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# Detection of metastable solid solution in doped LiFePO4 by synchrotron nuclear resonance techniques

Sergey Yaroslavtsev, Susanne C. Müller

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Sergey Yaroslavtsev, Susanne C. Müller. Detection of metastable solid solution in doped LiFePO4 by synchrotron nuclear resonance techniques. Materials Today Chemistry, 2024, 39, pp.102159. 10.1016/j.mtchem.2024.102159. hal-05128589

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# Detection of metastable solid solution in doped LiFePO₄ by synchrotron nuclear resonance techniques

Sergey Yaroslavtsev*, Susanne C. Müller

ESRF-The European Synchrotron, 38043, Grenoble, France

## ARTICLE INFO

### Keywords:

- Li-ion batteries

- Synchrotron Mössbauer spectroscopy

- Nuclear forward scattering

- Nuclear inelastic scattering

- Operando

- Lithium iron phosphates

## ABSTRACT

In this work we study one of the popular cathode materials based on doped lithium iron phosphate LiFeₓMn₁₋ₓPO₄. Synchrotron operando Mössbauer measurements reveal the existence of metastable states at different stages of the charge and discharge processes, with a lifetime in a wide range from 5 to 140 min. The existence of such states is associated with the formation of a metastable solid solution with the composition LiₓFeₓMn₁₋ₓPO₄ during cycling. Afterwards, this solution dissolves due to the slow diffusion of manganese and iron ions together with lithium. The presence of metastable states and their rapid decay indicate that cycling is not an equilibrium process. The influence of the manganese migration on the mechanism of the cycling process is discussed in this study.

## 1. Introduction

One of the promising cathode materials is lithium iron phosphate (LFP) [1–5], because of its low cost, easy synthesis, eco-friendliness, performance stability, etc. However, it has a low ionic and electronic conductivity [6,7], which limits its applications in fields, that require high currents. Resolving this issue will enable the development of a more efficient battery material for a wider range of applications. Several approaches exist to increase the capacity and to gain stability at high currents, such as carbon coating [8–10] or reducing the particle size [11, 12]. Another possibility is doping [13,14]. In order to avoid a decrease in the material capacity with doping, it is reasonable to use ions, such as manganese, which can also change the oxidation state. However, to gain efficiency with doping, it is necessary to understand how exactly doping changes the cycling process. Since doping improves the stability and the performance at high currents, it is important to study its influence at high cycling rates. In this case, the process could be in a non-equilibrium state and one of the interesting details is the possibility of the formation of metastable states during the cycling process, which could be relatively fast compared to the internal process within the material.

Mössbauer spectroscopy provides information on the local states of the iron ions including the change in symmetry of the nearest environment, which also allows one to indirectly get information on the dopant state. This makes the Mössbauer spectroscopy a widely used approach to study lithium-ion battery materials [15–17], even doped ones [18–22].

Unfortunately, the most common studies are *ex-situ* measurements due to limitations of the laboratory setup. To study metastable states (mentioned above) only an *operando* approach is suitable. Mössbauer *operando* studies are rare [19,20,23–25], and in all of them the batteries were cycled at low rates. The main reason for this is the long duration of the measurements, that is required to obtain reasonable statistics. In this case, only slow quasi-equilibrium processes can be studied, but not metastable states themselves. To reduce the measurement time, an optimization of the electrochemical cell design is required. In this study we used a new electrochemical cell designed specifically for synchrotron nuclear resonance techniques [26]. The cell was used in a three-electrode scheme. Together with a sample optimization, it finally allows us to perform fast Mössbauer *operando* studies.

In practice, a low level of doping is usually used to improve the battery performance. However, our aim is to investigate the effect of doping on the charge-discharge processes. Therefore, to study the influence of doping we have used a high concentration of manganese in iron sites to have an explicit demonstration of this effect.

