Nanoscale Detection of Intermediate Solid Solutions in Equilibrated

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Nanoscale Detection of Intermediate Solid Solutions in Equilibrated LixFePO4 Microcrystals Brian M. May, Young-Sang Yu, Martin Holt, Fiona C. Strobridge, Ulrike Bösenberg, Clare P. Grey, and Jordi Cabana Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.7b03086 • Publication Date (Web): 22 Nov 2017 Downloaded from http://pubs.acs.org on November 23, 2017

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Nanoscale Detection of Intermediate Solid Solutions in Equilibrated LixFePO4 Microcrystals

Brian M. May1, Young-Sang Yu1,2, Martin V. Holt3, Fiona C. Strobridge4, Ulrike Boesenberg2, Clare P. Grey4, Jordi Cabana1,* Affiliations: 1

Department of Chemistry, University of Illinois at Chicago, Chicago, Illinois, 60607, USA

2

Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, California, 94720,

USA 3

Center for Nanoscale Materials, Argonne National Laboratory, Argonne, Illinois, 60441, USA

4

Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW,

United Kingdom

*Corresponding Author: Jordi Cabana [email protected]

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Abstract Redox-driven phase transformations in solids determine the performance of lithium-ion batteries, crucial in the technological transition from fossil fuels. Couplings between chemistry and strain define reversibility and fatigue of an electrode. The accurate definition of all phases in the transformation, their energetics and nanoscale location within a particle produces fundamental understanding of these couplings needed to design materials with ultimate performance. Here we demonstrate that scanning Xray diffraction microscopy (SXDM) extends our ability to image battery processes in single particles. In LiFePO4 crystals equilibrated after delithiation, SXDM revealed the existence of domains of miscibility between LiFePO4 and Li0.6FePO4. These solid solutions are conventionally thought to be metastable, and were previously undetected by spectromicroscopy. The observation provides experimental verification of predictions that the LiFePO4-FePO4 phase diagram can be altered by coherency strain under certain interfacial orientations. It enriches our understanding of the interaction between diffusion, chemistry, and mechanics in solid state transformations. Keywords – LiFePO4, Li-ion battery materials, Nanoscale chemical imaging, Redox phase transitions


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The cathode material, LiFePO4, used in commercial lithium-ion batteries, provides a model system to study the consequences of phase energetics in battery reactions. In conditions close to equilibrium, it undergoes a first order transformation to FePO41, involving a large anisotropic misfit between the lithiated and delithiated phases. The misfit imposes mechanical stress which creates kinetic bottlenecks to reversibility and, ultimately, can lead to fracture2,3. The outstanding performance of modern LiFePO4 electrodes stems from a combination of nanosizing, to avoid fracture3 and the stabilization solid solution pathways under large overpotentials, which reduce lattice misfits4,5. The solid solution pathways are metastable, with relaxation to two phases occurring when the electrochemical stimulus is removed4. Nonetheless, formation of boundaries at ac interfaces imposed by 1-dimensional Li diffusion along b has been predicted to stabilize Li0.6FePO4 in the LiFePO4-FePO4 phase diagram6. This phase has only been detected by cooling LixFePO4 crystals from above the miscibility gap (~300°C)1,7, or in very thin interfacial domains in charged nanomaterials8. Verification of the stability of LixFePO4 solid solutions upon delithiation at room temperature would refine our understanding of the mechanism of transformation under different experimental conditions and, particularly, the role of lattice misfits on the fundamentals of battery electrodes. Given the dependence on domain orientation, such observations would be most valuable when spatially resolved within single particles, requiring nanoscale resolution. Chemical imaging techniques with high spatial resolution are increasingly applied to probe the distribution of phases in single particles of a battery electrode9. While electron microscopy achieves the greatest spatial resolution, issues of beam damage10,11 and experimental constraints requiring thin samples call for complementary techniques. Transmission X-ray microscopy is one such technique; its coupling with X-ray spectroscopy results in the ability to locate chemical domains using redox states, at resolutions below 10 nm12. In contrast, scanning x-ray diffraction microscopy (SXDM) produces discrete Bragg diffraction patterns for each individual nanoscale area illuminated by a rastering X-ray beam. As a result, it combines chemical insight from crystallographic d-spacings with the ability to 3 ACS Paragon Plus Environment

