Hidden Two-Step Phase Transition and Competing ... - ACS Publications

Mar 8, 2017 - ABSTRACT: LiFePO4 is a well-known electrode material that is capable of high- rate charging and discharging despite a strong ...
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Hidden Two-Step Phase Transition and Competing Reaction Pathways in LiFePO4 Yukinori Koyama,*,†,∥ Takeshi Uyama,† Yuki Orikasa,‡,⊥ Takahiro Naka,† Hideyuki Komatsu,† Keiji Shimoda,† Haruno Murayama,† Katsutoshi Fukuda,† Hajime Arai,†,□ Eiichiro Matsubara,§ Yoshiharu Uchimoto,‡ and Zempachi Ogumi† †

Office of Society-Academia Collaboration for Innovation, Kyoto University, Gokasho, Uji, Kyoto 611-0011, Japan Graduate School of Human and Environmental Studies, Kyoto University, Yoshida-Nihonmatsu, Sakyo, Kyoto 606-8501, Japan § Department of Materials Science and Engineering, Kyoto University, Yoshida-Honmachi, Sakyo, Kyoto 606-8501, Japan ‡

S Supporting Information *

ABSTRACT: LiFePO4 is a well-known electrode material that is capable of highrate charging and discharging despite a strong phase-separation tendency of the lithium-rich and poor end-member phases. X-ray diffraction measurements (XRD) with high time-resolution are conducted under battery operation conditions to reveal the phase-transition mechanism of LiFePO4 that leads to the high rate capability. We here propose a hidden two-step phase transition of LiFePO4 via a metastable phase. The existence of the metastable phase, not just a member of a transient solid solution, is evidenced by the operando XRD measurements. Our two-step phase-transition model explains the behavior of LiFePO4 under the battery operation conditions. It also explains asymmetric behavior during the charging and discharging at high rates and low temperatures, as well as apparent single-step two-phase reaction between the end members at low rates at room temperature. This model also suggests underlying, rate-dependent electrochemical processes that result from a competing disproportion reaction of the metastable phase.

1. INTRODUCTION Use of LiFePO4 as an electrode material for lithium-ion batteries was first proposed by Padhi et al. in 1997.1 Lithium insertion into and removal from this material are recognized to proceed by a two-phase reaction between the end members: lithium-rich Li1‑βFePO4 (LFP) and lithium-poor LiαFePO4 (FP) phases.1−4 This is because of the thermodynamic nature of the LixFePO4 system: strong tendency for phase separation and low miscibilities of lithium in the end members at room temperature. Although nucleation and growth processes in twophase reactions are considered to be kinetically unfavorable, LiFePO4 is capable of high-rate charging and discharging; thus, its phase transition dynamics is of great interest.5 A phase transition pathway proceeding through a transient solid solution to bypass the nucleation−growth process has been proposed on the basis of theoretical models.6−9 Based on phase transition behavior in a single particle, electrochemical behavior of electrodes consisting of multiparticles has been discussed.10−12 The phase transition has been experimentally investigated by operando X-ray diffraction (XRD) measurements, and emerging intensities have been observed between the diffraction peaks originating from LFP and FP, suggesting the transient solid solution.13−15 The diffraction patterns have been analyzed by a peak deconvolution technique assuming a variety of lattice constants due to a variation in lithium composition.14,15 On the other hand, Orikasa et al. reported emergence of an intermediate LixFePO4 (x ∼ 0.6−0.75), © 2017 American Chemical Society

named LxFP, during high-rate charge−discharge cycles at room temperature by operando XRD measurements.16 Such an independent intermediate has not been taken into account in the previous theoretical models. A similar additional diffraction peak was also reported by Zhang et al.13 It is a subject of discussion whether LxFP is a real phase or just a member of the transient solid solution; in other words, whether LxFP can exist in steady states or only during the phase transition. Recently, several research groups have reported asymmetric phase-transition behavior of LiFePO4 between charging and discharging by observation of individual particles. Li et al. reported asymmetric dependence of population of active particles on charging and discharging rates observed by ex situ scanning transmission X-ray microscopy (STXM).17,18 Zhang et al. also reported a different dependence of the activeparticle population as well as a large difference in local current density between LiFePO4 and FePO4 investigated by operando XRD.19 As the simple phase-transition mechanism between the end-member phases of LFP and FP hardly explains such asymmetric behaviors between charging and discharging, a revised phase-transition mechanism including the intermediate is worth considering. This is because LxFP emerged during Received: November 24, 2016 Revised: February 23, 2017 Published: March 8, 2017 2855

