Local Structure Evolution and Modes of Charge Storage in Secondary Li − FeS 2 Cells

: In the pursuit of high-capacity electrochemical energy storage, a promising domain of research involves conversion reaction schemes, wherein electrode materials are fully transformed during charge and discharge. There are, however, numerous di ﬃ culties in realizing theoretical capacity and high rate capability in many conversion schemes. Here we employ operando studies to understand the conversion material FeS 2 , focusing on the local structure evolution of this relatively reversible material. X-ray absorption spectroscopy, pair distribution function analysis, and ﬁ rst-principles calculations of intermediate structures shed light on the mechanism of charge storage in the Li − FeS 2 system, with some general principles emerging for charge storage in chalcogenide materials. Focusing on second and later charge/discharge cycles, we ﬁ nd small, disordered domains that locally resemble Fe and Li 2 S at the end of the ﬁ rst discharge. Upon charge, this is converted to a Li − Fe − S composition whose local structure reveals tetrahedrally coordinated Fe.


■ INTRODUCTION
Detailed mechanistic understanding of the processes associated with the intercalation cathode material LiCoO 2 and related layered transition metal oxides has been essential to the development of modern Li-ion batteries. 1In contrast, conversion reaction-based schemes for Li-ion batteries have not advanced as rapidly. 2,3Conversion reaction batteries involve electrodes that are not topochemical in their mode of charge storage and instead undergo dramatic structural and compositional changes during cycling.The broad range of chemistries (including oxides, fluorides, and sulfides) and structures capable of storing charge by conversion make it difficult to elucidate mechanistic trends that are applicable across the many candidate materials.
A general trend of conversion systems is the first discharge reaction, which can be considered for a transition metal (M) anion (X) compound as (eq 1): Another established phenomenon in conversion systems is the significant nanostructuring that accompanies the phase changes during the first discharge. 4,5The formation of new interfaces during the first discharge is accompanied by a large overpotential and results in cycling products with limited long-range order, if any.The disordered nature of products contributes to the difficulty of elucidating the mechanism of charge storage and makes average structure methods, including X-ray diffraction (XRD), ill-suited to the study of conversion systems. 6,7Rather, local structure methods, including pair distribution function (PDF) analysis and X-ray absorption This is an open access article published under a Creative Commons Attribution (CC-BY) License, which permits unrestricted use, distribution and reproduction in any medium, provided the author and source are cited.
−13 In particular, operando characterization provides valuable information about the charge storage mechanism as the chemistry is occurring.FeS 2 has compelling performance relative to other conversion materials, including transition metal oxides, and was originally investigated as a cathode for high-temperature batteries with molten salt electrolytes. 14,15It was later studied for room temperature secondary batteries with organic electrolytes, 16,17 with a focus on the mechanism of charge storage.A primary Li−FeS 2 battery has since been commercialized by Energizer. 18Recent work by Shao-Horn and co-workers revisited earlier mechanistic studies. 19Neartheoretical storage by FeS 2 in an all-solid state cell operating at 60 °C has been reported recently, 20 as have cells based on ionic liquid electrolytes. 21n pyrite FeS 2 , Fe 2+ forms a face-centered cubic lattice with each Fe octahedrally coordinated by disulfide bonds of the form S 2 2− (Figure 1a).FeS 2 can theoretically store 4 mol of Li per formula unit, with a complete first discharge (eq 2): FeS 2 is not recovered when charged at room temperature, 24 and consequently eq 2 is representative of only the very first discharge.With some exceptions, 9 including for FeS 2 , 25 mechanistic studies of conversion materials have typically focused on the first discharge or first cycle. 19,26,27The first discharge is unique from subsequent cycles, and consequently, monitoring structural evolution after the first discharge is essential to elucidating processes representative of battery performance.For FeS 2 , there is near consensus that an intermediate phase forms during cycling.Pyrrhotite and other off-stoichiometry binaries are among those proposed, 27−29 while other literature suggests a ternary Li−Fe−S intermediate stable over a range of Li compositions. 24,25,30Among the postulated ternary intermediates are those with layers of FeS 6 octahedra with Li in the van der Waals gap (Figure 1b), 17,31 layers of Li and Fe tetrahedrally coordinated by S between layers of LiS 6 octahedra (Figure 1c), 22 or a three-dimensionally connected, disordered structure with mixed and partial occupancies of Li and Fe tetrahedrally coordinated by S (Figure 1d). 23e report new mechanistic and structural information about the reaction of FeS 2 with Li based on operando and ex-situ local structure methods.The nature of the local structure of products at various states of charge is consistent from complementary operando PDF and ex-situ XAS data.Ternary structures predicted by first-principles calculations are in good agreement with the PDF data of intermediate and charge products.The mechanism(s) of charge storage for FeS 2 depend(s) on cycling conditions including rate, temperature, and electrolyte.We focus on later cycles, as stated earlier, and find for the applied conditions dual mechanisms including (i) conversion between small, disordered domains that locally resemble Fe and Li 2 S and a Li−Fe−S ternary local structure with tetrahedrally coordinated Fe at low potentials and high Li content and (ii) insertion-extraction behavior of the ternary structure at high potentials and low Li content.

