Structure of Manganese Oxide Nanoparticles Extracted via Pair Distribution Functions

: The structure of nanoparticles has been di ﬃ cult to determine accurately because the traditional structure methods rely on large monocrystals. Here, we discuss the structure of nanoparticles based on real-space modeling of the pair distribution function obtained by a Fourier transformation of the high-energy X-ray scattering structure factor. In particular, we consider X-ray scattering data taken from colloidal manganese oxide nanoparticles used in Lithium-ion batteries, air-puriﬁcation, and biomedical systems, which are known to exist in various nanometer-sized polymorphs. Insight is thus obtained into characterizing the structural relaxation of the MnO 6 octahedra, which are the key building blocks of oxide nanoparticles, important in many technologies.

X-ray scattering techniques are useful for characterizing the sizes of crystals and particles as well as their crystallographic phases, which taken together control their physical properties. These techniques are generally non-destructive and measure properties averaged over an ensemble of many particles. Most crystal structures have been determined via X-ray diffraction (XRD) experiments. The scattering pattern from a crystal typically consists of several tens or even hundreds of Bragg reflections from various atomic planes in the lattice. Crystal structures can be specified in terms of just a few variables, such as the unit cell parameters and the positions of the symmetry-independent atoms.
Direct imaging techniques such as electron microscopy also provide unique opportunities for structure analysis at a more local scale and thus complement diffraction techniques [12,13]. A transmission electron microscope (TEM), for example, can provide multidimensional analysis

Experimental Details
MnO nanoparticles were obtained by adapting the protocol of Gallo et al. [38] as follows. First, a manganese (II) oleate complex was produced via an exchange chemical reaction between manganese (II) chloride and sodium oleate. A quantity of 1.24 gm of the resulting manganese (II) oleate and 10 gm of 1-hexadecene were then combined in a 50 mL round-bottom flask attached to a Schlenk line. The mixture was degassed at 80 • C for 90 min, and then the vacuum was switched to Ar atmosphere. Next, the flask was heated to 280 • C and held at this temperature for 30 min, followed by cooling to room temperature. Nanoparticles were precipitated by adding 10 mL of acetone, collected by centrifugation at 9000 rpm for 10 min, re-dispersed in hexane, washed again with acetone and collected by centrifugation. Finally, the nanoparticles were re-dispersed in toluene to obtain a 10 mg·mL −1 stock of colloidal MnO nanoparticles.
Thin Si wafer substrates measuring 1 cm × 1 cm were first cleaned using ultrasonication in acetone, ethanol, and isopropanol, and then dried by flashing compressed air. The stock dispersion of the nanoparticles in toluene was drop-casted onto a substrate, and, then, the solvent was allowed to evaporate slowly in ambient conditions. Morphology of the synthesized nanoparticles was determined by transmission electron microscopy (TEM) using a JEOL JEM 2100 working at 200 kV TEM. The average diameter of the nanoparticles was determined by measuring the diameters of 200 particles and fitting the histograms to a Gaussian distribution function. Figure 1 shows a high resolution (HR)-TEM image of the as-synthesized colloidal MnO nanoparticles. The TEM picture was taken before deposition on the silica substrate. As discussed below, the silica substrate seems to alter the crystallinity of the sample. Fast Fourier transform (FFT) images including plane-spacing calculations are shown in the Supplementary Material.

