Research Article

Capturing metastable structures during high-rate cycling of LiFePO4 nanoparticle electrodes

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Science  27 Jun 2014:
Vol. 344, Issue 6191, 1252817
DOI: 10.1126/science.1252817

Structured Abstract


The ability to achieve high cycling rates in a lithium-ion battery is limited by the Li transport within the electrolyte; the transport of Li ions and electrons within the electrodes; and, when a phase transformation is induced as a result of the Li compositional changes within an electrode, the nucleation and growth of the second phase. The absence of a phase transformation involving substantial structural rearrangements and large volume changes is generally considered to be key for achieving high rates. This assumption has been challenged by the discovery that some nanoparticulate electrode materials, most notably LiFePO4, can be cycled in a battery at very high rates, even though they cycle between two phases during battery operation. This apparent contradiction has been reconciled by the hypothesis that a nonequilibrium solid solution can be formed during reaction to bypass the nucleation step.

Embedded Image

Phase transformation from LiFePO4 (blue) to FePO4 (red). The delithiation (indicated by yellow arrows) proceeds at high rates via the formation of a nonequilibrium solid solution phase LixFePO4 (intermediate purple color), avoiding a classical nucleation process (indicated by dashed arrows). When the reaction is interrupted, the particles relax into the equilibrium configuration (shaded region), where only single-phase particles of LiFePO4 and/or FePO4 are present.


To test this proposal, in situ techniques with high temporal resolution must be used to capture the fast phase transformation processes. We performed in situ synchrotron x-ray diffraction (XRD), which readily detects the structural changes and allows for fast data collection, on a LiFePO4-Li battery at high cycling rates, conditions that are able to drive the system away from equilibrium. We used an electrode comprising ~190-nm LiFePO4 particles, carbon, and binder (30:60:10 weight %), along with an electrochemical cell designed to yield reproducible results over multiple cycles, even at high rates. The high carbon content ensures that the reaction at high rates is not limited by either the electronic conductivity or ionic diffusion within the electrode composite. We compared the experimental results with simulated XRD patterns, in which the effects of strain versus compositional variation were explored. We then adapted a whole-pattern fitting method to quantify the compositional variation in the electrode during cycling.


The XRD patterns, collected during high-rate galvanostatic cycling, show the expected disappearance of LiFePO4 Bragg reflections on charge and the simultaneous formation of FePO4 reflections. In addition, the development of positive intensities between the LiFePO4 and FePO4 reflections indicates that particles with lattice parameters that deviate from the equilibrium values of LiFePO4 and FePO4 are formed. The phenomenon is more pronounced at high currents. Detailed simulations of the XRD patterns reveal that this lattice-parameter variation cannot be explained by a LiFePO4-FePO4 interface within the particles, unless the size of the interface is similar to or greater than the size of the entire particle. Instead, the results indicate compositional variation either within or between particles.


The results demonstrate the formation of a nonequilibrium solid solution phase, LixFePO4(0 < x < 1), during high-rate cycling, with compositions that span the entire composition between two thermodynamic phases, LiFePO4 and FePO4. This confirms the hypothesis that phase transformations in nanoparticulate LiFePO4 proceed, at least at high rates, via a continuous change in structure rather than a distinct moving phase boundary between LiFePO4 and FePO4. The ability of LiFePO4 to transform via a nonequilibrium single-phase solid solution, which avoids major structural rearrangement across a moving interface, helps to explain its high-rate performance despite a large Li miscibility gap at room temperature. The creation of a low-energy nonequilibrium path by, for example, particle size reduction or cation doping should enable the high-rate capabilities of other phase-transforming electrode materials.

Watching battery materials in action

When batteries get rapidly charged and discharged repeatedly, they will often stop working. This is especially true when the cycling changes the crystal structure of the battery components. Liu et al. examined the structural changes in components of a type of lithium battery (see the Perspective by Owen and Hector). Their findings explain why LiFePO4 delivers unexpectedly good electrochemical performances, particularly during rapid cycling.

