Atomic scale determination of cation inversion in spinel-based oxide nanoparticles.

The atomic structure of nanoparticles can be easily determined by transmission electron microscopy. However, obtaining atomic resolution chemical information about the individual atomic columns is a rather challenging endeavor. Here, crystalline monodispersed spinel Fe 3 O 4 /Mn 3 O 4 core/shell nanoparticles have been thoroughly characterized in a high-resolution scanning transmission electron microscope (STEM). Electron Energy-Loss Spectroscopy (EELS) measurements performed with atomic resolution allow direct mapping of the Mn 2+ /Mn 3+ ions in the shell and the Fe 2+ /Fe 3+ in the core structure. This enables a precise understanding of the core/shell interface and of the cation distribution in the crystalline lattice of the nanoparticles. Considering how the different oxidation states of resolution. X-ray absorption measurements on the whole sample confirm the presence of cation inversion. These results present a significant advance towards a better correlation of the structural and functional properties of nanostructured spinel oxides.


Introduction
Nanoparticles are gaining increased interest owing to their numerous applications in widespread fields [1][2][3][4] . Spinel oxides have been frequently used in nanoparticle synthesis due to the appealing fundamental properties linked to their unique structure, with uses ranging from everyday materials, like ceramics, to advanced applications in biotechnology [5][6][7][8][9] . In fact, given the structural similarities, spinel materials are particularly suited to grow core/shell structures with enhanced multifunctional properties [10][11][12][13][14][15][16][17] . inverse spinel, while x is equal to 2 ⁄3 for a completely random cation distribution 18 . Although, the different spinel materials are normally classified in specific spinel categories (e.g., FeAl2O4 is a normal spinel), depending on different factors such as the synthesis approach (e.g., thermal decomposition, sol-gel), processing methods (e.g., quenching, ball-milling), morphology (e.g., thin films, nanoparticles) or size, a cation inversion different from the nominal one can take place, leading to a change in the inversion parameter with respect to bulk materials. Interestingly, the degree of inversion has been shown to play an important role in the functional properties (e.g., electronic, transport, optical, magnetic, mechanical or structural) of spinel materials [19][20][21][22][23][24][25][26][27] . However, despite its relevance, the inversion parameter is seldom studied in detail, particularly in nanostructured materials. Several techniques exist that can assess the coordination of chemical species in a crystal, such as x-ray and neutron diffraction refinement, Mössbauer spectroscopy, x-ray absorption or nuclear magnetic resonance [28][29][30][31] . In general, these techniques yield averaged information, typically from rather large volumes. Nonetheless, when dealing with complex systems such as core/shell nanoparticles, a few unit cells can determine the resulting overall properties of the system, often making classical bulk approaches unsuitable. In fact, the atomic scale determination of the inversion parameter has never been reported. Therefore, it is clear that novel approaches are required to selectively characterize the different ions in nanoparticles with high spatial resolution.
In this framework, aberration-corrected transmission electron microscopy (TEM) is an extremely useful technique to probe materials at the atomic scale. Moreover, when coupled to electron energy-loss spectroscopy (EELS), the oxidation state of chemical species [23][24][25][26][27] and their distribution in a crystalline lattice can be mapped 32,33 .
Here we report on the atomic resolution study of the oxidation state and the cation inversion

Synthesis
The Fe3O4/Mn3O4 core/shell nanoparticles were synthesized using a seed-growth approach. Fe3O4 nanoparticles were previously synthesized and used as seeds for the subsequent growth of the Mn3O4 shells 11,32 .
The Fe3O4 seeds were synthesized by thermal decomposition of iron(III) oleate in 1-octadecene in the presence of oleic acid. 1.82 g (2mmol) iron(III) oleate and 0.1 g (0.4 mmol) oleic acid were dissolved in 20 mL of 1-octadecene. The reaction mixture was heated up to 320 ºC with a heating rate of 3 ºC/min under argon flow and kept at this temperature for 30 min. The reaction mixture was then cooled down to room temperature. The purification process subsequently involves several centrifugation cycles with a mixture of hexane and ethanol. Finally, the particles were dispersed in hexane. The subsequent growth of a Mn3O4 layer onto the Fe3O4 seeds was performed by dispersing 200 mg of Fe3O4 nanoparticles and 0.1 g (0.4 mmol) of oleic acid in 40 mL of dibenzyl ether, degassed under several cycles of vacuum/argon to remove any hexane traces. Then, the suspension was heated up to 220 ºC under an argon flow. At this moment, a solution of 0.2 g (0.6 mmol) of manganese(II) acetylacetonate, 0.2 g (2 mmol) of 1,2-hexadecanediol and 0.8 g (3 mmol) of oleylamine, previously heated up to 100 ºC, was injected at fast rate. The reaction mixture was kept at 220 ºC for 60 min and then cooled down to room temperature. The core/shell nanoparticles were purified several times by magnetic separation after mixing with hexane and acetone.