Condens. Matter 2019, 4, x FOR PEER REVIEW
3 of 10 of the nanoparticles in toluene was drop-casted onto a substrate, and, then, the solvent was allowed to evaporate slowly in ambient conditions. Morphology of the synthesized nanoparticles was determined by transmission electron microscopy (TEM) using a JEOL JEM 2100 working at 200 kV TEM. The average diameter of the nanoparticles was determined by measuring the diameters of 200 particles and fitting the histograms to a Gaussian distribution function. Figure 1 shows a high resolution (HR)-TEM image of the assynthesized colloidal MnO nanoparticles. The TEM picture was taken before deposition on the silica substrate. As discussed below, the silica substrate seems to alter the crystallinity of the sample. Fast Fourier transform (FFT) images including plane-spacing calculations are shown in the Supplementary Material. HE-XRD measurements with a photon wavelength of 0.21 Å were performed at beamline BL04B2 at the Japanese synchrotron facility SPring-8. An ionization chamber was used for monitoring the intensity of the incident X-rays. Three CdTe detectors were used to measure the intensity of the scattered X-rays. The small-angle scattering part of the signal was measured with a two-axis diffractometer to cover the low-Q region (0.1 Å -1 ). A vacuum chamber at HE-XRD setup was used to suppress air scattering around the sample. The HE-XRD setup at this beamline is described in more detail elsewhere [39]. Although radiation damage to individual nanoparticles should be reduced as much as possible, nanoparticles on a metallic substrate can be healed through a healing mechanism that involves a neutralization process [40].
Experimental I(Q) data were obtained for MnO nanoparticles of approximately 10 nm size. Background intensity was determined by carrying out a measurement on a bare substrate. The proper subtraction of the background is important for capturing the diffuse scattering signal in the data properly. Figure 2 shows the experimental I(Q) results for the MnO film sample. Only one Braggtype peak, centered at 3.3 Å -1 , is seen. Other peaks are an order of magnitude weaker and represent diffuse scattering. It is likely that the diffraction peaks of the MnO film are too weak to be observed due to the strong and sharp diffraction peaks of the silicon substrate, as has been reported previously for MnOx on stainless steel [6]. TEM analysis provides grain size information. The particle size obtained via TEM is usually larger than the crystallite size given by XRD. This is to be expected since a particle typically consists of several crystallites. Information on crystallite size can be obtained by analyzing X-ray diffraction peaks where the peak width is inversely proportional to crystallite size, HE-XRD measurements with a photon wavelength of 0.21 Å were performed at beamline BL04B2 at the Japanese synchrotron facility SPring-8. An ionization chamber was used for monitoring the intensity of the incident X-rays. Three CdTe detectors were used to measure the intensity of the scattered X-rays. The small-angle scattering part of the signal was measured with a two-axis diffractometer to cover the low-Q region (≈0.1 Å −1 ). A vacuum chamber at HE-XRD setup was used to suppress air scattering around the sample. The HE-XRD setup at this beamline is described in more detail elsewhere [39]. Although radiation damage to individual nanoparticles should be reduced as much as possible, nanoparticles on a metallic substrate can be healed through a healing mechanism that involves a neutralization process [40].
Experimental I(Q) data were obtained for MnO nanoparticles of approximately 10 nm size. Background intensity was determined by carrying out a measurement on a bare substrate. The proper subtraction of the background is important for capturing the diffuse scattering signal in the data properly. Figure 2 shows the experimental I(Q) results for the MnO film sample. Only one Bragg-type peak, centered at 3.3 Å −1 , is seen. Other peaks are an order of magnitude weaker and represent diffuse scattering. It is likely that the diffraction peaks of the MnO film are too weak to be observed due to the strong and sharp diffraction peaks of the silicon substrate, as has been reported previously for MnO x on stainless steel [6]. TEM analysis provides grain size information. The particle size obtained via TEM is usually larger than the crystallite size given by XRD. This is to be expected since a particle typically consists of several crystallites. Information on crystallite size can be obtained by analyzing X-ray diffraction peaks where the peak width is inversely proportional to crystallite size, effects of other factors that contribute to the peak width such as instrumental resolution, temperature and microstrain notwithstanding.
effects of other factors that contribute to the peak width such as instrumental resolution, temperature and microstrain notwithstanding.

Computational details
Note that the intensity of diffuse scattering, which is related to short and medium range order, is orders of magnitude smaller than that of the Bragg peaks. Fourier transformation of experimental total scattering data gives the pair distribution function, which is a direct probe of interatomic distances in real space. The window in Q-space, which depends on the radiation source, defines the accuracy of the data in the real space. For elastic scattering, the diffraction vector, Q, has a magnitude | | = ( ) where λ is the wavelength of incident photons and 2 is the scattering angle. Since sin ≤ 1, the experimentally accessible range of Q is limited to less than 4π/λ. For example, the CuKα radiation, which is a common radiation source, has a wavelength of 1.54 Å with a Q-range of about 8 Å -1 , but for investigating nanoparticles, a Qmax larger than 20 Å -1 is needed. For our MnO data here, we have Qmax = 25 Å -1 , which enables us to achieve relatively good real-space accuracy.
We will use the PDF approach as a 'small-box modelling', where one considers relatively small unit cells with periodic boundary conditions. For periodic model structures, the PDF, G(r), can be computed in real space as: where bi,j are related to thermal movements of the scattering atoms, rij are the relative positions of the scattering atoms, N is the number of particles and ρ0 is the particle density.
The PDF provides atomic-scale structural insights from the distribution of atom-atom distances ranging from the local coordination scale to several nanometers. In addition to atom-pair separations (peak positions), the PDF also provides direct information about coordination number (integrated peak intensity), static and dynamic disorder (peak shape), and the coherent scattering-domain size (peak attenuation). Modelling the PDF for known periodic structures allows us to assess the effects of modifying the lattice constant, thermal vibration parameters, atomic positions and site occupancies. In addition, PDF-dependent shape parameters can also be used for extracting the radius of a spherically shaped nanoparticle.

