Computational Identification and Experimental Realization of Lithium

Feb 12, 2015 - NMR spectroscopy and calculations reveal that the energy barrier to site-to-site hopping is 0.3–0.5 eV, comparable with best-in-class...
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Computational Identification and Experimental Realization of Lithium Vacancy Introduction into the Olivine LiMgPO4 Leopoldo Enciso-Maldonado,† Matthew S. Dyer,† Michael D. Jones,† Ming Li,† Julia L. Payne,† Michael J. Pitcher,† Mona K. Omir,† John B. Claridge,† Frédéric Blanc,*,†,‡ and Matthew J. Rosseinsky*,† †

Department of Chemistry, University of Liverpool, Crown Street, Liverpool, L69 7ZD, United Kingdom Stephenson Institute for Renewable Energy, University of Liverpool, Crown Street, Liverpool, L69 7ZD, United Kingdom

S Supporting Information *

ABSTRACT: Calculation of the energetics of aliovalent substitution into the olivine LiMgPO4 suggests that replacement of Mg2+ by In3+ is the most effective way to introduce lithium vacancies and thus generate Li ion conductivity. Experimental synthesis accesses materials with up to 17% Li vacancy content. An order-of-magnitude increase in the high-temperature hopping rates probed by 7Li NMR spin−lattice relaxation, and over 2 orders of magnitude increase in the room-temperature Li+ ion conductivity measured by impedance spectroscopy is observed upon the introduction of In3+ ions and Li vacancies. NMR spectroscopy and calculations reveal that the energy barrier to site-to-site hopping is 0.3−0.5 eV, comparable with best-in-class nonoxide systems such as argyrodite, but NMR-derived hopping rates, and impedance spectroscopy shows that longer range transport is less facile with activation energies in the range of 0.7−1 eV. Calculations suggest that this is because the Li vacancies are strongly bound to the In3+ dopants, suggesting that high lithium mobilities in oxides are accessible but high conductivities require strategies to separate defect from dopant.

anisotropic conductivity.9 LiFePO4 adopts the olivine structure (Figure 1a) in which a close-packed array of O2− ions is

INTRODUCTION Recently, there has been considerable attention toward the development of fast solid-state Li+ ion conductors,1,2 largely driven by their proposed use as electrolytes in all solid-state Li+ ion batteries3 that are safer to operate than conventional Li+ ion batteries containing flammable organic liquid electrolytes. However, the most challenging issue associated with solidstate Li electrolytes remains the low bulk Li+ ion conductivity at room temperature. Substantial progress has recently been made, with the development of inorganic crystalline solids, which have competitive bulk ionic conductivities of ∼10−2 S cm−1 at room temperature,4−6 in the same range as established liquid electrolytes, although there are still potential challenges with environmental issues and electrochemical stability. The identification of new families of lithium ion conductors and the development of methodologies that enable this is thus an important problem. One approach to the development of new solid-state Li+ ion electrolytes is to consider electronically insulating analogues of known Li electrode compounds, which must support sufficient Li+ ion diffusion to allow Li intercalation and deintercalation. Since the discovery of the reversible Li extraction from LiFePO4 and Li insertion in FePO4 by Goodenough et al. in 1997,7 LiFePO4 has emerged as a leading Li+ ion battery cathode material. 8 Although the mechanism of (de)intercalation remains under extensive debate,9 Li+ ions must be mobile in bulk LiFePO4, and appear to have highly © 2015 American Chemical Society

Figure 1. (a) Olivine structure of LiFePO4/LiMgPO4, showing layers of corner-sharing Fe/Mg octahedra (orange) alternating with layers of edge-sharing Li octahedral chains (green), linked by PO4 tetrahedra (purple). Oxygen atoms are shown in red. (b) One-dimensional (1-D) chain of Li+ ions, showing (with arrows) a proposed Li+ ion transport pathway through a tetrahedral interstitial site (yellow). Received: December 9, 2014 Revised: February 6, 2015 Published: February 12, 2015 2074

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10−10 cm2 s−1 obtained by converting the local hopping rate determined by μSR to a long-range diffusion coefficient.27 Defects in LiFePO4 have been shown to affect properties such as capacity and diffusivity. Samples reported to have a high degree of Li/Fe disorder have been shown to have a low diffusion coefficient (5.83 × 10−14 cm2 s−1, measured using impedance spectroscopy) with this value increasing to 2.56 × 10−13 cm2 s−1 for LiFePO4 with a lower defect content.30 An improvement in specific capacity in hydrothermally prepared LiFePO4 after annealing at 773 K was attributed to the removal of Fe from the Li channels.22 Electronically insulating olivines related to LiFePO4 have been computationally screened as potential Li+ ion conductors for use as solid-state electrolytes.31 A low-energy diffusion pathway was identified in which Li+ ions move along the chain of edge-sharing octahedra, traveling through connecting tetrahedral sites (Figure 1b); however, it was noted that Li+ ion conductivity in these systems would rely on the presence of Li+ ion vacancies. Vacancies within crystal structures can be created chemically by aliovalent substitution, in which a proportion of cations within the crystal structure are replaced with cations with a higher charge, creating charge compensating vacancy defects. We present the successful doping of an electronically insulating olivine with the concurrent creation of Li+ ion vacancies and increase in Li+ ion conductivity. The olivine LiMgPO432,33 contains only abundant, nontoxic elements and is predicted to have a low barrier to Li+ ion diffusion of 0.3 eV,31 comparable to that of known good Li+ ion conductors.5,6,34 Previously, LiMgPO4 has been doped with up to 20% Zn2+ for Mg2+ to improve dielectric properties,35 with ∼1% lanthanides to create phosphors36,37 and with 0.1% Co2+ and up to 10% Fe3+ for Li+ in magnetic studies.38−40 No increase in ionic conductivity was observed alongside Li+ vacancy creation with aliovalent doping with Fe3+, presumably due to Coulombic trapping of Li+ ion vacancies by dopant ions and the blocking action of heavy dopant ions within 1-D Li+ chains.40 Solid-state NMR has proven a very valuable technique to investigate the atomic-scale structure and dynamics of inorganic materials,41 and, in particular, in fast solid-state Li+ ion conductors, taking advantage of the fact that both 6Li (spin I = 1, natural abundance = 7.5%) and 7Li (spin I = 3/2, natural abundance = 92.5%) isotopes of lithium are NMR-active nuclei. While 6Li solid-state NMR spectra in combination with magic angle spinning (MAS) are used for structural elucidation, because of the high resolution (often) obtained in 6Li NMR, 7 Li solid-state NMR spectra of diamagnetic Li-containing materials are often broad and lack any spectral features, because of the combination of both 7Li−7Li dipolar coupling and quadrupolar broadenings.41 However, these interactions are very sensitive to mobility on the NMR time scale (Hz to MHz), and high-temperature 7Li NMR line shape analysis and spin− lattice relaxation rates have been used to successfully probe lithium mobility, including the quantitative measurements of Li diffusion hopping frequencies, in fast solid-state Li+ ion conductors.6,42−52 Such an approach to the understanding of the Li mobility cannot be used in LiFePO4,53−55 because the 7 Li NMR line shape is dominated by the large hyperfine coupling between the electronic magnetic moment of Fe2+ and the Li nuclei, and the bulk magnetic susceptibility.56 In addition, the spin−lattice relaxation rates are dominated by the short paramagnetic relaxation times and not by long-range Li diffusion.

occupied by interstitial cations forming one-dimensional (1-D) chains of edge-sharing LiO6 octahedra, corner-sharing FeO6 octahedra, and PO4 tetrahedra. Li+ ion transport is proposed to occur via hopping along the chains of LiO6 octahedra, and is probably hindered by the presence of Fe2+ in the chains resulting from low concentrations of Li+/Fe2+ antisite defects.8−10 The defect chemistry and doping limits in LiFePO4 have been subject to debate, with the precise degree and nature of cation disorder being dependent on the synthetic route and preparation temperature.11−18 A range of aliovalent and isovalent substitutions have been explored in LiFePO4. Meethong et al. outlined five possible substitution mechanisms and explored these experimentally, finding that the mechanism in Li1−nxMn+xFePO4 (M = Mg2+, Al3+, Zr4+, Nb5+), with dopant and vacancy located on the Li site, showed the largest change in cell parameters.12 Doping with Zr4+ was possible up to x ≈ 0.1. Wagemaker et al. also studied aliovalent substitution in Li1−nxMn+xFePO4 and found that Cr3+, Zr4+, or Nb5+ could be accommodated on the Li site at a level of up to 3% in LiFePO4, with the formation of charge-compensating Li vacancies on the Li site.13 In the same study, less than 1% Li on the Fe site was also reported.13 When prepared via a conventional solid-state route, LiFePO4 is free of Li−Fe antisite defects at 958 K, but annealing just below the melting point at 1248 K results in 4% Li−Fe antisite defects, and this process can be reversed.19 In contrast to this true cation antisite defect mechanism, Fe-rich LiFePO4, Li1−2xFexFePO4, has also been reported when LiFePO4 has been synthesized hydrothermally or as single crystals (from an iron-rich flux).20−22 A recent pair distribution function study has shown that hydrothermally prepared LiFePO4 consists of a Li1−2xFexFePO4 phase (x = 0.075) which coexists with an amorphous phase.20 This mixed crystalline−amorphous phase becomes fully stoichiometric LiFePO4 by increasing the duration and temperature of the hydrothermal reaction.20 Other “nonstoichiometric” olivines (Li1−nxMn+xMPO4 where in this case M = Ni, Co, Mn or Fe) have been reported, with a recent study showing that a structural distortion from orthorhombic to monoclinic also occurs.23 Several studies have also shown that vacancies may be accommodated on the Fe site. For example, Gibot et al. have reported a composition of (□0.07Li0.89Fe0.04)(□0.08Fe0.92)PO4 (where □ = vacancy) for nanosized “LiFePO4” prepared via a low-temperature precipitation method,24 while LiFe1−3x/2Vx□x/2PO4 (0 ≤ x ≤ 0.2) has also been reported.25 Transmission electron microscopy techniques have been used by Chung et al. to study the antisite defect ordering in both LiMnPO4 and LiFePO4, and have found that, in LiFePO4, defect clusters occur, while in LiMnPO4 defects are randomly distributed, indicating that the ordering is dependent on the M2+ cation.26 Lithium mobility in LiFePO4 has been probed experimentally by a range of different techniques, including muon spin relaxation (μSR)27 and the galvanostatic intermittent titration technique (GITT).28,29 However, the room temperature bulk diffusivity of LiFePO4 is difficult to determine in ceramics due to material inhomogeneities, with only a fraction of grains contributing to diffusion at any one time.8,9 Using a model as an attempt to include the effect of solid-solution regions and phase coexistence in LixFePO4, Churikov et al. reported a RT diffusion coefficient of 8 × 10−11 cm2 s−1 for Li0.999FePO4, as determined by the potentiostatic intermittent titration technique.29 This is in reasonable agreement with the 5 × 2075

