RMCProfile method. Typical configurations obtained for each compound (1 of the 100 performed for each) are illustrated in Figure 3, with the quality of the fits to the real space G(r) and reciprocal space F(Q) datasets shown in Figures 4 and 5, respectively. The simultaneous fitting to the Bragg data gave similar quality fits to those obtained by Rietveld analysis of the Bragg data alone (Figure 2) and are shown as Figure S4 in the Supporting Information. From the full ionic configurations for each compound, it is possible to extract the partial radial distribution functions, gij(r), averaged over the 100 individual runs. As shown in Figure 6, the cation−anion distributions appear largely consistent with the bond lengths extracted from the averaged structural models (Table 3). This indicates the absence of significant local disorder within the crystalline lattice, of the sort seen in other systems.42 The anion−anion partial radial distribution functions, shown in Figure 7, show peaks that are rather broader than the cation−anion ones, consistent with their larger values of anisotropic thermal vibrations (Table 2). Closer inspection of the gOO(r) distributions from the crystallographically distinct O1, O2, and O3 anions provides some evidence of limited disorder involving the O1 and O2 D


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Figure 3. Typical RMC-derived configurations for (a) LiFePO4 and (b) FePO4. The configuration boxes comprise 9 × 14 × 17 unit cells and show the Li (black), Fe (blue), P (green), O1 (red), O2 (pink), and O3 (purple) ions.

indicate significant anisotropy in the thermal vibrations of the anions in both LiFePO4 and FePO4. In the former case, there is also significant anisotropy in the distribution of the Li+ density around the octahedral center. Interestingly, this does not extend directly in the [010] direction (i.e., in the preferred Li+ diffusion direction) but is consistent with the curved onedimensional Li+ density distribution reported previously on the basis of the maximum entropy analysis of neutron powder diffraction data.27 The nature of the structural disorder within the LiFePO4 and FePO4 samples will be discussed further in Section 4.2. 4.2. Short-Range Correlations. As discussed in Section 3.2, the ionic distributions within the unit cell of LiFePO4 derived from the RMC modeling of the total neutron scattering data are broadly in line with the averaged structure determined by the Rietveld refinement of the Bragg diffraction data alone. However, this is not the case for FePO4. Specifically, around 1.7% of the O1 anions within the RMC refined configurations is displaced from their regular positions by more than 0.6 Å and around 2.3% of the O2 anions is displaced by more than 0.45 Å (where the cut-off values have been chosen based on the overall distribution of displacements as the point between the main peak and the second, smaller one). We denote these displaced anion sites as O1′ and O2′, and although the concentrations of anions occupying these sites are very small (and comprise around 1% of all of the anions), their presence is very consistent across all of the 100 refined configurations. On that basis, it is reasonable to believe that they represent real features within the FePO4 sample, especially as we observe no significant disorder around the O3 site. There is also an indication of these features within the Rietveld refinements of the Bragg scattering data from FePO4, where the anisotropic thermal vibration parameters shown in

sites specifically in the case of FePO4, which can be more clearly seen by transforming all of the ions in the supercell into a single unit cell, such that each individual cloud consists of 2142 individual ions. The shape of each cloud then represents the position and anisotropic thermal displacements for atoms in the given crystallographic position. As illustrated in Figure 8, a fraction of both the O1 and O2 anions in FePO4 is significantly displaced away from the idealized positions, in roughly [010] directions. The nature of this disorder is discussed further in Section 4.2. For completeness, the gij(r) partial radial distribution functions for cation−cation pairs are shown in Figure S5 of the Supporting Information.

4. DISCUSSION 4.1. Average Structure. The fitted parameters presented in Table 1 are in good agreement with those published previously,17,43,44 though with significantly lower estimated standard deviations reported in this work. It is clear that lithium insertion does not change the FePO4 structure significantly, although it causes anisotropic lattice expansion: positive in the [100] and [010] directions and negative in the [001] direction. As a consequence, the overall volume of the unit cell increases by 7.18%, and the total atom density of LiFePO4 is 8.85% higher than that of FePO4. The anion co-ordinations around each of the cation species within LiFePO4 and FePO4 are illustrated in Figure 9, derived from the positional parameters listed in Table 1. The reduction in atom density on going from LiFePO4 to FePO4 can be seen in terms of a shortening of some of the Fe−O bonds in the FeO6 octahedra (presumably associated with the change from Fe2+ to Fe3+) and a tilting of the PO4 tetrahedra roughly around the [010] direction. The thermal ellipsoids are also shown in Figure 9, using the information listed in Table 2, and E


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Figure 4. Plots of the fits to the radial distribution function, G(r), of (a) LiFePO4 and (b) FePO4. The dots are the experimental data points and the solid line is the calculated profile, with the difference profile shown in the lower plot.