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measure strain and microstructure in one measurement, at ~30nm spatial resolution13,14. Thus far, this technique has been used primarily to study thin films15. Here, we apply SXDM to detect and locate different phases in chemically delithiated (using bromine) particles of LiFePO4 that were equilibrated for months. The measurements unexpectedly revealed domains of miscibility between LiFePO4 and an intermediate phase close to Li0.6FePO4. They add novel insight compared to both bulk diffraction, where no spatial resolution exists, and spectromicroscopy, where only different Fe redox states, not crystallographic phases, can be detected. In the specific case of LiFePO4 crystals, these different states have typically been interpreted as mixtures of the end members, LiFePO4 and FePO4 (or Li-rich and Lipoor phases, respectively).3,16–18 The presence of these domains was consistent with predictions of the phase diagram that consider strain energy, challenging the expectation that LixFePO4 solid solutions are always metastable. Beyond extending our knowledge of this canonical battery material, this study sheds light into the chemical and physical effects that define phase stability in electrochemical reactions in solids.

Figure 1: Experimental setup for single particle scanning x-ray diffraction microscopy (SXDM) at 26ID-C, Advanced Photon Source, Argonne National Laboratory. The exemplar pattern above the diffracted beam represents the signal when a single phase is present in the specific mapping position,


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while the pattern below the beam represents a situation where a separate phase (different 2θ) with inhomogeneity in grain orientation (χ) exists.

In SXDM, the diffraction signal resulting from the interaction between a nanoscale X-ray beam and the sample is detected by a camera at a 2θ angle near a Bragg reflection of interest (Figure 1). After initial alignment of both the beamline optics as well as the particle into the diffraction geometry, the position of the camera is kept fixed, while the sample is scanned (in X-Y) relative to the beam to map the scattered intensity at one θ position. The process is repeated after subsequent rotation of the sample about θ, generating two-dimensional (2θ vs. χ) Bragg diffraction patterns at each nanoscale mapping position. The detector dimension out of the diffraction plane, χ, is sensitive to the orientation of domains with respect to the beam and each other, whereas the dimension within the diffraction plane (2θ) is sensitive to crystalline phase. When a single crystalline phase is present, the Bragg diffraction peak appears as a donut-shaped annulus (Figure 1) as a result of the combination of a Fresnel Zone Plate (FZP) focusing optic with a central beam stop. This ideal annulus defines the instrumental broadening. When separate chemical phases are present, the different lattice d-spacings lead to shifts of the signals along 2θ, according to Bragg’s law. The resulting 2θ positions can be used for phase identification if appropriate knowledge exists, as in LixFePO4.7 Chemical maps result from the analysis of the diffraction signal as a function of 2θ at each mapping position. Alternatively, maps representing relative domain misalignments can be built from the analysis along the azimuthal angle, χ.


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Figure 2. (A) Fe fluorescence map of a Li1 (pristine) particle. (B) Summed 2D diffraction pattern of the entire particle. The dashed line denotes the theoretical positions of LiFePO4, based on literature data19. The red circle denotes the size of the beam annulus, which corresponds to the instrumental broadening. The single spot is indicative of a single phase and single grain within the particle. (C) Chemical phase map of the particle, extracted from the intensity and position of any diffraction peaks present, compared to known values in the literature. Red corresponds to LiFePO4, the only phase present in this particle. (D) χ map pertaining to the diffraction intensity centroid in the vertical dimension of the detector, per each mapping position.

