Direct Monitoring of the Potassium Charge Carrier in Prussian Blue Cathodes using Potassium K-edge X-ray Absorption Spectroscopy

: Prussian Blue is widely utilized as a cathode material in batteries, due to its ability to intercalate alkaline metal ions, including potassium. However, the exact location of potassium or other cations within the complex structure, and how it changes as a function of cycling, is unclear. Herein, we report direct insight into the nature of potassium speciation within Prussian Blue during cyclic voltammetry, via operando potassium K-edge X-ray Absorption Near Edge Structure (XANES) analysis. Clear and identifiable spectra are experimentally differentiated for the fully intercalated (fully reduced Fe 2+ Fe II Prussian White), partially intercalated (Prussian Blue; Fe 3+ Fe II ), and free KNO 3(aq) electrolyte. Comparison of the experiment with simulated XANES of theoretical structures indicates that potassium lies within the channels of the Prussian blue structure, but is displaced towards the periphery of the channels by occluded water and/or structural water present resulting from [Fe(CN) 6 ] 4-vacancies. The structural composition from the charge carrier perspective was monitored for two samples of differing crystallinity and electrochemical stability. Reproducible potassium XANES spectral sequences were observed for crystalline Prussian blue, in agreement with retention of capacity; in contrast, the capacity of the poorly crystalline sample declined as the potassium became trapped within the partially intercalated poorly-crystalline Prussian blue. The cause of degradation could be attributed to a significant loss of [Fe(CN) 6 ]-[Fe(NC) 6 ] ordering and the formation of a potassium-free non-conducting ferrihydrite phase. These findings demonstrate the potential of XANES to directly study the nature and evolution of potassium species during an electrochemical process.


INTRODUCTION
Prussian blue (PB) is an important porous metal-cyanide framework structure (A x Fe 3+ [Fe II (CN) 6 ] y .nH 2 O) with exchangeable A cations.1][12] In particular, K + ions can be readily accommodated by the open structure of PB, which allows for reversable intercalation processes that are challenging in layered transition metal oxide cathodes.
Despite the identified potential, unexpected complexities within the PB structure have made fundamental understanding of intercalation processes difficult.4][15][16] In addition, the structure can accommodate significant amounts of uncoordinated occluded water. 17,18These structural variations influence the location of A site alkali cations within PB, which has ramifications in understanding the balance of charges during redox processes. 15,17,19,20In an ideal structure (Scheme 1a), reduction of Fe 3+/III sites is balanced by the intercalation of K + within the vacant channels of the structure, with the fully reduced Fe 2+ Fe II structure, known as Prussian white (PW) having a 1:1 K:Fe ratio.In the fully oxidized Fe 3+ Fe III structure, commonly referred to as Berlin Green (BG), K + is fully deintercalated.However, the influence of (H 2 O) 6 clusters, which are prevalent within the defective structure, has been debated, with some work concluding that these sites can inhibit ion insertion into the channels, while others deducing that K + sits within the (H 2 O) 6 cluster itself (Scheme 1b). 15,21The complications in understanding K + ion location have resulted in ambiguity when assigning the charge-balancing species during framework redox processes, with suggestions that in aqueous electrolytes H 3 O + or K + can act as counterions. 15,22,23Indeed, similar uncertainty is also observed for other cations that can be incorporated into the structure, such as Mg 2+ . 24other challenge in utilizing PB for energy storage applications is its varied stability over repeated cycling.Highly crystalline materials, considered to have a limited number of defects, are reported to favor superior cycle-life and rate capability.The importance of [Fe(CN) 6 ] 4- defects in contributing to structural collapse is stated to be due to their inhibition of ion insertion and decrease in electronic conductivity. 25- 28However, understanding the loss of capacity is again complicated by the differing process mechanisms that are suggested for charge balancing and K + intercalation.
Importantly, current understanding of the location of K + in PB is deduced from general long range structural information such as diffraction data, or via theoretical simulation.Herein, we show that operando potassium K-edge X-ray absorption near edge structure (XANES) can successfully be employed to understand, with the aid of theoretical simulations, the local structure of K + in PB cathodes.While XANES has previously been employed to follow sulfur species (at the S K-edge) in batteries during operation, [29][30][31] there have been few attempts to monitor group 1 or 2 species in battery cathodes.Villevieille and co-workers have identified different Na K-edge spectra of ex-situ isolated charged and discharged Na x MnO 2 cathodes, 32 while Weatherup and co-workers showed that ex-situ Mg K-edge XANES could be used to identify changes at the solid electrolyte interface of a Mg anode. 33Yet neither of these studies are performed during battery operation.We show that such XANES studies can be employed simultaneously with electrochemical testing in an operando experiment.Two samples of varying crystallinity and electrochemical stability are studied, and the evolution of K + within the structure monitored over repeated cyclic voltammograms.