## 2. Experimental part

The lithium iron phosphates LiFeₓMn₁₋ₓPO₄/C (x = 0, 0.2, 0.5, 0.7) were synthesized by the sol-gel method. In order to optimize the Mössbauer experiment, all samples were synthesized in a way that ⁵⁷Fe occupied 15 % of metal (Fe, Mn) sites. With a higher enrichment the

<figure><img src="image_3.png" /></figure>

<footnote>* Corresponding author.</footnote>

<footnote>E-mail address: sergey.yaroslavtsev@esrf.fr (S. Yaroslavtsev).</footnote>
<figure><img src="image_4.png" /><figcaption>**Fig. 1.** (a) Evolution of the quadrupole shift with time during pause for maximum charged 20 % Mn doped material. Squares - first and last measurements during pause. Red triangles - measurements before and after pause (presented for comparison of changes). Blue circles - measurements during pause. Yellow line - exponential fit. (b) Spectra at the start (purple) and at the end (orange) of pause and their difference (black). (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)</figcaption></figure>

sample would be too thin, leading to a significant thickness in-homogeneity. The samples were characterized with X-ray diffraction and scanning electron microscopy, which reveal a homogeneous distri-bution of the elements over the samples, absence of impurities and no priority in the growth direction. All samples have only one ortho-rhombic phase (space group *Pnma*). The average particle size is est-mated to be less than 100 nm. During electrochemical cycling, two clearly defined plateaus were observed, corresponding to a change in the oxidation state of Fe and Mn ions. For more details about material characterization see Ref. [27].

To prepare the electrodes, the synthesized cathode materials were mixed with PVDF and carbon black. Afterwards, this mixture was pasted onto the 15-µm aluminum foil. In the next step, the electrode was dried and pressed. Finally, the area density of electrode active material was about 8–10 mg/cm². Further details are described in Ref. [27].

Electrochemical cycling was performed using the pothentiostat Bio-Logic SP300. At all pauses during the cycling, the pothentiostat was automatically switched to OCV mode, to prevent any current leakage through the cell. For this *operando* experiment, the electrochemical cell, designed specifically for nuclear resonance techniques was used. Electrochemical cycling was performed in the range of 2.4–4.2V with an increase to 2.3–4.6V for doped samples at high current. 1 M LiPF₆ with EC/EMC/DMC (1:1:1 mixture) from Sigma-Aldrich was used as electrolyte, and *Celgard* as separator. The experiment on each sample was started with one full cycle, to estimate its capacity. The further experiment was done at a ~1C cycling rate (current equal experimentally estimated discharge capacity divided by 1 h).

All Mössbauer spectra were collected at the nuclear resonance beamline ID18 [28] (recently moved to ID14) at the ESRF (European Synchrotron Radiation Facility). Initial measurements were done using the energy domain spectroscopy - synchrotron Mössbauer source (SMS) [29]. The SMS spectra were measured in the non-timing mode to reach a maximum count rate for this technique. SMS is a unique technique, which is available at the ESRF, Spring-8 and DESY. The stability of the nuclear monochromator (iron-borate crystal) was checked by measuring a standard single-line absorber (K₂Mg⁵⁷Fe(CN)₆). This was done before and after the measurements to account for the shift and broadening of the experimental spectrum. No instability was detected during the experiment. Further measurements have been carried out using nuclear forward scattering (NFS). The NFS (time domain) spectra were measured in a timing (16 bunch) mode of the synchrotron. The initial synchrotron pulse was cut with “veto” and only the delay quanta were measured (see Refs. [30,31] for details). During the *operando* measurements in both SMS and NFS cases, the spectra were recorded every

minute, but for SMS they were subsequently summed by three to obtain a tolerable statistic. During one week of experiments, more than 2500 NFS spectra were collected.

In addition to NFS, several in-situ measurements (loop of cycle/pause/measurement) applying nuclear inelastic scattering (NIS) were conducted. In order to obtain a signal with both inelastic and elastic scattering, one detector is placed close to the sample on its side. Additionally, a second detector behind the sample along the beam can detect the forward scattering (mainly elastic signal). To proceed nuclear in-elastic scattering, the energy of the initial radiation must be measured together with the elastic and inelastic signals [32]. However, to measure an inelastic signal, the cell should be rotated almost 90° so that the window faces the side detector. Thus, the battery cell body blocks the forward scattering signal and the simultaneous measurement of elastic and inelastic signals is not possible. The standard sample (NH₄)₂Mg⁵⁷Fe(CN)₆ was used for the energy calibration and its elastic signal was applied for further data processing.