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NMR parameters were calculated using the periodic DFT code CASTEP.63 The structures of LiMgPO4 and the lowest energy configuration of Li31/32Mg31/32In1/32PO4 were relaxed in CASTEP with ultrasoft pseudo-potentials and an increased cutoff of 700 eV; otherwise, DFT settings were equivalent to those described above. Chemical shielding and electric field gradient tensors were calculated using the GIPAW64−67 method, as implemented in CASTEP. MD calculations were performed using GULP,68 with classical force fields describing interactions between ions. The polarizability of the O2− ions was included in the summation of long-range Coulomb interactions through a core−shell approach,69 with a shell charge of −2.96qe and a spring constant of 65 eV Å−2. Buckingham potentials were used to model short-range interactions between ions, with the parameters listed in Table 1 taken from literature.70−72 An additional

Impedance spectroscopy, which is a well-established technique in the study of ionic conductivity,57 can be used to probe long-range diffusion in ceramics. Used in combination, solid-state NMR and impedance spectroscopy provide information on a range of length and time scales, allowing for a more complete description of the potential energy landscape of ionic conductors.58 Alongside the experiment, computation has played an important role in increasing the understanding of the transport processes present within Li+ ion conductors.10 In an integrated study, we computationally identify suitable dopants to introduce Li+ ion vacancies into LiMgPO4 and successfully access the predicted doped compositions experimentally, demonstrating the key role of entropy. The composition, structure, and ionic transport properties of doped compounds were experimentally characterized by a wide range of techniques including X-ray and neutron diffraction. Impedance and solid-state NMR spectroscopies show that Li+ ions are more mobile following aliovalent doping, and reveal the characteristic energies that are related to shortand long-range Li+ ion transport. Density functional theory (DFT) calculations and classical molecular dynamics (MD) calculations are used to aid interpretation of the experiment, investigating the nature of the Li+ ion transport pathways within the structure.

Table 1. Parameters of Short-Range Buckingham Potentials Used during This Study

( )−

E = A exp −

Calculations. The assessment of relative doping enthalpies was based on periodic DFT calculations performed using VASP.59 Substitution was performed in a 2 × 2 × 2 supercell of LiMgPO4, in which one cation was replaced by another with a higher charge, with the removal of Li+ ions to balance charge. All symmetrically unique supercells for a given composition were constructed using the in-house code, which uses a method similar to that of Grau-Crespo and co-workers.60 These configurations were structurally optimized using the projector augmented wave method,61 the PBE functional,62 a planewave cutoff of 600 eV, and a 1 × 2 × 2 k-point grid, until all forces were below 0.01 eV/Å. A doping enthalpy was obtained by comparing the calculated energy of the supercell with that of the parent-phase LiMgPO4 and other competing phases, using ternary oxides where reported in the ICSD, and binary phases otherwise. For example, the doping enthalpy ΔHdoped for introducing one In3+ ion, forming a supercell with composition Li31Mg31InP32O128, was calculated as

C r6

ion pair

A (eV)

ρ (Å)

C (eV Å6)

Li −O Mg2+−O2− In3+−O2− P5+−O2− O2−−O2−

632.1018 1428.5 1495.6 897.2648 22764.3

0.2906 0.2945 0.331 0.3577 0.149

0.0 0.0 0.0 0.0 44.53



r ρ


harmonic three-body term was included to constrain O2−−P5+−O2− angles to values of ∼109.47° with a spring constant of 1.3558 eV rad−2. A time step of 0.5 fs was used for all MD calculations. The shells on O2− ions were treated as massless particles, with their positions optimized at each time step and without extrapolation between time steps. Equilibration of structures was performed using a 10 ps trajectory within the NPT ensemble, with a pressure of 0 GPa and a set temperature. The final structure from the equilibration trajectory was then used to start a production run within the NVE ensemble. MD calculations were run on 2 × 4 × 4 supercells of undoped and Indoped LiMgPO4. The initial supercell of In-doped LiMgPO4 was selected as the lowest-energy relaxed structure of 1000 supercells in which a random distribution of 19 Mg2+ (15%) had been substituted for In3+, and 19 random Li+ ions have been removed. Temperatures for MD calculations are quoted as the mean and standard deviation of the temperature over the NVE production run. Synthesis. All samples were synthesized by a conventional solidstate ceramic route. High-purity Li2CO3 (>99.995%, Fluka Analytical, used as received), MgO (99.95%, Alfa Aesar, dried at 950 °C for 3 h), In2O3 (99.995%, Alfa Aesar, dried at 220 °C for 3 h), and (NH4)H2PO4 (99.999%, Sigma−Aldrich, dried at 120 °C for 3 h) were used as precursors. The 7Li-enriched samples were prepared using 7Li2CO3 (99% 7Li atom, Sigma−Aldrich, used as received). (NH4)H2PO4 and 7Li 2CO3 were ground to fine powders prior to use. The parent material LiMgPO 4, and its doped derivatives Li1−xMg1−xInxPO4 were synthesized by adapting a published protocol for LiMg0.5Ni0.5PO4,73 using stoichiometric amounts of the reactants, which were intimately ground in an agate mortar and pestle. First, the reaction mixture was lightly homogenized and loaded as loose powder in alumina crucibles, then heated at 648 K for 12 h using a heating rate of 0.5 K min−1 and a cooling rate of 5 K min−1. The resulting powders were then thoroughly reground and pressed into a pellet by applying a uniaxial pressure of 30 MPa. For the undoped parent material LiMgPO4, pellets were then placed in an alumina crucible and held at 1073 K for 20 h using a heating rate of 1 K min−1 and a cooling rate of 2 K min−1, to obtain samples that appeared to be single phase by laboratory PXRD. Higher temperatures were required for the synthesis of single-phase (as determined by laboratory PXRD) doped materials, Li1−xMg1−xInxPO4, which required a single heating step of 1273 K for 20 h.

ΔHdoped = E(Li31Mg31P32O128) − 31E(LiMgPO4 ) − E(InPO4 ) Finite temperature effects on the stability of doped compounds were included by introducing the entropy of mixing due to partially occupied crystallographic sites. Assuming a completely disordered distribution of species at these sites, the mixing entropy is calculated as ΔSmix = − kB∑I ∑i fIi ln(fIi ) where f Ii is the fraction of species i occupying the crystallographic site I, and kB is the Boltzmann constant. A doping free energy (ΔFdoped) was then calculated as a function of temperature (T) and doping concentration (x):

ΔFdoped = xΔHdoped − T ΔSmix using the doping enthalpy (ΔHdoped ) of the lowest energy configuration. For example, for Li1−xMg1−xInxPO4, the Li+ site is occupied by (1 − x) Li+ ions and x vacancies, and the Mg2+ site by (1 − x) Mg2+ ions and x In3+ ions. Hence, the doping free energy is calculated as