■ EXPERIMENTAL AND THEORETICAL METHODS
Ex-Situ Cell Assembly, Cycling, and Sample Preparation.Cycling was carried out in Swagelok cells with loose-powder electrodes of FeS 2 (Alpha Aesar, 99.9%) and conductive carbon additive Ketjen Black (KB) (AkzoNobel EC-600JD) in a 9:1 ratio by weight.Powders were ground in air with an agate mortar and pestle.LiPF 6 (1 M) in ethylene carbonate−dimethyl carbonate (EC−DMC) (1:1 ratio by volume) electrolyte and two Whatman glass filter dryer (GFD) separators were used.Li metal served as both the counter and reference electrode in these half-cells.Cells were assembled in an Arfilled glovebox and cycled galvanostatically at a rate of C/40 (Q/10), calculated for the theoretical reaction of FeS 2 with 4 mol of Li (per formula unit) in 40 h, with potential limitations of 1 and 3 V for discharge and charge, respectively.Cells were cycled using a Bio-Logic VMP-3.
For ex-situ total scattering and X-ray absorption spectroscopy (XAS), loose-powder Swagelok cells were cycled to a specified potential or capacity.Cells were disassembled in an Ar glovebox, and the cathode powder was collected, washed with DMC, and dried under vacuum.For total scattering experiments, washed powders were loaded into 1.2 mm diameter kapton tubes sealed with epoxy at both ends.For XAS, powders were painted into homogeneous films on kapton tape.All ex-situ samples were prepared and transported under Ar.
First-Principles Calculations.Structure prediction was performed using the ab initio random structure searching (AIRSS) method. 32For a given system, AIRSS initially generates random structures, which are then relaxed to a local minima in the potential energy surface (PES) using density functional theory (DFT) forces.By generating large numbers of relaxed structures it is possible to widely cover the PES of the system.On the basis of general physical principles and systemspecific constraints, the search can be biased in a variety of sensible ways. 33About 2200 Li−Fe−S structures were generated by AIRSS at stoichiometries of x = 0.5,1,1.5, 2, 3, and 4 in Li x FeS 2 .
AIRSS calculations were undertaken using the CASTEP DFT planewave code. 34The gradient corrected Perdew Burke Ernzerhof (PBE)  22 and (d) Li 1.77 Fe 1.17 S 2 (P3) with mixed and partial occupancy (white) of Li and Fe in corner-sharing tetrahedra. 23xchange-correlation functional 35 with spin-polarization was used in all calculations presented in this work.The core electrons were described using Vanderbilt "ultrasoft" pseudopotentials, and the Brillouin zone was sampled using a Monkhorst−Pack grid 36 with a k-point spacing finer than 2π × 0.07 Å −1 .The plane wave basis set was truncated with a cutoff value of 350 eV.
The thermodynamical phase stability of a system was assessed by comparing the free energy of different phases.From the available DFT total energy of a given binary phase of elements A and B, E{A a B b }, it is possible to define a formation energy per atom as eq 3: The formation energies of each structure were then plotted as a function of the B element concentration, u = b/(a + b), starting at u = 0 and ending at u = 1.A convex hull was constructed between the chemical potentials at (u,E f /atom) = (0,0);(1,0) by drawing a tie line to join the lowest energy structures, which is valid provided it forms a convex function.This construction gives access to the 0 K stable structure, as the second law of thermodynamics demands that the (free) energy per atom is a convex function of the relative concentrations of the atoms.
Average voltages for the structures lying on the hull were calculated from the available DFT total energies.For two given phases on the hull, A x 1 B and A x 2 B with x 2 > x 1 , the following two-phase reaction is assumed as eq 4: The voltage, V, is given by eq 5, 37 where it is assumed that the Gibbs energy can be approximated by the internal energy, as the pV and thermal energy contributions are small. 37he low energy structures obtained by the AIRSS search were refined with higher accuracy using a k-points spacing finer than 2π × 0.03 Å −1 and an energy cutoff of 800 eV with more accurate pseudopotentials (see the Supporting Information).The DFT+U approach implemented in CASTEP was used to correct self-interaction error in the GGA by adding the U parameter to the d orbital of the transition metal. 38The U parameter can be chosen to assimilate any experimental band gap.−41 We have used a value of U eff = 4 eV, as was used for Li−Fe−S−O compounds, 42 which falls within the range of reported U values.
X-ray Absorption Studies.Ex-situ XAS at the Fe K-edge was carried out at 20-BM-B at the Advanced Photon Source at Argonne National Laboratory for cells cycled at C/40, as described above.Spectra were collected in transmission mode.The data was calibrated to 7.112 keV 43 and normalized by aligning the E 0 for each Fe foil to a reference spectra.Data was deglitched, normalized and averaged using the open source program ATHENA. 44perando Pair Distribution Function Studies.Operando total scattering experiments were carried out at 11-ID-B at the Advanced Photon Source at Argonne National Laboratory.A PerkinElmer amorphous Si-based area detector enabled rapid-acquisition of X-ray scattering measurements with an X-ray wavelength of 0.2112 Å (≈58 keV).An AMPIX electrochemical cell 45 was assembled in an Ar-filled glovebox with a free-standing pellet cathode composed of FeS 2 − graphite/VulcanC (1:1 by weight)−polytetrafluoroethylene (70:20:10 by weight).The free-standing pellet cathode was about 160 μm thick and 13 mm in diameter.The electrolyte was 1 M LiPF 6 in EC−DMC in a 3:7 by volume, which soaked a GFD separator.Li metal served as both a reference and counter electrode.The cell was galvanostatically cycled with an applied current of 0.8722 mA and a C-rate of about C/17, based on the reaction of 1 mol of FeS 2 with 4 mol of Li in 17 h and with potential limits of 1 and 3 V.Because of time constraints of beamtime and our interest in characterizing later cycles in addition to the first discharge, operando studies were carried out at a faster rate than other cycling discussed here.
The background contribution of the operando cell was collected using an AMPIX cell assembled without the cathode.Experimental geometries were calibrated using CeO 2 powder and Fit2D freeware. 46it2D was also used to integrate collected 2D data, which was acquired once every 30 min.From each set of integrated data, the real-space pair distribution function (PDF) was calculated by a Fourier transform using PDFgetX2, 47 with the structure factor taking into account the relative Li content based on a constant Fe−S ratio of 1:2 and with a Q max = 19 Å −1 .PDFgui 48 was used to simulate PDFs and to fit data to published and calculated structures.Similar data collection and processing were carried out for ex-situ PDFs.Principal component analysis (PCA) was used to assess the local structure evolution during the first discharge.PCA was carried out using Origin Pro (OriginLab, Northampton, MA), which yielded three significant principle components (PCs).Linear combinations were taken of the raw PCs such that there was a single component at the beginning of the reaction and a single component at the end of the reaction. 49The weightings for these revised PCs were evaluated with a least-squares linear combination analysis.