Ex-situ Characterization and Electrochemical Performance.
Prior to analysis of the local structure of K + within the samples, electrochemical properties and ex-situ structural analysis was performed to identify any informative structure-function properties that may enhance our analysis of the potassium K-edge XANES.The PB samples of high crystallinity (HC-PB) and low crystallinity (LC-PB) can both be assigned by XRD to crystalize with a face-centered Fm3 � m PB structure, with varying average crystallite sizes of 103 ±3 nm and 14 ± 2 nm, respectively (Figure S1 and Table S1).IR spectroscopy further confirmed the formation of PB through the presence of a single ν(C≡N) mode at 2086 cm -1 (HC-PB) and 2081 cm -1 (LC-PB), as shown in Figure S2.The morphology of the two samples is notably different when imaged with scanning electron microscopy (SEM) (Figure S3), with HC-PB comprised of 140 ± 30 nm faceted crystalline particles, and LC-PB of ill-defined <18±4 nm particles that agglomerate into >10 µm aggregates.Notably, the large aggregates of LC-PB proved harder to disperse amongst the conductive carbon black during electrode preparation (Figure S4).
Elemental analysis and TGA (Figure S5 and Table S2) result in structural formulae of K 0.55 Fe[Fe(CN) 6 ] 0.92 •3.3H 2 O and K 1.04 Fe[Fe(CN) 6 ] 0.94 •4.1H 2 O for HC-PB and LC-PB, respectively.Given that values of <1 were observed for [Fe(CN) 6 ] 4-, defect sites are concluded to be present in both samples.Fe K-edge EXAFS analysis of the samples is indicative of the PB structure (Figures 1a and S6), with features associated with the Fe-C/N 1 st and 2 nd shells and the Fe-Fe 1 st shell.The intensity of Fourier Transform magnitude features is similar between samples, indicating that the short-range order was comparable.Room temperature 57 Fe Mossbauer spectra of the two samples (Figure 1b and Tables S3 & S4) also show limited differences, with similar average quadrupole splittings and the ratio of Area Fe(III) : Area Fe(II) is equal to 1.5][36] The results are in contrast to the impactful assumption that small crystallite size equated to a more defective structure, which was applied in previous studies of PB electrochemical stability. 28In the present study, both high and low crystallinity samples contain a notable, but comparable, number of defects, despite their very different crystallite size.
A cyclic voltammogram (CV) of HC-PB within the operando XAS cell, in 0.1 M KNO 3 (aq) electrolyte, is shown in Figure 2a.The reduction and oxidation peaks at 0.034 V and 0.22 V are due to the transition of PB to PW (and vice versa).The reduction peak suggests intercalation of K + ion into the HC-PB lattice although, as noted previously, contributions from H + or OH -cannot be excluded (see Scheme 1). 15The observation of an oxidation peak at 0.22 V, with an identical area and height to the reduction peak, indicates the deintercalation of K + ion as well as the quasi-reversibility of the process.The 186 mV peak separation suggests that the rate of intercalation and deintercalation of the hydrated K + ion in and out of the HC-PB lattice is slow and Nernstian concentration is not maintained throughout these processes.The peaks corresponding to the transition of BG to PB (and vice versa) are at 0.88 V and 0.73 V, respectively, and appear to be quasi-reversible with peak-to-peak separation of 150 mV.