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Figure 1. (top left) Operando XRD patterns of LiFePO4/Li cells during five galvanostatic charge−discharge cycles, (right) corresponding potential profiles, and (bottom) XRD patterns during the first charging and discharging. Charge−discharge cycles were conducted (a) at a rate of 1 C (170 mA g−1) and a temperature of 25 °C, (b) at 10 C (1700 mA g−1) and 25 °C, (c) at 1 C and −5 °C, and (d) at 10 C and −5 °C. Colors of the XRD patterns in the bottom panels represent states of charge (SOCs) of the cells; blue of low SOC to red of high SOC. Black lines denote the patterns at the beginning of the charging or at the end of the discharging; red lines denote the patterns at the end of the charging.

member of the transient solid solution, is evidenced by the temperature-controlled operando XRD measurements. The asymmetric charge−discharge behaviors can be explained in consideration of different kinetics between LFP−LxFP transition and LxFP−FP transition. Numerical simulation for the two-step phase transition based on a first-order reaction model21 reveals underlying, rate-dependent electrochemical processes that result from a competing disproportionation reaction of metastable LxFP.

discharging but did not appear during charging in the previous study,16 showing asymmetric behavior. To obtain further insights on the phase-transition mechanism and the asymmetric charge−discharge behavior of LiFePO4, temperature-controlled operando XRD measurements have been conducted in this study with a variation of rates and temperatures. As electrochemical lithium insertion and removal are thermal activation reactions, exchange current densities are expected to be reduced at low temperatures. Hence, much higher rates could be simulated by charging and discharging at low temperatures. Recently, Yan et al. reported temperaturecontrolled operando XRD measurements using a laboratory Xray,20 but broad diffraction peaks obtained at 273 K result in difficulty to distinguish the intermediate from LiFePO4 and FePO4. To enhance time and angle resolutions of XRD measurements, we have conducted the temperature-controlled operando XRD measurements using a synchrotron radiation Xray. On the basis of the results of the operando measurements, we propose a novel phase-transition mechanism of LiFePO4 that proceeds through two steps via metastable LxFP. This mechanism is in contrast to the conventional single-step phase transition between LFP and FP. LxFP of a real phase, not a

2. METHODS Sample Preparation and Electrochemical Cells. Carboncoated LiFePO4 was prepared through a hydrothermal method.16 LiOH·2H2O (Wako, 98%), H3PO4 (Wako, 85%), FeSO4·7H2O (Wako, 99%), and ascorbic acid (Wako, 99.6%) were dissolved at a ratio of 3:1:1:0.2 in water deoxygenized by bubbling nitrogen gas. The solution was heated in a quartz vessel sealed in a stainless-steel autoclave (MMJ-200, OM Lab-Tech) at 190 °C for 12 h at 1.4 MPa. After the product was washed with deionized water and acetone and dried in a vacuum oven, it was calcined at 700 °C in a 97% argon/3% hydrogen atmosphere for 1 h. The product was characterized by XRD and scanning electron microscopy (SEM) (see Figure S1 in the Supporting Information). The XRD measurement was performed on a 2856