■ RESULTS
Electrochemical Cycling of FeS 2 .For the first several cycles of FeS 2 unoptimized loose-powder Swagelok cells in carbonate electrolytes, we saw surprising reversibility and Coulombic efficiency (Figure 2).The discharge−charge curves give clues about the mechanism(s) of Li storage.For example, there is ambiguity as to the presence of one or two plateaux in the first discharge (Figure 2a), which would suggest either one or two reactions occur.This has been addressed in the previous literature, and the mechanism (one vs two reactions) appears to depend on the rate and/or temperature at which the cell is cycled. 19,27t is typical for the first discharge plateau of conversion materials to occur at lower potentials than in subsequent discharges. 2 The higher overpotential on the first discharge is ubiquitous and has been attributed to the extra energy associated with the creation of new interfaces of the many nanoscale domains formed during the first discharge. 4,5There is also a contribution to the difference in potential of the first and subsequent discharges that arises from the difference in structure and composition of the first charge product from the initial material.For FeS 2 we saw a marked difference in both the potential and character of the first discharge compared to later cycling.During the first charge, there were two distinct plateaux separated by about 0.75 V. We observe a sloped region between the plateaux that contributes nearly one-third of the charge capacity.The features of the second discharge are more similar to those of the first charge than the first discharge.This is suggestive of a distinct reaction on the first discharge, which differs from subsequent cycles.
First-Principles Calculations.About 2200 Li−Fe−S structures were generated by AIRSS for the reaction of FeS 2 with 1, 1.5, 2, 3, and 4 mol of Li.While it is known that the discharge product resembles a combination of Fe and Li 2 S after reacting with 4 mol of Li, treatment of multiple phases quickly becomes computationally expensive and so AIRSS calculations over the range were carried out to yield descriptions as single phase products.For the same reasons, the electrochemical curve is calculated based on the pseudobinary phase diagram (Figure 3).
The formation energies of calculated structures are plotted as a function of composition (Figure 3a).Detailed information about the phases on the hull and several just above it are provided in Table 1.
Among the structures included in Table 1 are two previously published Li 2 FeS 2 phases shown in Figure 1.We found the P3̅ m1 with octahedrally coordinated Fe (Figure 1b) to be 0.110 eV/atom above the hull.For the P3̅ m1 structure with sites half occupied by Li and Fe tetrahedrally coordinated by S (Figure 1c), two 1 × 2 supercells (provided in the Supporting Information) were adapted with different patterning of Li and Fe on the sites, such that each is fully occupied by one or the other.These supercells were found to have formation energies about 0.050 eV/atom above the hull.While more rigorous methods would be needed to more exactly provide the relative energies of the these published phases to the hull, this would require computationally intensive efforts and have relatively low returns for this study.As such, we provide these formation energies to show that from a first pass, it is more likely that the MP or AIRSS phases, especially those in Table 2, are descriptive of the cycling products.
Tie lines connect the minimum energy structures and end members, FeS 2 and Li, to create the convex hull.The hull represents the thermodynamic equilibrium phases predicted to form as Li reacts with FeS 2 in the simplification of the ternary system to a pseudobinary.Assuming each phase transformation occurs as a two-phase reaction upon lithiation, a potential curve was calculated for the lowest energy structures (Figure 3b) using eq 5.
We were not surprised to find differences between predicted and experimental potential curves for the first discharge.We expect the plateau of the experiment to have a lower potential than was thermodynaically calculated due to the overpotential associated with kinetics of the reaction, especially the formation of many new surfaces during the nanostructuring that is welldocumented for conversion materials. 4,5Our experimental first discharge is at only a slightly lower potential than the calculated electrochemical curve (Figure 3b).If treated as a true ternary, the combination of Fe and Li 2 S would be energetically favorable to the predicted Li 4 FeS 2 .The predicted curve is not in agreement with second and later discharges either because, as will be discussed, the charge product is distinct from FeS 2 and so a different phase evolution occurs for the second and subsequent discharges.
Since batteries do not necessarily operate under equilibrium conditions, we considered several metastable phases near the hull.Despite variations of the relative stability, structures with similar structural motifs were near the hull for a range of Li content (1−2 mol of Li).As such, we considered structures with Li−FeS 2 ratios of 1:1, 1.5:1, and 2:1 in comparing the local structure measured by PDF to predicted structures.FeS 2 did not achieve theoretical capacity during operando PDF studies, so for intermediate cycling products, we considered structures with corresponding Li content.We chose to focus on those of the stoichiometry Li 3 Fe 2 S 4 (also referred to in the text as Li 1.5 FeS 2 ), previously described in Table 1.We also calculated the relative formation energies of selected structures at this composition when relaxed with DFT+U (Table 2).
The energetics of the system do not seem to change significantly after adding the U eff parameter.However, an average increase of 15% in the cell volume is observed.The increment of the lattice parameters with increasing U eff value has been observed in other studies. 38,53-ray Absorption Studies.Ex-situ Fe K-edge XAS was carried out at various states of charge to probe the oxidation state and coordination of Fe during the cycling of the Li−FeS 2 electrochemical system.Samples were prepared by stopping cells at a particular capacity or potential during the cycling of loose-powder Swagelok cells at C/40 (Q/10).For complex and nonequilibrium systems, such as conversion materials, in situ and operando experiments are ideal for the most representative data.However, we compared operando and ex-situ PDF for similar states of charge and saw good agreement between features of each (Figure S1), which gave us confidence in the ex-situ XAS.For both ex-situ PDF and XAS, samples were prepared just prior to experiments to minimize changes of the material between cycling and measurements.Because of extreme disorder in these materials after cycling, we focus on the near-edge energy range of the XAS data, rather than attempting to carry out an analysis of the fine structure.The discharge−charge curves for the first 1.5 cycles are shown in Figure 4a and are marked at each point a cell was stopped for an ex-situ measurement.The first discharge differs slightly from that shown in Figure 2a, which is due to cell-to-cell variation from the nonoptimized loose-powder cells employed.In this cell, a slight increase in potential can be seen at about 2 mol of Li; this could arise from the change in the particle size upon lithiation, as the bulk particles are broken into smaller domains. 7,54The XAS measured at each state of charge, and of FeS 2 as a reference, are shown for each half cycle (Figure 4b−d).
During the first discharge, we observed a slight change of slope with the reduction of Fe 2+ in FeS 2 .The product of the first discharge differed from bulk Fe (Figure S2a), which is in part due to the incomplete reaction of FeS 2 over the first   discharge.The nature of the XAS of the discharge product was also impacted by the small domain size and disorder of Fe clusters that formed with discharge.This has been observed for FeS 2 by XAS previously and will be discussed in more detail in the PDF analysis and discussion sections.