TEM characterization
For the TEM observation the samples were dispersed in hexane and, after 30 min sonication, were deposited on a holey-carbon coated copper grid.
Scanning TEM high angle annular dark field images (STEM-HAADF) and EELS spectrum images were acquired in an aberration-corrected Nion UltraSTEM200 TEM equipped with a cold field emission gun and a Gatan Enfina high-resolution EELS spectrometer. The experiments were performed at 100kV. The convergence and collection angles for spectroscopy were 35 and 80 mrad respectively. The beam current was between 40-60 pA for all spectrum images.
EELS analysis was performed in python using the open-source EELS analysis suite Hyperspy 34,35 and the Gatan Digital Micrograph software.

X-ray Absorption Spectroscopy
The room temperature x-ray absorption spectra at the Fe and Mn L2,3-edges were acquired in total electron yield mode at the BM-26 beamline (BOREAS) of the ALBA-CELLS synchrotron. The spectra were fitted using the CTM4XAS program 36 . Figure 1A-B) show rounded monodisperse particles exhibiting a 14.7 nm average size and a standard deviation of 1.2 nm ( Figure 1C). EEL-Spectrum Imaging at high resolution for the region in figure 1D reveals the core/shell nature of the nanoparticles. Oxygen, iron and manganese quantification maps ( Figures 1E-G), demonstrate that the nanoparticles are composed of iron oxide cores surrounded by irregular manganese oxide shells with a 1-2 nm thickness ( Figure 1H). From measurements in the elemental quantification maps of several nanoparticles, the core/shell interface was found to extend 0.31 ± 0.05 nm ( Figure S1), which can be considered as atomically sharp. The observed oxygen relative composition 37 is around 58% ( Figure S2), which is only compatible with a magnetite (Fe3O4) core. In concordance with these measurements, hausmannite (Mn3O4) is the most likely phase of the manganese oxide shell. This was further studied by analyzing the fine structure of the Mn L2,3-edge. An EELS spectrum acquired over several nanoparticles was analyzed using our open source code OxideWizard and also compared to reference data, 38,39 demonstrating that the shell is indeed hausmannite ( Figure S3-4).