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Chemistry of Materials Rigaku SmartLab diffractometer using a Cu Kα radiation (45 kV, 200 mA) at a 2θ range of 10−90° and a step of 0.03° at room temperature. The obtained XRD pattern indicates that the sample was a single phase of LiFePO4 with an olivine structure (space group Pnma, a = 10.2961(4) Å, b = 5.9876(2) Å, c = 4.6794(2) Å). SEM images were recorded on a SU6600 (Hitachi) operated at 5.0 kV. The particles had a flaky appearance and a diameter of ca. 1 μm. Another LiFePO4 sample having a particle size of ca. 60 nm was synthesized by a solidstate reaction method22 for comparison. Three-electrode aluminum-laminated pouch-type cells were fabricated for operando XRD measurements. LiFePO4/C, carbon black (Denka), and polyvinylidene fluoride (Kureha) at 75:15:10 ratio were mixed with 1-methyl-2-pyrrolidone (Wako, 99%). The slurry was coated on aluminum foil current collectors, dried in a vacuum oven at 80 °C for 24 h, and roll-pressed. The prepared LiFePO4 composite electrodes were used as working electrodes in the cells with lithium foil as counter electrodes and reference electrodes, 1 mol dm−3 LiPF6 solution in an ethylene carbonate/ethyl methyl carbonate mixture (3:7 v/v, battery grade; Kishida) as electrolytes, and microporous polyolefin films as separators. The cells were fabricated in an argon-atmosphere glovebox. The cells were first conditioned by a few cycles of charging and discharging between 2.0 and 4.3 V (versus Li/Li+) at room temperature. Operando XRD Measurements. Operando XRD measurements were conducted at BL28XU of SPring-8 (Hyogo, Japan). An incident X-ray beam (λ = 0.9998 Å) monochromated by a Si (111) double crystal in a transmittance mode was used. The beam size was 0.2 × 0.5 mm2. XRD patterns were recorded by a one-dimensional detector (MYTHEN 1K, DECTRIS), which covers a 2θ range of 17.7−21.3°. In this range, 211 and 020 diffraction peaks of LixFePO4 phases were measured. A pair of beryllium plates used to press the cells and used as an X-ray window were installed to obtain homogeneous current distribution in the cells. Charge−discharge processes of the cells were performed by using potentiogalvanostat equipment (SP300, BioLogic). Before the operando XRD measurements, the cells were potentiostatically charged to 3.35 V at room temperature to fix initial states.16,22 The cells were then used at various temperatures (−5, 5, and 25 °C) fixed by temperature-controlled jackets.23 The cells were galvanostatically charged and discharged at rates of 1 C (170 mA g−1), 5 C (850 mA g−1), and 10 C (1700 mA g−1) between 2.0 and 4.3 V (versus Li/Li+) for five cycles. A fully discharged cell and a fully charged cell were also prepared at room temperature for comparison. The former was obtained by galvanostatic discharging at 0.2 C (34 mA g−1) followed by potentiostatic discharging at 2.0 V for 30 min; the latter was obtained by galvanostatic charging at 0.2 C followed by potentiostatic charging at 4.3 V for 3 h. Wide-range XRD patterns were obtained at a 2θ range of 10−40° at a step of 2.5°, and each section of ca. 3.6° was recorded by the onedimensional detector. Stability of LxFP was evaluated under opencircuit conditions by observing the XRD patterns at the 2θ range of 17.7−21.3°. XRD intensities were estimated by fitting the 211 and 020 diffraction peaks with pseudo-Voigt functions.

overlapping LFP 211 and 020 diffractions disappear, and FP 211 and 020 diffractions simultaneously appear. Conversely, the FP diffractions disappear, and the LFP diffractions appear as the cell is discharged. Charge−discharge cycles at 10 C rate at 25 °C resulted in a larger polarization and a less capacity (Figure S3b). The residual capacity after the first cycle, i.e. the difference in capacity between the charging and discharging, is 24 mA h g−1, which is significantly larger than that at 1 C and 25 °C (5 mA h g−1). The charge and discharge capacities in the subsequent cycles are nearly the same as that in the first discharging. The residual capacity in the first cycle is not due to an irreversible reaction, since it recovered upon slow discharging. The operando XRD pattern during the first charging (Figures 1b and S2c) is similar to that at 1 C and 25 °C. However, a distinct peak at 2θ = 19.4° emerged during the discharging (Figure S2d). This peak can be ascribed to diffraction from LxFP.16 During charge−discharge cycles at 1 C and −5 °C, the potential in the first charging was higher than those in the subsequent cycles (Figure S3c). We observed such a higher potential during the first charging at 10 C and 25 °C (Figure S3b), although the potential difference was small. The residual capacity in the first cycle was ca. 34 mA h g−1, whereas the Coulombic efficiency was nearly 100% in the subsequent cycles. The behavior of the operando XRD patterns in the first charging (Figures 1c and S2e) was different from that at 1 C and 25 °C. At the end of the charging, the FP 020 and 211 diffraction peaks had significant tails on the low-2θ side, and baselines of the diffraction intensity between the LFP 211/020 and FP 211 peaks (ca. 19.3−19.4°) and between the FP 211 and FP 020 peaks (ca. 19.6−19.7°) were remarkably high. The large tails and the high baselines could be ascribed to the transient solid solution as similar to the observations in the literature.13−15 The same tendency was seen at 10 C and 25 °C, whereas it is more significant at 1 C and −5 °C. The effect of low temperatures on the phase-transition behavior is similar to that of high rates, as the same current density corresponds to relatively large quantities at low temperatures due to reduced exchange current densities. The peak at 19.4° became clear by discharging the cell (Figures 1c and S2f). The potential profile at 10 C and −5 °C showed higher potential in the first charging than those in the subsequent cycles (Figure S3d), as similar to the case at 1 C and −5 °C. The residual capacity in the first cycle was ca. 34 mA h g−1. The diffraction peaks became more diffuse in the first charging than those at 1 C and −5 °C, and the pattern finally became an almost trapezoidal shape at the end of the charging (Figures 1d and S2g). The solid-solution pathway would play a more important role at such higher rates and lower temperatures. The diffuse diffraction pattern showed the strongest intensity at ca. 19.4° at the end of the first charging. Although the formation of LxFP was not observed in the first charging at room temperature,16 the intermediate was seen even in the first charging at 10 C and −5 °C. The diffuse diffraction pattern disappeared and diffraction peaks at 19.2° and 19.4° grew, as the cell was discharged (Figures 1d and S2h). This suggests that the discharge reaction stopped at the formation of LxFP and did not reach the formation of LFP. The behavior in the operando XRD pattern was rechecked using another LiFePO4 sample synthesized by a solid-state reaction method, which had a much smaller particle size (60 nm) than that so far described (1 μm). As a result, the same behavior of the diffraction pattern during charge−discharge