The character of the postedge, above 7.12 keV, changes from the pristine material with reduction halfway through and at the end of the first discharge (Figure 4b).Over the first charge, the slope of the edge increases with oxidation.Also, a more welldefined, sharper pre-edge peak emerges upon charging to 1.9 V (Figure 4c), just beyond the lower potential plateau (Figure 4a).This pre-edge peak grew during the rest of the charge process, over which there were relatively minor changes to the edge and postedge features (Figure 4c).The evolution of the postedge during the slope and high potential plateau of the electrochemistry could correspond to slight changes in the local coordination of Fe, for example, bond distances and bond angles.
The evolution of the XAS over the second discharge was quite different than that observed for the first discharge.Over the high potential plateau and the sloped region (above 1.5 V), the edge remained quite similar and the postedge evolved slightly (Figure 4a,d).Over the lower potential plateau, the XAS saw a more pronounced change suggestive of the reduction of Fe (Figure 4a,d).The second discharge product, similar to that of the first discharge, differed from bulk Fe (Figure S3a), likely due to small domain sizes of Fe.At these cycling conditions, there is ambiguity as to whether an intermediate phase forms on the first discharge.It has been previously reported to vary with electrolyte, temperature, rate, and particle size. 19,26,27The XAS of the first and second discharge products were similar and resembled small clusters of metallic Fe and, possibly, remaining FeS 2 or a ternary structure (Figure S2a). 55Differences between the spectra of the discharge products and the bulk Fe reference are likely a consequence of small clusters of Fe and local disorder, 26 which we also see evidence of by operando PDF.
The difference of XAS evolution over the lower and higher potential plateaux of the cycling was revealing about the mechanisms at play.There was a clear conversion over the lower plateau, but relatively minor changes in the XAS at higher potentials, suggesting a different mechanism of Li reaction in this potential range, one with minimal changes to the local environment of Fe.The similarity of the XAS at higher potentials suggests the products are structurally similar.In previous work, Totir et al. interpreted the similarity of the Fe Kedge to mean that S redox was predominant at higher potentials. 24However, a follow-up study using S K-edge XAS did not see clear evidence for oxidation of S to disulfide. 30hese studies led Totir et al. to believe that the charge product consisted of pyrrhotite (of the form Fe x S y ) and S, 30 as had been proposed by other work. 28We find the XAS of the charge product to be distinct from that of Fe 7 S 8 (Figure S2a).In particular, the pre-edge character of XAS above the lower plateau is suggestive of tetrahedrally coordinated Fe, 56 similar to that of a cubanite (CuFe 2 S 3 , F4̅ 3m) 57 standard (Figure S2b), in which Cu and Fe share tetrahedrally coordinated sites and Fe has an average 2.5+ oxidation state.Previous XAS studies of FeS 2 that did not see a pre-edge peak were carried out using ether-based electrolytes, in which the electrochemical behavior of S will vary. 27perando Pair Distribution Function Studies.Operando PDF of a cycling Li−FeS 2 cell was collected over the first 4.5 cycles (Figure S3).On the first discharge, FeS 2 reacted with Li over a single, sloping plateau near 1.5 V, yielding a capacity of 2.6 mol of Li (Figure 5a).This differs slightly from slower cycling in which it was unclear if one or two plateaux were present on the first discharge (Figure 2a).The general behavior and features of the discharge−charge curves of the operando cell were similar to those seen in the cycling of loose-powder Swagelok cells.
Over the first discharge, operando PDF shows a change in local structure from FeS 2 to Fe-and Li 2 S-like domains (Figure 5b).PCA was carried out to discern if intermediate local structures evolved during the first discharge.By PCA and linear combination transformations to satisfy criteria, as described by Chapman et al., 49 we determined three significant PCs.The first PC is FeS 2 and matches the pattern before cycling (Figure 5b,i).The second PC is representative of the product of the first discharge, which resembles Fe and Li 2 S (Figure 5b,ii).The third PC forms intermediately and is then consumed.This third PC does not resemble the ternary local structures observed in later cycles but does have some features in common with the product of the fifth discharge.The PCs and the percentages in which they appear over the first discharge can be found in Figures S4 and S5, respectively.For the discharge product, the intensity of peaks at even 14 Å was low, indicating poor longrange order, as is expected for conversion materials. 4,5Further analysis of the discharge product will be discussed in the following sections.
The first charge took place over two plateaux and a sloped region between them and achieved a charge capacity of about 2.3 mol of Li (Figure 6).The first plateau (Figure 6a,ii to iii), near 1.9 V, contributed 1 mol of Li to the capacity and the second (Figure 6a, iv to v), at about 2.5 V, contributed 0.7 mol of Li. Between them, the sloped region (Figure 6a, iii to iv) contributed a non-negligible 0.6 mol of Li.Over the first charge, there was a conversion from the Fe-and Li 2 S-like domains (Figure 6c, ii) to another local structure (Figure 6c,v) distinct from both FeS 2 (Figure 6b,i) and the first discharge product (Figure 6b,ii).Above the lower plateau (Figure 6a,iii to v), the first three major peaks between 1.5 and 5 Å, shifted to The corresponding PDFs for the first discharge show conversion of (i) FeS 2 to (ii) Fe-and Li 2 S-like products.The PDF also shows a decrease in crystallinity with cycling by the decreased intensity of peaks beyond 6 Å. lower r.As was observed for the first discharge product, the higher r peaks decreased in intensity, indicating a decrease in long-range order.
We found electrochemical features during the second discharge similar to those of the first charge, with plateaux near 2 V (Figure 7a,v to vi) and 1.5 V (Figure 7a, vii to viii) and a total discharge capacity of about 2.2 mol of Li.During the second discharge, the local structure initially evolved with the shifting of low and moderate r peaks to higher r (Figure 7b,v to vii), followed by a change of the local structure to resemble the first discharge product (Figure 7b,vii to viii).
Considering the first 1.5 cycles of operando PDF together, a few key observations can be made.Similar to XAS, PDF showed that the discharge products locally resembled Fe and Li 2 S (Figure 5b,ii and Figure 7b,viii) and that FeS 2 (Figure 5b,i) was not recovered on charge (Figure 6b,v).The shifting of peaks during the first charge and second discharge (as well as during subsequent cycles) suggests the charge product is structurally similar to an intermediate.This is in line with the minor changes of the postedge of XAS in this regime of potential and Li content.In the high potential regime of the second discharge, we propose there is some storage of Li by a host structure by an insertion-extraction mechanism at lower Li content, followed by conversion to Fe-and Li 2 S-like domains at higher Li content and lower potentials.Further analysis of discharge, charge, and intermediate products are discussed in greater detail following.
Pair Distribution Function Analysis of Intermediate Ternary Products.Several structures have been proposed to form during the cycling of FeS 2 .Among those are phases hypothesized to accommodate a range of Li content and, accordingly, store charge by a Li insertion-extraction mechanism at high potentials and low Li content.We also see evidence for this mechanism in our study.By the analysis of operando PDF, we elucidate new information about the local structure of the ternary intermediate and a related charge product.
Among the calculated and published ternary Li−Fe−S phases we considered, there were a number of local structural motifs present.At the smallest correlation distance, we saw a difference of Fe octahedrally or tetrahedrally coordinated by S in the simulated PDF.Fits to intermediate cycling products (collected at 1.56 V and 1.3 mol of Li, along the sloped region of the second discharge) show that published Li 2 FeS 2 with FeS 6 octahedra 17 does not capture the features of the measured PDF as well as structures with FeS 4 tetrahedra (Figure S6).This is consistent with the pre-edge peak in XAS at these potentials, which is indicative of tetrahedrally coordinated Fe (Figure 4).