Science, this issue p. 10.1126/science.1252817; see also p. 1451


The absence of a phase transformation involving substantial structural rearrangements and large volume changes is generally considered to be a key characteristic underpinning the high-rate capability of any battery electrode material. In apparent contradiction, nanoparticulate LiFePO4, a commercially important cathode material, displays exceptionally high rates, whereas its lithium-composition phase diagram indicates that it should react via a kinetically limited, two-phase nucleation and growth process. Knowledge concerning the equilibrium phases is therefore insufficient, and direct investigation of the dynamic process is required. Using time-resolved in situ x-ray powder diffraction, we reveal the existence of a continuous metastable solid solution phase during rapid lithium extraction and insertion. This nonequilibrium facile phase transformation route provides a mechanism for realizing high-rate capability of electrode materials that operate via two-phase reactions.

Rechargeable lithium-ion batteries are important electrochemical storage devices for portable electronics and increasingly for electrical vehicles. An electrode operates by reversible Li-ion insertion (lithiation) and extraction (delithiation) during charge and discharge. High-rate lithium-ion battery electrode compounds generally form solid solutions with Li over a large composition range so that no phase transformation is induced during (de)lithiation. Phase transformations, if they occur during cycling, are associated with small or negligible volume changes. For example, the Li-excess spinel Li1.06Mn2O4.10 forms a solid solution throughout the delithiation process (1), as does the layered compound LiNi1/3Mn1/3Co1/3O2 (2, 3), whereas the high-voltage spinel Lix(Ni0.5Mn1.5)O4 (0 < x < 1), shows only a small volume change (3%) for the two-phase region (4). Moreover, a clear correlation between cation ordering, reaction mechanism, and rate has yet to be fully established. LiFePO4 (5) represents an exception to this rule, because it displays excellent high-rate performance when nanosized (6), despite undergoing a first-order phase transformation to FePO4 upon delithiation, a process involving a volume change of 6.8% (5). The very limited Li solubility in LiFePO4 and FePO4 suggests that (de)lithiation occurs via a two-phase reaction (711), where the relative LiFePO4:FePO4 phase ratio is changed by a moving phase boundary, and not via a solid solution. Although the Li solubility is found to increase with decreasing particle size (12, 13) as a result of the increased interfacial energy per unit volume, a substantial Li miscibility gap still exists. Taking this interfacial energy into consideration, ex situ diffraction studies of LiFePO4 nanoparticles propose that once an energetically unfavorable LiFePO4-FePO4 interface is formed, this interface will quickly propagate through the particle so as to return to the most stable LiFePO4 or FePO4 state (the “domino-cascade” mechanism) (14), explaining why only LiFePO4 and FePO4 particles are observed ex situ (15). Thus, at any time during the charge cycling, only a very small subset of particles should be reacting, making it difficult to observe this mechanism in situ.

Because all electrochemical processes operate at an overpotential, the pathways taken during the reaction are not necessarily governed by the thermodynamic properties of the system. As LiFePO4 and FePO4 phases coexist under equilibrium, an overpotential that lowers the Li chemical potential of one phase relative to the other is required to drive the reaction. It has been postulated that this reaction overpotential modifies the phase transformation pathway. Ab initio calculations (16) have predicted that instead of forming an interface, the (de)lithiation of a single particle proceeds via nonequilibrium single-phase LixFePO4 (0 < x < 1), which bypasses nucleation and proceeds at a much lower overpotential. Once the overpotential is removed, the nonequilibrium LixFePO4 particle relaxes to form the thermodynamic LiFePO4 and FePO4 phases releasing or taking in Li+ ions from the electrolyte. Making use of this theory, continuum modeling has suggested that a higher fraction of the electrode will react simultaneously via this nonequilibrium solid solution at high rates than at low rates; that is, the fraction of the electrode particles present as LixFePO4 will be higher (17). A second continuum modeling study has argued that LiFePO4-FePO4 phase separation (within a single particle) is not seen at high rates due to the dynamic stabilization of the intermediate phases (18).

Diffraction methods using neutron or x-ray sources are commonly used for in situ characterization of the structural changes that occur in the crystalline phases within the electrode during electrochemical cycling. Recent in situ x-ray diffraction (XRD) studies of micrometer-sized LiFePO4 at high current rates have shown the appearance of a metastable crystalline phase with an intermediate lithium composition of Li0.6-0.75FePO4 (19). However, investigations of smaller particles have been limited to low (<0.1 C; n C is the current required to either charge or discharge the electrode fully in 1/n hours) (20) and moderate (1 C) (21) current rates, and only small deviations in stoichiometry from LiFePO4 and FePO4 were observed (via changes in lattice parameters) during cycling. Because nanoparticles generally have faster transport kinetics, a higher current rate is required to reach the kinetic limit of a phase transformation.