The fitting of the NFS spectra was performed using SYNCmoss [33] in a 'logarithmic' mode, to fit all features of the spectra, as they contain more information about the hyperfine parameters. Otherwise, the earlier part of the spectra will statistically dominate the later part (see Ref. [33] for more details). A useful feature of the software in this case was the ability to automatically fit a set of spectra in a sequence (one after the other). In the case of SMS, the instrumental function does not have a symmetric shape [34], which could lead to uncertainties in the fitting results. As all the changes in hyperfine parameters discussed in this article are very small, it was necessary to fit the spectra with high accuracy. Therefore, the fitting of the SMS spectra was done in SYN-Cmoss as it is specifically designed to fit synchrotron Mössbauer spectra, taking into account the shape of the instrumental function.

To fit the NIS spectra, the first step is to summarize all scans and to subtract the background. Then the elastic part can be subtracted and the energy scale is extended to the full range of phonon energies. Finally, the partial density of phonon states (pDOS) is derived and normalized. All spectra were fitted and processed using nisDOS (provided by Ilya Ser-geev, P01 at DESY) and the following information from the iron envi-ronment can be extracted: the pDOS, the Lamb-Mössbauer factor (f<sub>LM</sub>), the force constant, the entropy, the internal energy and the heat capacity.
<figure><img src="image_5.png" /><figcaption>**Fig. 2.** (a) The evolution of the NFS spectrum during the discharging process for $Li_xFe_{0.8}Mn_{0.2}PO_4$. (b) Spectra of $LiFe_{0.8}Mn_{0.2}PO_4$ at different charging states. Blue - before cycling measured for 30 min, red - maximum charged (30 min), green - partially discharged (1 min). (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)</figcaption></figure>

# 3. Results and discussion

## 3.1. Results of SMS measurements

The typical Mössbauer spectrum of doped lithium iron phosphate has four components [27]. The hyperfine parameters of two of these (the main $Fe^{2+}$ and secondary $Fe^{3+}$ components) do not change during the cycling process. The parameters of two others could change depending on the charge state of the sample. The most significant change appears in the quadrupole shift of the main $Fe^{3+}$ component. It has been shown that the evolution of the Mössbauer spectrum parameters during cycling depends on the cycling rate [27]. This clearly indicates a change in the dynamics of the cycling process and probably a switch from an equilibrium to a non-equilibrium process. The reason for this phenomenon lies in the formation of solid solution at the interphase layer, which is at least partly due to the switch from the two-state mechanism to the solid solution mechanism of the cycling process.

To investigate the dynamic nature mentioned above, we carried out an inhouse study using the same SMS technique. We were able to detect the metastable state for the maximum charged state by pausing the cycle at the end of the charging process for quite a long time and measuring spectra every minute. As expected, the relaxation (the decay of the metastable state) mainly affects the value of the quadrupole shift 0.74–0.69 mm/s of the main $Fe^{3+}$ component (Fig. 1 a). Based on the exponential dependence of the quadrupole shift on time, the lifetime of the metastable states can be estimated to be ~140 min. Due to the small (≤0.05 mm/s in total) monotonic change of the hyperfine parameter it is much easier to detect it by fast *opera*do measurements. Such changes are small even by the standards of the Mössbauer spectroscopy, and standard deviations of the parameters could be comparable to them. However, in this case we are not interested in absolute values, but only in differences, which have significantly higher accuracy. The estimated standard deviation of the quadrupole shift from the fitting procedure is about 0.002 mm/s (the absolute value definitely has a larger deviation). Furthermore, the results are based not only on the start and end points, but also on the number of points with a visible downward trend. Thus, we consider the fitting result to be unambiguously reliable. To dispel any doubt, the change in the spectra can be seen even without any fitting (see Fig. 1 b).