Figure 5. Plots of the fits to the total neutron scattering factor, F(Q) of (a) LiFePO4 and (b) FePO4. The dots are the experimental data points and the solid line is the calculated profile, with the difference profile shown in the lower plot.

Figure 9 are (subject to the constraints imposed by the space group symmetry) consistent with the additional anion density around the O1 and O2 sites in the directions of the O1′ and O2′ positions, respectively. The comparison is shown in Figure S6 in the Supporting Information supporting this manuscript. With such a small number of anions occupying the O1′ and O2′ sites, it is not straightforward to analyze their origin. However, it is possible to make a number of observations. The occupied O1′ and O2′ sites appear to be randomly distributed throughout the configuration boxes, with no evidence of clusters of anions residing on O1′ or O2′ sites. Nevertheless, around half of all of the O1′ and O2′ anions form O1′−O2′ pairs with a separation of 2.5−3.1 Å. As illustrated in Figure 10a, virtually all of these O1′−O2′ pairs are aligned along the [010] direction. To clarify the nature of these pairs, we note that nondisplaced O1 and O2 anions within the ideal structure of FePO4 approach each other in two ways, with O1−O2 contacts of ∼2.48 Å in essentially ⟨101⟩ directions along one edge of the PO4 tetrahedra and longer contacts of 2.96 Å in chains along the [010] axis, which link the oxygen anions, which form the vertices of the corner sharing FeO6 octahedra and PO4 tetrahedra. These contacts are illustrated in Figure 10b. The lengths and orientation of the O1′−O2′ close contacts observed in the RMC configurations of FePO4 essentially correspond to those O1−O2 contacts along the [010] direction in FePO4.

As the O1′−O2′ pairs form edges of the octahedra occupied by Li+ in LiFePO4, the discussion above initially points to the presence of some Li+ cations remaining within the empty octahedral cavities in the FePO4 sample, which are filled in the LiFePO4 material. However, the situation is less straightforward, as a detailed analysis of the RMC configurations for FePO4 shows that all of the O1′ anions are within 2.3 Å of the octahedral center (which is straightforward to identify, as it is the crystallographic origin), and all of the O2′ anions are within 2.2 Å of these sites. On the one hand, this indicates that none of the displaced anions has moved into positions that give implausible distances but provides only a limited indication of what the central cation might be. Considering the ionic radii45 and the average of the bond distances from the Rietveld refinements of LiFePO4 and FePO4 listed in Table 3, it is likely that Fe3+ is too small, but Li+ and Fe2+ are plausible. Unfortunately, bond valence calculations, performed by placing each cation species at the center of the “empty” octahedra, do not give a clear preference. As discussed in Section 3.1, no significant improvement to the quality of the Rietveld fit to the FePO4 diffraction data was obtained through placing either Li or Fe onto the empty site, and there was no significant residual nuclear density in these positions in a Fourier difference map. Given that the neutron scattering lengths of Li and Fe are of opposite sign (bLi7 = −2.22 fm and bFe = 9.4535), the most likely explanation is that both species are present in low F


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Figure 6. Partial radial distribution functions gij(r) for cation−anion pairs in (a) LiFePO4, (b) FePO4 obtained from the final RMC configurations. The tick marks along the top of the plot show the cation−anion distances (first co-ordination shell) calculated from the averaged structure derived from Rietveld refinements of the Bragg scattering (see Table 3).

Figure 7. Partial radial distribution functions gij(r) for anion−anion pairs in (a) LiFePO4, (b) FePO4 obtained from the final RMC configurations. The contributions to the total gOO(r) from the contacts between the symmetry-independent anion sites are shown.

Li+ arises from incomplete delithiation, whereas the Fe2+ is suggestive of some antisite disorders within the FePO4 sample. As there is no evidence of any significant ionic disorder in either the Rietveld or RMC analysis of the LiFePO4 diffraction data, the latter must occur during the delithiation process of LiFePO4. Although the extent of the lattice disorder within the FePO4 sample is limited to only around 1% of all anions, this is consistent with the 5% solid solubility limit of Li+ in FePO4 reported previously.21 For the alternative explanation, computational studies have shown that Li−Fe antisite defects are the most energetically favorable instrinsic defects within LiFePO4,24,46−48 with a formation energy ranging from 0.51− 0.5549,50 to 0.74 eV.24,47 Such defects are a significant hindrance to the widespread use of LiMPO4 (M = Fe, Co, Ni, and Mn)-based cathode materials in rechargeable batteries, where the disappointing electrochemical properties shown by materials synthesized by hydrothermal methods at relatively low temperatures have been attributed to the formation of Li− M antisite defects in which the M cation blocks the Li+ diffusion channels in the [010] directions.49−53 As a consequence, the Li+ are forced to hop across channels, which have a higher energy barrier.54,55 The concentration of antisite defects under ambient conditions is typically also rather low (of the order of a few %), making it difficult to