To analyze the PDF of the intermediate and related charge products of cycling, we focused on PDF measured over the sloped region of the second discharge at 1.74 V with about 1.2 mol of Li.Since the full capacity was not achieved and calculated structures at various compositions had similar local motifs, we considered several metastable calculated phases at the composition Li 1.5 FeS 2 with FeS 4 tetrahedra (Figure 8).The metastable Li 1.5 FeS 2 structures considered generally consist of Li between 1D or quasi-1D chains of FeS 4 tetrahedra, each with a unique local motif beyond the first coordination shell.The P1̅ structure (Figure 8a) consists of disrupted corrugated chains, which meet to form a group of four corner-sharing tetrahedra, referred to hereafter as a "tetrad" motif (Figure 9i) (GGA+U structure used, see Table 2).The P2 1 structure (Figure 8b) has edge-sharing FeS 4 tetrahedra that arrange as corrugated chains (Figure 9ii), with Li between them (by PBE, see Table 2).The Pnma phase (Figure 8c) has linear chains of edge-sharing FeS 4 tetrahedra (Figure 9iii) (derived from Materials Project, 51 relaxed by PBE, see Table 2).Among the other calculated structures with tetrahedrally coordinated Fe, each had one of these three motifs.
We fit the three representative structures shown in Figure 8 to an intermediate product along the slope of the second discharge at 1.74 V and 1.2 mol of Li.The data was fit between 1.5 and 5.5 Å and lattice parameters, nonspecial angles, a correlated motion parameter (delta1 in PDFgui), and the  U iso of each atom were refined in a single-phase fit with a nanoparticle size (the parameter spdiameter in PDFgui) of 40 Å.It is important to note that the "tetrad" phase has the more complex local structure and the lowest symmetry; this enables refinement of more Fe−Fe correlation distances and parameters that contribute to the goodness of fit of this local motif to measured PDF.
Fitting over this small range, on the same length scale of the structural motifs, gave good fits with small difference curves (Figure 9).While the corrugated and linear chains (Figure 9ii,iii) fit the local structure quite well (Figure 9b,c), there are still several correlations not completely captured by these motifs.Both the fit and the nature of the difference curve show the tetrad structural motif (in the P1̅ phase) best models the local structure of the measured PDF (Figure 9i,a).The low symmetry of the P1̅ structure and the corresponding larger number of refined parameters undoubtedly contribute to the goodness of fit to the measured data.This structure also has the most variety of connectivity, with both edge-and cornersharing tetrahedra, which enables it to fit the local structure.When refined to higher r, the overall quality of fit decreases, which suggests the local and average structures are different.In particular, it appears that the local structure resembles the local motifs described by the calculated phases, but there is insufficient correlation of these units to give a periodic structure.We carried out fits to the three published structures (shown in Figure 1 and described above) with similar fitting conditions as the calculated structures and less satisfactory fits (Figure S7).
Of the local structures considered, the tetrad motif present in the Li 1.5 FeS 2 with P1̅ symmetry gave the best local fit.Accordingly, this is a possible structural unit in the intermediate products.However, there could be a variety of local motifs contributing to the measured PDF.From PDF and XAS, we know the local structure of the intermediate and charge products are similar.By fitting the P1̅ structure to 15 Å at various states of charge above the lower potential plateau, on both the first charge and second discharge, we see many of the features are captured (Figures S8 and S9).It is important to note that the average structure is not well-defined by the P1̅ , or any other, of the phases we considered; when we extend the good local fit for the tetrad motif to even 15 Å, the overall fit is not as good (Figure S8).
Pair Distribution Function Analysis of Discharge Products.By XAS, 24,25,54 transmission electron microscopy, 4,5,58 and 26 Fe Mossbauer, 26 among other methods, researchers have previously found that the metal formed during the discharge of conversion electrodes tends to occur as disordered clusters of metal atoms on the order of 10 Å to 50 Å in diameter.Deviations of the structure of nanoparticles from the bulk structure has been observed for several systems, including gold nanoparticles. 59s previously mentioned, for FeS 2 the first and second discharge products locally resembled Fe and Li 2 S. Upon a closer look we found equilibrium body-centered cubic (bcc) Fe did not fully capture the local structure of the first discharge product (Figure S10), which has been previously observed for other Fe-based conversion electrode materials. 11,13Comparing the PDF of the first discharge product to a two-phase fit of Li 2 S and bcc Fe, bcc Fe contributes an extra peak at 5.6 Å and does not capture the peaks at 6.3 and 8.7 Å (Figure S10).From similar comparisons to the local structure of face-centered cubic and body-centered tetragonal Fe, we found these local structures were not a good match to the measured PDF.We also compared the local structure of the first discharge to hexagonal close-packed (hcp) Fe, which was close, but like bcc Fe had extra or missing peaks (Figure S10); hcp Fe captured  the peaks at 6.3 and 8.7 Å that bcc Fe was missing but had extra features at 3.6 and 5.6 Å.
To better model the local structure, we employed a supercell of bcc Fe whose atomic positions were perturbed from their ideal sites, using the RMCProfile software suite. 60A 3 × 3 × 3 supercell of 54 atoms was generated from a single unit cell of Im3̅ m (bcc) Fe with Fe in the 2a Wyckoff site at (0,0,0).Atoms were allowed to translate a maximum of 0.01 Å per move, and a minimum approach distance of 2.46 Å was applied, employing approximately 5 × 10 6 Monte Carlo moves.The relaxation yielded a local structure that offered a good compromise between bcc and hcp Fe (Figure S10).The structure produced by the simulation was then used in a two phase fit of the discharge product with Li 2 S as the second phase.In combination with Li 2 S, the disordered Fe, with an approximate cluster diameter of 10 Å to 12 Å (set as spdiameter in PDFgui 48 ), captures the dominant features of the first discharge product in the range of 1.5 Å to 15 Å (Figure 10a).We know from previous work that diameter of a particle or cluster will relate to the damping of the signal from that material in the PDF. 59For these fits, the lattice parameters and U iso of all atoms were refined.Visualization of the initial bcc Fe supercell and the disordered Fe structures are available in Figure S11.
The local structure of the first, second, and third discharge products were similar (Figure 11a), and can therefore be described by clusters of disordered Fe and Li 2 S. The PDF of the fourth and fifth discharge products were different than the previous and better described as a combination of hcp Fe and Li 2 S. A two-phase fit of the fifth discharge product with about 20 Å diameter clusters of hcp Fe and Li 2 S model the local structure well (Figure 10b).This analysis of the discharge products does not preclude other species that may be present in small amounts.
It appears that Fe clusters grow with subsequent discharges, possibly as the crystallinity of the system decreases with each cycle, which could enable increased Fe diffusion.Despite the evolution of the discharge product with cycling, there are only minor changes to the charge product (Figure 11a).Despite the apparent growth of clusters and their resemblance to hcp Fe at discharge in later cycles, the cluster formation appears to be mostly reversible, as no major changes are evident in the four charge products over which PDF was collected (Figure 11b).