This change could not be explained by the self-discharge process, since previous results have shown that such a difference in the quadrupole shift corresponds to the charging/discharging for more than 20 % of its capacity. Moreover, the opposite effect is expected to occur during the dissolution (to a fully delithiated and lithiated phases) of the solid solution driven by lithium diffusion only. This is because the highest value of the quadrupole shift was observed for $FePO_4$ (see Ref. [27]), so the formation of such phases should increase the quadrupole shift of the

subspectral corresponding to $Fe^{3+}$ ions.

The relaxation behaviour is not related to macroscopic redistribution of lithium ions between particles of different charge levels, which could theoretically occur due to particle size distribution or polarization of the electrode. Since, there is no change in the $Fe^{3+}/Fe^{2+}$ ratio during relaxation, which also rules out the idea of lithium migration from the second nearest environment of Fe ions to Mn ions (or vice versa) during relaxation. Moreover, the relaxation occurs also at the voltage plateau (see below), when the surfaces of each particle are at the same potential and contain only the $FePO_4$ phase.

## 3.2. Results of NFS measurements

It was necessary to check if faster relaxation effects occur in other charge/discharge states. Thus, to investigate metastable states in more detail, we used the NFS technique. NFS allows us to measure spectra faster (1 min is sufficient for the studied case). A typical NFS spectra and their evolution during the discharge process is shown in Fig. 2. NFS spectra are more complicated and have an uncertainty in the fit. However, these uncertainties can be resolved by results obtained with the SMS technique (inhouse research described above), which clearly show that the only parameter that changes significantly during the observed relaxation is the quadrupole shift of the main $Fe^{3+}$ component. Thus, first the spectra were summed and fitted to find the average values of each hyperfine parameter for all subspectra at the specific charge stage of the battery. Then, each parameter except the quadrupole shift of the main $Fe^{3+}$ component was fixed and the spectra were fitted individually.<fnref n="1" /> In order to detect metastable states, the cycling process was paused at several charge/discharge stages. During these pauses we observed (except for one case, see below) either no pronounced relaxation effect (Fig. 3 b) or relaxation with some decrease of the $Fe^{3+}$ quadrupole shift (by 0.01 – 0.04 mm/s) (Fig. 3 a) during the pause (about half an hour).

Worse still, the relaxation is strongly dependent on the ratio between the iron and manganese concentrations in the cathode material. The same concentrations of these two metals seem to be the most favorable to observe relaxation. In the case of pure $LiFePO_4$, the relaxation was only observed close to the maximum discharge state, for $LiFe_{0.8}Mn_{0.2}PO_4$ it also appears at the partially charge state, finally for $LiFe_{0.5}Mn_{0.5}PO_4$ it also could be observed at the partially discharge

<footnote n="1">¹ There have been several attempts of fitting with varying other parameters (effective thicknesses and widths) but they all give similar results with no pronounced dependence on time. Varying too many parameters leads to uncertainties as it was mentioned above and the dependencies become chaotic and have no physical meaning.</footnote>
<figure><img src="image_6.png" /><figcaption>Fig. 3. (a, b, c) Three different cases of the quadrupole shift evolution with time during the pause. Tendency type (decreasing (a), stable (b), increasing (c)) depends on when specifically, the cycle process was paused and on Mn concentration. Squares - first and last measurements during the pause. Red triangles - measurements before and after pause (presented for comparison of changes). Blue circles - measurements during the pause. Yellow line – exponential fit. (d, e, f) Spectra at the start of the pause (orange) with the fit (red). The spectra at the end of the pause (purple) with the fit (blue). The difference between the two spectra (black) and the difference between their fits (lime). (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)</figcaption></figure>

state. Further increase of the Mn concentration causes the relaxation to disappear. The lifetime of the metastable states with pronounced decay was estimated to be about 10–25 min. If the relaxation is not pronounced it means that the decay is too slow and the quadrupole shift has a linear trend with a very small change (~0.01 mm/s) or no change at all. All maximum charged cases have long lifetimes not on a scale of several minutes as it was shown using the SMS.