Figures 2a-d present X-ray fluorescence and diffraction data collected around the (020) reflection for one particle in pristine LiFePO4 (Li1). The fluorescence map (figure 2a) represents the concentration of Fe delineating a particle measuring 4x2 µm. Separate electron microscopy analyses of similar particles revealed a thickness of less than 0.5 µm3,16. Scanning electron microscopy revealed a few small agglomerated fragments on the outside edge of the particle (Figure S1a), which account for the 6 ACS Paragon Plus Environment

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enhanced fluorescence intensity in the same area. The collection of individual diffraction patterns acquired at each X-Y-θ mapping position were summed in order to build a representative 2D (2θ-χ) pattern of the integrated diffraction intensity within the entire crystal (figure 2b). This summation is useful to assign physical regions of interest for phase identification within the spatial maps. Most of the signal intensity fell within the boundary defined by the annulus, denoted by a red circle in the figure. Therefore, the particle was single phase and single crystalline. Signal broadening was largely instrumental, with minor deviations due to slight imperfections within the particle. The diffraction intensity was narrowly centered around 2θ = 26.44 ± 0.05˚ (figure S2 and Table 1). A vertical dashed line drawn over the 2D pattern demonstrates good agreement with the predicted location of the (020) reflection in LiFePO4, taking cell parameters from the literature19. The chemical map confirmed the sole presence of LiFePO4 within the whole particle (figure 2c). The χ value was fairly uniform over the majority of the particle (figure 2d), with minor inhomogeneities along the outside edges. Individual XY maps of total diffraction intensity were also generated at each θ (figure S3) to verify sufficient angular range was collected for analysis. The systematic change in diffraction intensity across the particle upon rotation suggested that it exhibited a slight surface curvature. These observations are consistent with the rounded edges reported for similar crystals,3,16,20 which would cause a shift in χ, when resulting from domains in different orientations. The same analyses were performed for a particle in a partially delithiated, Li0.5, sample (figure 3). Fluorescence mapping (figure 3a) and SEM (figure S1b) confirmed that the overall morphology was not altered.16,21 However, delithiation introduced significant complexity on the diffraction signals, as evidenced by the smearing of intensity over both 2θ and χ in the integrated diffraction pattern (figure 3b). Representative diffraction patterns of individual nanoscale positions are provided in figure S4. Broadening was larger than the size of the beam annulus, indicating it was caused by the sample. Along


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2θ, the smear produced complete signal overlap between 26.4 and 27°, with a gap in the intensity existing up to ~27.4°. The integration of the intensity along the χ dimension for each 2θ value to produce a 1D pattern (figure S2) confirmed the existence of at least 3 peaks, implying that several phases were present. These peaks were centered at 2θ1 = 26.61 ± 0.09°, 2θ2 = 26.85 ± 0.07°, and 2θ3 = 27.50 ± 0.06°, corresponding to d1 = 2.99 ± 0.01Å, d2 = 2.965 ± 0.008Å, and d3 = 2.897 ± 0.007Å, respectively (Table 1). The first value was slightly lower than expected for stoichiometric LiFePO4, (see vertical dashed line in figure 3b). This discrepancy signaled a slight understoichiometry, Li1αFePO4

with α being small, due to a slight lithium miscibility in these conditions22. It is worth noting

that a small set of individual nanoscale positions showed diffraction peaks close to the theoretical value of LiFePO4 (Figure S4e), indicating that it was present, but in small amounts. The signal at the highest d matched literature data for FePO423. The peak and smeared diffraction intensity appearing at intermediate d-spacings were assigned to the (020) reflection of intermediate LixFePO4 phases rather than the (211) reflection of FePO4, despite the two reflections diffracting at similar angles in a powder pattern,24 because the momentum transfer of the diffraction geometry was aligned a priori to the symmetric lattice vector from the ac plane, corresponding to the large facet of the crystal21. This diffraction geometry is fundamentally insensitive to a family reflection without significant (65°) realignment of the crystallographic axes. The morphological changes that would accompany this distortion were not observed in SEM (figure S1b). The intermediate LixFePO4 solid solution showing the lowest d-spacing (d3 = 2.897 ± 0.007Å) would correspond to x≈0.65, based on the linear relationship between composition and unit cell parameter along the b direction.7 The striking smearing of the diffraction signal along 2θ between the peaks at 26.6 and 26.85°, is an indication of miscibility between LiFePO4 and this intermediate. This interpretation is further supported by the existence of individual nanoscale positions where the diffraction pattern showed coexistence of two discrete signals