ΔFdoped = xΔHdoped − 2kBT[x ln(x) + (1 − x) ln(1 − x)] 2076

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Chemistry of Materials 7

Diffraction. Initial crystallographic analysis to establish phase purity and lattice parameters, from both powder samples and sintered pellets, was conducted using XRD data from a Panalytical X’Pert Pro diffractometer using Co Kα1 radiation in Bragg−Brentano geometry and an X’Celerator detector. The data from powder samples were collected in the range of 5° < 2θ < 130° with a step size of 0.0167° and a time per step of 0.47 s. The secondary standard LaB6 was used as an internal standard for the determination of lattice parameters, as a function of composition. For detailed structural analysis, synchrotron X-ray powder diffraction (SXRD) data were collected using the I11 powder diffractometer at Diamond Light Source (UK), operating in Debye− Scherrer geometry with five multianalyzer crystal detectors, and timeof-flight neutron powder diffraction (NPD) data were collected at ISIS (U.K.) using the POLARIS and GEM instruments. All samples studied by NPD were synthesized with 7Li2CO3 to minimize neutron absorption by 6Li and the neutron data were corrected for absorption, using the instrument data manipulation software Mantid,74 prior to Rietveld refinement. SXRD samples were contained within 0.7 mm borosilicate capillaries and a small absorption correction was applied to all Rietveld refinements (estimated μR = 0.3 for x = 0, up to a maximum of μR = 0.7 for x = 0.17), with neutral element scattering factors used for all atoms. On close inspection the SXRD patterns of LiMgPO4 and Li1−xMg1−xInxPO4 were found to contain sets of weak impurity peaks at low angles (2θ < 20°), which were not visible in standard laboratory PXRD patterns or by NPD. In LiMgPO4, peaks corresponding to Li4P2O7 and to Li9Al3P8O29 were assigned using the pattern-matching function of the XPert Highscore software with the PDF2 database and this phase was included in the Rietveld fits. A second set of peaks could not be assigned to a known Li−Mg−Al−P−O phase, but were indexed to an orthorhombic cell with dimensions of a = 10.5904(1) Å, b = 8.3102(2) Å, and c = 9.0478(2) Å. Cross-referencing this cell against the ICSD database75 found several entries with similar cell size but none that had a suitable compositions containing Li, Mg, or Al (which may be present by reaction with the Al2O3 crucible). There was no overlap between these peaks and those of LiMgPO4, so this phase was modeled with a Pawley fit in the final stages of refinement. Li0.95Mg0.95In0.05PO4 was found to contain this orthorhombic phase as the only secondary phase. In Li0.83Mg0.83In0.17PO4, a set of peaks corresponding to a single minority orthorhombic phase with cell dimensions of a = 18.9388(5) Å, b = 9.1154(3) Å, and c = 8.3463(3) Å were observed, which could not be assigned to a known phase using the methods above, and was also modeled by a Pawley fit in the final stages of refinement (with care being taken to ensure no overlap with olivine peaks). The SXRD patterns of the intermediate compositions (x = 0.10, 0.15) were found to contain both of these minority orthorhombic phases. Rietveld refinements were carried out using Topas Academic (Version 5).76,77 Processing. Several steps were required in order to make >90% dense pellets for AC impedance measurements. First, the powder samples of phase-pure Li1−xMg1−xInxPO4 were ball-milled in ethanol, using 45-mL zirconia pots and zirconia balls, in a Fritsch Pulverissette 7 planetary mill. The total milling time was between 45 min and 2.5 h, for powder amounts of 0.5−2.8 g, at 350 rpm. The milled powder was dried and then pressed into a thin pellet (∼1−2 mm thick) 13 mm in diameter by applying a uniaxial pressure of 60 MPa. These pellets were then cold isostatically pressed by applying a hydrostatic pressure of 200 MPa. Finally, the pellets were sintered at 1273 K for 5 h using heating and cooling rates of 5 K min−1. The final pellets of undoped LiMgPO4 were sintered inside an alumina crucible. For the Incontaining samples, pellets were loaded on top of a presintered buffer pellet of identical composition to prevent the reaction observed occasionally in samples directly in contact with the alumina crucible. XRD patterns were collected from both sides of each sintered pellet to confirm their phase purity, and their densities were calculated from their mass and physical dimensions. Samples of LiMgPO4, Li0.9Mg0.9In0.1PO4, and 7Li0.9Mg0.9In0.1PO4 were prepared for ICP-OES analysis by dissolving the powders in hot nitric acid. TEM-EDX samples of Li 0.9 Mg 0.9 In 0.1 PO 4 and

Li0.9Mg0.9In0.1PO4 were prepared using a Cu grid from a suspension of the powders in methanol. Impedance. Impedance spectroscopy measurements were performed using a Solartron Model 1255B frequency response analyzer coupled with a Solartron Model 1296 dielectric interface or using a stand-alone Solartron Model 1260 system (Solartron Analytical, Farnborough, U.K.) over a frequency range from 0.01 Hz to 1 MHz and a temperature range of 25−500 °C. Au paste was applied on both sides of the pellet and fired at 600 °C for 1 h to make the electrode. To minimize any possible effect of moisture on electrical conductivity,78 measurements were performed in a flow of dry air, unless otherwise stated. Impedance data were corrected for sample geometry (thickness/area of pellet) and analyzed using ZView (Version 2.9b, Scribner Associates, Inc., USA). After geometry correction, resistance (R) becomes resistivity (ρ). The capacitance (C = ε0εrA/d, where ε0 is the permittivity of free space (ε0 = 8.854 × 10−14 F cm−1, εr is the relative permittivity, A the pellet electrode area, and d the pellet thickness) becomes Ccorr (Ccorr = ε0εr) and effective εr can be calculated using the relation Ccorr/ε0. NMR. 6Li (spin I = 1) solid-state NMR experiments were carried out on a 9.4 T Bruker Avance III HD spectrometer with a Bruker 4 mm HXY Magic Angle Spinning (MAS) probe (in double resonance mode) tuned to 6Li at ν0(6Li) = ω0(6Li)/2π = 58.88 MHz and on a 20 T Bruker Avance II spectrometer with a Bruker 4 mm HX MAS probe tuned to 6Li at ν0(6Li) = ω0(6Li)/2π = 125.11 MHz. 6Li spectra were obtained with π/2 pulse length of 5 μs at a radio-frequency (rf) amplitude of ν1(6Li) = ω1(6Li)/2π ≈ 50 kHz. 7Li (spin I = 3/2) solidstate NMR experiments below 440 °C were carried out on a 9.4 T Bruker Avance III HD spectrometer with a Bruker 4 mm HX HighTemperature MAS probe tuned to 7Li at ν0(7Li) = ω0(7Li)/2π = 155.51 MHz. 7Li NMR experiments above 440 °C were carried out on a 9.4 T Bruker Avance spectrometer using a single channel static NMR probe tuned to 7Li at ν0(7Li) = ω0(7Li)/2π = 155.33 MHz and a homemade CO2 laser (λ = 10.6 μm, 250 W) heating system developed in Orléans (CNRS − CEMHTI).79,80 The boron nitride crucible containing the sample is placed inside the rf coil, in the center of the cryomagnet. The sample is heated by two laser beams, passing axially through the NMR probe, and the temperature is controlled by the laser power. 7Li spectra were obtained with π/2 pulse length of 2.5 μs at an rf field amplitude of ν1(7Li) = ω1(7Li)/2π = 100 kHz below 440 °C and with π/2 pulse length of 16 μs at an rf amplitude of ν1(7Li) = ω1(7Li)/2π = 8 kHz above 440 °C. Spin−lattice relaxation times T1 in the laboratory frame were recorded with a saturation recovery pulse sequence, and were fitted to a single exponential of the form 1 − exp[−(τ/T1)] (where τ are variable delays). Spin−lattice relaxation times T1ρ in the rotating frame were obtained with a spin-lock sequence at frequencies of ν 1(7Li) = ω1(6Li)/2π ≈ 12.5 below 440 °C and ∼13 kHz above 440 °C, and were parametrized successfully to a single exponential exp[−(τ/T1ρ)] (where τ are variable delays). All measurements were reproducible upon temperature cycling. Temperature calibration of the probe was performed in separate experiments using the 207Pb NMR resonance of Pb(NO3)2,81,82 the 63Cu resonances of CuIBr across the γ-to-β phase transition at 658 K and of CuII across the γ-to-β phase transition at 642 K83,84 (below 440 °C) or by the direct measurement of the melting points of reference samples (above 440 °C).79,80 The sample temperatures quoted subsequently have all been corrected according to this calibration, and have an accuracy of approximately ±10 K. All 6Li and 7Li shifts were externally referenced to solid LiCl at 0.0 ppm.

RESULTS AND DISCUSSION Introduction of Vacancies by Doping. DFT calculations were performed to investigate distinct substitution mechanisms to introduce Li vacancies. Doping enthalpies were calculated for a range of dopants substituting each cation within LiMgPO4, by assessing the energies of all symmetrically unique configurations of doped 2 × 2 × 2 supercells (Figure 2a). These calculations reveal that the most favorable substitution is In3+ 2077

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Figure 2. (a) Doping enthalpies calculated for a range of dopant ions substituting Li+ ions (green), Mg2+ ions (orange), and P5+ ions (purple) in LiMgPO4. (b) Doping free energy for the compound Li1−xMg1−xInxPO4, as a function of temperature (T) and doping fraction (x). Contours are labeled in units of eV/FU.

on the Mg2+ site, which, although calculated to be endothermic, is predicted to become entropically stabilized by mixing at above 600 K at 10% In doping (Figure 2b). Other substitutions that are predicted to have a relatively low doping enthalpy include Mg2+ for Li+, and Ga3+ and Sc3+ for Mg2+(see Figure 2a). Following the computational prediction, synthesis of the Indoped series Li1−xMg1−xInxPO4 (x = 0.05, 0.10, 0.15) was attempted. Synthesis with a final firing at 1173 K produced polyphasic samples in which the lattice parameters increased with x for the majority olivine phase. Increasing the synthesis temperature to 1273 K produced samples that appeared phase p u r e v i a la b o r a t o r y PX R D . P X R D d a t a o f t h e Li1−xMg1−xInxPO4 series show trends in relative peak intensities and peak positions that correspond to an inclusion of the larger, stronger scattering In3+ ion on the Mg2+ site and a resulting increase in lattice parameters (see Figure 3). The refined lattice parameters, cell volume and In occupancies vary linearly up to a doping limit of x = 0.17, following Vegard’s law (see Figures 3b and 3c). The composition of the x = 0.10 material, Li0.9Mg0.9In0.1PO4, was confirmed by ICP and EDX analysis (see Table 2 and Figure S1 in the Supporting Information). The effect of cooling rate on the synthesis of Li0.9Mg0.9In0.1PO4 was investigated by cooling from the synthesis temperature of 1273 K by quenching on an aluminum block, and by slow cooling to room temperature at 0.5 K min−1. Both procedures produced Li0.9Mg0.9In0.1PO4 samples with phase purity equivalent to that obtained when the standard cooling rate of 2 K min−1 was used; hence, the cooling rate of 2 K min−1 was used for all subsequent samples. Refinement of the site occupancies using combined X-ray and neutron diffraction data (described in detail below) suggests straightforward vacancy creation at the Li site across the compositional series.