Computational Details
Note that the intensity of diffuse scattering, which is related to short and medium range order, is orders of magnitude smaller than that of the Bragg peaks. Fourier transformation of experimental total scattering data gives the pair distribution function, which is a direct probe of interatomic distances in real space. The window in Q-space, which depends on the radiation source, defines the accuracy of the data in the real space. For elastic scattering, the diffraction vector, Q, has a magnitude where λ is the wavelength of incident photons and 2θ is the scattering angle. Since sinθ ≤ 1, the experimentally accessible range of Q is limited to less than 4π/λ. For example, the CuK α radiation, which is a common radiation source, has a wavelength of 1.54 Å with a Q-range of about 8 Å −1 , but for investigating nanoparticles, a Q max larger than 20 Å −1 is needed. For our MnO data here, we have Q max = 25 Å −1 , which enables us to achieve relatively good real-space accuracy. We will use the PDF approach as a 'small-box modelling', where one considers relatively small unit cells with periodic boundary conditions. For periodic model structures, the PDF, G(r), can be computed in real space as: where b i,j are related to thermal movements of the scattering atoms, r ij are the relative positions of the scattering atoms, N is the number of particles and ρ 0 is the particle density.
The PDF provides atomic-scale structural insights from the distribution of atom-atom distances ranging from the local coordination scale to several nanometers. In addition to atom-pair separations (peak positions), the PDF also provides direct information about coordination number (integrated peak intensity), static and dynamic disorder (peak shape), and the coherent scattering-domain size (peak attenuation). Modelling the PDF for known periodic structures allows us to assess the effects of modifying the lattice constant, thermal vibration parameters, atomic positions and site occupancies. In addition, PDF-dependent shape parameters can also be used for extracting the radius of a spherically shaped nanoparticle.

An Illustrative Analysis of the MnO Data
Manganese can exist in the form of a variety of stable oxides (MnO, Mn 3 O 4 , Mn 2 O 3 , MnO 2 ) [41,42], which crystallize in different types of structures. Associated with this wide diversity of crystal forms, defect chemistry, morphology, porosity and textures, manganese oxides exhibit a variety of distinct electrochemical properties. For example, MnO 2 exists in six different polymorphs (pyrolusite, ramsdellite, hollandite, intergrowth, spinel, and layered), all of which share basic structural features-small Mn 4+ ions in a spin-polarized 3d 3 configuration and large, highly polarizable O 2− ions in a spin-unpolarized 2p 6 configuration, which are arranged in corner-and edge-sharing MnO 6 octahedra. These octahedral units are characteristic for each oxidation state of manganese oxide and play a crucial role in determining the electrochemical properties of various oxides.
MnO crystallizes in the so-called rock-salt structure, which is a face-centered cubic (fcc) lattice with a 6:6 octahedral coordination. The experimental lattice constant at room temperature is a = 4.444 Å [43]. We obtained the PDF by using PDFgetX3 [44], which is a command-line utility for extracting atomic pair distribution functions from X-ray diffraction data. Data up to Q = 25.00 Å −1 were used using the Fourier transform, giving a real-space resolution of ∆r ≈ 0.25 Å. The PDF data were further analyzed using the DiffPy-CMI package [45], which is a library of Python modules for robust modelling of nanostructures in crystals, nanomaterials, and amorphous materials. Figure 3 shows the PDF for MnO obtained by converting the experimental I(Q) data of Figure 2. The coherent scattering domain size is seen to be only about 5 Å, with the peaks attenuating rapidly at larger distances. This feature may reflect the glass-like film assembly because the particles are crystalline.