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between 26.4° and 26.9°, 2θ, without continuity of intensity between them (Figure S4d and S4f). While the existence of small atomic displacements due to mechanical strain cannot be discarded, the absence of signal smearing at the nanoscale indicates that the different signals are primarily due to the existence of individual chemical phases. In contrast, the diffraction data systematically indicated that there was a miscibility gap between this intermediate and FePO4 in this particle.

Figure 3. (A) Fe fluorescence map of a Li0.5 particle. (B) Summed 2D diffraction pattern of the entire particle. The 3 main areas of intensity are centered at d-space values of 2.99, 2.965, and 2.897Å. The dashed lines denote the theoretical positions of LiFePO4 and FePO4, based on literature data7,19,23. The red circle denotes the size of the beam annulus, which corresponds to the instrumental broadening. (C) Chemical phase map of the particle. Red corresponds to LiFePO4, green corresponds to intermediate compositions close to Li0.65FePO4, and blue corresponds to FePO4. The arrow denotes an area in which 9 ACS Paragon Plus Environment

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a large amount of dispersion of χ values is observed (see D), which corresponds to a small FePO4 domain, according to the phase map. (D) χ map pertaining to the diffraction intensity centroid in the vertical dimension of the detector, per each mapping position.

A chemical phase map was constructed by analyzing the 2D pattern of each X-Y mapping position (figure 3c). The diffraction intensity was integrated in the 2θ region for FePO4, and within equally sized regions centered at the two extremes of intensity in the smeared region, 26.6 and 26.85°, 2θ, to account the absence of discrete peaks in the summed 2D diffraction pattern. The right side of the particle was mostly unreacted. In contrast, the top and bottom edges of the particle showed the highest degree of delithiation. A significant fraction of FePO4 was also detected on the left particle edge (see arrow in figure 3c). The remainder of the particle presented a mixed composition dominated by the intermediate phase(s). Previous analysis of similar crystals by X-ray spectromicroscopy revealed the existence of varying amounts of Fe3+ in regions located in the center of the crystal,16 which contain large areas assigned here to intermediate phases based on their d-spacings. Furthermore, no domains that contained only Fe2+ were found. This observation further supports that the changes in lattice parameter reflect mostly the composition of the phase in a given domain. Significant broadening was also found along the χ dimension of the integrated 2D diffraction pattern, the spread again being larger than in Li1. This observation is indicative of significant changes in microstructure upon delithiation. Sudden changes in intensity were observed in the χ map (figure 3d), rather than the gradual changes in Li1, confirming that slight misalignment of the domains occurred due to the formation of grain boundaries. Some level of correlation was found between the χ and composition maps. For instance, the largest contribution of the intermediate species (green) was observed, in the bottom left portion of the particle, appearing to coincide with an area at a high χ value. Significant gradients in χ were observed when transitioning from this region to adjacent areas with 10 ACS Paragon Plus Environment

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increased delithiation, at the bottom of the particle, or less reacted, to the right. The isolated delithiated domain on the left edge (see arrows in figures 3c and d) also appeared to contain a large heterogeneity in grain orientations.

Figure 4. (A) Fe fluorescence map of a FePO4 particle. (B) Summed 2D diffraction pattern of the entire particle. The observed d-space values are centered at 2.897, and 2.96Å. The dashed line denotes the theoretical position of FePO4, based on literature data7,23. The red circle denotes the size of the beam annulus, which corresponds to the instrumental broadening. (C) Chemical phase map of the particle. Green corresponds to Li0.6FePO4 and blue corresponds to FePO4. (D) χ map pertaining to the diffraction intensity centroid in the vertical dimension of the detector, per each mapping position.