Figure 3. (a) Co Kα1 PXRD patterns of the Li1−xMg1−xInxPO4 series as a function of the In doping level (x). The intensity of the (200) reflection and the relative intensities of the (111) and (201) reflections are strongly dependent on In content. The (100) peak from the LaB6 internal standard is marked with an asterisk (*). (b) Relative cell parameters for the In-doped series, Li1−xMg1−xInxPO4. The straight lines are present as guides to the eye. (c) Refined In occupancy from synchrotron XRD refinements (x = 0.17) and combined NPD-PXRD refinements (x = 0.05, 0.10, 0.15) with the dashed line indicating the nominal stoichiometry. Error bars in panels (b) and (c) are shown as ±3 × the estimated standard deviation (esd).

Crystal Structure of Li1−xMg1−xInxPO4. The parent olivine LiMgPO4 was analyzed by high-resolution synchrotron XRD (I11, Diamond Light Source, λ = 0.825625(3) Å) collected using five multianalyzer crystal detectors, with the literature model of Hanic et al.32 used as a starting model for the Rietveld refinement. The known chemistry of the isostructural olivine LiFePO4 suggests that the Li site may be able to accommodate small concentrations of M2+ cations.12,20,21,26,30,85 In order to test the nature and extent of antisite defects in this system, two refinement models were constructed: (1) The first (Model 1) is fully stoichiometric, with Li and Mg allowed to populate both cation sites, and is represented as [Li1−yMgy][Mg1−yLiy]PO4 with y refined; and (2) In the second (Model 2), the antisite defects cause nonstoichiometry with Mg partially populating the Li 2078

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Chemistry of Materials Table 2. Compositional analysis of Li1xMgxInxPO4 samplesa Composition (Analytical Result) nominal composition













0.897(7) −

0.91(1) 0.85(2)

0.0975(4) 0.096(5)

1.000(5) 1.00(3)



0.908(9) −

0.906(8) 0.85(3)

0.0964(6) 0.088(9)

1.000(7) 1.00(4)


Uncertainty shown as ±1σ. A dash is shown when the technique is not suitable for that element (EDX for Li) or when the value was below the detection limit. a

Figure 4. Rietveld refinement of LiMgPO4 against high-resolution PXRD data from I11. Three inset plots show expanded regions of the pattern. Black tick marks represent LiMgPO4, green tick marks represent Li4P2O7, purple tick marks represent Li9Al3P8O29, and pink tick marks represent an orthorhombic impurity.

no evidence for this type of disorder from either diffraction or compositional analysis, Model 2 was discarded. The intensity of the (200) peak was found to be highly sensitive to the disorder imposed by Model 1, with the calculated intensity decreasing strongly as y increases. This peak is fitted well when 0 < y ≤ 0.02, while the calculated intensity becomes too weak to fit the peak adequately in the range of y > 0.02, implying that the upper limit for this type of antisite defect in LiMgPO4 lies between y > 0.02 and y < 0.03. Analysis of the Rwp values obtained at fixed values of y show a shallow minimum at y ≈ 0.02, while Biso values for the Li site were found to increase sharply with increasing y. After testing fixed values of y, this parameter was allowed to refine freely and gave a value of 0.015(1), with a corresponding Biso (Li) value of 2.17(6) Å2. In the final refinement, Model 1 was used with y refined from a starting value y = 0.015, and temperature factors refined anisotropically in the final stages of refinement; this resulted in a larger refined value of y = 0.0214(8) and an improvement in fit, compared to the previous isotropic model (Rwp = 7.367 vs Rwp = 8.128). The shapes of the refined thermal ellipsoids and their evolution with composition and temperature are discussed, together with the refined structures of the Indoped materials from combined PXRD−NPD refinements, below. The refined structural parameters are shown in Table S1

site, and is represented as [Li1−2yMgy]MgPO4 with y refined. In Model 2, this type of nonstoichiometry might be expected to result in Li-rich impurity phases in the sample. In order to estimate the sensitivity of the refinement to y in both systems, a set of Rietveld refinements were conducted in which fixed values of y (0.00 ≤ y ≤ 0.07) were imposed and the corresponding Rwp values and Li Biso values plotted, with the fit to the low-angle (200) peak also taken into consideration. The calculated intensity of this peak is sensitive to cation ordering; however, its observed intensity is ∼2% of that of the most intense peak (which is (101)) and, therefore, a poorly fitting (200) peak is not expected to have a large effect on Rwp, even though it may imply that the cation ordering has been modeled incorrectly. Isotropic temperature factors were used for these tests. The Rwp values, (200) fit, and Biso value for the Li site are plotted in Figure S2 in the Supporting Information for Model 1 and Figure S3 in the Supporting Information for Model 2. Imposing nonzero values of y on Model 2 was found to result in a systematically poorer fit to the data (Rwp increases monotonically with y). However, the (200) peak intensity was found to be relatively insensitive to this type of disorder. A free refinement of y resulted in a value of y = 0.001(2). Furthermore, the composition determined by ICP analysis showed the material to be stoichiometric (see Table 2). With 2079

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Figure 5. (a) Refined structure of Li0.85Mg0.85In0.15PO4 with atoms displayed as 99% thermal displacement ellipsoids. (b) Simplified structural diagram with fractional occupancies of Li, Mg and In shown in a pie-style chart at each cation site. Atom colors in both structural diagrams are as follows: green, Li; orange, Mg; blue, In; purple, P; and red, O. (c, d) Fits to diffraction data from combined Rietveld refinement of Li0.85Mg0.85In0.15PO4 against high-resolution PXRD (I11, λ = 0.825685(2) Å) and NPD (GEM 154° bank) at ambient temperature.

Allowing z to refine freely yields a value of z = 0.0031(2). Based on these parameters, In3+ shows a strong preference for the Mg (4c) site, and z was set to zero in subsequent refinements. The second site-ordering model to be tested was Li−Mg antisite disorder (Model 4: analogous to “Model 1” for the parent phase, above). In this model, In3+ was fixed on the Mg (4c) site with Li and Mg allowed to exchange sites i.e., [Li0.85−zMgz][Mg0.85−zLizIn0.15]PO4. In this model, vacancies are formed on the Li site only, with the Mg site fully occupied by cations. Fixed values of z = 0.00−0.07 were applied and their effect on the fit analyzed in the same way as for the parent phase (see Figure S5 in the Supporting Information). Rwp was found to go through a shallow minimum at z ≈ 0.02, while the fit to the (200) peak (by PXRD) was found to get systematically poorer when z > 0.02. Allowing z to be refined freely in this model yielded a value of 0.0126(8) and a refined Biso (Li) value of 1.73(5) Å2 (compared to 1.40(5) Å2 when z = 0.00). This behavior is consistent with that of the parent phase discussed above, and suggests that antisite defects of this type are present in this system, up to a limit of z = 0.02. The third In-substituted site-ordering model (Model 5) is a variation of the above, with vacancies allowed on both cation sites represented by [Li0.85Mgz][Mg0.85−zIn0.15]PO4. In this model, Mg may occupy a Li site, but Li may not reciprocate by occupying the resulting vacancy on the Mg site. The same analytical route was followed as previously described. From this model, a minimum in Rwp was observed when z ≈ 0.01. Allowing z to refine freely resulted a value of 0.0121(7). Again, this is consistent with a small amount of Mg defects occupying Li sites with a limit of z ≈ 0.02. However, Rwp values and Biso (Li) were shown to increase more rapidly with z than the corresponding values in Model 4 (see Figure S6 in the Supporting Information); therefore, this model was not used in subsequent refinements.