The short lifetime of metastable states makes this study impossible without fast *operando* measurements. The obtained results provide a new insight into the dynamics of the cycling process. Moreover, they do not

contradict previous studies on similar materials [18–20].

The nature of the relaxation process is one of the most interesting questions arising from the results of this study. Most probably, the reason for the relaxation behavior is the formation of solid solutions and local inhomogeneity of manganese ions. Due to the low solubility of the $LiFePO_4$ and $FePO_4$ phases [35] in terms of thermodynamics, the existence of the solid solutions $Li(Fe,Mn)PO_4/(Fe,Mn)PO_4$ with comparable concentrations is unfavorable, leading to instability of such a system. This is the reason why in the partially charged state the migration of manganese ions from $(Fe,Mn)PO_4$ to $Li(Fe,Mn)PO_4$ is possible along
<figure><img src="image_7.png" /><figcaption>**Fig. 4.** NIS spectra (a, b) of initial (a, c) and maximum charged (b, d) samples $Li_xFe_{0.8}Mn_{0.2}PO_4$ and the corresponding, derived pDOS (c, d). The red single line is the instrumental function was measured independently using the standard sample. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)</figcaption></figure>

with counter-diffusion of iron ions. Such migration inevitably leads to the formation of small “islands” of divalent ions. Lithium ions should migrate together with divalent ions to maintain charge neutrality. Of course, the diffusion of divalent and trivalent metal ions is much slower but it can be detected due to the small size of particles and clusters. Relaxation does not affect the momentum kinetics of the cycling process which depends more on the much faster diffusion of lithium ions. This is why we were only able to detect it clearly during the pauses by change in the quadrupole shift of the Mössbauer subspectrum. This hypothesis fits perfectly with the fact that the relaxation is more pronounced for compounds with the same concentration of Mn and Fe ions and is in agreement with previous results, which show the inhomogeneity of Mn distribution [18].

After the pause in the cycling process, the redistribution of divalent ions together with lithium ions takes place in the interphase, which supposed to occupy a relatively large area due to the high cycling rate. Despite the small particle size, Mn ions could not reach the center of the particle in a short time, but they form clusters (“islands”), which are supposed to merge later. However, the merge process appears to be so slow that even after a few weeks the interphase boundary is still long and contains a lot of iron ions [18]. The disproportionality of the two phases and the differences in the local environment of the iron ions in these phases lead to significant distortion and asymmetry of the local states of $Fe^{3+}$ ions located at the boundary of the “islands” as well as at the phase boundary. Instability and significant distortion lead to changes in the quadrupole shift observed during relaxation. Worse still, in the case of the maximum charged state, when the concentration of divalent ions becomes smallest, the lifetime of the metastable state increases dramatically due to the size of the divalent “islands” becoming too small, i.e. longer diffusion paths. In maximum discharge state the situation is mirrored and the behavior of the system remains the same.

In undoped samples the relaxation proceeds much faster, because it

is only limited by lithium diffusion. The only relaxation process observed has a lifetime of ~6 min and is smaller than for doped material. This is why the relaxation could only be observed closer to the final states when the diffusion path is the longest. There could be no “islands” but only a solid solution layer formed during cycling. Its thickness increases as the layer gets closer to the particle core at the final charge states. Of course, one could even assume that “islands” could exist in undoped material due to structural defects of various kinds, but this seems unlikely.

Thereby, manganese ions can be slowly redistributed, which means that the Mn distribution changes dynamically during cycling (as well as during pauses). This should be taken into account in any model describing charge-discharge processes. Moreover, the relaxation was not only observed for the first charge, thus, another redistribution of manganese ions could take place during discharge. Such an “opposite” relaxation (with an increase in the quadrupole shift) was observed for the slightly discharged sample $Li_xFe_{0.5}Mn_{0.5}PO_4$ (see Fig. 3 c). This relaxation is much faster – the lifetime is ~5 min. Note, that further discharge leads to relaxation, again with a decreasing tendency of the quadrupole shift, meaning that the relaxation behavior depends on both the process type and the specific state. The redistribution of manganese ions during the cycling could be the reason for the asymmetry of the hyperfine parameter dependencies during charge and discharge processes [27], since these two processes actually occur in the same particles, but with a different distribution of Mn inside them.