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Figure 4 shows data for a particle in the sample at nominally complete delithiation, Li0, with the same approximate morphology (figure 4a and S1c). Two major signals were observed in the average 2D diffraction pattern (figure 4b), centered at 2θ1 = 27.46 ± 0.05˚ and 2θ2 = 26.9 ± 0.1˚, corresponding to d1=2.897 ± 0.005Å and d2=2.96 ± 0.01Å, respectively (Table 1). The highest d value is again in agreement with FePO4. Applying Vegard’s law, the lowest value would correspond to the intermediate composition being Li0.6FePO4. However, 2θ2 was within error of 2θ2 in Li0.5 (Table 1), indicating that their actual Li contents of the two intermediates could well be the same. Most of the diffraction intensity in the crystal was found around FePO4 (figure 4b and S2), with the intermediate as a minority phase. It is likely that the overall content of Li0.6FePO4 in the sample ensemble was small, handicapping detection by powder diffraction.7 Similar to Li0.5, there was significant broadening in both 2θ and χ dimensions. A miscibility gap was again observed in 2θ between Li0.6FePO4 and FePO4, suggesting that broadening along 2θ was mostly due to the reduction of crystalline domain size. The phase map (Figure 4c, with representative individual patterns in Figure S5), shows that Li0.6FePO4 was located almost exclusively in the center of the particle, surrounded by FePO4. The presence of unreacted fractions in Li0 was validated by an independent measurement by full field transmission Xray microscopy coupled with X-ray absorption spectroscopy (FF TXM-XANES) at the Fe K-edge. Figure 5a shows the averaged transmission image above the edge, with the corresponding phase map (b) derived by linear combination (LC) fitting of single pixel spectra (figure 5c). Pure LiFePO4 and FePO4 standards had to be used in the fits because of the absence of reliable spectra for Li0.6FePO4. In these conditions, the assignment of LiFePO4 to a domain is simply a proxy for the existence of (partly) lithiated domains (i.e., containing Fe2+), and not a statement of precise composition. The central regions of the particles clearly presented some level of remaining lithiation, with the edge regions being almost fully oxidized. Some pixels showed apparent Fe2+-Fe3+ ratios close to 2:1, and close to the 12 ACS Paragon Plus Environment

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composition of the intermediate solid solution detected by SXDM.

Table 1. Summary of phases identified in each sample, along with corresponding 2θ and d-spacing. sample

phase

2θ (λ=1.377Å)

d-spacing (Å)

Li1

LiFePO4

26.44 ± 0.05°

3.008 ± 0.006Å

Li0.5

LiFePO4

26.61 ± 0.09°

2.99 ± 0.01Å

Li0.65FePO4

26.85 ± 0.07°

2.965 ± 0.008Å

FePO4

27.5 ± 0.06°

2.897 ± 0.007Å

Li0.6FePO4

26.9 ± 0.1°

2.96 ± 0.01Å

FePO4

27.46 ± 0.05°

2.897 ± 0.005Å

Li0


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Figure 5. (A) Average transmission above the Fe-K absorption edge of FePO4 particles obtained in FF TXM. (B) Chemical map of the particles. (C) Single pixel XANES and results of LC fitting with FePO4 and LiFePO4 standards of the two points marked in (B).