STEM-HAADF images (
The detailed structural analysis from atomic resolution STEM-HAADF images shows that the manganese oxide shell is a tetragonal spinel phase 40 while the iron oxide core is a cubic spinel phase 41 ( Figure S5).  42 . This crystallographic adaptation of the crystals has an associated mismatch of 3.3% (see SI), which probably leads to some of the planar crystal defects observed in Figure S8. EELS L2,3-edge intensity maps (Figure 2) of the nanoparticle oriented along a high symmetry zone axis (survey image at low magnification in figure S9) further confirm the spinel structure of both the magnetite core and the hausmannite shell. Figure Figure 2C) and the core ( Figure 2D), respectively. From these images it was possible to understand the core/shell interface at the atomic level, schematically shown in Figures 2E,F. However, to gain further insight into the intimate configuration of these nanoparticles, the location of 2+ and 3+ species of each element in the different oxygen coordination sites must be unveiled.  One possible way to obtain an oxidation state mapping is through the analysis of the energyloss near edge structures (ELNES) related to a given element 39,[43][44][45] . Potentially, these ELNES features allow the determination of divalent/trivalent cation lattice distribution from spectrum images acquired at sufficient energy and spatial resolution. In many transition metals the ELNES display two sharp peaks (L3 and L2), often referred to as white lines, where the associated ELNES parameters are the onset of the peaks, their relative position or their relative intensity. In the particular case of manganese, the determination of the oxidation state is carried out by using the Mn L3/Mn L2 intensity ratio and the onset of the Mn L3 peak 38,44,46 . On the other hand, for iron, the onset of the Fe L3-edge has been reported to shift to higher energies as its oxidation state increases from Fe 2+ to Fe 3+ 45,47-49 .
Interestingly, these ELNES features allow the calculation of the cation inversion, provided that spectra from individual atomic columns can be obtained. In particular, the following expression, valid for most transition metal spinel oxides, can be used to calculate the cation inversion parameter: where S is the measured L3 shift between two atomic columns and Sref and C are parameters related to the particular element that is being considered and the zone axis in which the crystal lattice is measured (the details of the derivation are provided in the Supplementary Information).
This approach was pursued with the spectrum image shown in Figure 3. Figure 3A shows an atomic resolution STEM-HAADF image. The particle is oriented along a low symmetry zone axis: [541] (the plane indexation of the image can be found in Figure S10). An atomic resolution EELS spectrum image was acquired from the highlighted region of panel A, which shows the expected (111) planes in this zone axis ( Figure 3B). Notably, the (111) planes of magnetite (labeled with numbers in the image) contain iron atoms only in octahedral coordination (12 per unit cell). On the other hand, between these planes, in the regions with darker contrast in Figure 3B, iron atoms are distributed in both octahedral and tetrahedral coordination (8 Th and 4 Oh positions per unit cell; Figure 3C). The bright planes have been labeled with a number (i), in figure 3B-C while the darker planes will be referred as i'.
A spectrum image was acquired from the region displayed in figure 3B. To improve the signal to noise ratio, and given the symmetry in the image, spectra were added along the vertical direction to obtain a spectrum line (displayed in figure 3D), where the horizonal axis is the same as in figure 3B and the vertical one corresponds to the energy loss. As an example, the spectra corresponding to positions 5(5´) (highlighted in blue(orange) in Figure 3D) are plotted in Figure 3E. The onset of the Fe L3 edge was calculated as the energy at which half the intensity of the peak was attained. The variation of the Fe L3 onset along the direction [111] is plotted in Figure 3F (blue line). A shift is observed between adjacent i-i' of planes, as can be observed in the example of Figure 3E, which demonstrates an uneven distribution of iron ions with different oxidation states. This Fe L3 shift between the two types of planes was calculated to be of 0.3 eV on average (see S11). From this measurement, expression (1) can be applied to calculate the cation inversion parameter of the magnetite core in the nanoparticle. After taking Sref = 1.7 eV from 47 and C = -3/2 from the analyzed planes, the inversion parameter of the iron oxide core was found to be x = 0.84 ± 0.02, where the error was estimated from the standard deviation of the Fe L3 shifts.
A similar approach was used to calculate the inversion parameter of the hausmannite shell. Figure 4A shows an enlarged view of the Mn3O4 shell of the same nanoparticle as in Figure 2.
The comparison with the atomistic model ( Figure 4B) demonstrates that, in this orientation, the observed atomic columns contain exclusively either ions in tetrahedral coordination (orange) or in octahedral coordination (green). The Mn L 3 onset was mapped, as shown in Figure 5A, where regions with low Mn signal (the Fe3O4 core and vacuum) have been masked. A histogram of the Mn L3 energy onset in pixels corresponding to columns of tetrahedral and octahedral coordination is shown in Figure 5B. The tetrahedral/octahedral column positions where manually chosen from the correlated HAADF image.  The centers of the distribution of the Mn L3 energy onsets are shifted 0.65 eV between octahedral and tetrahedral Mn coordination. From this measurement, the cation inversion parameter was calculated to be x = 0.39 ± 0.10, using C = 1 for the treated zone axis and atomic columns and Sref = 1.6. 46 The cation inversion uncertainty has been estimated from the width of the EELS energy onsets distributions of Figure 5B. It should be noted that the uncertainty in this measurement is much larger than for the one corresponding to magnetite.
An alternative way to unravel the contribution of the different cations in each crystallographic site can be considered. Multivariate analysis (MVA) and spectral decomposition techniques have been used in the past to obtain maps related to the density of a specific ion 34,50,51 . If such maps are obtained at atomic resolution, for a spinel crystal the cation inversion can be estimated simply as the fraction of signal from the 3+ ion at the tetrahedral coordination positions: Principal component analysis (PCA) was applied to the spectrum image shown in Figure 2 for the energy range corresponding to the Mn L3,2-edge. The results revealed that 3 components were enough to describe the whole dataset ( Figure S12). Then, a 3-component spectral decomposition was performed through Non-negative Matrix Factorization (NMF) 52 , yielding the components depicted in Figure 6A. The component C0 has no relevant spectral features, and is considered a background, basically related to the thickness at each point of the image. On the other hand components C1 and C2 show Mn L-edges with very distinct features. In particular, the L3/L2 intensity ratio is much higher for C1 than for C2 and the L3 peak is at lower energies for C1 than for C2. By further comparison with reference spectra 44,46,49 it is possible to assign C1 to be proportional to the Mn 2+ ion density and C2 to the Mn 3+ ion density. The score maps for the three individual components are shown in Figure S13. In Figure 6B, the score maps of C1 (orange color scale) and C2 (green color scale) are combined, highlighting the Mn 2+ and Mn 3+ sublattices. The maps have an excellent correspondence with the different oxygen coordination sites, similarly to previously atomic resolution EELS maps obtained through multilinear least square fitting in hausmanite 33 , with the map of C1 and C2 having higher intensity in the Th and the Oh sites, respectively ( Figure 6B). Once the maps proportional to the Mn 2+ (C1) and Mn 3+ (C2) are obtained, they must be normalized so that Equation 2 can be reliably used. In this case, each map was divided by the integrated signal of their corresponding spectrum. The resulting information is plotted in Figure 7. Figure 7A shows an image of the manganese oxidation state, calculated by the weighted average of 2+ and 3+ ions  Interestingly, the measurements shown in Figure 7 allow the observation of an "inversion gradient" from the core/shell interface to the surface of the particle. The spatial variation can be better observed if the inversion parameter for the tetrahedral atomic columns is averaged for each (002)Mn3O4 plane ( Figure 7C). It can be clearly observed that x is smaller closer to the interface than at the surface of the nanoparticle.
Remarkably, x-ray absorption experiments (a well-stablished method to asses cation coordination inversion 53 Figure S14a and  Figure S14b and Table  S2). The small differences in cation inversion between the two techniques probably stem from the statistical average character of the x-ray absorption and to a certain extent from the somewhat non-univocal nature of the x-ray absorption fits.