3. RESULTS Operando XRD Measurements. Operando XRD patterns of LiFePO4/Li cells during five galvanostatic charge−discharge cycles are displayed in Figure 1. The patterns during the first charging and the first discharging are separately shown in the figure, and enlarged patterns are shown in Figure S2 in the Supporting Information. Potential profiles and capacities in the operando measurements are presented in Figure S3 in the Supporting Information. The potential profile obtained at a charge−discharge rate of 1 C and a temperature of 25 °C is typical of LiFePO4 electrodes with a flat plateau at ca. 3.4 V versus Li/Li+ (Figure S3a). The corresponding operando XRD pattern (Figures 1a and S2ab) is typical of the two-phase reaction between LFP and FP. During the cell charging, 2857

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Figure 2. (a) Wide-range XRD patterns of LiFePO4/Li cells after five galvanostatic charge−discharge cycles at a rate of 5 C (850 mA g−1) and a temperature of −5 °C (LxFP); after potentiostatic discharging at 2.0 V versus Li/Li+ at room temperature (LFP); and after potentiostatic charging at 4.3 V at room temperature (FP). The XRD patterns are indexed to single olivine structures. Diffractions from cell components and X-ray windows are denoted by asterisks (*). Insets show enlarged images for the 211 and 020 diffractions. (b) Estimated unit-cell volumes and lattice constants a, b, and c for LxFP, LFP, and FP cells. The size of the marks denotes the standard error (±1σ) of the estimated values. Lithium composition of the LxFP cell estimated from the cumulative capacity is 0.76.

cycles was observed. The operando XRD patterns measured at 10 and 30 C rates and at 25 °C are shown in Figure S4 in the Supporting Information. The additional diffraction peaks at ca. 2θ = 19.4° were overlapped with the tails of the LFP 211/020 diffraction peaks; the overlapping is due to the broad diffraction peaks resulting from the smaller particle size. Similar evolution of the additional diffraction between the LFP 211/020 and FP 211 diffraction peaks has been reported by other researchers.14,15 These results show that the emergence of LxFP is not specific to the synthesis method of samples. Large particle LiFePO4 (ca. 1 μm), the thin electrodes (18 μm), and the highly coherent synchrotron X-ray with a reasonably long wavelength (λ = 0.9998 Å) were used in most of this study to distinguish the diffraction originating from LxFP with high angle- and high time-resolutions. Wide-Range XRD for Intermediate LixFePO4. At the end of discharging at a temperature of −5 °C and rates of 5 and 10 C, no diffraction peaks from LFP and FP were observed (Figures 1d and S2h). Furthermore, the diffraction peak at 19.4° originating from LxFP had remained strong for several hours under open-circuit conditions as shown in Figure S5 in the Supporting Information. This is in sharp contrast to the behavior at room temperature, where the diffraction peak of LxFP disappeared within 30 min to 1 h (Figure S5 and ref 16). The extended lifetime of metastable LxFP enabled us to conduct wide-range XRD measurements. Figure 2a shows the XRD pattern of a cell after five charge− discharge cycles at 5 C and −5 °C (LxFP cell, hereafter). The cumulative charge−discharge capacity was 40 mA h g−1, which