The spread in χ was much greater in FePO4 than Li0.6FePO4 (figure 4b). Nonetheless, the microstructure map (figure 4d) showed moderate gradients in orientation along any given direction, in contrast with the sharp differences in Li0.5. Only weak correlation was observed between the phase and microstructure maps. The fracture of the crystals found in morphological observations by TXM and SEM are consistent with the distortion of the initial diffraction features from large single crystalline domains upon delithiation, accompanied by a random, yet small, spread in the orientation of the newly formed domains. This fact consequently reinforces the idea that delithiation in these microcrystals induces significant defects, from domain misalignment (detected by diffraction) to fracture (detected by morphological imaging)12,16. Accumulation of these defects, especially fracture, is likely to severely handicap complete delithiation, explaining the observations from particles in Li0. The overall distribution of delithiated domains observed in equilibrated crystals by SXDM agrees well with measurements by X-ray spectromicroscopy.16 This correlation confirms that changes in d-spacing are primarily caused by gradients in Fe oxidation state, although there could be a small contribution by coherency strain at interfaces between domains of different composition. SXDM revealed the existence of LixFePO4 solid solutions showing miscibility at 0 < x ~ 0.6, and spatially located them at the nanoscale. The observation significantly enriches earlier insight from chemical maps using spectromicroscopy, where oxidation states, as opposed to crystallographic phases, are locally identified. These earlier maps were interpreted as mixtures of LiFePO4 and FePO4,16 , based on existing knowledge of the phase diagram. Very high spectral (i.e., energy) resolution is required to differentiate mixtures of Fe2+ and Fe3+ occurring at the atomic scale (LixFePO4) or at nanoscale dimensions smaller 14 ACS Paragon Plus Environment

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than the spatial resolution (LiFePO4 and FePO4),25 especially since local Fe2+ and Fe3+ clustering exists for LixFePO4 (x=0.34 and 0.6).26 Such high chemical resolution is typically out of reach due to limited measurement time. In contrast, changes in Li content have a large effect on the spacing of Bragg diffraction planes, leading to easily resolvable signals along 2θ for LixFePO4 solid solutions compared to xLiFePO4 + (1-x) FePO4 mixtures. Bulk powder XRD patterns of similar samples were previously interpreted as a mixture of end members.7 However, close inspection of the data (e.g., figure 1a in ref. 6) reveals complex peak shapes around the LiFePO4 reflections, at angles which could be indicative of the presence of intermediate phases. Further, it is likely that the ratio of crystals in the sample containing domains of solid solution is low, especially if the number of particles actively reacting is small.3,27 This effect would lead to weak features in bulk XRD, obscured by large peaks nearby. This effect highlights the ability of SXDM to spatially resolve diffraction patterns and detect minority phases. Miscible solid solution domains in the LiFePO4-FePO4 phase diagram can be reached either at high temperature1 or, in the case of nanoparticles, through electrochemical cycling,4,5 driven by interface and surface energies and anisotropic lithium diffusion.28,29 A eutectoid exists at Li0.6FePO4 in the phase diagram. A miscibility gap between this eutectoid and FePO4, as found here, also exists at temperatures where miscibility with LiFePO4 is already complete.1,10,11 However, all solid solutions are considered metastable at room temperature.30,31 Most often, they quickly equilibrate to the end members, Li1αFePO4

and LiβFePO4,4,7,30 where α and β account for the slight miscibility depending on particle

size.32 In this study, the as-delithiated particles were allowed to rest at room temperature for many months before the experiments were carried out. Therefore, full equilibration would be expected. Long term stabilization of discrete domains containing the Li0.6FePO4 eutectoid has only been observed at narrow (under 10nm) interfaces in electrochemically cycled nanoparticles8 and after the decomposition


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of high temperature solid solutions, in mixtures with one of the end members, with limited miscibility.7 Considerations of mechanical energy could explain the existence of Li0.6FePO4 domains showing miscibility with LiFePO4 in a particle delithiated at room temperature. Van der Ven et al. predicted that coherency strain would activate a thermodynamic pathway involving the formation of Li0.6FePO4 if delithiation was preferential along the b direction, leading to ac interfacial planes.6 More recently, Abdellahi et al. proposed that linear concentration gradients could occur between surface and crystal interiors under these conditions.29 The b dimension corresponds both to the thickness of the plates,7 and the direction of highest Li diffusion.33 Gradients of concentration into the particle cannot be evaluated by SXDM, as the diffraction data is representative of the entire volume probed at each mapping position. However, we have previously proposed that delithiation of LiFePO4 plates proceeds under limitations of solid state 1-dimensional diffusion, based on local correlations between chemical composition and fracture points that exposed otherwise interior domains.12 This limitation leads to predominant delithiation of the (010) surface(s) before propagation into the crystal, and, therefore, formation of ac interfacial planes. As a result, the existence of miscibility along LiFePO4-Li0.6FePO4 in equilibrated crystals is consistent with existing theoretical models predicting that coherency strain into the crystal alters the energetics of the phase diagram, creating a new equilibrium situation. These novel observations enrich our understanding of the coupling of chemistry and mechanics in battery systems by providing experimental verification to theoretical models. The work highlights that SXDM increases our ability of imaging phase transformations in solids. The sensitivity to different crystallographic phases within an individual particle renders it particularly powerful when seeking to determine the order of the transformation mechanism, and thereby establish strain relationships. It complements chemical insight with the ability to probe microstructural effects of the reaction and, when combined with spectromicroscopy, can deconvolute the chemical phase composition from mechanical strain. Since batteries fundamentally rely on extensive phase transformations that can 16 ACS Paragon Plus Environment