Our approach involves the use of a dilute electrode in a customized electrochemical cell (22), which is capable of achieving high cycling rates, with high reproducibility over multiple cycles, as well as an in situ XRD set-up with high x-ray intensity and a fast read detector to allow the reaction to be probed with high time resolution. The use of the dilute electrode improves both the electronic conductivity and the ion diffusion within the electrode composite (23, 24) and is critical to probe the process intrinsic to the active material, LiFePO4. By studying the nanoparticles under high current rates, we are able to force enough particles to transform simultaneously so that the reacting particles can be detected and the nature of the phase transformations that occur at an overpotential can be determined.

Intermediate LixFePO4 phases induced at high currents

In situ diffraction patterns during the first five cycles of a 10-C galvanostatic charge-discharge of LiFePO4 of average size 186 nm (fig. S1) are shown in Fig. 1A, where the contributions from the cell background and polytetrafluoroethylene (PTFE) peaks are subtracted for clarity. All diffraction peaks can be indexed to either the Li-rich Li1–αFePO4 phase or the Li-poor LiβFePO4 phase in the space group Pnma. As expected, Li1–αFePO4 peaks disappear on charge and are restored on discharge; conversely, LiβFePO4 peaks start to form and grow on charge and disappear on discharge. Unexpectedly, we observed the development of appreciable positive intensities within the 8.15° to 8.4°, 13.95° to 14.1°, and 15.15° to 15.4° 2θ ranges, which indicate the existence of phases with lattice parameters that deviate from those of LiFePO4 and FePO4 under equilibrium. A closer examination of individual diffraction patterns for selected 2θ regions is provided in Fig. 1B. The phenomenon is more pronounced at high current rates, as illustrated by Fig. 2, which compares the results obtained at 5-, 10-, and 20-C rates.

Fig. 1 In situ XRD patterns during galvanostatic charge and discharge at a rate of 10 C.

(A) The image plot of diffraction patterns for (200), (211), (020), and (301) reflections during the first five charge-discharge cycles. The horizontal axis represents the selected 2θ regions, and time is on the vertical axis. The diffraction intensity is color coded with the scale bar shown on top. The corresponding voltage curve is plotted to the right. LFP, LiFePO4; FP, FePO4; a.u., arbitrary units. (B) Selected individual diffraction patterns during the first two cycles stacked against the voltage profile. The baseline is represented by horizontal dashed gray lines. Black vertical lines mark the positions of LiFePO4 peaks at the start of reaction; red vertical lines mark the position of FePO4 peaks formed during the first cycle.

Fig. 2 In situ XRD pattern of LiFePO4 under different electrochemical cycling conditions.

(A to C) Images show the second galvanostatic cycle at 5, 10, and 20 C, respectively. (D) Images show the evolution of the charge-relax experiment, where a current equivalent to 10 C is applied for 90 s (highlighted with the horizontal gray bands) followed by an open-circuit relaxation of 10 min. The dashed white lines indicate the peak positions of the LiFePO4 and FePO4 phases at the end of the second relaxation period, which are used to draw the boundaries of the miscibility gap, as determined from the (200) and (301) reflections.

All of the reflections exhibit highly symmetrical profiles at the onset of the first charge [shown in Fig. 1B, pattern (a)], but as charging proceeds, the LiFePO4 (200) and (301) reflections start to broaden asymmetrically toward higher angles [pattern (d)]. The most severe asymmetrical broadening is shown on discharge in patterns (f) and (g), where the (200) reflections from both phases are connected by a positive intensity band. Similar behavior is also found in the second cycle [most notably, patterns (l) and (p)]. Neither the peak position nor the peak shape of LiFePO4 is restored to that of the original state by the end of the second cycle: As shown in pattern (r), all selected peaks shift toward higher angle and broaden. The peak shift indicates a decrease in the unit cell volume, which is attributed to the reduced accessible capacity at high rates. Because the lithium composition is not restored to LiFePO4 at the end of each cycle, a solid solution (Li1–αFePO4) is formed, which has a smaller unit cell volume than stoichiometric LiFePO4. This phase is also more disordered and/or has a shorter coherence length than LiFePO4, resulting in peak broadening.