While the same oxidation and reduction features are observed in LC-PB, the electrochemical behavior is somewhat different (Figure 2a).The redox processes show a significantly greater peak separation of 460 mV (transition of BG to PB) vs 150mV seen for HC-PB versa), illustrating a quasi-reversible process with much slower kinetics than HC-PB.This could be due to slower charge transfer or alternatively greater particle and contact resistance seen with LC-PB.Unwin and co-workers clearly illustrated that increased electrical resistance increased CV peak separation in scanning electrochemical cell microscopy measurements of LiMn 2 O 4 at fast scan rates of 1 V s -1 . 37Although the impact of resistance on peak separation is anticipated to be reduced by the slow scan rate of 0.77 mV s -1 used in our study, the impact of the relatively poor conductivity of PB (ca 1x 10 -7 S cm -1 ) 38 should not be discounted.In particular the large aggregates of LC-PB seen by SEM (Figure S4) with relatively poor dispersion, when compared to HC-PB, in the conductive carbon of the assembled matrix could well account for substantial resistance within the LC-PB cathode.
The varying stability of HC-PB and LC-PB was further investigated over repeated CV cycles, with calculated discharge capacities given in Figure 2b (Specific changes in CVs are discussed in Section 2.4 with XANES analysis).HC-PB capacity was mostly retained with a 35% reduction over 13 cycles, while LC-PB showed significant instability with 80% loss of capacity over 9 cycles.
Ex-situ analysis of electrodes after cycling showed a loss of structural order in both cathodes, but to a significantly greater extent in LC-PB (Figure 1).Specifically, Fe K-edge EXAFS showed reductions in 2 nd shell Fe-C/N and Fe-Fe path intensities, indicating a loss of short-range order in both samples, although to a far greater extent for LC-PB.There is a clear correlation from EXAFS between the loss in intensity of 2 nd shell Fe-C/N and the loss of capacity of the PB samples on cycling.No change in phasing was observed in the EXAFS of HC-PB, indicating no bulk formation of a new structure.In contrast, an increased contribution of a Fe-O path, as indicated by a shift in the 1 st feature of the FT towards 1.5 Å, is seen in LC-PB after cycling, attributable to the presence of a new additional oxidic phase. 57Fe Mössbauer analysis (Figure 1b and Tables S3 & S4) shows no degradation to HC-PB after cycling, while significant changes were seen for LC-PB.For the spectrum of the LC-PB material, the conventional fitting with 2 Fe (III) doublets was not valid and a further 3rd Fe (III) component with a larger quadrupole splitting was needed to satisfactorily fit the data.The resultant ratio of Area Fe(III) : Area Fe(II) for LC-PB after cycling changed from 1:1 to 3:1, which is far beyond the reasonable limit for PB and implies the presence of an additional Fe (III) phase.A further fit of the LC-PB after cycling spectrum using the original PB components revealed hyperfine parameters of two doublets, which is consistent with the poorly crystalline phase, ferrihydrite (Figure S7). 39The presence of ferrihydrite within the sample is further evidenced when comparing Fe-K edge XANES and EXAFS of the LC-PB used electrode and a ferrihydrite standard (Figures S8 & S9).There was no change in microstructure, formation of cracks, or exfoliation from the current collector observed in the used samples by SEM (Figure S10).
The combination of techniques provides an overall picture a relatively stable HC-cathode with a small but notable loss of long-range order over cycling, and a LC-PB cathode that undergoes rapid degradation through loss of PB short-range order and formation of non-conductive ferrihydrite.The analysis provides an understanding of differences in framework electrochemical properties and associated bulk structural changes, though further work is necessary to provide information on the K + charge carrier speciation and evolution during charge/discharge cycling.