Table 3. Bond Lengths within LiFePO4 and FePO4, Derived from the Parameters Obtained by Least-Squares Rietveld Refinement of the Neutron Powder Diffraction Data Given in Table 1 LiFePO4 Li−O (octahedral)

Fe−O (octahedral)

P−O (tetrahedral)

polyhedral bond lengths Li−O2 2.0876(2)Å × 2 Li−O1 2.1715(2)Å × 2 Li−O3 2.1884(2)Å × 2 average = 2.1492 Å Fe−O3 2.0647(2)Å × 2 Fe−O2 2.1068(3)Å Fe−O1 2.2011(4)Å Fe−O3 2.2499(3)Å × 2 average = 2.1562 Å P−O1 1.5223(4)Å P−O2 1.5362(4)Å P−O3 1.5534(3)Å × 2 average = 1.5413 Å

FePO4

Fe−O1 1.9104(2)Å Fe−O2 1.9265(2)Å Fe−O3 2.0370(2)Å × 2 Fe−O3 2.1349(2)Å × 2 average = 2.0301 Å P−O2 1.5078(4)Å P−O1 1.5100(3)Å P−O3 1.5665(2)Å × 2 average = 1.5377 Å

concentrations within the empty octahedral cavities in the FePO4 sample, with their ratio such that the effective scattering length of the site is close to zero. It is likely that the presence of G


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quenched from high temperatures. Additional evidence has been provided by scanning tunneling electron microscopy,48 and a combined nuclear magnetic resonance and Monte Carlo simulation study concluded that although the concentration of such defects on LiFePO4 was only ∼0.5%, around 80% of the diffusion channels contains such defects64 and the capacity fading in LiCoPO4-based batteries has been attributed to the formation of antisite defects during battery discharge.65,66 Finally, other polyanionic iron-based compounds also show a propensity toward forming Li−Fe antisite defects during lithium extraction.67 Thus, the factors which influence and, ideally, restrict the formation of such antisite defects, are a key issue for the successful future use of LiMPO4-based cathodes in future lithium battery technologies.

5. CONCLUSIONS The crystal structures of LiFePO4 and FePO4 have been investigated using neutron powder diffraction, with the Rietveld refinement of the Bragg scattering and reverse Monte Carlo (RMC) modeling of the total scattering data used to provide a model of the long-range and short-range ionic distribution. Although the average structures are consistent with previous reports of the crystal structure and the RMC modeling of the LiFePO4 data is consistent with the averaged structure, a small number of significantly displaced anions are observed in the RMC configurations of FePO4, which have been discussed in terms of incomplete delithiation of the sample and/or antisite (Li+−Fe2+) defects. Finally, from the technique point-of-view, it is clear that this work sits at the limits of what can currently be achieved using the total neutron scattering method, though its ability to identify such a low concentration of defects in FePO4 is rather impressive. Looking to the future, the development of new, high-countrate powder diffractometers and high-intensity neutron sources will increase the sensitivity of the technique, with the ultimate goal of performing time-resolved total scattering studies on the neutron diffractometer, using in situ electrochemical cells to probe the structural properties during charge/discharge cycling.

Figure 8. Density of ions within the unit cells of (a) LiFePO4 and (b) FePO4 derived from the final RMC configurations. The ions shown are Li (black), Fe (blue), P (green), O1 (red), O2 (pink), and O3 (purple).

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.chemmater.9b00552. Bond lengths and bond angles within LiFePO4 and FePO4, derived from the parameters obtained by the Rietveld refinement of the neutron powder diffraction data; fits to the neutron powder diffraction data for LiFePO4 and FePO4 collected in the medium, low-angle and very low-angle detector banks, fit to the neutron powder diffraction data for LiFePO4 and FePO4 as a part of the RMC fitting procedure; selected partial radial distribution functions for LiFePO4 and FePO4 obtained from the final RMC configurations; comparison of the anisotropic thermal ellipsoid of the O1 anions obtained from the average structure refinement with the ionic density derived from the RMCProfile modeling of the local structure; discussion of possible multiple phase models of FePO4 (PDF)

Figure 9. Anion co-ordinations around the (a) Li+, (b) Fe2+, and (c) P5+ in LiFePO4 and around the (d) Fe3+ and (e) P5+ in FePO4, derived from the results of the Rietveld refinement of the Bragg diffraction data listed in Table 1.

probe them experimentally.15,48,49,56−61 Diffraction studies of LiFePO462 and LiFe1−xMnxPO463 have shown the presence of an antisite disorder, with the former study observing changes in the lattice parameters and site occupancies in samples H


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Figure 10. (a) Typical plot of a final RMC configuration of FePO4, showing the locations of the displaced O1′ and O2′ atoms (see text) and illustrating their tendency to form pairs in the [010] direction. (b) A polyhedral representation of the structure of FePO4 showing the two shortest O1−O2 contacts.