An Illustrative Analysis of the MnO Data
Manganese can exist in the form of a variety of stable oxides (MnO, Mn3O4, Mn2O3, MnO2) [41,42], which crystallize in different types of structures. Associated with this wide diversity of crystal forms, defect chemistry, morphology, porosity and textures, manganese oxides exhibit a variety of distinct electrochemical properties. For example, MnO2 exists in six different polymorphs (pyrolusite, ramsdellite, hollandite, intergrowth, spinel, and layered), all of which share basic structural features-small Mn 4+ ions in a spin-polarized 3d 3 configuration and large, highly polarizable O 2ions in a spin-unpolarized 2p 6 configuration, which are arranged in corner-and edge-sharing MnO6 octahedra. These octahedral units are characteristic for each oxidation state of manganese oxide and play a crucial role in determining the electrochemical properties of various oxides.
MnO crystallizes in the so-called rock-salt structure, which is a face-centered cubic (fcc) lattice with a 6:6 octahedral coordination. The experimental lattice constant at room temperature is a = 4.444 Å [43]. We obtained the PDF by using PDFgetX3 [44], which is a command-line utility for extracting atomic pair distribution functions from X-ray diffraction data. Data up to Q = 25.00 Å -1 were used using the Fourier transform, giving a real-space resolution of Δr ≈ 0.25 Å. The PDF data were further analyzed using the DiffPy-CMI package [45], which is a library of Python modules for robust modelling of nanostructures in crystals, nanomaterials, and amorphous materials. Figure 3 shows the PDF for MnO obtained by converting the experimental I(Q) data of Figure 2. The coherent scattering domain size is seen to be only about 5 Å, with the peaks attenuating rapidly at larger distances. This feature may reflect the glass-like film assembly because the particles are crystalline.      Figure 5 shows the computed partial PDFs for bulk MnO. The calculated total PDF shown in Figure 6 is the sum of these partial PDFs. Partial PDFs help in assigning the peaks with their corresponding bonds. Notably, the PDF method can be used to assess the degree of structural coherence in a sample in terms of the experimental PDF. In particular, positions of peaks in the PDF can be related to the distribution of characteristic inter-atomic pair distances in the sample (In our case, the data are seen to be sensitive to only the first few pair distances). A PDF can be easily computed for any model configuration of atoms and thus allows convenient testing and refining of three-dimensional structure models of materials with varying degrees of structural coherence. In this way, periodic and non-periodic models can be evaluated on the same footing and different levels of structural information can be extracted. For crystalline samples, atomic structure can be determined completely, but for less ordered samples, the information obtained is more limited. Figure 5 shows that the experimental data have the highest intensity at the Mn-O distance, indicating that we have MnO6 octahedral building blocks or at least distorted/strained octahedral units. The arrangement of the neighboring octahedra is probably quite "random", resulting in destructive signals. A simple fitting to the PDF data has been done in order to extract the lattice constant for the MnO data. The result of the analysis is shown in Figure 6, and the fitted structure is illustrated in Figure 7 with the lattice constant given by a = 4.56 Å. A fit based on a hypothetical 57-atom cluster is discussed in the Supplementary Material.   Figure 5 shows the computed partial PDFs for bulk MnO. The calculated total PDF shown in Figure 6 is the sum of these partial PDFs. Partial PDFs help in assigning the peaks with their corresponding bonds. Notably, the PDF method can be used to assess the degree of structural coherence in a sample in terms of the experimental PDF. In particular, positions of peaks in the PDF can be related to the distribution of characteristic inter-atomic pair distances in the sample (In our case, the data are seen to be sensitive to only the first few pair distances). A PDF can be easily computed for any model configuration of atoms and thus allows convenient testing and refining of three-dimensional structure models of materials with varying degrees of structural coherence. In this way, periodic and non-periodic models can be evaluated on the same footing and different levels of structural information can be extracted. For crystalline samples, atomic structure can be determined completely, but for less ordered samples, the information obtained is more limited. Figure 5 shows that the experimental data have the highest intensity at the Mn-O distance, indicating that we have MnO 6 octahedral building blocks or at least distorted/strained octahedral units. The arrangement of the neighboring octahedra is probably quite "random", resulting in destructive signals. A simple fitting to the PDF data has been done in order to extract the lattice constant for the MnO data. The result of the analysis is shown in Figure 6, and the fitted structure is illustrated in Figure 7 with the lattice constant given by a = 4.56 Å. A fit based on a hypothetical 57-atom cluster is discussed in the Supplementary Material.   Figure 5 shows the computed partial PDFs for bulk MnO. The calculated total PDF shown in Figure 6 is the sum of these partial PDFs. Partial PDFs help in assigning the peaks with their corresponding bonds. Notably, the PDF method can be used to assess the degree of structural coherence in a sample in terms of the experimental PDF. In particular, positions of peaks in the PDF can be related to the distribution of characteristic inter-atomic pair distances in the sample (In our case, the data are seen to be sensitive to only the first few pair distances). A PDF can be easily computed for any model configuration of atoms and thus allows convenient testing and refining of three-dimensional structure models of materials with varying degrees of structural coherence. In this way, periodic and non-periodic models can be evaluated on the same footing and different levels of structural information can be extracted. For crystalline samples, atomic structure can be determined completely, but for less ordered samples, the information obtained is more limited. Figure 5 shows that the experimental data have the highest intensity at the Mn-O distance, indicating that we have MnO6 octahedral building blocks or at least distorted/strained octahedral units. The arrangement of the neighboring octahedra is probably quite "random", resulting in destructive signals. A simple fitting to the PDF data has been done in order to extract the lattice constant for the MnO data. The result of the analysis is shown in Figure 6, and the fitted structure is illustrated in Figure 7 with the lattice constant given by a = 4.56 Å. A fit based on a hypothetical 57-atom cluster is discussed in the Supplementary Material.    Our results are quite different from those for synthetic crystalline MnO2 birnessite obtained by Petkov [25], where sharp Bragg peaks are fitted with a model based on a hexagonal lattice rather than the cubic model invoked in our case. Petkov [25] has also shown that very diffuse XRD patterns for bacterial and fungal MnOx can be described with monoclinic and triclinic lattices.