Understanding the Local K + Coordination from Potassium K-edge XANES.
Potassium K-edge XANES of HC-PB were recorded at voltages of 0.41 V during charging, and 0.9 V and -0.1 V during discharge (indicated on the CV in Figure 3a, with spectra shown in Figure 3b).At 0.41 V, the spectrum was comparable with that recorded for PB prior to the addition of electrolyte (Fig S9 ) with notable features at 3610.1 eV (pre-edge), 3612.3 eV (white line shoulder), 3614.3 eV (white line), 3617.7 eV and 3619.8 eV (small doublet peaks after white line), and extended features beyond 3625 eV.Significantly, the XANES spectra of the KNO 3(aq) electrolyte alone is clearly distinguishable, through a more intense pre-edge feature, and a broad single structure centered at 3616.7 eV.The observations show the potential of operando K-edge potassium XANES, as the spectrum of K + within the cathode and electrolyte can be easily differentiated.At 0.9 V (discharge), the spectrum of the cathode is comparable to the electrolyte with residual features associated with PB, showing that almost all K + has been deintercalated from the now oxidized BG structure.The result suggests that K + is acting as a charge carrier under the conditions monitored and can be fully deintercalated from the structure.Lastly, holding at -0.1V resulted in a 3 rd XANES spectrum, which is associated with the fully reduced Fe 2+ Fe II PW structure, with full K + intercalation.The features of the XANES spectrum for the postulated PW structure differ from that of PB, with an enhanced pre-edge feature, a change in intensity ratios of the split main feature, and emergence of another strong shoulder at 3616.3 eV.
By comparison, LC-PB analyzed prior to addition of electrolyte, or an applied voltage, shows subtle difference in K + speciation (Figure S11).Linear combination fitting (LCF) allows assignment of 68% K + within a comparable environment to HC-PB, and 32% adsorbed K + in a solvated environment.Subsequently, the structural formula determined by elemental analysis can be revised to K 0.71 Fe[Fe(CN) 6 ] 0.94 .4.1H 2 O + 0.33K + (ads) .Introduction of electrolyte results in the XANES spectrum of LC-PB changing to that seen for HC-PB, which shows the removal of adsorbed K + from the PB surface.At the same voltages of -0.1 V, 0.4 V, and 0.9 V that were applied to HC-PB, potassium XANES of LC-PB gives comparable pre-edge positions, main feature splitting, and extended structural features for K + in PB, PW and electrolyte environments, as seen for HC-PB (Figure S12).Interestingly, these results show that the local environment of K + is comparable in both samples after residual K + (ads) is washed from the surface by the aqueous solvent.This observation correlates to information from the framework perspective, as provided by Fe K-edge XAS and 57 Fe Mössbauer, which showed similar structural order and defect formation in both samples.
To rationalize the observed spectra, several theoretical structures were validated by density functional theory (DFT) simulation before being used to simulate the potassium K-edge XANES.The electronic and structural properties of K + inclusion within the ideal PB structure verified that the ion sits in half of the center of the primitive cubic structural cavities (8c sites), in an ordered tetrahedral pattern (as shown in Scheme 1a).Analysis of the electronic density of states (DOS) is consistent with the expected changes in Fe oxidation and spin states on removing all K + (BG), or when fully oxidizing the system by filling all 8c sites (PW) (Figure S13).Next, the inclusion of H 2 O was considered in competition with K + for the 8c site, which would increase the distance between intercalated K + , as it is pushed towards the corners of the primitive cell into the 32f' position (Figures S14 & S15).Increasing the water content from 4 to 16 H 2 O molecules per unit cell pushes the K + further away from the central 8c site, with the inclusion of 8 H 2 O calculated as the most thermodynamically viable.Finally, the influence of the Fe II (CN) 6 defects was considered by the removal of the central Fe II (CN) 6 octahedra and addition of a (H 2 O) 6 cluster.In this scenario K + has been considered in two locations (Figure S16).When K + was considered within the cavities, it was pushed away from the 8c site towards the 32f' position, relative to the ideal water free PB structure.The enthalpy of formation (ΔH form ) of this intercalated structure is higher with the inclusion of the defect, supporting notions that structural defects would inhibit K + intercalation. 27Alternatively, K + was considered within the central (H 2 O) 6 cluster (equivalent to Scheme 1b), with ΔH form at comparable K + loading less favorable than for the defective system with K + within the channel.Therefore, K + is unlikely to be located within this defect site.
Simulation of the XANES spectrum of the ideal PB structure, with K + on the 8c site, is compared in Figure 4a with the experimental spectra of HC-PB.The pre-edge (Feature A), white line shoulder (Features B & C) and white line (Feature D) were successfully simulated.These features are attributed from the projected DOS (Figures 4b and 4c) to low lying K p-states overlapped with Fe orbitals (A), hybridized K pstates with CN anti-bonding π orbitals (B & C), and isolated K p-states (D), respectively.While most features are well represented, the intensity of feature C is significantly underestimated in the original simulation.Given that K + at the 8c site is a significant distance from CN π anti-bonding orbitals, a lack of overlap between K p-states and these π orbitals can account for the low intensity of feature C and dominance of D. As noted, when performing the DFT simulations, the inclusion of water molecules or defects pushes K + towards the Fe 3+ -N corners of the primitive cube (32f' position), which would increase orbital overlap of states associated with feature C. XANES simulation of K + within this 32f' position (Figure 4c) did indeed show an increased contribution to the XANES from feature C and brought the XANES simulation into closer agreement with experiment.The greater ΔH form calculated by DFT suggests that that K + does not reside within the defect (Fig. S16); with the evidence is more compelling for K + being forced into the corners of the channels by these defect sites or occluded water within the structure.
The XANES spectrum calculated for the PW structure (Figure 4d) replicated the experimental features seen at -0.1 V, including the additional feature at 3616.3 eV (Feature E) that is not observed for PB.The results validate the assignment of the experimental XANES spectrum to a fully intercalated PW structure, where the sample is fully reduced.Using simulation to validate the spectrum is particularly important given that PW readily oxidized under ambient conditions to PB, making validation via the use of a synthesized material analyzed ex-situ unsuitable.As seen with the simulated spectra of PB with K + within the 8c site, the shoulder of the white line is mispresented in the simulated spectrum of PW, showing that K + continues to be off center from the 8c site within the fully intercalated structure.