Unfortunately, it is difficult to accurately estimate the size of the “islands” mentioned above and the distances between them. It can be assumed that the typical size should be at least 5–10 times smaller than the particle size of the cathode material, i.e. 5-10 nm (the length of the diffusion path is half of it). Another indirect evidence of such size (less than 10 nm) is the observation of the relaxation-type subspectrum corresponding to $Fe^{2+}$ ions in the interface [18]. The distance between the
“islands” should be of the same order as their size. Knowing, that the average life-time is about 15 min, the diffusion coefficient of iron and manganese ions could be estimated to be $\lesssim 3 \cdot 10^{-20} \text{ m}^2/\text{s}$, which is a reasonable value for solid solutions.

### 3.3. Results of NIS measurements

The NIS measurements were started ~30 min after the pause in cycling and the collection time varied from 1 to 4 h. Due to the long collection time for NIS spectra, we could not investigate metastable states.<fnref n="2" /> Fig. 4 shows the typical spectra (Fig. 4 a, b) and the derived partial density of states (pDOS, Fig. 4 c, d). The peaks of pDOS correspond to optical and acoustic modes of iron with its environment. The modes can give insights into vibrations of Fe and therefore, bond properties between iron ions and bonding elements. However, especially at low energies optic and acoustic modes are hardly distinguishable and therefore cannot be unambiguously assigned to a specific bond. Comparing the pDOS for Mn doped phases with the pure $LiFePO_4$-phase at the initial charge state, no significant differences are observed. However, the charging process changes pDOS dramatically (Fig. 4 c, d). The most striking difference is the peak at ~42 meV in the maximum charge state. This peak most likely corresponds to an optical mode from $Fe^{3+}$, which appears during the charging process. This behavior is in good agreement with calculations [36].

It is almost impossible to fit each individual peak of pDOS as at low energies there are a lot of peaks overlapping with each other. However, one can apply binning and smoothing to the data (Fig. 5), which provides a guideline to compare pDOS of different charge/discharge states more easily. Thus, it becomes clear, that the pDOS for Mn-doped material in the partially dis-/charged state does not plot between the pDOS for initial and maximum charged states (Fig. 5 b, c). From a structural point of view this indicates, that the intermediate state is not a sum of the extreme cases, suggesting that a slight change in the structure should take place during the cycling. At around 42 meV the peak shifts during charging, which indicates a hardening of a specific Fe-bond (with i.e. O, P). While for undoped $Li_xFePO_4$ the intermediate state plots in between the two extreme cases and the peak shift is not seen (Fig. 5 a), meaning that it is their proportional sum. This is in agreement with the fact, mentioned before, that the Mn incorporation leads to the formation of a solid solution during cycling. Moreover, it allows us to conclude that the fast relaxation mentioned above proceeds from one solid solution state to another, while further dissolution into two separate phases seems to require much more time.

Fig. 6 demonstrates the dependencies of the Lamb-Mossbauer factor on the $Fe^{3+}$ fraction (the fractions were determined from the corresponding NFS spectra). The most interesting result in our case is the decreasing tendency of $f_{LM}$ with increasing Mn concentration, which means, that the averaged rigidity of the Fe-bonds decreases. Moreover, $f_{LM}$ values can be used for corrections in the determination of the $Fe^{3+}$ and $Fe^{2+}$ concentration in these materials from Mössbauer spectroscopy. It may be useful for further studies to compare different samples at the same cycling stage. We should mention that the $f_{LM}$ dependency (Fig. 6) is linear, because this parameter depends mainly on the low-energy part of the pDOS, which is driven by acoustic modes. This is why a significant change occurs with the $Fe^{2+} \leftrightarrow Fe^{3+}$ transition and only the mean value changes with the Mn concentration.