The unusual evolution of peak shapes comes as a result of the microstructural changes induced during high-rate cycling. In diffraction theory (25), the peak shape is a convolution of the instrumental profile, which is symmetrical in this case, and the sample-induced profile due to small crystallite sizes and/or lattice distortions that can originate from strain, composition variations, etc. The size effect produces a symmetrical profile, whereas the lattice distortion effect can give rise to either a symmetrical or asymmetrical profile (25), depending on the nature and distribution of the distortion. Thus, the development of an asymmetrical peak profile in this system is solely attributed to lattice distortions and/or compositional distributions. The experimental peak asymmetry exhibits a certain hkl dependence—the (200), (210), (211), (020), and (301) reflections skewing in the opposite direction to the skew observed for the (101) reflection (fig. S2)—that is consistent with that predicted for varying lithium composition between FePO4 and LiFePO4 (i.e., a solid solution). Some anisotropic peak shift and/or asymmetry could also be induced by a mechanical strain built up from the coherent interface between the LiFePO4 and the FePO4 domains during the reaction, which although of different physical origin, will also cause variations in lattice parameters.

Continuous distribution of LixFePO4 phases beyond the thermodynamic miscibility gap

The distribution of lattice parameters can be quantified if its contribution to the peak profile (broadening) can be separated from other sources. One common approach to treat an asymmetrical profile is to deconvolute contributions due to size and lattice-parameter variations by applying a Warren-Averbach Fourier analysis (25) to a series of diffraction peaks arising from the same class of reflection. This is difficult to implement in our system because of the low crystal symmetry and severe peak overlap. An alternative approach, adopted here, involves fitting the peak profile by convoluting separate contributions from size and lattice-parameter variations with appropriate analytical functions (see materials and methods). To carry this out, we performed Pawley whole-powder-pattern fitting (26) with two phases representing LiFePO4 and FePO4. The effect on the profile from the small crystallite size was modeled by an isotropic size-broadening term, whereas that due to lattice-parameter variations was modeled by convoluting an isotropic microstrain-like broadening term, accounting for the symmetrical distribution of lattice parameters, with spherical harmonics to fit the hkl-dependent asymmetry (27) caused by the asymmetrical lattice-parameter distribution. We then used the TOPAS structural refinement package (28) to refine the size and lattice-parameter variations in the fitting process, and we achieved satisfactory fits to the observed profile (fig. S3), demonstrating the success of our model in accounting for the asymmetrical peak profiles. Our fittings capture the asymmetry of all the classes of reflections [fig. S3; see, for example, the (200), (211), (020), and (301) reflections], which indicates that the lattice-spacing variation is not limited to only a few crystallographic directions. The scale factor of LiFePO4 + FePO4 remains constant during the reaction (fig. S4), providing evidence that our model is able to capture the bulk of the sample, even during the phase transformation. Instead of a single set, we extracted a distribution of all lattice parameters for each diffraction pattern from this analysis.

Contour plots in Fig. 3 show the population density distribution of a, b, and c lattice parameters from both phases during the first two cycles. The LiFePO4 phase initially has a very narrow lattice-parameter distribution, but during the first charge, the lattice parameters from both LiFePO4 and FePO4 become more widely distributed, with an asymmetric tail toward the cell parameters corresponding to the lower and the higher Li compositions, respectively. Although analogous features are found in subsequent discharge and charge cycles, the Li composition range between x = 0.2 and 0.8 (for x in LixFePO4) in the middle of (dis)charge becomes more populated than in the first charge. A similar population density distribution (fig. S5) can be obtained consistently by fitting the (200) and (301) reflections with multiple peaks representing a distribution of lattice parameters.

Fig. 3 Lattice-parameter distributions during galvanostatic cycling.