Operando Potassium K-edge XANES of PB Cathodes
Unnormalized operando spectra, obtained throughout a CV of HC-PB, are shown in Figure 5a, alongside the determined compositions of potassium within PB, PW, and electrolyte environments (Figure 5b).The compositions are determined from the potassium K-edge step values and associated fractions of each K + species determined by LCF analysis (Figure S17).Visual inspection of the unnormalized spectra in Figure 5a shows a clear evolution of speciation through the voltage sweep, and a change in edge step height.As K + speciation evolves through the different environments of PB and residual electrolyte, the edge step decreases as K + is removed from the cathode.The edge step then increases as the sample is oxidized to PB and then PW.Consequently, comprehensive analysis of both K + speciation and its relative concentration within the PB cathode, with respect to applied potential and current response, can be made during charge/discharge cycling.
The changes in K + for the 1 st full CV, starting from PW, are shown in Figure 5b.Deintercalation of K + , as evidenced by the decrease in the step edge, clearly occurs in two stages and at the same potentials of 0.22V and 0.88V as seen from the current responses in the voltammogram.When observing the evolution of individual K + species, the stages that occur are the deintercalation of K + from within PW due to its oxidation to PB, and then further deintercalation from oxidation to BG.The evolution of specific K + environments associated with these framework structures can be directly correlated to redox features within a CV.Each deintercalation event is followed by further small and gradual losses in K + signal (i.e., poorly defined plateaus of K + concentration), which occur within the voltage windows of 0.4-0.8V and 1.0 V charging cycle to 1.0 V discharge cycle.Analysis of the individual XANES components shows that this gradual loss of K + concentration between oxidation events is due to deintercalation of kinetically hindered K + from within PW and PB environments respectively.Furthermore, the sluggish deintercalation of K + from residual PB sites within the cathode is particularly apparent from the LCF of the normalized spectra (Figure S17).Zampardi et al. noted that the deintercalation of K + from PB to BG can be sluggish in composite electrodes, corresponding to the slow K + evolution seen in the XANES. 40Interestingly, this kinetically hindered K + was hypothesized not to be an intrinsic property of PB but of the assembled electrode and associated electrostatic effects, as supported by the resent multiscale measurements by Unwin and co-workers using scanning electrochemical microscopy on LiMn 2 O 4 . 37e corresponding two step intercalation of K + during reduction of BG to PB, and then to PW, can also be directly observed from the increases in K + concentration and the evolution of K + environment.In contrast to oxidation, a clear plateau in K + concentration, and PB speciation, is observed between the two reduction events.The result suggests that the reduction process is more facile, with no residual intercalation being observed.Given that the total edge step intensity does not return to its initial value the apparent improvement in kinetics could be the consequence of poorly conductive intercalation sites seen during reduction not participating in the subsequent oxidation.Evidently, throughout the entire redox process of PB, K + acts as the predominant charge-balancing species through intercalation processes, with no clear discrepancies seen between this process and the recorded current response during cycling.It is important to note that the apparent loss of solvated K + associated with electrolyte when the sample is fully reduced to PW is likely an artifact of the analysis, as the PW standard XANES spectrum used in LCF analysis itself contained an electrolyte component.
Operando XANES of LC-PB (Figure 6 & Figure S18) revealed significantly different behavior to HC-PB.Starting from -0.2 V of the 2 nd CV cycle, a very low current response is seen when sweeping the potential between 0.1 to 0.5 V.The lack of current response suggests minimal oxidation of species, either due to minimal PW being formed from the preceding PB reduction or a lack of oxidation of PW.Interestingly, XANES analysis of K + speciation shows that ca.20% of K + was already within a PB environment at -0.2 V, partially explaining the low current response.However, the remaining ca.80% of K + was present within a PW environment and the deintercalation of the K + from the PW environment is clearly observed during the oxidative potential sweep.The rate of deintercalation from PW was incredibly sluggish, with considerable K + being retained in LC-PB up to 0.8 V (i.e., within PW) and no clear plateau of K + concentration exists.Surprisingly, the deintercalation process shows minimal current response, suggesting a non-faradaic chemical process is responsible for a significant proportion of the PW deintercalation.
Further oxidation of PB to BG was facile, with rapid K + deintercalation and a strong simultaneous current response.Given that little difference in defect structure has been demonstrated for HC-PB and LC-PB, these differences are attributed to variation in composite film microstructure seen by SEM (Figure S4), as reported by Zampardi et al. 40 From the XANES analysis, it is evident that K + is almost completely deintercalated from PB, with the remaining K + that is seen after the current response attributed with the electrolyte.Therefore, while the high spin redox process appears to be incomplete (i.e., K + is not completely converted from a PB environment to a PW one), the K + removal during low spin PB to BG is far more favorable and goes to completion.The subsequent intercalation of K + from BG to PB also appears facile, although observation of the total edge step shows that significantly less K + is present within the sample after the low spin redox process, in agreement with the reduced current response (i.e., K + signal at the two relevant current response plateaus).Finally, unlike during oxidation, the intercalation of K + during PB reduction to PW corresponds to a clearly observable current response, indicating that this process is faradaic in nature.