and S2 in the Supporting Information, and the corresponding Rietveld fit is shown in Figure 4. For In doped compositions Li1−xMg1−xInxPO4 (x = 0.05, 0.10, 0.15), high-resolution PXRD data (beamline I11, DLS) were collected at room temperature, and used in combined Rietveld refinements with neutron powder diffraction (NPD) data from the Polaris (x = 0.05, 0.10) and GEM (x = 0.15) diffractometers at ISIS, U.K. NPD data were also collected upon warming up to 623 K for the x = 0.15 sample; and hightemperature PXRD data were collected at T ≤ 1073 K for the x = 0.10 composition, using the I11 position-sensitive detector for rapid collection of data suitable for space group confirmation and lattice parameter determination. The starting model for these refinements was based on that of the parent olivine LiMgPO4 discussed above. The inclusion of In3+ allows potential for more-complex defect models than those considered for the parent olivine, and the potential for three different atoms to occupy the same cation site means that candidate models must be distinguished using combined refinements with X-rays and neutrons. Initially, it is important to establish the location of In3+. For this, the x = 0.15 sample was chosen (representing the highest In content from which both PXRD and NPD data were collected) and a model applied (Model 3) such that In3+ may occupy either the Li+ or Mg2+ site, with Li+ and Mg2+ localized on their respective sites to constrain the overall composition to Li0.85Mg0.85In0.15PO4, according to the formula [Li0.85Inz][Mg0.85In0.15−z]PO4. As with the preliminary analysis of the parent phase, thermal parameters were allowed to be refined isotropically. The overall Rwp value, the fit to the (200) peak in the XRD pattern, and the Biso value for the Li site were evaluated for values of z = 0.00, 0.01, 0.02, and 0.03, and these are plotted in Figure S4 in the Supporting Information. Rwp was found to increase strongly with increasing z, while the fit to the (200) peak becomes systematically poorer and Biso values rapidly become unphysical. 2080

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Figure 6. Selected interatomic distances in Li1−xMg1−xInxPO4 plotted as a function of composition: (a) refined Li−O distances and (b) refined Mg− O distances. Error bars (3 esd) are approximately the size of the data points. (c) Structural fragment showing refined thermal displacement ellipsoids (99% probability) for Li0.85Mg0.85In0.15PO4 with atoms labeled according to the interatomic distances plotted in panels (a) and (b). (d) Refined area of the two octahedral faces parallel to the Li diffusion pathway, plotted relative to LiMgPO4. Black markers indicate the “open” faces, whereas red markers indicate the “closed” faces.

For the final ambient temperature refinement, Li−Mg antisite disorder was allowed, according to Model 4 [Li0.85−zMgz][Mg0.85−zLizIn0.15]PO4, with In3+ partially occupying the Mg site only and z refined freely. Anisotropic thermal parameters were refined for all atoms in the final stages. Structural parameters are tabulated in Table S1 in the Supporting Information. This yielded a refined structure with a cation distribution of [Li0.8350(7)Mg0.0150(7)][Li0.0150(7)Mg0.8350(7)In0.15]PO4. Finally, the compositional constraint was removed to test the robustness of the refinement. Li and Mg occupancy were allowed to be refined freely on each site, with In fixed to the Mg site and its occupancy refined from a starting (nominal) value of 0.15. This resulted in a marginal improvement in fit, with a refined composition of [Li0.884(6)Mg0.000(1)][Li0.00(5)Mg0.83(2)In0.148(8)]PO4, which is consistent with the nominal composition and implies a minimal number of Li−Mg antisite defects. Considering this, together with the systematic analysis of antisite models against combined X-ray and neutron data, the possibility that a small number of Li−Mg antisite defects are present in Li0.85Mg0.85In0.15PO4 cannot be excluded, although it is clear that their concentration is small and must be limited to z < 0.02. This constrained model (Model 4) was then used in the combined PXRD-NPD refinement of the x = 0.05 and x = 0.10 samples, and in the high-temperature refinements of x = 0.15. The resulting Rietveld fits and structural parameters are given in Figures 5 and 6, respectively. The mean Li−O and Mg−O distances both show a linear increase with increasing In3+

concentration, consistent with the increase in average O−O distance and expansion of the unit cell. Of the two cation sites, it is the Li site that expands most rapidly. Examination of the O−O distances that make up the edges of the LiO6 octahedra shows that the Li coordination environment does not expand isotropically; instead, the area of the “open” faces of the octahedra (which form the windows to the tetrahedral site through which Li travels on the proposed diffusion pathway, Figure 1b) increases more rapidly than the area of the “closed” faces (which form a window to a small tetrahedral site adjacent to phosphate groups), which might be expected to lower the energy barrier to intersite hopping. The Li−Li distance along the 1-D channels, which is defined by the b parameter, shows an increase of ∼0.4% across the entire compositional range from 2.953 Å in LiMgPO4 to 2.965 Å in Li0.83Mg0.83In0.17PO4. The structural trends observed on doping are also reflected in the behavior of Li0.85Mg0.85In0.15PO4 upon heating to 623 K (tabulated in Tables S3 and S4 in the Supporting Information). A linear expansion of the unit-cell volume is accompanied by monotonic increases in the Li−O, Mg−O distances and a distortion of the LiO6 octahedron with the area of the “open” faces increasing at the fastest rate, analogous to that observed as a function of In content. For each refinement, superior agreement factors were obtained by using anisotropic, rather than isotropic, temperature factors. The shape and orientation of the refined thermal displacement ellipsoids shows a strong similarity to those reported in an NPD study of LiFePO4.86 The P and Mg atoms remain almost isotropic, while the Li atom 2081

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Chemistry of Materials Table 3. Calculated 7Li NMR Parameters for the Undoped Parent LiMgPO4, and Lowest-Energy Configuration with Composition Li31/32Mg31/32In1/32PO4a σiso (ppm)


σaniso (ppm)



90.52−90.71 90.62 ± 0.05

(−7.23)−(−6.02) −6.5 ± 0.2

ηCS LiMgPO4 0.70 Li31/32Mg31/32In1/32PO4 0.62−0.81 0.71 ± 0.04

|CQ| (kHz)




67.1−93.4 77 ± 5

0.67−0.97 0.81 ± 0.07

Data for the doped compound is given as a range, and as a mean and standard deviation over the 31 Li+ ions within the supercell.

Figure 7. Selected variable temperature static 7Li solid-state NMR spectra of LiMgPO4 and Li0.9Mg0.9In0.1PO4 obtained at 9.4 T. Line shape simulations to fit the quadrupolar powder pattern at room temperature are shown in green under the experimental spectra.

(all points lying within 3 standard deviations) as a function of composition (see Table S1 in the Supporting Information). Upon heating Li0.85Mg0.85In0.15PO4 to 623 K, the shape and orientation of the Li thermal ellipsoids remain constant, while their magnitudes increase linearly, implying that increased thermal motion does not translate into increased long-range diffusion by displacement of Li toward the tetrahedral transition site at these temperatures. Finally, Pawley fits to the high-temperature PXRD patterns from composition 7Li0.9Mg0.90In0.10PO4 showed a linear increase in unit cell parameters up to 1073 K, consistent with an isotropic expansion of the unit cell and retention of the orthorhombic (Pnma) structure throughout this temperature range. These data are plotted in Figure S8 in the Supporting Information.

shows a pronounced anisotropy, manifested principally as an elongation along the O1−Li−O1 axis of its octahedron: this is the longest axis of the octahedron (e.g., the x = 0.15 sample at ambient temperature has a refined Li−O1 distance of 2.2109(4) Å, compared to 2.1244(4) and 2.1552(4) Å for Li−O2 and Li−O3, respectively) and it is perhaps unsurprising that there is uncertainty in the Li position along this direction. A view of the LiO6 octahedron along the O1−Li−O1 axis shows that the Li ellipsoid is also distorted toward the long equatorial O2−O3 edge in preference to the short edge, and this represents displacement toward the larger “open” faces of the octahedron, which offer the lowest-energy Li diffusion pathway. These characteristics were exhibited by all of the Indoped compositions and the nondoped LiMgPO4 phase, but the dimensions of the Li ellipsoid were found to be invariant 2082

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Li and 7Li NMR of LiMgPO4 and Li0.9Mg0.9In0.1PO4. The Li MAS NMR spectra of both LiMgPO4 and Li0.9Mg0.9In0.1PO4 recorded at 9.4 and 20 T are given in Figure S9 in the Supporting Information. All spectra display a single narrow peak (∼15 Hz broad or ∼0.2 ppm at 9.4 T) at ∼0.4 ppm, in agreement with Li sites in 6-fold coordination as anticipated for the olivine structure. Although a distribution of isotropic chemical shifts is calculated over the multiple Li sites of the lowest energy Li31/32Mg31/32In1/32PO4 configuration (Table 3), the standard deviation of site-averaged calculated 6Li isotropic chemical shielding obtained from GIPAW calculations is ∼0.05 ppm, which accounts for the experimental observation of only one 6Li resonance. The 7 Li static NMR spectra of LiMgPO 4 and Li0.9Mg0.9In0.1PO4 obtained at a resonance frequency of 155 MHz and in the 100−1400 K temperature range are given in Figure 7. The spectra at room temperature showed the typical line shape of a spin I = 3/2 nucleus, such as 7Li, consisting of a line at 0 ppm corresponding to the central transition and broad lines spanning ∼400 ppm (or ∼65 kHz) for the quadrupolar satellite transitions. The room-temperature spectrum of LiMgPO4 could be fitted with a 7Li quadrupolar coupling of CQ ≈ 52 (±10) kHz (Figure 7) in agreement with previous report (CQ ≈ 60 kHz)40 but slightly lower that the current GIPAW calculations (87 kHz). In the case o f Li0.9Mg0.9In0.1PO4, the quadrupolar splitting gives a quadrupolar constant of CQ ≈ 72 kHz, in agreement with the calculations (CQ ≈ 77 kHz with a standard deviation of 5 kHz across the 31 Li sites in the lowest-energy Li31/32Mg31/32In1/32PO4 configuration (Table 3)). The broadening of the central transition at room temperature (∼5 kHz) is similar to that observed previously at a much lower field of 2 T for LiMgPO440 and results from 7Li − 7Li homonuclear dipolar broadenings (the so-called rigid-lattice regime). As the temperature is increased, the 7Li−7Li dipolar interactions are averaged out due to the increase of Li+ ion mobility. Figure 8 plots the central transition NMR line width as a function of temperature where a significant line narrowing is only observed at a rather high temperature, indicating limited Li mobility in these two olivine phases. Nevertheless, it is clear that the onset of motional narrowing occurs at a much lower temperature for Li0.9Mg0.9In0.1PO4 (∼470 K) than for LiMgPO4 (∼750 K), indicating faster Li+ ion dynamics in the In-doped olivine. The Li jump rate (τ−1) is on the order of the line width of the central transition in the rigid-lattice regime νrl = ωrl/2π, and yields a value for τ−1 of ∼3 × 104 s−1 at ∼470 K for Li0.9Mg0.9In0.1PO4 and ∼750 K for LiMgPO4. In addition, the jump rate of the motion τc−1 describing the ionic translational motion can be obtained from the NMR central transition line width ν(T) = ω(T)/2π at a given temperature and in the rigidlattice regime using the following equation: 6