The refined LiFePO4 and FePO4 lattice-parameter distributions are shown for the first two charge-discharge cycles at the 10-C rate. The relative population density is color coded, as shown at atop the figure. Given the very narrow distribution and, hence, the very high population density at the beginning of the first charge, the lowest contour is drawn at 7.5% intensity of the maximum intensity (indicated by the solid black circles) in subsequent cycles. The corresponding voltage profile is shown at the bottom. Dashed lines mark the positions where lattice-parameter distributions are most asymmetrical.

To identify the dominant cause for the asymmetrical distribution of lattice parameters, we need to separate the effects of compositional variations and strain between two different lattices (LiFePO4 and FePO4). The following observations indicate that the compositional variation mechanism dominates. First, we note that the peak asymmetry of reflections from LiFePO4 persists, even in the absence of any reflections from FePO4, as shown in patterns (i) and (k) of Fig. 1B; this can only be caused by compositional variation because an interface requires the coexistence of both phases. Second, we consider the effect of a possible region affected by the strain introduced by a coherent interface between LiFePO4 and FePO4 on the XRD patterns. Because the interface has been shown to align with the bc plane by transmission electron microscopy studies (7), it is most relevant to examine the effect of the interface width on the (200) reflections. Figure 4A shows the simulated (200) reflection profiles for a series of widths of the bc interface in a particle that is 186 nm long along the a axis. We used the strain distribution derived from a coherent twin boundary (29), which leads to the a lattice-parameter profile at an interface along the a axis as Embedded Image (1)where a0 and a1 are the a lattice parameters of FePO4 and LiFePO4, respectively; L is the interfacial width; and x is the distance from the center of the interface. The Li composition profile (and also the structure factor) is discrete and remains constant on either side of the interface, as shown in the right panel of Fig. 4A. We find that for a 10-nm interface, which is approximately the relaxed interface width found in both a micrometer-sized (7) and a 172-nm (8) particle, the (200) profile remains almost unaffected. Although the simulated profile shows more asymmetry as the interface becomes wider, the asymmetry is mostly associated with the FePO4 reflection, which is opposite to the experimental observation where the asymmetrical broadening is more associated with the LiFePO4 reflection. When the Li composition (and also the structure factor) is allowed to vary continuously across the interface, the a lattice-parameter distribution profile follows the exact form described by Eq. 1 if (i) Vegard’s law is assumed (i.e., a linear change in the lattice parameters is observed as the lithium composition varies between FePO4 and LiFePO4) and (ii) the regular solution model (30) is assumed (Li and vacancy ordering is random). The simulated profile (Fig. 4B) finds much better agreement with the experimentally observed one, but only for interfaces of 100 nm or wider (i.e., of the same order of magnitude as the size of the crystallites). Qualitatively similar trends are expected for interfaces with different orientations (for example, the ab and ac interfaces). Hence, the experimental profile cannot be explained by an interface maintained solely by mechanical strains, as suggested by the domino-cascade argument (14), and must be associated with continuous compositional variations. This is only plausible for a system that can form a solid solution—in this case, only under nonequilibrium conditions.

Fig. 4 Simulated reflection profiles.

(A and B) The (200) reflections are simulated for different interface widths between LiFePO4 and FePO4. Left panels compare the simulated profiles with the experimentally measured one (top). Right panels show the corresponding Li composition (shaded areas) and the a lattice-parameter profiles (solid black lines) used in the simulation for various interfacial widths. The particle dimension along the a axis is 186 nm, and the interface is positioned in the center. The results based on a discrete Li composition profile (mechanical strain only) and a continuous Li compositional variation are shown in (A) and (B), respectively.

In a real system, multiple interfaces and/or reaction fronts may exist within a single particle, which can lead to an even more homogenous Li composition distribution within a single particle. Furthermore, increased inhomogeneity may result from the finite one-dimensional (1D) Li+ transport in the 1D tunnels of the olivine structure. Li+ concentration gradients in the electrolyte induced by the high current rate will also give rise to an inhomogeneous state of lithiation across the electrode (24); that is, the Li composition varies between particles. Consequently, the asymmetrical broadening of the observed reflection profile cannot be solely attributed to the Li compositional variation within a particle, and at least a substantial part of the broadening is due to compositional variation between particles and across the electrode.