Conclusions
MnO nanoparticles have attracted much interest due to their potential applications in many fields. In this work, we used HE-XRD at the SPring-8 synchrotron facility to extract important octahedral information, despite the challenging small size of the nanoparticles (about 10 nm) and the effect of deposition on the substrate, which results in a glassy thin film as indicated by our X-ray measurements. Our analysis reveals that Mn atoms are mostly present in an octahedrally coordinated MnO6 form, consistent with a cubic phase with a lattice constant of a = 4.56 Å, which is modified by significant glass-like disorder effects. In this way, atomic PDF analysis of HE-XRD data can be used to characterize structural and disorder properties of MnO nanocrystalline materials used in battery and air purification applications. Clearly, a fundamental understanding of the redox reactions and their relationship with magnetism occurring at the MnO6 sites requires a robust extraction of the octahedron size [47].

Supplementary Materials:
The following are available online at www.mdpi.com/xxx/s1, Figure S1: FFT images for several individual NPs including plane-spacing calculations; Figure S2: Comparison of experimental G(r) with the corresponding simulated results for a hypothetical 57 atom (relaxed) MnO cluster.   Our results are quite different from those for synthetic crystalline MnO2 birnessite obtained by Petkov [25], where sharp Bragg peaks are fitted with a model based on a hexagonal lattice rather than the cubic model invoked in our case. Petkov [25] has also shown that very diffuse XRD patterns for bacterial and fungal MnOx can be described with monoclinic and triclinic lattices.

Conclusions
MnO nanoparticles have attracted much interest due to their potential applications in many fields. In this work, we used HE-XRD at the SPring-8 synchrotron facility to extract important octahedral information, despite the challenging small size of the nanoparticles (about 10 nm) and the effect of deposition on the substrate, which results in a glassy thin film as indicated by our X-ray measurements. Our analysis reveals that Mn atoms are mostly present in an octahedrally coordinated MnO6 form, consistent with a cubic phase with a lattice constant of a = 4.56 Å, which is modified by significant glass-like disorder effects. In this way, atomic PDF analysis of HE-XRD data can be used to characterize structural and disorder properties of MnO nanocrystalline materials used in battery and air purification applications. Clearly, a fundamental understanding of the redox reactions and their relationship with magnetism occurring at the MnO6 sites requires a robust extraction of the octahedron size [47].

Supplementary Materials:
The following are available online at www.mdpi.com/xxx/s1, Figure S1: FFT images for several individual NPs including plane-spacing calculations; Figure S2: Comparison of experimental G(r) with the corresponding simulated results for a hypothetical 57 atom (relaxed) MnO cluster.  Our results are quite different from those for synthetic crystalline MnO 2 birnessite obtained by Petkov [25], where sharp Bragg peaks are fitted with a model based on a hexagonal lattice rather than the cubic model invoked in our case. Petkov [25] has also shown that very diffuse XRD patterns for bacterial and fungal MnO x can be described with monoclinic and triclinic lattices.

Conclusions
MnO nanoparticles have attracted much interest due to their potential applications in many fields. In this work, we used HE-XRD at the SPring-8 synchrotron facility to extract important octahedral information, despite the challenging small size of the nanoparticles (about 10 nm) and the effect of deposition on the substrate, which results in a glassy thin film as indicated by our X-ray measurements. Our analysis reveals that Mn atoms are mostly present in an octahedrally coordinated MnO6 form, consistent with a cubic phase with a lattice constant of a = 4.56 Å, which is modified by significant glass-like disorder effects. In this way, atomic PDF analysis of HE-XRD data can be used to characterize structural and disorder properties of MnO nanocrystalline materials used in battery and air purification applications. Clearly, a fundamental understanding of the redox reactions and their relationship with magnetism occurring at the MnO 6 sites requires a robust extraction of the octahedron size [47].