corresponds to 24% state of charge (SOC). By excluding contribution of other cell components and a beryllium X-ray window, the diffraction pattern of LxFP cell can be indexed to a single olivine structure. Since the diffraction pattern shows no evidence on coexistent LFP or FP, the lithium composition of LxFP can be estimated to be 0.76 from the cumulative charge− discharge capacity of the cell. Note that the diffraction peaks of LxFP cell are 2−4 times broader than the corresponding peaks of the fully charged (FP) and fully discharged (LFP) cells, as shown in the insets of Figure 2a. This suggests that LxFP has much larger miscibility of lithium than the end members of LFP and FP. The broader peaks also suggest a certain variation in the lithium composition among particles. Thus, the lithium composition estimated from the cumulative capacity is an average in the cell. Quantitative estimation of peak intensities for LxFP cell is difficult because of overlapping of diffraction from the cell components and the X-ray window; this interferes with detailed structural analysis of atomic positions and other structural data. Therefore, the lattice constants of LxFP were estimated as a = 10.207(7) Å, b = 5.943(6) Å, and c = 4.724(4) Å by fitting peak positions (see Table S1 in the Supporting Information). The unit-cell volume and lattice constants a, b, and c of LFP, FP, and LxFP are plotted with lithium composition in Figure 2b. The unit-cell volume and the lattice constant a of LxFP are on the interpolation lines between LFP and FP; they follow Vegard’s law. On the other hand, the lattice constant b of LxFP is slightly below the interpolation line, and the lattice constant c is above the line. The lithium composition estimated from the 2858

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has been reported in the literature16,18,19 and is also seen in the operando XRD measurements in this study at 10 C rate or −5 °C or both (Figures 1 and S2). Li et al. used a charge transfer coefficient α = 0.2 in generalized Butler−Volmer kinetics to capture the experimentally observed asymmetry.18 The cause of the asymmetric phase-transition behavior might be asymmetry in chemical potential of lithium6 or in lithium diffusivity28 suggested by density functional theory (DFT) calculations, but such bulk characters are often assumed to be negligible in the theoretical models for the phase transition.6−8,18 Moreover, we used thin electrodes of 18 μm thickness to avoid electrolyte depletion, which might lead to asymmetric behavior.29−31 Instead, through the observation of LxFP, we here propose that the phase transition of LiFePO4 proceeds in two steps via metastable LxFP as follows: Consecutive electrochemical processes proceed from FP to LxFP (step α, hereafter) and from LxFP to LFP (step β) during discharging and from LFP to LxFP (step β) and from LxFP to FP (step α) during charging. The existence of LxFP as a metastable phase is evidenced by the operando XRD measurements (Figures 1 and 2), as discussed above. Different kinetics between the two consecutive electrochemical processes can naturally explain the asymmetric behavior in the phase transition without assuming asymmetric kinetics between charging and discharging. As LxFP is metastable, its disproportionation to the thermodynamically stable phases of LFP and FP competes with the electrochemical processes, resulting in rate-dependent phase transition behavior. We here employed a simplified, macroscopic, and phenomenological model to discuss the phase transition behavior during the charging and discharging. This macroscopic model deals with fractions of LFP, LxFP, and FP averaged in the electrodes. Single lithium composition is assumed for LxFP (experimentally evaluated as 0.76). A first-order reaction model21 is applied to both the electrochemical processes and the disproportionation of LxFP. The proposed model is applicable to the battery operation conditions in the present study and lower rates, whereas it is not to ultrahigh rates (much more than 10 C and −5 °C), at which the system does not have time to form LxFP. Under these simplification and assumption, the phase transition kinetics, namely the phase fractions (cX; X = LFP, LxFP, and FP) and reaction rates as functions of time, are formulated using reaction-rate parameters: kα for step α, kβ for step β, and kd for the disproportionation. We focused on galvanostatic charging and discharging and thus a constant rate of the entire electrochemical process (re) in this study. Then, the kinetic equations can be reformulated with normalized time τ = ret as follows:

cumulative capacity (0.76) was larger than the previously reported range (0.61−0.66)13 that was estimated from the lattice constant b assuming Vegard’s law. The smaller b value of LxFP relative to the value obtained by the linear interpolation resulted in underestimation of the lithium composition. Recently, Nishimura et al. reported24 a refined superstructure of metastable Li0.67FePO4, which was a part of a mixture sample obtained by quenching Li0.6FePO4 solid solution at 623 K. Despite the different lithium composition and the different synthesis route, the reported lattice constants are very close to our values. More appropriate methods are needed to determine the lithium composition and the miscibility in LxFP. The intermediate lattice constants of LxFP can mitigate the lattice mismatch between the two end-members of LFP and FP.16,24

4. DISCUSSION LxFPMetastable Phase or Transient State? In the present study, two points are discussed hereafter: the state of the intermediate LxFP and the origin of the asymmetric charge−discharge behavior of LiFePO4. An important question is whether LxFP is just a member of the transient solid solution in the phase transition between LFP and FP. The following is our explanation why we believe that LxFP is a real phase and not a member of the transient solid solution.25−27 As shown in Figures 1 and S2, diffraction intensities between the LFP 211/020 peaks and the FP 211 peak (ca. 19.3−19.4°) were stronger during the first charging than those at the beginning and at the end of the charging at the conditions of 1 C and 25 °C, 10 C and 25 °C, and 1 C and −5 °C (Figure S2ace). On the other hand, no stronger intensity than that at the end of the charging was observed between the FP 211 and 020 peaks (ca. 19.6−19.8°). The large tails of the diffraction peaks and the high baselines at 19.6−19.8° could be ascribed to the transient solid solution. However, the 020 diffraction of LixFePO4 was never remarkable in this range (roughly x ∼ 0.1− 0.4 on the basis of Vegard’s law) despite the growth of the endmember FP. In the first discharging, no remarkable intensity was observed at 19.6−19.8° despite the clearly emerging peaks at 19.4° at 10 C and 25 °C and 1 C and −5 °C (Figure S2df). Emerging diffraction intensities between the LFP 211/020 and FP 211 peaks with less growth between the FP 211 and 020 peaks were also reported by Liu et al.14 and Hess et al.,12 although they analyzed the diffraction patterns assuming a variety of lithium composition. Although theoretical studies have suggested homogeneous and continuous solid solutions in the transient state,6−9 the continuous solid solutions can hardly explain such miscibility-gap-like behavior during the charging and discharging. The front of the phase transition in particles, which can be very diffuse, would be another possible place for transient solid solutions to appear,9,11,25−27 but such inhomogeneous solid solutions are inconsistent with the observation results in this study; LxFP exists without coexistent LFP or FP (Figure 2a). Instead, consideration of LxFP as a distinct phase with a contribution of the transient solid solutions between LFP and LxFP and between LxFP and FP can simply and reasonably explain the operando XRD patterns. The additional diffraction intensities at 19.3−19.4° during the first charging could be ascribed to the formation of LxFP. The idea that LxFP is a phase is not contradictory to the previously reported transient solid solution in the phase transition; this is discussed in the following section. Two-Step Phase Transition of LiFePO4. Asymmetric charge−discharge behavior in the phase transition of LiFePO4

dc LFP xc = −κc LFP + LxFP dτ ρ dc LxFP c = κc LFP − γκc LxFP − LxFP dτ ρ (1 − x)c LxFP dc FP = γκc LxFP + dτ ρ 1 = (1 − x)κc LFP + xγκc LxFP

for charging and 2859

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Figure 3. (top) Phase fractions of LFP, LxFP, and FP (cX) and (bottom) contribution of two electrochemical steps in the entire electrochemical reaction (fα and fβ) and contribution of disproportionation in the entire consumption of LxFP (fd) for the two-step phase transition model with normalized time (τ) during (a, c, e) charging and (b, d, f) discharging. The relative charging and discharging rate to the disproportionation (ρ) is set to (a, b) 0.0005, (c, d) 0.5, and (e, f) 500, and the ratio of the reaction rate parameters for step α to step β (γ) is set to 5.