It should be noted that a wide distribution of particle size could potentially lead to asymmetrical peak profiles, due to the particle-size–dependent Li solubility (12, 13, 31), which could lead to a composition variation based on the particle size. However, the change in the Li solubility is substantial only when the particle size is smaller than 50 nm. Although there are some particles smaller than 50 nm in the sample (fig. S1C), their volumetric fraction is negligible (~6%). Because the phase fraction by x-ray diffraction scales with the total volume of the respective phase, the very small particles (<50 nm) will contribute almost no intensity to the diffraction pattern and will not appreciably affect the peak profile.

Proof of the metastable nature of the LixFePO4 phase

The lithium composition interpolated by Vegard’s law is shown on the right axes in Fig. 3. We find that at around 400, 700, and 920 s, where the asymmetrical lattice-parameter distribution is most pronounced, ~20% of the entire electrode probed by the x-ray beam exists with a composition between that of Li0.25FePO4 and Li0.65FePO4. In comparison, the solubilities obtained by Vegard’s law in 35- and 140-nm particles with coexisting LiFePO4 and FePO4 domains are Li~0.9FePO4 and Li~0.1FePO4, and Li>0.95FePO4 and Li<0.05FePO4, respectively, even by taking the most generous estimation (31). The application of a high current rate thus extends the solid solution into the regime that is thermodynamically prohibited and exists only under nonequilibrium conditions.

To confirm the metastability of the extended solid solution, we carried out an intermittent charging experiment and collected diffraction patterns during both the 10-C charging and the relaxation processes (Fig. 2D). The same whole-powder-pattern fitting method was used to generate the a, b, and c lattice-parameter distribution contour plots (Fig. 5). As expected, asymmetry in the lattice-parameter distribution develops on the LiFePO4 side in the shaded region that highlights the periods during which current is applied, and the distribution gradually becomes more symmetrical once the current is removed and the system is allowed to equilibrate.

Fig. 5 Lattice-parameter distributions during intermittent charging.

The refined LiFePO4 and FePO4 lattice-parameter distributions are shown for the 10-C charging pulse (shaded region) and the subsequent relaxation period. The application of a 10-C current pulse for 90 s (corresponding to the removal of 0.25 Li per LiFePO4 formula unit) is followed by a 10-min relaxation in open-circuit mode. The low FePO4 phase fraction during the first relaxation period is responsible for the greater fluctuation in the lattice parameters. The relative population density is color coded (see top). The lowest contour is drawn at 7.5% intensity of the maximum population density for the FePO4 phase at the end of the second relaxation period (indicated by the solid black circles). In the bottom graph, voltage (red lines) and current (blue lines) are plotted as a function of time.


In contrast to the formation of an intermediate Li0.6-0.75FePO4 phase under high cycling rates in micrometer-sized particles (19), our model reveals the development of a continuous solid solution that extends from the two end-member phases into the thermodynamic miscibility gap. A higher fraction distributed on the LiFePO4 than on the FePO4 side is in good agreement with the nonequilibrium stability phase diagram constructed from the phase-field simulation (18), which predicts an asymmetrically vanishing spinodal region with increasing current rate. This asymmetry is also consistent with the thermodynamic phase diagram with greater lithium solubility on the LiFePO4 side at room temperature (12, 13) and a higher solid solution formation temperature on the low Li composition side (32, 33), which indicates a higher energy barrier to form a homogeneous solid solution with low Li composition. Phase transformation via a single-phase solid solution mechanism is generally thought to manifest itself in diffraction studies as a continuous shift in the peak position; that is, all of the particles react at essentially the same time. The distribution of Li compositions seen here is a consequence of the inhomogeneous nature in the reacting nanoparticulate electrode, which has been shown in various studies to react particle by particle (14, 15, 34, 35). The high current rate induces more particles to undergo phase transformations at similar times during charge and discharge. The different electronic wiring of the particles and distributions in particle sizes all contribute to the onset of the phase transformation reactions and the variation of the Li compositions between the particles and within the particle (17). Detection of the solid solution by powder diffraction is still, however, very difficult due to the small number of reacting particles at any one time. The application of a high current not only induces an overpotential that is large enough to deliver a dynamic phase transformation pathway but also increases the number of reacting particles and, potentially, reaction fronts within a particle, so that the reacting particles can be observed via a bulk measurement technique. However, a large portion of the electrode still remains inactive at any one time, and the diffraction pattern is still dominated by the equilibrium phases LiFePO4 and FePO4.