Discussion
In this work two main objectives have been pursued: (i) the thorough characterization of Fe3O4/Mn3O4 core/shell nanoparticles at the atomic scale has been achieved, and (ii) two different methods to calculate the cation inversion parameter of spinel crystals with unprecedented spatial resolution have been demonstrated. These methods will be referred to as the "ELNES" approach, associated with Equation (1) and demonstrated in Figures 3 and 5, and the "MVA" approach, associated with Equation (2) with the corresponding results shown in Figures 6-7.
The iron oxide cores have been found to be Fe3O4, i.e., nominally, an inverse spinel with x = 1. However, the cation inversion parameter of the iron oxide core was found to be x = 0.84 ± 0.02 through the ELNES analysis approach. Although this value is smaller than that expected for Fe3O4, this is not overly surprising, since magnetite nanoparticles, prepared by different methods, with inversion parameters lower than 1 have already been reported 56,57 . This cation inversion can stem from different factors such as structural defects, surface effects or iron vacancies in the lattice.
The cation inversion for the hausmannite shell has been evaluated to be x = 0.39 ± 0.10 following the ELNES analysis approach. However, the rather broad distribution of the Mn L3 energy onset leads to a high uncertainty in the value of the cation inversion parameter (Δx = 0.10). Actually, the MVA approach, depicted in Figures 7, evidenced that this uncertainty is related to a spatial variation of the cation inversion rather than an intrinsic lack of precision of the method. This illustrates a possible drawback of the ELNES approach. Namely, the inversion is measured relative to, at least, two different atomic columns and, therefore, it is not possible to determine the x values with a higher resolution than the distance between the two columns. Moreover, the two different atomic columns used to calculate S are unavoidably chosen arbitrarily in this approach. Additionally, the evaluation of the inversion through Equation (1) requires a reference value (Sref) for the energy shift of an edge related to the oxidation state of a given element. Nonetheless, reference spectra are available for most elements that can be found in a spinel lattice. Finally, the assumption of a linear dependence between onset shift and oxidation state may not always hold, although Equation (1) may be adapted to higher order dependences.
Remarkably, all of these issues are avoided with the spectral decomposition ("MVA") approach. As shown in figures 7, cation inversion measurements with true atomic resolution can be achieved through Equation (2) with the only limitation being the ability to obtain a sufficiently good spectral decomposition. The average x value obtained by this approach is consistent with the one from the ELNES approach. However, it is worth emphasizing that the MVA approach has allowed the unprecedented observation of an atomic resolution spatial variation in the cation inversion in the hausmannite shell ( Figure 7C).
Although the origin of this spatial variation is not clear at present, it may lie in the fact that the hausmannite is actually stressed, as it grows epitaxially onto the magnetite as shown in Figures  S5-7. In fact, cation inversion can act as an accommodation mechanism. As for the inversion drop at the surface of the nanoparticle, surface reordering of the free bonds does surely affect the electronic environment of the lattice and may also play a role in how the Mn 2+ /Mn 3+ populations are distributed. Similarly, the vacancy distribution (which could affect x) in the Mn3O4 may be different at the interface than at the surface.