Figure 8. 7Li NMR central transition line width ν = ω/2π of both LiMgPO4 (red circles) and Li0.9Mg0.9In0.1PO4 (blue circles), as a function of temperature (T). Data were measured at a Larmor frequency of ν0(7Li) = ω0(7Li)/2π = 155.5 and 155.3 MHz below and above 713 K, respectively. The dotted lines show the extrapolation of the onset of motional narrowing on the 7Li NMR line width. The solid lines show the fit to the equation of motional narrowing given in the text.45,87

Further increases in T, up to temperatures of 1373 K, reveals a significant narrowing of the quadrupolar satellite transitions while the line width of the central transition remains constant at ∼0.8 kHz. This suggests fast Li+ ion diffusion with Li jump rates (τ−1) larger than ∼6 × 105 s−1 at ∼1200 K. At 1423 K, the 7Li NMR spectra of both LiMgPO4 and Li0.9Mg0.9In0.1PO4 show no satellite transitions and a very narrow line width of ∼200 Hz, indicating liquid-state samples and that the measurements went above the melting point (this was confirmed by visual inspection of the samples after returning to room temperature and synthesis in a muffle furnace). The 7Li spin−lattice relaxation rates in the laboratory frame (T1−1) or the rotating frame (T1ρ−1) are a measure of the rate for the spin population to recover to equilibrium after a perturbation and are mediated by fluctuations of the local magnetic fields. T1(ρ)−1 are quantified by the correlation times of the motion τc, with frequencies τc−1 that are on the order of the Larmor frequency for T1, (i.e., MHz) or the spin lock frequency for T1ρ (i.e., kHz). The T1−1 values measured at various temperatures can be converted to τc, assuming isotropic motion, random walk of the Li+ ions, and a dominant quadrupolar relaxation mechanism by using a standard expression88,89 (see Supporting Information for further details), as often found for 7Li spin−lattice relaxation of Li ionic conductors.6,44,45 The temperature dependences of T1(ρ)−1 in LiMgPO4 and Li0.9Mg0.9In0.1PO4 at temperatures between 160 K and 1400 K are given in Figure 9a (and Figure S11 in the Supporting Information) and are significantly different, clearly indicating different Li+ ion dynamics between the parent and the In-doped LiMgPO4 olivine. At temperatures below ∼400 K, T1−1 is largely temperature independent for both compounds (Figure 9a). This lowtemperature regime, which was measured previously for LiMgPO4,40, is also observed in other Li-containing com-

2⎤ ⎡ ⎛ π ⎞⎛ υ(T ) ⎞ ⎥ τc−1 = 2πaυ(T ) tan−1⎢⎜ ⎟⎜ ⎟ ⎢⎣⎝ 2 ⎠⎝ υd ⎠ ⎥⎦

where α is a factor that is dependent on the NMR line shape and taken to be equal to one.45,87 Faster jump rates were obtained for Li0.9Mg0.9In0.1PO4 (τc−1 ≈ 4 × 105 s−1 at ∼770 K; see Figure S10 in the Supporting Information) than for the undoped LiMgPO4 (τc−1 ≈ 4 × 104 s−1 at ∼770 K; see Figure S10 in the Supporting Information), verifying experimentally the success of the In doping strategy found by the simulation discussed above. 2083

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Figure 9. Arrhenius plot of the (a) 7Li spin−lattice relaxation rates T1−1 obtained at ν0(7Li) = ω0(7Li)/2π = 155.5 and 155.3 MHz below and above 713 K, respectively, and T1ρ−1 obtained at the spin-locking frequencies ν1(7Li) = ω1(7Li)/2π ≈ 12.5−13 kHz as a function of the temperature (T). (b) Li hopping frequencies τc−1 evaluated from spin−lattice relaxation rates T1−1 obtained at ν0(7Li) = ω0(7Li)/2π and assuming a quadrupolardriven relaxation mechanism. Data for LiMgPO4 and Li0.9Mg0.9In0.1PO4 are given in red and blue, respectively. A plot giving the full temperature range is given in Figure S11 in the Supporting Information.

pounds,45 and does not probe diffusive Li+ ion mobility between sites.42 We concentrate on the higher-temperature regime, where the 7Li T1−1 increases with temperature from ∼800 K in LiMgPO4 and ∼450 K in Li0.9Mg0.9In0.1PO4 up to ∼1400 K (the temperature at which the samples melt; see above discussion). The increase in T1−1 with temperature indicates a slow motional regime (ω0τc ≫ 1) and that the rates are sensitive to local site-to-site hopping processes of the Li+ ions, rather than long-range translational diffusion.90,91 The fact that the inflection point occurs at a much lower temperature in Li0.9Mg0.9In0.1PO4 (∼440 K) than in LiMgPO4 (∼700 K) clearly shows that the In-doped sample has faster Li mobility, confirming the In doping strategy. This is also corroborated by the quantification of the activation energies, from the log(T1−1) vs 1/T plot in Figure 9a, where values of ∼0.5 eV for LiMgPO4 and ∼0.3 eV for Li0.9Mg0.9In0.1PO4 (below ∼900 K) are obtained, and reflect the smaller energy barrier for a single site−site hopping transition in Li0.9Mg0.9In0.1PO4 than in LiMgPO4. Above ∼900 K for Li0.9Mg0.9In0.1PO4, the T1−1 rates increase further and follow an Arrhenius behavior with an activation energy on the order of ∼0.2 eV. This value is different than that determined below ∼900 K, and it probably reflects a different motional process. The plot of the rotating frame relaxation rates T1ρ−1 vs 1/T is given in Figure 9a (and Figure S11 in the Supporting Information) and pass through a maxima, indicating that the rates are induced by diffusion processes. At the peak maximum, the jump rate τc−1 can be directly determined from the following expression ω1τc ≈ 0.5 and a value of τc−1 ≈ ν1(7Li) × 2π/0.5 ∼ 1.6 × 105 s−1 is obtained for Li0.9Mg0.9In0.1PO4 at a

lower temperature (∼900 K) than for LiMgPO4 (∼1000 K), again indicating enhanced Li diffusion upon In doping. In the slow motional regime (ω1τc ≫ 1, i.e., at temperatures lower than those giving the maximum hopping rates), activation energies of ∼0.5 eV for LiMgPO 4 and ∼0.1 eV for Li0.9Mg0.9In0.1PO4 were estimated and are in fair agreement with those obtained from T1−1 relaxation rates, highlighting that the same site-to-site motional process is probed. More interestingly, in the fast motional regime (ω1τc ≪ 1), the Arrhenius fit to the T1ρ−1 vs 1/T data given in Figure 9a yield activation energies of ∼1.0 eV (at T above ∼1000 K) and ∼0.9 eV (at T above ∼900 K) for LiMgPO4 and Li0.9Mg0.9In0.1PO4, respectively. These energy barriers obtained from the hightemperature flank of the T1ρ−1 data reflect long-range Li+ ion transport.90,91 and could be directly compared with the results obtained with the conductivity data given below. We note that translational Li diffusion could also potentially be obtained from the laboratory frame relaxation rates T1−1 in the fast motional regime (ω0τc ≪ 1); however, this regime could not be reached here, because the samples melt at (∼1400 K) before the T1−1 maximum. Using the Einstein−Smoluchowski equation, the Li diffusion constant from NMR (DNMR) could be obtained from the jump rates τc−1 by D NMR =

fa 2τc−1 6

where a is the mean Li−Li jump distance obtained from the crystal structure (recall Figure 6) and found to be 2.953 Å in LiMgPO4 to 2.960 Å in Li0.9Mg0.9In0.1PO4 (Table S1) and f is a correlation factor (taken to 1 for uncorrelated motion). All the 2084

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Chemistry of Materials NMR diffusion coefficients obtained from the jump rates determined from the 7Li NMR onset of line narrowing, 7Li NMR central transition line narrowing and 7Li NMR relaxation rates T1ρ−1 are plotted in Figure 10. The values obtained at

Figure 11. DFT calculated configurations of a Li+ ion in the tetrahedral transition state for Li+ ion hopping (a) close to and (b) far away from a dopant In3+ ion. Arrows highlight the tetrahedral Li+ ion (shown as green tetrahedra), vacant octahedral Li+ sites are indicated by white spheres, and octahedra containing In3+ ions are drawn in blue. Mg atoms, Li atoms, PO4 tetrahedra, and O atoms are shown in orange, green, purple, and red, respectively.

