X-ray studies bridge the molecular and macro length scales during the emergence of CoO assemblies

The key to fabricating complex, hierarchical materials is the control of chemical reactions at various length scales. To this end, the classical model of nucleation and growth fails to provide sufficient information. Here, we illustrate how modern X-ray spectroscopic and scattering in situ studies bridge the molecular- and macro- length scales for assemblies of polyhedrally shaped CoO nanocrystals. Utilizing high energy-resolution fluorescence-detected X-ray absorption spectroscopy, we directly access the molecular level of the nanomaterial synthesis. We reveal that initially Co(acac)3 rapidly reduces to square-planar Co(acac)2 and coordinates to two solvent molecules. Combining atomic pair distribution functions and small-angle X-ray scattering we observe that, unlike a classical nucleation and growth mechanism, nuclei as small as 2 nm assemble into superstructures of 20 nm. The individual nanoparticles and assemblies continue growing at a similar pace. The final spherical assemblies are smaller than 100 nm, while the nanoparticles reach a size of 6 nm and adopt various polyhedral, edgy shapes. Our work thus provides a comprehensive perspective on the emergence of nano-assemblies in solution.

We account the large structures visible between 10 and 15 min to precipitation of unreacted intermediate Co(acac)2 or precursor Co(acac)3. Only the sample after 20 min shows distinct CoO assemblies, together with a strong crystalline ED signal. In the sample after 15 min, nanosized precipitate is observed. However, the very weak ED signal excludes the presence of final crystalline nanoparticles.

Supplementary Notes 1. MCR-ALS method for analysis of in situ HERFD-XANES
The Multivariate Curve Resolution by Alternating Least Squares (MCR-ALS) method [3][4][5] used for extracting the reaction pathway from the in situ HERFD-XANES data is briefly explained, followed by detailed fit results. Generally speaking, MCR-ALS is a factor analysis tool, thus it searches for the number and nature of uncorrelated variables explaining the variance in a set of observed, correlated variables. For this, the observed data set needs to be decomposable in the underlying bilinear model given by In Equation (1) and for our case of time-resolved HERFD-XANES spectra, D is the experimental data with each row corresponding to a measured spectrum, rows of S T are spectra of uncorrelated variables (we call them components) and columns of C are the concentration profiles of each component over time. E represents variance in the data not explained by the model. After an initial guess for C and S T , which we do by means of the purest variables detection method, 4, 6 a set of linear equations is iteratively solved, alternatingly keeping C or S T constant until the change in the standard deviation of E falls below a certain convergence criterion. Additional constraints can be imposed on the optimization problem (spectral and/or concentration dimension) to facilitate convergence, one being non-negativity and the other one being unimodality. Quality estimates of a converged fit arise from the unexplained residuals E, or the difference between the experimental data and the bilinear model, with the lack of fit given by where is a data matrix element and is the corresponding element of the residuals matrix E. Additionally, the variance explained in the model can be estimated from and the standard deviation of the residuals is given by where , refer to the dimensions of D. For the MCR-ALS analysis in the main article, we show the quality estimates in Supplementary Table 1. The MCR-ALS optimization can only start after the dimensions of C and S T have been defined, thus the number of components must be defined beforehand. For this purpose we use Singular Value Decomposition (SVD) which computes a set of eigenvalues and corresponding eigenvectors from the input data set. 3 Both of them contain information to determine the number of components. A higher eigenvalue means that the respective component explains more variance of the data, while the graphical representation of the eigenvector of a meaningful component should display a distinctive profile, independent of its absolute values. Such meaningful components correspond to HERFD-XANES spectra of chemical compounds in the reaction mixture.  Table 2. Additionally, looking at the eigenvector representations in Supplementary Figure 7b, we see clear profiles only for components 1 to 3, while components 4 and 5 only punctually exceed the noise level, which we assign to fluctuations due to changing positions of the incident beam on the reaction container throughout the collection of the in situ data set. The wall thickness of the reaction container could vary in a certain range, and we have to note that no stirring was applied during the in situ studies. From both measures combined, we conclude that there are 3 independent components in the data set. Additionally, MCR-ALS optimization with 4 and more components would not give physically meaningful results.