Operando XANES of PB Cathodes During Repeat Cycling
Operando XANES was used to follow changes in K + speciation within HC-PB between CV cycles 3 and 10 (Figure 7a), over which time a 15% loss in capacity was observed.While minor shifts in the CV peak positions occurred during HC-PB cycling, the electrochemical properties of the sample remained relatively consistent.Based on the edge step of the unnormalized XANES (Figure 7b), clear repeatable cycles of K + concentration can be observed.Notably, the plateaus and maxima of K + concentration reduce slightly, by 30%, while the minima remain constant.LCF of the potassium XANES across the repeated cycles is shown in Figure 7c, with the cycling of the three K + environments being relatively consistent as expected.Therefore, it can be concluded that the intercalation sites present, while dropping slightly in absolute number, continuing to effectively cycle between the K + species discussed over the 8 CV cycles investigated.The modest loss of structural order and intercalation sites on cycling of HC-PB, as determined by Fe K-edge EXAFS analysis (Section 2.1), explains the decrease in K + intercalation seen from edge step analysis.Nevertheless, the effective cycling of the remaining K + species shows that sufficient framework order is retained to maintain conductivity and electrochemical efficiency.
In contrast, LC-PB showed clear instability over the 8 cycles when studied by operando XANES, with 62.5% loss of capacity.(CV scans shown in Figure 7d).Changes to the CVs consist of a shift in peak potential by 0.08 V for PB → BG oxidation and a reduction in peak current magnitude.A shift to lower V for the BG reduction is also observed for the 1 st cycle, and then the peak position stabilized at 0.6 V but with a reduction in peak magnitude with increasing cycles.A minimal shift in peak potential was observed for the high spin redox couple, with a dramatic decrease in the magnitude of the features, which was particularly prominent for the current response associated with PW reduction to PB. Evidently a series of complex changes occur during cycling, which the operando XANES can help rationalize.
In accordance with the dramatic capacity loss seen for LC-PB, the Δ edge step, which corresponds to the change in un normalized potassium K-edge XANES edge step during charge/discharge, decreases by 54% over 7 cycles (Figure 7e).In LC-PB, the edge step values show a different trend to that observed for HC-PB on repeat cycling, with the maximum and minimum K + concentrations both converging on a relatively stable PB plateau.By contrast K + signal only decreased in respect to a loss of fully intercalated PW sites on cycling.LCF analysis (Figure 7f) of the LC-PB data shows a dramatic loss of K + signal variation associated with either electrolyte or PW as CV cycling progresses, with complementary increase of a signal associated with K + trapped within the PB structure.The entrapment of K + within an PB environment throughout the potential sweeps showed that LC-PB becomes electrochemically inactive.A loss of conductivity due to the collapse of the short-range order within PB and ferrihydrite formation (Section 2.1) explains the observed trapping of charge carriers in the remaining PB sites within the cathode.