ratio γ (kα/kβ) is assumed to be constant regardless of charging or discharging, values of kα and kβ, and temperature. The parameter kd is constant at a given temperature and independent from the electrochemical reaction rate, and it becomes smaller (ρ becomes larger) at lower temperatures. The kinetic equations and the ratio κ (kβ/re) were numerically solved. The experimental evidence of the discharging ending at single LxFP at 5 and 10 C rates and at −5 °C (Figure 2a) suggests that step β is slower than step α (γ > 1). As the phasetransition behavior is not very sensitive to γ (see Figure S6 in the Supporting Information), we used γ = 5. To quantify the contribution of the two electrochemical processes in the charging and discharging, the ratios of the reaction rates to the entire electrochemical reaction rate are evaluated as follows

dc LFP xc = κc LxFP + LxFP dτ ρ dc LxFP c = −κc LxFP + γκc FP − LxFP dτ ρ (1 − x)c LxFP dc FP = −γκc FP + dτ ρ 1 = (1 − x)κc LxFP + xγκc FP

for discharging. In the equations, x is the lithium composition of LxFP, γ is the ratio of the rate parameters for the two electrochemical processes (kα/kβ), κ is the normalized rate parameter for step β (kβ/re), and ρ is the relative (dis)charging rate to the disproportionation rate parameter (re/kd). The details are described in Note S1 and Scheme S1 in the Supporting Information. The rate parameters for the electrochemical processes, kα and kβ, are variable in the galvanostatic charging and discharging, which is analogous to controlling over- and underpotentials in experiments. In this study, the 2860

fα =

xrLxFP → FP = xγκc LxFP re

fβ =

(1 − x)rLFP → LxFP = (1 − x)κc LFP re DOI: 10.1021/acs.chemmater.6b05000 Chem. Mater. 2017, 29, 2855−2863

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Figure 4. Schematic illustration of the phase transition behavior in the two-step phase transition model during (a, c) charging and (b, d) discharging at (a, b) low rates and high temperatures and (c, d) high rates and low temperatures. Widths of arrows schematically represent relative reaction rates and gray arrows denote slow and insignificant reactions at each condition. In charging and discharging at low rates and high temperatures (a, b), LxFP is not observable because of its immediate disproportionation; in charging at high rates and low temperatures (c), LxFP is not observable because of the simultaneous electrochemical process of step α; in discharging at high rates and low temperatures (d), LxFP can be observed. The electrochemical process might not go to the later step β in the high-rate and low-temperature discharging; thus step β is denoted by a broken arrow.

for charging and fα =

xrFP → LxFP = xγκc FP re

fβ =

(1 − x)rLxFP → LFP = (1 − x)κc LxFP re

At a glance at the phase fractions, the charging and discharging appear to proceed through the single-step twophase reaction. In contrast, our model suggests that the underlying processes involve the combination of the electrochemical processes and the disproportionation. The asymmetric processes result in higher and lower potential during the charging and discharging, respectively, compared with the equilibrium potential of the LiFePO4/FePO4 system because of the metastable nature of LxFP. Dreyer et al. reported a voltage gap of 20 mV in LiFePO4 between charging and discharging even at a very low rate (C/1,000).10 The two-step phase transition explains such a voltage gap at a low rate, although overshooting in single particles of a multiparticle electrode is also a plausible cause of the voltage gap. At ρ = 500 (Figure 3ef), i.e. high rates and low temperatures, the disproportionation of LxFP is negligible compared with the electrochemical processes ( fd ∼ 0). During the charging, the contributions of steps α and β in the entire electrochemical reaction (fα and fβ) are respectively ca. x (0.76) and 1 − x (0.24), indicating that the reaction rates of rLFP→LxFP, rLxFP→FP, and re are almost the same. This suggests that step β is ratedetermining and also that LxFP produced at step β immediately converts into FP by the consecutive electrochemical lithiumremoval (step α). Thus, the charging appears to be a single-step two-phase reaction again, as schematically illustrated in Figure 4c. Although the charging appears to proceed in the two-phase manner at both the high and low rates, the underlying processes are quite different. In contrast to the charging, the discharging at high rates and low temperatures proceeds in a stepwise manner (Figure 4d), and thus LxFP becomes the majority halfway in the discharging. This asymmetry in the phase fraction between the charging and discharging is consistent with the operando XRD measurements (Figure 1 and ref 16). The experimental observation that the discharge reaction stopped at the formation of LxFP could be ascribed to the slow kinetics of step β. At ρ = 0.5, i.e. moderate rates and moderate temperatures, the charging proceeds with little disproportionation of LxFP (Figure 3c), similar to the case at high rates and low temperatures. This is because the electrochemical process to form FP (step α) is faster than the competing disproportionation of LxFP. On the other hand, LFP slowly forms in step β during the discharging, and thus the disproportionation of