■ DISCUSSION
By a combination of first-principles calculations, operando PDF, and ex-situ XAS, we bring new insight into the local structure evolution at the cathode in Li−FeS 2 cells.We make a point of examining later cycles in addition to the first discharge to understand the processes most representative of the system.In the cycling of micron-sized particles of FeS   potential plateau.The combination of this data is in contrast to previous literature that suggests octahedral coordination of Fe by S, either in ternary phases or in off-stoichiometry Fe x S y pyrrhotite. 27,28,30However, pyrrhotite has primarily been reported for ether-based electrolytes, in which S electrochemistry and solubility are known to differ and could impact the structural evolution.For our study in a carbonate-based electrolyte solution, we see a poor fit of phases with FeS 6 octahedra to our data (Figure S6).
There are previously proposed ternary phases with FeS 4 tetrahedra (Figure 1c,d); however, we found the local structure of these phases beyond the first coordination shell were not a good fit to measured PDF (Figure S7). 22,23To further explore the local structure, AIRSS was employed to predict a library of ternary structures with various local motifs.We found reasonably good fits for those motifs with linear or corrugated chains of edge-sharing FeS 4 tetrahedra at intermediate states of charge.The best local fit, however, was for a "tetrad" motif, which has both edge-and corner-sharing FeS 4 tetrahedra.All three motifs capture most of the local features of the intermediate PDF well, but none have great agreement to the average structure, indicating there is poor correlation at higher r.−7 The collection and analysis of PDF over 4.5 cycles allows a unique opportunity to relate structure and performance.We see over the five discharge products an increase in the size of Fe clusters, modeled in fits as spdiameter.As the clusters grow, there is also a change from disordered Fe to a local structure resembling hcp Fe.The larger diameter could enable the lower energy, more ordered Fe structure.Previous studies suggest that Fe-based conversion systems show favorable reversibility relative to Cu-based analogues due in part to the smaller size of Fe particles formed, with the cluster size limited by the diffusivity of the metal during discharge. 5The combination of small-angle X-ray scattering and PDF has been previously employed by Wiaderek et al. to reveal a dependence of cluster size on anion chemistry for Fe-based conversion electrodes, with fluorides forming larger particles than oxides (35 Å compared to 20 Å). 13 For FeS 2 , we find Fe clusters for the first discharge on the order of 10 Å in diameter.Combining the results of the study by Wiaderek et al. with this one, 13 it is possible that nanoparticle size varies with anion electronegativity.However, it is unclear if this trend is exclusively applicable to Fe-based materials or is more general.Other factors, such as the degree of ionicity or covalency of bonds, could be at play in the impact of anion chemistry on metal cluster size.Despite the evolution in the discharge products, the first four charge products remain quite similar, even as the charge capacity fades slightly.Operando PDF at later cycles could further inform failure mechanisms for this system.
The intriguing difference between FeS 2 and a number of other conversion systems is the dual modes of storage.FeF 2 , 4 MnO, 7 CuF 2 , 8 and many others store Li by a single conversion step.In isostructural pyrite CoS 2 , which does have multiple reactions, the observed intermediate products are a combination of Li 2 S and Co−S binaries. 61We present here strong evidence that the cathode of an Li−FeS 2 cell operates by two different mechanisms beyond the first discharge under cycling conditions similar to those employed here.At slower rates or higher temperature, the first discharge can involve an intermediate product, but this would be two conversion steps, rather than the pairing of insertion-extraction and conversion reactions.The combination of insertion-extraction and conversion seen in the second and subsequent cycles of FeS 2 system are similar to observations for VS 4 , which on charge undergoes conversion from V clusters and Li 2 S to a ternary Li 3+x VS 4 structure that is stable over a range of Li content, and so then undergoes an insertion-extraction mechanism from the host structure at higher potentials. 9The reversible behavior of FeS 2 could arise from the two types of charge storage mechanisms that occur.