Classical MD calculations were performed to investigate Li+ ion motion on the atomic scale. MD simulations on the parent LiMgPO4 compound were carried out at four temperatures between 298 ± 6 K and 1092 ± 21 K, and in all cases showed no site-to-site hopping or long-range Li+ ion motion, with a constant mean square deviation (MSD) of the Li+ ions with time (see Figure 12). Hopping events were evident in the Li+

Figure 10. Diffusion coefficients D as a function of temperature obtained from 7Li NMR onset of line narrowing (triangles, ▲), 7Li NMR line narrowing (circles, ●), 7Li NMR relaxation rates T1ρ−1 (squares, ■) obtained from the Einstein−Smoluchowski relation and compared with the room-temperature impedance conductivity measurements determined from the Nernst−Einstein expression (diamonds, ⧫) (see text for further details). Data for LiMgPO4 and Li0.9Mg0.9In0.1PO4 are given in red and blue, respectively.

these high temperatures suggest relatively slow Li+ ion diffusion as diffusion coefficients of ∼10−9−10−12 cm2 s−1 determined from 7Li NMR, have been obtained for faster Li+ ion conductors near room temperature,6,44,46,51,52 including the very fast Li diffusion of argyrodite-type Li6PS5Br (∼10−9 cm2 s−1) at only 263 K.6 Calculation of Hopping Barriers and Dynamics. The activation energy of 0.3 eV obtained for Li0.9Mg0.9In0.1PO4 from 7 Li NMR spin−lattice relaxation rates between 500 K and 900 K is in good agreement with the value of 0.30 eV calculated by Jalem and co-workers31 for LiMgPO4 with a single Li+ vacancy in a 1 × 2 × 2 supercell. We performed further DFT calculations to obtain the energy barrier for a single hopping event (ΔHhop) in the In3+-doped compound, assuming a pathway through the previously suggested tetrahedral transition state.31 A Li+ ion was placed in a tetrahedral sites between two vacant octahedral sites in two configurationsone close to a dopant In3+ ion and one further away (see Figure 11)and the structure relaxed fully. The energy was then compared to the configuration in which one of the two vacant sites is occupied by a Li+ ion. A slightly lower barrier of ΔHhop = 0.24 eV was calculated for the hop close to the In3+ ion, compared to 0.29 eV further away; both values consistent with those calculated previously and those obtained by high temperature 7Li NMR T1−1 relaxation rates (∼0.3 eV, Figure 9).

Figure 12. Mean square displacement (MSD) of Li+ ions in LiMgPO4, plotted as a function of time. Data were obtained from 120 ps MD production runs at 298 ± 6 K (black), 674 ± 13 K (blue), 880 ± 17 K (green), and 1092 ± 21 K (red). Pale lines show the MSD of individual Li+ ions, and the darker lines the mean over all Li+ ions.

ion trajectories of the 15% In 3+ -doped compound (Li0.85Mg0.85In0.15PO4) at 685 ± 14 K and 888 ± 17 K (see Figure 13 and Figure S12 in the Supporting Information). Hops always occurred along chains of Li+ ions in the bdirection, with no crossover between channels observed within the time scale of these simulations (700 ps at 685 ± 14 K (Figure 13) and 470 ps at 888 ± 17 K (Figure S12 in the Supporting Information)). This confirms the extreme 1-D nature of Li+ ion transport, which leads to no observable hopping in chains that do not contain Li+ ion vacancies (see Figures 12 and 13, as well as Figure S12 in the Supporting Information). By identifying hopping events within the trajectories, hopping rates for each Li+ ion can be calculated at each 2085

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Chemistry of Materials

impossible for LiFePO4.53−55 Extrapolation of the site-to-site hopping rate obtained from high-temperature NMR τc data (Figure 9b) to room temperature would give hopping rates of ∼5 × 105 s−1 for Li0.9Mg0.9In0.1PO4, similar to the roomtemperature hopping rate of 5 × 105 s−1 for LiFePO4 obtained by μSR.27 A much lower value, below ∼104 s−1, is extrapolated at room temperature for LiMgPO4. Analysis of a single hopping event in the MD trajectory shows that the Li+ ion does not pass through the tetrahedral transition state identified in DFT (Figures 1b and 11), instead following a path which is closer to the line connecting two octahedral sites (Figure 15). The configuration around the migrating Li+ ion at the midpoint of the trajectory between two octahedral sites has Li−O distances of 1.93, 2.16, 2.36, and 2.76 Å to the four surrounding O2− ions, avoiding the center of the tetrahedral space that it is traveling through. This pathway is closer to the curved pathway

Figure 13. Li+ ion positions throughout a 700 ps NVE trajectory of Li0.85Mg0.85In0.15PO4 at 685 ± 14 K. Initial equilibrated positions of Li+ ions are plotted as circles, and lines trace the trajectory of each Li+ ion viewed down the crystallographic a-axis. A plot is made for each layer of Li+ ions within the supercell. Chains without Li+ ion vacancies are indicated with blue arrows.

temperature (see Figure 14). The mean hopping rate of the Li+ ions at 685 ± 14 K is 2 × 109 s−1, about an order of magnitude

Figure 14. Hopping frequencies of Li+ ions taken from MD trajectories of Li0.85Mg0.85In0.15PO4 at 685 ± 14 K and 888 ± 17 K, calculated as the number of hops in the full trajectory/total time.

greater than the τc−1 value of ∼2 × 108 s−1 obtained at ∼700 K for Li0.9Mg0.9In0.1PO4 by 7Li NMR and extracted from the spin−lattice relaxation rates T1−1 data (see Figure 9b, as well as eqs S1 and S2 in the Supporting Information), but close enough to suggest that both techniques probe the same motional processes (i.e., site-to-site hopping rates). By investigating an olivine system without transition-metal cations, we have been able to use 7Li NMR to investigate the short-range hopping process which is likely to be common for all LiMPO4 compounds without the deleterious effect of hyperfine coupling, which makes such an investigation

Figure 15. (a) Positions of a Li+ ion (green) throughout a hopping event at 888 ± 17 K are shown over a period of 1 ps by the small green spheres, with 5 fs between each sphere. The other spheres show the positions of the Li+ ion and surrounding ions when the Li+ ion was halfway between the two equilibrium octahedral sites at the start and end of the trajectory. (b) Direct octahedral−octahedral (blue) and octahedral−tetrahedral−octahedral (black) paths shown for comparison. Mg octahedra, PO4 tetrahedra, and oxygen atoms are shown in orange, purple, and red, respectively. 2086

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Figure 16. (a) Impedance complex plane plot and (b) combined spectroscopic plots of the imaginary components of impedance (Z″) and electric modulus (M″) plots at 472 K for Li0.85Mg0.85In0.15PO4; temperature dependence of M″ plots for (c) bulk response and (d) grain-boundary response for Li0.85Mg0.85In0.15PO4; and (e) Arrhenius-type plots for both the bulk and grain-boundary responses for all compositions.

proposed computationally18 and seen experimentally in LiFePO4.86 Impedance Spectroscopy. The 7Li NMR T1−1 rates and DFT calculations of energy barriers only probe local site-to-site motion of Li+ ions. Impedance spectroscopy was used to obtain information about the long-range bulk transport of Li+ ions and was compared with the high-temperature regime of 7Li NMR T1ρ−1 rates. A typical impedance complex plane plot at 472 K for Li0.85Mg0.85In0.15PO4 (Figure 16a) consists of a slightly depressed arc at frequencies larger than ∼1 Hz and a spike at lower frequencies. The resistivity and capacitance associated with this arc is ∼0.6 GΩ cm and ∼60 pF cm−1 (corresponding εr ≈ 680), respectively. The permittivity value is much higher than the reported intrinsic εr value of ∼6.6 for the parent composition, measured in the GHz frequency range,92 suggesting that this arc is not associated with a bulk (grain) response. An expanded view of the high-frequency data does not reveal unambiguously whether another more conducting electro-active element is present. Since the impedance complex plane plot is dominated by the most resistive element, it is not always straightforward to detect the presence of a conducting bulk element from this type of plot alone.93 The imaginary component of electric modulus M″ is dominated by the element with smaller capacitance, since the M″ peak maximum is inversely related to the magnitude of capacitance. Bulk capacitance in polycrystalline samples is much smaller than that of grain boundary (due to thin grain boundary layer) and electrode processes (due to non-Ohimic contacts and/or electrochemical reactions at the sample/electrode interface). Therefore, the M″ plot is particularly useful to detect the bulk element.57,93 Combined spectroscopic plots of the imaginary components of impedance (Z″) and electric modulus (M″) (Figure 16b) exhibit a low-frequency (less than ∼1 Hz) incline in the Z″ spectrum that corresponds to the spike in Figure 16a. The Z″/ M″ peaks at ∼10 Hz correspond to the arc in Figure 16a. More importantly, the high-frequency increase in the M″ spectrum suggests that there is another M″ peak at frequencies of >1 MHz and therefore indicates the presence of a much more

conductive bulk element. The M″ peak frequency is determined by fmax =

1 2πρε0εr

and is independent of sample geometry.93 By lowering the measuring temperature, the resistivity increases and the M″ peaks associated with the conducting bulk element are brought into the measured frequency range at T < 400 K (Figure 16c). Figure 16d shows the temperature dependence of the M″ peaks associated with the resistive element at higher temperatures. Therefore, combined Z″/M″ plots clearly reveal that there are two electro-active elements. The resistive element is assigned as the grain-boundary response. As in the impedance complex plane plot (Figure 16a), the bulk arc is swamped by the grain-boundary arc; therefore, it is not possible to extract the bulk resistivity using this method. Nevertheless, the bulk resistivity can be estimated using the relation given above. The εr values are estimated from capacitance spectroscopic plots at room temperature (using the capacitance value at 500 kHz; see Figure S13 in the Supporting Information). The temperature dependence of εr is typically very small (for example, −55 ppm/K for LiMgPO492), compared to the temperature dependence of the resistivity. Therefore, it is reasonable to use the room-temperature εr value to calculate the resistivity at different temperatures. Arrheniustype plots for both the bulk and grain boundary responses are shown in Figure 16e, where the grain-boundary resistivity values are obtained from the impedance complex plane plots and the bulk resistivity values are obtained from the spectroscopic plots of the imaginary component of the electric modulus, M″. All compositions exhibit values of 0.7−0.8 eV for the activation energies for conduction (Ea) in the bulk and ∼1.0 eV at grain boundaries (see Table S5 in the Supporting Information), close to the ∼0.9−1.0 eV value obtained for long-range Li transport from the high-temperature regime of the 7Li NMR T1ρ−1 rates (recall Figure 9a). In3+ doping of 15% and 17% increases the bulk conductivity by more than 2 orders 2087