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induce mechanical damage, further use of SXDM should extend our understanding of chemomechanics in these devices. Methods Sample Preparation The LixFePO4 crystals employed in this study were the same studied by Boesenberg et al. using full field transmission X-ray spectromicroscopy16. LiFePO4 was synthesized under hydrothermal conditions reported by Chen et al.,21 and then chemically delithiated by mixing the particles in a 0.05M solution of bromine in acetonitrile, using the desired molar ratio. The compositions quoted for each delithiated sample correspond to the nominal average content of Li in the whole sample (e.g., 100%, 50%, 0%). For details on the powder X-ray diffractograms, the reader is referred to the data provided by Chen et al.21. In order to avoid confusion during the discussion, the three samples are referred to as Li1, Li0.5 and Li0, respectively, hereafter. The samples were allowed to equilibrate over several months before any microscopy measurements were made. Particles were dispersed over a copper transmission electron microscopy (TEM) reference grid with alphanumeric markers to precisely identify the exact location of the sample. A JEOL 7500F scanning electron microscope (SEM) was used at working distances of ~3mm and electron beam energy of 1.00 keV to identify candidate particles to be studied (figure S1 in the Supporting Information), based on morphology, orientation, and isolation from other particles. Scanning X-ray Diffraction Microscopy Diffraction and fluorescence maps were collected for each composition at the Hard X-ray Nanoprobe beamline operated by the Center for Nanoscale Materials (CNM) at Sector 26 of the Advanced Photon Source (APS), Argonne National Laboratory. A schematic of the experimental setup is displayed in Figure 1. A monochromatic beam is focused through a zone plate, passed through an order sorting aperture and shone onto the sample. Not pictured in the figure is an SII Vortex ME-4 4-element silicon 17 ACS Paragon Plus Environment

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drift diode energy dispersive detector that collects fluorescence data. The intensity of the diffracted beam was captured by a PIXIS 1024f CCD camera, resulting in 2D patterns. The beamline can be viewed in more detail in prior work13. The location of particles of interest was determined at the beamline by collecting maps of Fe X-ray fluorescence at the Kα emission line of ~6.4KeV. Particles were aligned so that diffraction signal could be observed from the (020) reflection, approximately 27.5° 2θ at a wavelength of 1.377Å. Once aligned, the sample was moved relative to the beam using a step size of 50-100nm and an exposure time of 1-2s. In this way, a two-dimensional map was collected. Each exposure, or mapping position, contained a single two-dimensional diffraction pattern, consisting of 1024x1024 pixels, tracking the diffraction signal by the 2θ angle (horizontal) and the azimuth, χ, angle (vertical). After the map was obtained, the particle was then rotated about an axis perpendicular to the beam by 0.2°, an amount that exceeds the angular range of the CCD detector, and another map was collected. This was repeated several times until diffraction intensity was no longer observed (in both directions of rotation). Each map was collected in approximately 2h. Data was collected using EPICS channel-access data acquisition and control software. Data Analysis Software packages for Matlab developed by the Advanced Photon Source were used to perform the analysis34. Several 2D images were constructed by selecting data from the maps collected over several degrees of rotation. In order to view the shape and dimensions of the particles of study, a fluorescence map for each one was constructed from the individual scan that displayed the highest intensity and plotting the values accordingly. Ensemble 2D diffraction patterns were obtained for each particle by taking a summation of all the patterns collected at each mapping position. This step revealed the number of chemical phases present in the entirety of the particle and where each one displayed intensity on the detector. A more traditional intensity vs. 2θ plot was generated by taking a summation of the total intensity collected at each horizontal position on the detector. From this plot, full width at 18 ACS Paragon Plus Environment