It is well known that in the mixed olivine system, where the Fe site is occupied by two or more transition metal ions, a thermodynamically stable phase is often observed at intermediate Li composition with extended Li solubility (3641). In cases where Fe, Mn, and Co are mixed at the appropriate ratios (41, 42), a single-phase reaction can even be induced. The solid solutions in the mixed olivine phases are distinct from those reported here because they are thermodynamic in origin (occurring for the bulk of the electrode at low current rates; i.e., under equilibrium conditions), resulting primarily from a random distribution of the transition metal ions and, as described in a recent report, from coherency strain between the two end-member phases (43).

In summary, the exceptionally high rates observed for LiFePO4 are explained by the existence of a facile nonequilibrium single-phase transformation pathway. Provision of the nonequilibrium solid solution phases may also underpin the high-rate capability of other materials that nominally operate via two-phase reactions.

Materials and methods

Materials synthesis

LiFePO4/C composites were synthesized by a solid-state reaction developed by Kobayashi et al. (13). 0.556 g lithium carbonate (Li2CO3, Aldrich 99.997%), 2.681 g iron(II) oxalate dihydrate [Fe(II)C2O4•H2O, Aldrich 99%], 1.714 g ammonium dihydrogen phosphate (NH4H2PO4, Aldrich 99.999%), and 0.261 g Ketjen black (EC-600JD AkzoNobel) were high-energy ball-milled for 40 min to produce homogeneously mixed precursors. The precursors were then pressed into a pellet and sintered at 600°C for 6 hours under flowing Ar gas.

In situ x-ray diffraction measurement

The AMPIX electrochemical cells were used in this experiment; a detailed description of the cell can be found elsewhere (22). To ensure optimal high-rate performance, the proportion of active material in the electrode was halved compared with typical experiments. LiFePO4 powder (3 mg) was mixed with Super P carbon (Alfa Aesar), carbon black (Vulcan XC-72, Cabot Corporation), and PTFE binder (Sigma-Aldrich) in the mass ratio 3:3:3:1 and was pressed (1.6 to 1.8 ton) into a pellet (13 mm in diameter, ~150 μm in thickness). The electrode pellet was assembled into the AMPIX cell with Li foil as the anode, glass fiber as the separator, and 1 M LiPF6 in 1:1 ethylene carbonate:dimethyl carbonate (Tomiyama Pure Chemical Industries) as the liquid electrolyte. The cells were cycled under conditions described in the text.

In situ synchrotron x-ray powder diffraction measurements were performed in transmission geometry at beamline 17-BM of the Advanced Photon Source at Argonne National Laboratory (wavelength 0.7270 Å, 500-μm-diameter beam). A 2D area detector (Perkin-Elmer), consisting of 2048 pixels by 2048 pixels of 200 μm by 200 μm, in size was used. Measurements were performed at two sample-to-detector distances, the first optimized for improved 2θ resolution. For the 10-C charge-discharge cycling presented in Fig. 1 of the main text, the following was used: 900-mm sample-to-detector distance, with a detector offset of 130 mm from the scattered beam, resulting in a 2θ range of 1° to 25°. The data collection time for each pattern was 4 s, corresponding to a change of 0.011 Li per formula unit of LiFePO4. For a larger 2θ range of 1° to 29°, a sample-to-detector distance of 500 nm, with the detector centered at the scattered beam, was used (data shown for 5-, 10-, 20-C cycling and the intermittent 10-C charge-discharge cycling, all in Fig. 2). The data collection time for each pattern was 3 s, corresponding to a change of 0.004, 0.008, and 0.017 Li per formula unit of LiFePO4 for galvanostatic cycling at 5, 10, and 20 C, respectively.

Whole-powder-pattern fitting of the in situ x-ray diffraction data

The background profile was measured for an assembled AMPIX cell without either electrode and was modeled with seven split pseudo-Voigt functions. These seven peaks were used to describe the background of the in situ patterns, and only the peak intensities were varied to account for the gradual changes in the background intensity. Because the sample thickness is less than the beam size, the instrumental broadening is dominated by the beam size. The instrumental profile was determined from the diffraction pattern of a thin layer of LaB6 powder (SRM 660a) placed in the same geometry as the LiFePO4 electrode.