■ CONCLUSIONS
This examination of the Li−FeS 2 secondary energy storage system provides new insights into the previously studied cycling mechanism at slow rates, room temperature, and in a carbonate-based electrolyte by operando PDF and ex-situ Kedge XAS.During the first discharge, FeS 2 undergoes conversion to Fe-and Li 2 S-like domains under these cycling conditions.Initially, the Fe clusters are disordered, not quite resembling bcc or hcp Fe.In continued cycling, the Fe clusters grow and the local structure more closely resembles hcp Fe, possibly stabilized by the growth of metal clusters.
The first charge product is not FeS 2 , and consequently, the second discharge follows a different evolution of local structure than the first.The first charge occurs as two steps: (i) conversion between Fe and Li 2 S and a ternary intermediate over the lower plateau and (ii) an insertion-extraction reaction with a host structure over the higher potential slope and plateau.The Li insertion-extraction is evidenced in the PDF by the shifting of low r peaks in real space, corresponding to expansion/contraction of the structure as bond lengths increase/decrease with reduction/oxidation.The related intermediate and charge products have tetrahedrally coordinated Fe.We suggest several structures with local motifs that capture the low r features of the measured PDF well and describe the local structure of the intermediate cycling products.The second discharge appears to follow the same steps as the first charge in the reverse order.We hypothesize that the hybrid modes of storage, insertion/extraction and conversion, could be important in identifying promising candidates for next-generation, high capacity electrode materials.
In addition to our contribution to the understanding of FeS 2 as a conversion electrode, we also show effective methodology for investigating dynamic and disordered systems, including conversion reaction electrode candidates.We especially highlight the utility of combined computational and local structure methods.Further, we show that the application of operando methods and structural characterization well beyond the first discharge reveal useful insight into the mechanisms of charge storage and even cell failure.This work also contributes to the literature on conversion electrodes by characterizing the mechanisms of a relatively reversible system.Mechanistic studies with advanced characterization methods permit the identification of general rules for more reversible candidates, toward realizing the promise of conversion reaction systems for electrochemical energy storage.