for discharging, where rX is the rate of reaction X. The fraction of LxFP decomposing through the disproportionation (reaction rate: rd) is also evaluated as follows fd =

rd 1 = rd + rLxFP → FP 1 + γκρ

for charging and fd =

rd rd + rLxFP → LFP

=

1 1 + κρ

for discharging. The phase fractions and the ratios of the reaction rates are illustrated in Figure 3 with normalized time at several values of ρ (the relative charging and discharging rate). The corresponding phase transition behavior is schematically illustrated in Figure 4. At ρ = 0.0005 (Figure 3ab), i.e. low rates and high temperatures, the phase fraction of LxFP is close to zero and the contribution of the disproportionation fd is close to unity during both the charging and discharging; most of LxFP produced by the earlier electrochemical step decomposes to LFP and FP by the disproportionation. Therefore, the charging proceeds through the following processes LiFePO4 → LixFePO4 + (1 − x)Li+ + (1 − x)e− (electrochemical charging; step β) → x LiFePO4 + (1 − x)FePO4 + (1 − x)Li+ + (1 − x)e− (disproportionation)

as schematically illustrated in Figure 4a. On the other hand, the discharging proceeds as follows (Figure 4b): FePO4 + x Li+ + x e− → LixFePO4 (electrochemical discharging; step α) → x LiFePO4 + (1 − x)FePO4 (disproportionation) 2861

DOI: 10.1021/acs.chemmater.6b05000 Chem. Mater. 2017, 29, 2855−2863

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Chemistry of Materials

BL28XU of SPring-8 (Proposal No. 2012B7601, 2013A7601, and 2013B7601).

LxFP is favored (Figure 3d), similar to the case at low rates and high temperatures. The different phase-transition kinetics between the two electrochemical steps with the competing disproportionation of LxFP in our model explains the asymmetric charge−discharge behavior of LiFePO4.

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5. CONCLUSION The operando XRD patterns support that LxFP observed during the charge−discharge cycles at high rates and low temperatures is not just a member of the transient solid solution but a real phase. This model can explain the asymmetric charge− discharge behavior of LiFePO4 under the battery operation conditions of the operando XRD measurements. The asymmetry between the charging and discharging as well as the underlying, rate-dependent electrochemical processes can be ascribed to the different phase-transition kinetics between the two electrochemical steps, as presented by the numerical simulation using the simplified macroscopic first-order-reaction model. The present study clearly demonstrates the importance of elucidating hidden but kinetically favorable phase-transition pathways, which contribute to development of electrode materials with high rate capability.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.chemmater.6b05000. Characterization of the LiFePO4 sample by XRD, SEM, and electrochemical tests, additional data for the operando XRD measurements, diffraction peak positions of LxFP, LFP, and FP measured by the wide-range XRD measurements, and phase-transition kinetics simulation based on the two-step phase transition model (PDF)

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REFERENCES

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Yukinori Koyama: 0000-0002-7090-4430 Katsutoshi Fukuda: 0000-0002-7895-650X Hajime Arai: 0000-0001-6695-637X Present Addresses ∥

(Y.K.) Center for Materials Research by Information Integration, National Institute for Materials Science, 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047, Japan. ⊥ (Y.O.) Department of Applied Chemistry, Ritsumeikan University, 1-1-1 Noji-Higashi, Kusatsu, Shiga 525-8577, Japan. □ (H.A.) School of Materials and Chemical Technology, Tokyo Institute of Technology, 4259 Nagatsuta, Midori-ku, Yokohama, Kanagawa 226-8502, Japan. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the Research and Development Initiative for Scientific Innovation of New Generation Battery (RISING) project under the auspices of New Energy and Industrial Technology Development Organization (NEDO), Japan. Operando XRD measurements were performed at 2862

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