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half maximum values could be determined for each peak, or chemical phase, which yielded the error, following the formula: FWHM = 2.35σ (in which σ represents the standard deviation). Maps of chemical composition (2θ) and grain orientation (χ) were constructed from the series of 2D diffraction patterns collected. For each individual location, the 2D pattern that displayed the highest total intensity was selected to build the subsequent maps. Equally sized rectangular regions of interest were created around each area of intensity along the 2θ axis. For each mapping position the relative intensities of each phase were plotted according to an assigned color, yielding composition maps. In order to plot relative microstructure of the particles, the center of mass of the intensity over the vertical (χ) axis were calculated to yield single values. These values at each mapping position were then used to build the maps. Transmission X-ray microscopy FF-TXM-XANES data was collected at beamline 6-2 at the Stanford Synchrotron Radiation Lightsource (SSRL), SLAC National Accelerator Laboratory, CA. The microscope achieves a a single flat field of view (FOV) of about 20 × 20µm with a spatial and energy resolution of 30 nm and ∆E/E=10-5, respectively. For the measurements, the crystals were sprinkled directly onto 200 nm Si3N4 membranes (Silson Inc). 2D XANES images (0.5s exposure time, 50 repetitions, binning 2) were collected from 7080 to 7260 eV in 74 steps at varying energy intervals, with spectral sampling at 1 eV across the Fe K-edge. The zone plate was adjusted at each energy to maintain focus. A set of reference images was recorded at each energy in regions where the transmission of the beam was unobstructed by the sample and subtracted from the region of interest containing the sample. All data processing, including reference correction, averaging, magnification correction, XANES reconstruction and fitting, was performed using the TXM wizard software35,36. Details of the experimental procedure and data processing can be found in ref. 15.


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Data Availability The datasets generated during the measurements and post-experiment analysis are available from the corresponding author upon reasonable request. Author contributions M.V.H. and J.C. conceived and planned the experiments. Y.S.Y. performed SEM imaging. U.B. prepared the powder samples and performed the FF TXM-XANES experiments and analysis. B.M.M., Y.S.Y., M.V.H., and F.C.S. carried out the SXDM measurements. B.M.M. and M.V.H. performed the post-experiment data analysis and developed the data processing code. B.M.M., M.V.H., C.P.G. and J.C. established the interpretation of maps and diffraction patterns. B.M.M. and J.C. prepared the manuscript, which includes input from all authors. Competing financial interests The authors declare no competing financial interests Materials and correspondence Jordi Cabana [email protected] Supporting Information Available Electron microscopy and data analysis Acknowledgements This material is based upon work supported as part of the NorthEast Center for Chemical Energy Storage (NECCES), an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under Award Number DE-SC0012583. Use of the Advanced Photon Source and the Center for Nanoscale Materials, both Office of Science User Facilities, was supported by the US Department of Energy, Office of Science, Office of Basic Energy Sciences, under Contract No. DE-AC02-06CH11357 Use of the Stanford Synchrotron Radiation 20 ACS Paragon Plus Environment

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Lightsource, SLAC National Accelerator Laboratory, is supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under Contract No. DE-AC02-76SF00515. We would like to thank Yijin Liu, Florian Meirer and Joy C. Andrews for assistance using beamline 6-2-c. The authors thank M.R. Plews (UIC) for assisting in the creation of figure 1. References (1)

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Nanoscale Detection of Intermediate Solid Solutions in Equilibrated

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