The sample profile is a convolution of the size and the strain effects and is modeled separately. A Lorentzian peak profile is used to model the size broadening, and the apparent size is assumed to be isotropic with respect to different (hkl) reflections. The dependence of the full width at half maximum (FWHM), β, on θ is given byEmbedded Image (2)where λ is the wavelength, and L is the refined apparent size parameter. Because the strain and/or compositional effect induces an asymmetrical profile, it is described by a convolution of a symmetrical and an asymmetrical profile function. A Gaussian profile peak function is chosen to model the symmetrical broadening due to strain, and this strain is also assumed to be isotropic with respect to different (hkl) reflections. The θ dependence of FWHM is given byEmbedded Image (3)where E is the refined symmetrical strain parameter. The asymmetrical profile is modeled by an exponential functionEmbedded Image (4)where εhkl is the refined parameter, and θ is defined in the range [θhkl, +∞] if εhkl > 0 and [–∞, θhkl] if εhkl < 0. Due to the anisotropic change in the lattice parameters from LiFePO4 to FePO4, where a and b contract and c expands, we have to include an hkl-dependent description of the asymmetrical profile, which is done by including symmetrized spherical harmonics series in εhklEmbedded Image (5)where Yij(ω,ϕ) are the symmetrized spherical harmonics that can be found in (44, 45), and Cij are the refined parameters.

The purely strain-induced profile for a certain (hkl) reflection is obtained by convoluting the symmetrical Gaussian function and the exponential function defined at the corresponding θhkl. This profile is scaled by the scale factor of the respective phase to represent the population density distribution. The whole-powder-pattern fitting of the in situ diffraction patterns within the 2θ range between 7.5° and 22.95° was carried out sequentially in the TOPAS structural refinement package (28).

Simulations of XRD reflection profile

Because it has been shown by experiment (7) that the LiFePO4-FePO4 phase boundary is in the bc plane, we only considered the case of a 1D 186-nm particle along the (h00) direction composed of unit cells that continuously vary in the a lattice parameter, as described by Eq. 1. Each unit along the (h00) direction is assigned with a unique index. We followed the treatment of small coherent domains with continuously varying unit cell parameters by Warren (25). For an (h00) reflection, the diffraction power as a function of diffraction angle 2θ can be expressed asEmbedded Image (6)where the subscripts m and m′ represent the indices of the unit cells, fm and fm′ are the structure factors of unit cells m and m′, Rm and Rm are the position coordinates of unit cells m and m′, λ is the x-ray wavelength, and K is a factor independent of θ. The summation is performed over all unit cells in the 1D particle. The structure factor f for the (200) reflection is assumed to vary linearly with the Li composition c (46)Embedded Image (7)where f(0) and f(1) are the structure factors for the (200) reflections of FePO4 and LiFePO4, respectively.

Supplementary Materials

Supplementary Text

Figs. S1 to S5


References and Notes

  1. Acknowledgments: This work was supported as part of the Northeastern Center for Chemical Energy Storage, an Energy Frontier Research Center funded by the U.S. Department of Energy (DOE), Office of Science, Office of Basic Energy Sciences under award no. DE-SC0001294. Work performed at Argonne National Laboratory and use of the Advanced Photon Source, an Office of Science User Facility operated for the DOE Office of Science by Argonne National Laboratory, were supported by DOE under contract no. DE-AC02-06CH11357. H.L. acknowledges the funding from European Union FP7-265368 via the Eurolion Project and the Cambridge Overseas Trust. F.C.S. acknowledges the funding from the Engineering Physical Science Research Council via a Doctoral Training Partnership Award. We thank B. Orvananos, H. C. Yu, K. Thornton, R. Malik, A. Abdellahi, G. Ceder, and M. S. Whittingham for helpful discussions and comments. H.L., F.C.S., O.J.B. and K.M.W. carried out the experiments; H.L., K.W.C., P.J.C. and C.P.G. performed the analysis; and C.P.G. and H.L. wrote the manuscript with help from all coauthors.
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