Figure 1 .
Figure 1.(a) FeS 2 (Pa3̅ ) consists of a fcc lattice of Fe atoms (green) octahedrally coordinated by disulfides, highlighted in yellow.Published Li−Fe−S ternary phases proposed to be intermediate products during the cycling of FeS 2 : (b) Li 2 FeS 2 (P3̅ m1) with layers of FeS 6 octahedra with Li (gray) in tetrahedral sites between the layers, 17 (c) Li 2 FeS 2 (P3̅ m1) with layers of mixed occupancy Li and Fe tetrahedrally coordinated by S,22 and (d) Li 1.77 Fe 1.17 S 2 (P3) with mixed and partial occupancy (white) of Li and Fe in corner-sharing tetrahedra.23

Figure 2 .
Figure 2. (a) Discharge−charge curves for FeS 2 at C/40 show good capacity retention for a conversion material over the first five cycles.Broken lines indicate later cycles, as numbered.(b) Capacity per cycle and Coulombic efficiency show surprising reversibility for the first five cycles.

Figure 4 .
Figure 4. (a) Representative 1.5 cycles of galvanostatic cycling at C/40 marked at each potential or capacity at which a cell was stopped for exsitu XAS.(b) The corresponding XAS for the first discharge, (c) the first charge, and (d) the second discharge.FeS 2 is plotted in each panel for reference.

Figure 5 .
Figure 5. (a) The first 1.5 cycles of operando electrochemistry at ≈C/ 17.(b) The corresponding PDFs for the first discharge show conversion of (i) FeS 2 to (ii) Fe-and Li 2 S-like products.The PDF also shows a decrease in crystallinity with cycling by the decreased intensity of peaks beyond 6 Å.

Figure 6 .
Figure 6.(a) First 1.5 cycles of operando electrochemistry at ≈C/17.(b) PDF of the FeS 2 before cycling.(c) The PDFs for the first charge show conversion of (ii) discharge products (Fe-and Li 2 S-like domains) to (iii) an intermediate phase and then (iii) to (iv) the shifting of pairwise interactions to lower r over the sloped region and (iv) the high potential plateau with continued charging.The local structure shows that (c,v) the charge product has much less long-range order and is not FeS 2 (b,i).

Figure 7 .
Figure 7. (a) First 1.5 cycles of operando electrochemistry at ≈C/17.(b) The corresponding PDFs for the second discharge suggest a similar mechanism as the first charge, which is distinct from the first discharge.(v to vi) Over the high potential plateau and (vi to vii) the sloped region, there is an increase in the pairwise interaction lengths with reduction, an expansion of the local structure, suggestive of Li insertion into a host structure.(vii to viii) Over the low-potential plateau, at about 1.5 V, there is a conversion to (viii) Fe-and Li 2 S-like products, similar to (Figure 5b,ii) the products of the first discharge.

Figure 9 .
Figure 9. Fits of three calculated structures with the composition Li 1.5 FeS 2 with tetrahedrally coordinated Fe to data collected at 1.74 V and 1.2 mol of Li during the second discharge and various local structure motifs.(a) Li 1.5 FeS 2 with P1̅ symmetry has both edge-and corner-sharing FeS 4 tetrahedra, which we refer to as (i) a "tetrad".(b) Li 1.5 FeS 2 with P2 1 symmetry has (ii) corrugated chains of edge-sharing tetrahedra.(c) Li 1.5 FeS 2 with Pnma symmetry has (iii) linear chains of edge-sharing tetrahedra.
2 at room temperature at C/17 in carbonate electrolyte, we observed conversion to Fe-and Li 2 S-like domains during the first discharge by operando PDF.On the first charge we observed a conversion from Fe and Li 2 S to an intermediate, ternary local structure over the lower potential plateau.With continued oxidation, the low r peaks shift, rather than forming a new local structure.The shift of these peaks with oxidation and reduction corresponds to the expansion and contraction of bond lengths and, consequently, cell parameters with cycling, suggestive of a Li insertion-extraction mechanism (similar to the intercalation of Li for Li 1−x CoO 2 ) above the lower potential plateau between the ternary intermediate and a related charge product.Ex-situ Fe K-edge XAS also shows only minor changes above the lower potential plateau.An insertion-extraction regime has been proposed in previous reports and our operando PDF enables visualization of this mechanism.The combination of operando PDF and ex-situ XAS also allows us to expand upon hypothesized phases to describe the intermediate, ternary local structure, and the related charge product.The pre-edge feature in Fe K-edge XAS and the first correlation peak in PDF indicate an intermediate product with tetrahedrally coordinated Fe.The tetrahedral features persist in both the PDF and XAS for all electrochemistry above the lower

Figure 10 .
Figure 10.(a) Two-phase fit of the first discharge and contributions from each phase: disordered Fe from the relaxation of a bcc Fe supercell with a particle diameter of 10 Å and Li 2 S with a particle diameter of 60 Å.(b) Two-phase fit of the fifth discharge and contributions from each phase: hcp Fe with a particle diameter of 20 Å and Li 2 S with a particle diameter of 60 Å.

Figure 11 .
Figure 11.(a) PDFs of the first through fifth discharges of FeS 2 show changes in the local structure with cycling.The first through the third discharge products are similar, corresponding to clusters of disordered Fe and Li 2 S locally.The fourth and fifth discharge products have a different local structure, better matched to small clusters of hcp Fe and Li 2 S. The fits of the first and fifth discharge products can be found in Figure 10.(b) PDFs of the first through fourth charge products show similar local structures.

Table 1 .
Description of the Experimental and Predicted Li x FeS 2 Phases a a We indicate with a star (★) the stable phases which are found on the convex hull.Descriptions of the structures obtained by AIRSS are presented in the Supporting Information.

Table 2 .
Li 3 Fe 2 S 51Structural Formation Energies, Cell Volumes and Spin Arrangements Using GGA+U Correction with U eff = 4 eV relative formation energy (meV/atom) symmetry volume (Å 3 /f.u.)a Derived from Materials Project ID:mp-768360.51