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Chemistry of Materials of magnitude over the parent composition. For example, at room temperature, the parent composition and the 10% and 17% In3+-doped compositions exhibit bulk conductivities of ∼5 × 10−12, ∼ 4 × 10−10, and ∼2 × 10−9 S cm−1, respectively (see Table S5 in the Supporting Information). The similar Ea values for all compositions suggest that (i) the mechanism of Li+ ion conduction does not change significantly and (ii) the increase of bulk conductivity is related to the increase in the number of Li vacancies in the In-doped compositions. This proves the validity of the doping strategy identified by simulation, although the bulk conductivity of In-doped compositions is still far lower than that of the best-known Li+ ion conductors. The bulk conductivity σ obtained above could be converted to a diffusion constant Dσ. Assuming a simple Nernst−Einstein relation for the motion of Li+ ions,

Dσ =

σkBT Nq2

where T is temperature, N the density of Li+ ions, and q their charge, we obtain a room-temperature value of Dσ ≈ 6 × 10−17, 6 × 10 −15 , and ∼3 × 10 −14 cm2 s−1 for LiMgPO4 , Li0.9Mg0.9In0.1PO4, and Li0.83Mg0.83In0.17PO4, respectively. The latter value is close to the value reported for Li0.83FePO4 (∼10−14 cm2 s−1).29 In addition, extrapolation of the diffusion coefficients obtained by 7Li NMR (recall Figure 10) in the temperature range of 500−1100 K to room temperature gives a diffusion constant of ∼2 × 10−17 cm2 s−1 for LiMgPO4 and ∼8 × 10−14 cm2 s−1 for Li0.9Mg0.9In0.1PO4, in fair agreement with the data obtained from impedance measurements. Impedance measurements were also performed in flowing O2 and Ar (see Figure S14 in the Supporting Information). The impedance complex plane plots at 776 K (Figures S14a and S14b in the Supporting Information) and the M″ plots at 382 K (Figure S14c in the Supporting Information) reveal no difference in both grain-boundary and bulk conductivity by varying the measured oxygen partial pressure (pO2) from O2 to Ar. The behavior of conductivity dependence on pO2, together with the low-frequency spikes observed in impedance complex plane plots (see Figure 16a, as well as Figure S14d in the Supporting Information) suggests that the electrical conduction is indeed associated with Li+ ion conduction rather than electronic conduction. Dopant Trapping of Vacancies. It has previously been suggested that Li+ ion conduction in doped LiFePO4 is prevented by trapping of Li+ ion vacancies by dopant ions introduced into the structure.40 The DFT energies of the configurations used to predict the doping enthalpy of In in LiMgPO4 can be used to assess the strength of the interaction between the In3+ dopant ion and the Li+ ion vacancy created in the structure. A plot of energy versus the separation of these two species for each symmetrically unique configuration (Figure 17a) shows a clear energetic preference for the vacancy to reside close to the In3+ ion, likely due to simple Coulombic interactions. There is an energetic cost or trapping enthalpy (ΔHtrap) of ∼0.4 eV for removing the vacancy to a distance of >8 Å from the In3+ ion. The activation energy for long-range Li diffusion obtained from impedance spectroscopy of 0.7−0.8 eV and 7Li NMR of 0.9−1.0 eV is close to the sum of the calculated trapping enthalpy (ΔHtrap) and the hopping barrier (ΔHhop). This is consistent with a model in which there is an energy barrier related to ΔHtrap, with regard to releasing charge carriers, along

Figure 17. (a) Doping enthalpy of In3+ for Mg2+ substitution is plotted versus the separation between the dopant In3+ ion and the resulting Li+ vacancy for each of the symmetrically unique configurations in a 2 × 2 × 2 supercell. The relaxed structures of the configurations with the smallest and largest separations are shown as insets. Octahedra containing In3+ ions are drawn in blue, and those containing the Li+ vacancy are shown in yellow. Mg atoms, Li atoms, PO4 tetrahedra, and O atoms are shown in orange, green, purple, and red, respectively. (b) Trapping enthalpy of Li+ vacancies by dopant ions, plotted for substitutions of the Li+ ions (green), Mg2+ ions (orange), and P5+ ions (purple) in LiMgPO4.

with a hopping barrier ΔHhop, which is related to site−site motion of each released carrier, in a manner related to proton trapping in hydrated Y-doped BaZrO394 and to oxide ion trapping in Sc-doped CeO2.58 The charge carrier concentration then depends exponentially as exp(−ΔHtrap/(kBT)), leading to Arrhenius behavior of the form σ=

⎛ ΔHtrap ⎞ ⎛ ΔHhop ⎞ σ0 exp⎜− ⎟ exp⎜− ⎟ T ⎝ kBT ⎠ ⎝ kBT ⎠

The effect of dopant trapping is also observed in the MD data. Plots of the mean square deviation (MSD) with time do not show the linear behavior expected for random walk trajectories, and there is a pronounced distribution of MSD values for different Li+ ions reflecting the strong dependence of ionic mobility on local environment (see Figure 18). LiMgPO4 would be expected to be a good ionic conductor based on the barrier to local site hopping (ΔHhop), but is transformed into a poor conductor by the effect of dopant trapping. This effect is likely to be ameliorated in transitionmetal-containing olivines such as LiFePO4, in which correlated electronic and ionic transport allows the 3+ species to migrate with the Li+ ion vacancy, reducing the overall barrier to diffusion.9 Nevertheless, it is possible that the correct choice of parent compound and dopant species could lead to a considerably reduced trapping enthalpy and thus to improved transport properties. ΔHtrap, which is defined as the difference between the lowest-energy and highest-energy doped configurations, was obtained for every calculated substitution into LiMgPO4, and is plotted in Figure 17b. In3+ substitution for 2088

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S Supporting Information *

Additional data and figures for crystallography, EDX, NMR, MD, and impedance spectroscopy. This material is available free of charge via the Internet at


Corresponding Authors

*E-mail: [email protected] (F. Blanc). *E-mail: [email protected] (M. J. Rosseinsky). Figure 18. Mean square displacement (MSD) of Li+ ions during two MD runs of Li0.85Mg0.85In0.15PO4 at 685 ± 14 K and 888 ± 17 K.


The authors declare no competing financial interest.

ACKNOWLEDGMENTS We thank Dr. P. Adamson, Dr. C. Murray, Dr. S. Thompson, and Dr. C. Tang, for assistance on I11; Dr. R. I. Smith, for assistance on Polaris; and Prof. D. A. Keen, for assistance on GEM. We also thank Dr. A. Rakhmatullin and Dr. P. Florian (CEMHTI−CNRS Orléans) for access to the laser-heated high-temperature static NMR probe and useful discussions. This work is funded by the European Research Council (ERC Grant Agreement No. 227987 RLUCIM). It made use of computer facilities of N8 HPC provided and funded by the N8 consortium and EPSRC (EP/K000225/1) and the U.K.’s national high-performance computing service HECToR via our membership to the U.K.’s HPC Materials Chemistry Consortium funded by EPSRC (No. EP/L000202). The U.K.’s 850 MHz Solid-State NMR Facility used in this research was funded by EPSRC and BBSRC, as well as the University of Warwick, with partial funding through Birmingham Science City Advanced Materials Projects 1 and 2, supported by Advantage West Midlands (AWM) and the European Regional Development Fund (ERDF). The authors thank Dr. P. A. Chater for helpful discussion and comment.

Mg2+ has one of the lowest predicted values of ΔHtrap, second only to Ga3+ for Mg2+ substitution, which is experimentally inaccessible, suggesting that ΔHtrap has already been optimized for doped LiMgPO4. The ionic conductivity of LiFePO4 is affected by the presence of Li/Fe antisite defects in addition to the trapping of vacancies by charged point defects.8−10 The grains in the measured Li1−xMg1−xInxPO4 ceramics are 10−100 μm in size (see Figure S15 in the Supporting Information). At this length scale, the majority of 1-D conduction channels in Li1−xMg1−xInxPO4 are expected to contain antisite defects, reducing the Li+ ion conductivity, even at the concentrations of