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(7) Bruce, P. G.; Cahn, R.; Bagshaw, N. E.; Hamnett, A. Rechargeable lithium batteries. Philos. Trans. R. Soc., A 1996, 354, 1577−1594. (8) Delmas, C.; Ménétrier, M.; Croguennec, L.; Levasseur, S.; Pérès, J. P.; Pouillerie, C.; Prado, G.; Fournès, L.; Weill, F. Lithium batteries. A new tool in solid state chemistry. Int. J. Inorg. Mater. 1999, 1, 11− 19. (9) Goodenough, J. B.; Kim, Y. Challenges for rechargeable Li batteries. Chem. Mater. 2010, 22, 587−603. (10) Nishi, Y. Lithium ion secondary batteries. Past 10 years and the future. J. Power Sources 2001, 100, 101−106. (11) Owen, J. R. Rechargeable lithium batteries. Chem. Soc. Rev. 1997, 26, 259−267. (12) Palacín, M. R. Recent advances in rechargeable battery materials. A chemist’s perspective. Chem. Soc. Rev. 2009, 38, 2565− 2575. (13) Scrosati, B.; Garche, J. Lithium batteries. Status, prospects and future. J. Power Sources 2010, 195, 2419−2430. (14) Tarascon, J. M.; Armand, M. Issues and challenges facing rechargeable lithium batteries. Nature 2001, 414, 359−367. (15) Whittingham, M. S. Lithium batteries and cathode materials. Chem. Rev. 2004, 104, 4271−4302. (16) Nagaura, T.; Tazawa, K. Lithium ion rechargeable battery. Prog. Batteries Sol. Cells 1990, 9, 209−217. (17) Andersson, A. S.; Kalska, B.; Häggström, L.; Thomas, J. O. Lithium extraction/insertion in LiFePO4: an X-ray diffraction and Mössbauer spectroscopy study. Solid State Ionics 2000, 130, 41−52. (18) Manthiram, A.; Goodenough, J. B. Lithium insertion into Fe2(MO4)3 frameworks. Comparison of M = W with M = Mo. J. Solid State Chem. 1987, 71, 349−360. (19) Manthiram, A.; Goodenough, J. B. Lithium insertion into Fe2(SO4)3 frameworks. J. Power Sources 1989, 26, 403−408. (20) Padhi, A. K.; Nanjundaswamy, K. S.; Goodenough, J. B. Phospho-olivines as positive-electrode materials for rechargeable lithium batteries. J. Electrochem. Soc. 1997, 144, 1188−1194. (21) Yamada, A.; Koizumi, H.; Nishimura, S. I.; Sonoyama, N.; Kanno, R.; Yonemura, M.; Nakamura, T.; Kobayashi, Y. Room temperature miscibility gap in LixFePO4. Nat. Mater 2006, 5, 357− 360. (22) Wang, J.; Sun, X. Olivine LiFePO4. The remaining challenges for future energy storage. Energy Environ. Sci. 2015, 8, 1110−1138. (23) Li, J.; Yao, W.; Martin, S.; Vaknin, D. Lithium ion conductivity in single crystal LiFePO4. Solid State Ionics 2008, 179, 2016−2019. (24) Islam, M. S.; Driscoll, D. J.; Fisher, C. A. J.; Slater, P. R. Atomic scale investigation of defects, dopants, and lithium transport in the LiFePO4 olivine-type battery material. Chem. Mater. 2005, 17, 5085− 5092.

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Wojciech A. Sławiński: 0000-0002-9578-0374 Helen Y. Playford: 0000-0001-5445-8605 Torbjörn Gustafsson: 0000-0003-2737-4670 Kristina Edström: 0000-0003-4440-2952 William R. Brant: 0000-0002-8658-8938 Present Addresses ⊥

Pharmaceutical Technology and Development, AstraZeneca, Pepparedsleden 1, 431 83 Mölndal, Sweden (S.T.N.). ∥ Faculty of Chemistry, University of Warsaw, Pasteura 1, 02093 Warsaw, Poland (W.A.S.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The U.K. Science and Technology Facilities Council (STFC) is thanked for allocating beamtime at the ISIS Facility. W.A.S., S.T.N., and S.G.E. wish to thank Vetenskapsrådet (Swedish Research Council, grant number VR-2012-5240) for financial support.

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DEDICATION Paper dedicated to the memory of Prof. S.G. Eriksson, for his contribution to neutron science. REFERENCES

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Neutron Pair Distribution Function Study of FePO4 and LiFePO4

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