<figure><img src="image_8.png" /><figcaption>Fig. 5. Derived pDOS (points) and smoothed pDOS (lines) for different charge/discharge states of $Li_xFePO_4$ (a), $Li_xFe_{0.8}Mn_{0.2}PO_4$ (b), $Li_xFe_{0.3}Mn_{0.7}PO_4$ (c). Black dash circles indicate features referenced in text. Fraction of $Fe^{3+}/Fe$ was found from the fitting of corresponding NFS spectra.</figcaption></figure>

### 4. Conclusions

As shown by the results of the NIS measurements, doping with divalent Mn ions promotes the formation of solid solution in the phase

<footnote n="2">² For further experiments in the future the collection time could be reduced due to the higher flux at the ESRF in the 16-bunch mode (measurements were done at 30 mA in the storage ring, currently it is already 70 mA, and soon it will become 90 mA). It is also possible to use 100 % ⁵⁷Fe enriched samples if NIS will be the main technique of the study.</footnote>
<figure><img src="image_9.png" /><figcaption>**Fig. 6.** $f_{LM}$ values extracted from pDOS. Dashed lines represent linear approximations. Purple - $Li_xFePO_4$, blue - $Li_xFe_{0.8}Mn_{0.2}PO_4$, orange - $Li_xFe_{0.5}Mn_{0.5}PO_4$, red - $Li_xFe_{0.3}Mn_{0.7}PO_4$. Triangles – measured before cycling (initial samples), circles – measured after pause during charging process, squares – measured after pause during discharging process. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)</figcaption></figure>

boundary between $Li(Fe,Mn)PO_4$ and $(Fe,Mn)PO_4$. This solid solution can exist for at least a few hours after the pause in cycling. However, NFS reveals the initially formed solid solution during the cycling to be metastable, with a lifetime in the scale of minutes. Decay of the metastable phase takes place due to the ordering of the structure by slow migration of $Mn^{2+}$ and $Li^+$ into clusters ("islands") of $Li(Fe,Mn)PO_4$ together with counter diffusion of $Fe^{3+}$ ions into $(Fe,Mn)PO_4$, forming "matrix" around the clusters. Due to the formation of multiple clusters, the diffusion path is short enough to make the relaxation process relatively fast. However, further diffusion of polyvalent ions from the clusters is extremely slow. Doping has a positive effect on the cycling process and therefore, a redistribution of the dopant ions within the particles should directly affect the cycling process. In particular, there are stages of the cycling process, when long holding leads to a Mn clustering, which should have a certain effect on further cycling. Such relaxation and redistribution of dopant ions within the structure of cathode material plays an important role in the cycling mechanisms and could be one of the main reasons for the asymmetry of the charge and discharge processes in doped materials.

Considering these conclusions, we propose future research with different dopants, as the lifetime of metastable states should depend on the mobility of the dopant ions. Thus, varying the dopant type one should be able to suppress or accelerate the formation and decay of metastable states for a battery cycling optimization. Moreover, detailed studies of the effect of the cycling rate on metastable states, as well as the effect of the relaxation processes on cycling in the long term are required.

## CRediT authorship contribution statement

**Sergey Yaroslavtsev:** Writing – review & editing, Writing – original draft, Validation, Methodology, Investigation, Data curation, Conceptualization. **Susanne C. Müller:** Writing – review & editing, Validation, Investigation, Data curation, Conceptualization.

## Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence

the work reported in this paper.

## Data availability

Data will be made available on request.

## Acknowledgements

Authors acknowledge the European Synchrotron Radiation Facility (ESRF) for provision of synchrotron radiation facilities under proposal number MA-5363 at nuclear resonance beamline ID18 (moved to ID14 since September 2023).

The authors thank I. Stenina and T. Kulova for providing high quality cathode materials for this experiment and A. Yaroslavtsev for discussing the experimental results.

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