Conclusions
Precise determination of the oxidation state of iron and manganese in an Fe3O4/Mn3O4 core/shell nanoparticle has been performed. The analysis of the oxidation states, using either by ELNES or MVA approaches, has enabled the first determination of the cation inversion at atomic column resolution from a spinel oxide. The obtained mean cation inversion value for the magnetite core is x = 0.84, whilst for hausmannite it is x = 0.39 (confirmed by x-ray absorption measurements in the whole sample). The analysis also reveals that while the cation inversion in the Fe3O4 core is spatially uniform, in the Mn3O4 shell it exhibits a decrease in inversion close to the core/shell interface. These novel approaches set the stage for further exploration of oxide nanosystems through EELS at a very high resolution, which should lead to an improved control of the physiochemical properties of these materials. Figure S1. Fe L2,3 and Mn L2,3 edge integrated signals along core/shell interfaces of different nanoparticles. The interface limits were taken where Fe signal drops between 75% and 25% of the mean core signal. Figure S2. Oxygen relative composition from the spectrum image in Figure 1D-H, calculated through the Egerton quantification method 1 .   The FFT from the center of the core/shell nanoparticle, highlighted in blue in Figure S5B, where the manganese signal is very low, matches excellently the Fe3O4 spinel crystal lattice 4 , in agreement with the EELS characterization ( Figure S5A). In particular, Figure S5E  The FFT calculated from the shell region (in red in Figure S5B) corresponds to the [100] zone axis of the Mn3O4 Hausmanite phase 5 ( Figure S5D). The 2.9 Å planes in figure S5D correspond to the (020)Mn3O4 and the 2. The variations in lattice spacings of the crystal can be clearly visualized with Geometric Phase Analysis (GPA) ( Figure S6). GPA is able to obtain maps of distortions in a crystal lattice with respect to a reference region. In this case, the reference region was chosen in the Fe3O4 core. Figure S6 shows GPA strain maps of the nanoparticle seen in the HAADF image of Figure S5B. The Exx image shows the strain along the in-plane direction (named X in the axis). The image Eyy reveals the strain along the out-of-plane direction (named Y in the axis). The map of strain in the X direction is essentially flat with only a planar defect showing up in the form a bright line in the map. This demonstrates that the manganese oxide lattice grows adapted to the magnetite core. To probe that the lattice expansion along Y was solely in the manganese shell region, a superposition of the strain map and HAADF image is provided in Figure S7.

5.936Å
= 3.3%. This, together with the fact that hausmanite has a tetragonal space group, should induce strong stresses and frustration in the shell when growing onto a (cubic space group) magnetite core. Consequently, it is no surprise to see planar defects in the nanoparticles ( Figure S8). The STEM-Bright Field (BF) image in Figure S8A shows clear twinning planes at the surface in the three highlighted positions. A GPA strain map of the crystal ( Figure S8B) highlights the three domains in which the crystal is divided. A second type of defect can be seen in Figure S8C where a stacking fault is present near the edge of the particle. The stacking fault becomes more visible in the corresponding GPA strain map ( figure  8D). These two types of defects, both of which originate at the surface of the nanoparticles, are the most common among all the acquired images.

Cation inversion parameter calculation
When performing ELNES measurements in nanostructured materials, certain experimental issues can arise. For example, nanoparticles are usually in arbitrary zone axes, and signals from different ions and unit cells can be superimposed. Moreover, it is not always easy to obtain "absolute" data for some ELNES parameters. In particular, the position of an EELS edge may be offset by a detector-dependent value or by electron beam instabilities.
We propose to handle these problems by considering the shift in the EELS peak position instead of its absolute position cancelling any spectrometer misalignment. Also, if a linear relationship between the oxidation state and the L3 peak position is assumed (reasonably for many transition metals 3 ), the following expression for the spinel coordination inversion parameter can be derived: Assuming (i) that an EELS spectrum is being acquired from a given atomic column, labeled by P, of a spinel oxide and (ii) that the energy value of a certain EELS edge (EP) is given by theaverage between the value for 2+ ions (E 2+ ) and 3+ ions (E 3+ ) weighted by the number of atoms of each type in P. If in P there are A sites of tetrahedral oxygen coordination and B sites of octahedral oxygen coordination, and the coordination inversion parameter for that crystal is x, the expression for EP is the following: From the previous expression, it is just a matter of rearranging terms to obtain the following expression for the cation inversion parameter:    Figure S14. Experimental x-ray absorption spectra at the Mn (A) and the Fe (B) L3-edge (symbols) and the corresponding simulation (gray line) obtained as a combination of the theoretical spectra of the 2+ and 3+ ions in either Td or Oh environments (red, blue, magenta and green thin lines).