CONCLUSION
Potassium K-edge XANES has been used to understand the location of K + within the Prussian blue structure.Differentiated K + species were clearly observed, associated with the fully intercalated Prussian white structure, partial intercalation within Prussian blue, and within the aqueous KNO 3 electrolyte.Theoretical simulations of Prussian blue, and associated XANES simulations, show that K + resides within the cavities of the structure, but located away from the center of the primitive cubic cavities (8c site) and towards the corners of the cavities (32f' position), due to structural defects or occluded water.
Operando spectroscopy has been applied during electrochemical redox reactions of Prussian blue within an aqueous KNO 3 electrolyte, and definitively shows that K + is the predominant species that balances structural charge during the relevant redox reaction.Within a highly crystalline Prussian blue sample, the intercalation process was reproducible over repeated charge/discharge cycles, although full deintercalation of K + was kinetically hindered.with residual evolution of K + species being observed by XANES at potentials beyond that of the observed current response.
Significant degradation in electrochemical performance of a low crystalline Prussian Blue, with almost complete loss of capacity over 10 voltammetry cycles, was identified as being caused by K + becoming trapped within the partially intercalated Prussian blue structure.The degradation is caused by an increase in structural disorder on cycling, which can be observed from the perspectives of framework Fe and also the K + species.Specifically, non-conductive ferrihydrite forms on repeated cycling, which results in a loss of electrochemical activity, and K + becomes trapped within the remaining thermodynamically stable Prussian blue within the cathode.Potentially this process is exacerbated by the poor electrical conductivity of these small crystallite containing samples that aggregate together when forming composite electrodes.
The study shows that operando potassium K-edge XANES can be successfully employed to effectively study the evolution of charge carrier species during an electrochemical process.The potential of XANES to monitor the speciation of alkaline charge carriers, in a host of different battery and other electrochemical processes, has exciting future potential in characterization and development of new materials.EXPERIMENTAL SECTION Material Synthesis.LC-PB preparation is based on wet chemical precipitation method.Equimolar concentrations of Fe(NO 3 ) 3 and K 4 Fe(CN) 6 solutions (5 mmol in 15 mL in DI water) were mixed together through dropwise addition.The solution was heated to 60 °C and kept under vigorous stirring for 2 hours.The resulting blue precipitate was separated via centrifugation at 10,000 rpm for 5 minutes and washed 5 times with acetone and DI water.The resulting precipitate was dried in a vacuum oven at 80 °C for 3 hours.
HC-PB preparation is based on a previously described method with modifications. 28An equimolar ratio of K 3 (Fe(CN) 6 and K 4 Fe(CN) 6 (10 mmol) was dissolved in a 150 mL 0.6 M HCl solution.The solution was heated to 80 o C and stirred for 20 hours.The resulting precipitate was filtered under vacuum and washed with DI water several times.The powder collected was dried in a vacuum oven at 80 o C for 3 hours.
Material Characterisation.The thermogravimetric analyses were collected on a TA Q600 SDT system, the samples were heated to 900 o C under air with a 2 °C/min ramp rate.X-ray diffraction (XRD) patterns were collected on a Brucker D8 Discover diffractometer using Co Kα (λ = 1.79 Å) operating at 35 kV and 40 mA with a PSD Braun detector.CHN elemental analysis was performed on a Perkin Elmer 2400.Before measurements, the samples were degassed overnight at 90 °C.ICP-AES experiments were performed on reaction filtrates using an Agilient 4210 MP-AES fitted with a SPS4 autosampler.SEM images were taken using the lower electron detector in a JEOL 7100F REGSEM.Infrared measurements were taken using a Schimadzu IT Affinity-1 spectrometer, using an attenuated total reflection crystal sampling technique.The investigated spectral range was from 4000 to 400 cm -1 with a resolution of 4 cm -1 .The signal was obtained by averaging 16 scans. 57Fe Mössbauer spectra were recorded at room temperature in the transmission mode using a constant acceleration spectrometer and a 57 Co(Rh) source.The velocity scale was calibrated using a 6 μm thick α-Fe foil.All the spectra were computer-fitted and the isomer shifts referred to the centroid of the spectrum of α-Fe at room temperature.ELECTROCHEMCIAL EVALUATION.Electrochemical performances were performed in an operando cell (Figure S22).To compensate for the low energy of potassium XANES, 60 µm glassy carbon windows were used as both the current collector and X-ray window of the cell.The electrodes consisted of 80 % active material, 10 % C65 carbon black, and 10 % polyvinylidene fluoride (PVDF) binder, which were ground together into a paste and spread on the substrate with a K-Bar at ca. 100 μm thickness.The electrochemical performance of active material was evaluated using cyclic voltammetry (CV) at ambient temperature.The measurements were performed using an Ivium OctoStat30 potentiostat.Measurements were performed in a three-electrode cell.A Pt wire acted as the counter electrode, and a Ag/AgCl (3M NaCl) filled capillary tube as the reference electrode.The electrolyte comprised of flowing 0.1 M KNO 3 (aq).XANES MEASUREMNTS.XANES measurements was performed at B18 Beamline at Diamond Light Source, Didcot, UK.XANES were set-up with a fast-scanning silicon (111) double-crystal monochromator.Operando measurements were taken in fluorescence mode.For ex-situ measurements, sample preparation consisted of spreading a thin layer of material on carbon tape and taken in total electron yield (TEY).XANES data was processed using Athena software of the Demeter package.Linear Combination Fitting of operando XANES on normalised datasets was caried out in the energy window of 3593-3643 eV. 41Standards for PB and electrolyte were recorded within the operando cell environment to mitigate for self-absorption effect.The PW standard was taken at a fixed -0.1 V potential after the current response stabilised.
DFT simulations.Ab initio DFT calculations were performed using the numeric atomic orbital (NAO) package, FHI-aims, 42 which is an allelectron, full-potential electronic structure code.The generalised gradient approximation (GGA) of Perdew-Burke-Ernzerhof, reparametrized for solids (PBEsol), 43 was used as the exchange-correlation (XC) functional during geometry optimisations, with the XC functional of Heyd, Scuseria and Ernzerhof (HSE06) 44 and a screening parameter, w, of 0.11 bohr -1 used for subsequent single point energy calculations on the optimised structures.Dispersion interactions were accounted for using the Tkatchenko-Scheffler method, 45 which is a pair-wise additive approach to include van der Waals interactions within the system.Calculations were performed using a 'light' basis set of the 2010 FHI-aims release, with SCF convergence assumed when the change in density was 10 -6 e/a 0. Calculations were performed with a converged Monkhorst-Pack k-point 46 sampling grid of 4 x 4 x 4. Calculations were also performed spin-polarized to account for the iron spin-states, and the zeroth order regular approximations (ZORA) was used for relativistic treatments.

FeFigure 2 .
Figure 2. Electrochemical performance of HC-PB and LC-PB.(a) Cyclic voltammograms of HC-PB (Blue) and LC-PB (Red).Scan rate of 0.77 mVs -1 and a 0.1 M KNO 3 aqueous electrolyte.(b) Discharge capacities determined from repeated CV cycling.Grey box illustrates CV cycles that were subsequently investigated using operando potassium K-edge XANES.

Figure 3 .
Figure 3. (a) Cyclic Voltammogram of HC-PB (b) Potassium K-edge XANES of samples held at denoted points during the CV.CV measurements were made using 0.1 M KNO 3 (aq) electrolyte using a scan rate of 0.77 mV/s.

Figure 4 .
Figure 4. Comparison of experimental potassium K edge XANES (black dashed) and Simulated XANES (red).(A) Prussian Blue with K + within the ideal 8c cage site.(B) Projected p-type density of states for Prussian Blue with K + within the ideal 8c site: Potassium p-type DOS (Blue); N p-type DOS (Green); C p-type DOS.(C) Simulated XANES of Prussian Blue with K + being in the 32f site towards the high spin Fe 3+ corners of the cage (non-relaxed structure).(D) Simulated XANES of Prussian White with full K + occupancy.

Figure 5 .
Figure 5. Operando Potassium K-edge XANES of HC-PB during cyclic voltammetry.(a) XANES plot showing evolution of unnormalized spectra from 0.56 to 0.33 V. (b) Pseudo-concentration of potassium speciation with respect to applied potential and current density.Current density (Red dashed); total edge step value of potassium XANES (Purple); Potassium associated with PW structure (Black); Potassium associated with PB structure (Blue); Potassium associated with KNO 3(aq) (Green).Pseudo-concentration of potassium determined by multiplication of edge step date by fraction of potassium determined by linear combination fitting of XANES.

Figure 6 .
Figure 6.Pseudo-concentration of potassium speciation during Operando Potassium K-edge XANES of LC-PB cyclic voltammetry.Current density (Red dashed); total edge step value of potassium XANES (Purple); Potassium associated with PW structure (Black); Potassium associated with PB structure (Blue); Potassium associated with KNO 3(aq) (Green).Pseudo-concentration of potassium determined by multiplication of edge step date by fraction of potassium determined by linear combination fitting of XANES.

Figure S 1 .
Figure S 1. XRD patterns of HC-PB (Blue) and LC-PB (Red).Reference pattern of Prussian Blue, JCPDS no.52-1907 (Black), circle represents a peak from tape from the instrument.

Figure S 4 .
Figure S 4. SEM images of fresh electrodes of HC-PB (left hand-side) and LC-PB (right-hand side).

Figure
Figure S7.-Room temperature Mössbauer spectra recorded from sample LC-PB used fitted to a different model than that shown in Figure 1b (main paper).The dark and light brown doublets correspond to Ferrihydrite.The remaining components correspond to LC-PB fresh.The Mössbauer parameters and relative area ratios of the LC-PB fresh have been fixed to those deduced from the spectrum of LC-PB fresh.

Figure S 8 Figure S 9 Figure S 10 .
Figure S 8 Fe K edge XAFS of HC-PB before and after cycling in comparison to a Ferrihydrite standard (top) XANES, (bottom right) k space, (bottom left) Fourier Transform χR.HC-PB powder (Blue), LC-PB powder (Red), Ferrihydrite (Green)

Figure S12 .
Figure S12.(Top) Cyclic Voltammogram of LC-PB (bottom) Potassium K-edge XANES of samples held at denoted points during the CV.CV measurements were made using 0.1 M KNO3 (aq) electrolyte using a scan rate of 0.77 mV/s.

Figure S 14 .
Figure S 14. ∆Hform for addition of 4, 8, and 16 H2O molecules to unit cell of PB.

Figure S 16 .
Figure S 16. ∆Hform for soluble (blue triangles) and insoluble (reds square) structures as a function of K + loadings.

Figure S17 .
Figure S17.Operando Potassium K-edge XANES of HC-PB during cyclic voltammetry.(left) Comparison of unnormalized XANES edge step value (associated with K + concentration) at specific applied potentials and corresponding current density.(right) Comparison of fraction of K + species determined from linear combination fitting of normalized XANES.

Figure S18 .
Figure S18.Operando Potassium K-edge XANES of LC-PB during cyclic voltammetry.(left) Comparison of unnormalized XANES edge step value (associated with K + concentration) at specific applied potentials and corresponding current density.(right) Comparison of fraction of K + species determined from linear combination fitting of normalized XANES.

Figure S22 .
Figure S22.Image of electrochemical cell

Table S3 .
-Hyperfine parameters obtained from the fit of the spectra presented in Figure1b.(δ is the isomer shift; Δ is the quadrupole splitting and Γ is the full with at half maximum).

Table S4 .
-Average isomer shift and quadrupole splitting of the HS Fe(III) components in the spectra shown in Figure1b.AIII/AII is the AreaFe(III)/AreaFe(II) ratio.