Supplementary Notes 2. HERFD-XANES self-absorption correction
Self-absorption can affect the intensities of features in fluorescence-detected XAS. In order to correct for this, we apply the method described by Booth and Bridges 7 expressed by Equation (5): Here, 0 and f are the incident and fluorescence intensities, a ( ) is the fluorescence efficiency per unit solid angle, a ( ) is the absorption coefficient due to core hole excitation, ( ) is the total absorption coefficient, f = ( f ) is the absorption coefficient at the detected fluorescence energy, and are the angles of incident and outgoing X-rays with respect to the sample surface, ≡ sin / sin , and is the thickness of the sample. Energy dependencies are implicit in all equations. In our case of HERFD-XANES, = = 45°, a ≈ const. and if we assume a thick sample with respect to the absorption length, we can say that and we can additionally assume that a ( ) ≈ ( ). Thus, Equation (5) For the self-absorption corrected fluorescence intensity, f corr 0 , we can say that f corr 0~ for f corr 0 ≪ 1 and since we are not interested in absolute values for the absorption coefficient, we can use Equation (6) to perform self-absorption correction without knowledge of f or a . We do self-absorption correction based on Equation (6) for the CoO powder reference in a way that we minimize the difference to the MCR-ALS spectrum of CoO. Due to the relatively low concentration of nanoparticles in the solution, we can assume the MCR-ALS spectrum not to contain any significant self-absorption. The corrected reference spectrum, after re-normalizing the edge step, is shown in Supplementary Figure 8 together with the uncorrected MCR-ALS spectrum.

Supplementary Notes 3. Kinetic fit of MCR-ALS results
The reaction of Co(acac)3 with BnOH at 160 °C includes two steps, a reduction to Co(acac)2 followed by the formation of CoO. The concentration profiles obtained from the MCR-ALS analysis give a hint on the kinetics of the reaction steps. Supplementary Figure 9 shows

Supplementary Notes 4. Calculation of XANES spectra using the FEFF code
In addition to reference measurements, we verify the reaction components identified by MCR-ALS with theoretical calculations of Co K-edge XANES spectra that we obtain using the FEFF code. 10 From Supplementary Figure 10, we see that the calculated spectra of the reaction precursor, Co(acac)3, and the product, CoO, are in good agreement with the experimentally obtained spectra of these compounds. Additionally, we see that the 3d density of states (DOS) of the cobalt ion mainly determines the shape of the pre-edge transitions. Thus, the pre-edge features arise from hybridization of Co 4p and 3d states, allowing to a certain extent 1s→3d quadrupole transitions. The calculated spectrum of CoO is missing a feature ~8 eV above the absorption edge compared to the experiment, which we account to a final state effect in the HERFD-XANES measurement not reproducible with FEFF. Standard transmission XANES at the Co K-edge also excludes this feature. 11 showed that in the crystalline state, the molecule adopts the tetrameric form Co4(acac)8 13,14 . DFT calculations of the isolated molecule indicate a small energy difference between the square-planar and tetrahedral conformation, thus the interaction with the solvent plays an important role for the actual structure. 15 In Supplementary Figure 11, we present FEFF calculations for the possible structures of Co(acac)2. It is clear that only in the case of an octahedrally coordinated Co 2+ ion, the theory is in good agreement with the experiment. We conclude that for the reference that was measured as a powder, the molecule forms tetramers with octahedral coordination (c.f. Supplementary Figure 11d). In solution, the Co 2+ ion is additionally coordinated by oxygen atoms of two solvent molecules, forming a bis-adduct with octahedral coordination 13 (c.f. Supplementary Figure 11c). Note that since the actual coordination geometry of Co(acac)2 in BnOH is unknown, we used water as a model coordinating solvent for the FEFF calculations.

Supplementary
Supplementary Figure 11. Theoretical XANES spectra of Co(acac)2 calculated using the FEFF code. 10 We compare a square-planar, b tetrahedral, c solvent-coordinated with water as a model solvent and d tetrameric geometry. The spectra are plotted together with the local DOS for s, p and d states. The experimental HERFD-XANES spectrum of Co(acac)2 powder is shown as dotted line. The energy scale is relative to the absorption edge E0. Vertical dashed lines indicate the position of the Fermi level. The atomic positions in square-planar and tetrahedral Co(acac)2 were taken from reference 15 and the structure of the tetramer was adopted form reference 14 .
We used the FEFF code 10 in version 9.6.4 with the Hedin-Lundquist energy dependent exchange correlation potential for all calculations. The settings are listed in Supplementary Table 3. Note that no instrumental broadening (EXCHANGE card setting vi) needed to be applied since the experimental spectra were measured in HERFD mode. For the Co4(acac)8 tetramer, we averaged calculations with each of the Co ions set as the absorber, since their environments in the tetramer are not equivalent.

Supplementary Notes 5. In situ total scattering studies of the reaction at 140°C
The CoO reflections in time-resolved in situ total scattering data at 140 °C (Supplementary Figure 18a) occur after 64 min reaction time, which is 44 min later than at 160°C. Similarly, the long-range order correlations in the time-resolved PDFs emerge later. (Supplementary Figure 18b,c). We evaluate the structural parameters by the same sequential refinement method starting from the final product after 210 min and tracing the signal back towards earlier reaction times. The refinement results are depicted in Supplementary Figure 19. The evolution of the sp-diameter over time provides a value of ~26 Å at 70 min, which progressively increases and reaches ~64 Å at 210 min. Therefore, although the reaction at 140 °C yields CoO nanoparticles with a similar particle size as the reaction at 160 °C, the reaction takes ~2.3 times longer.
Supplementary Figure 18. In situ total X-ray scattering data for the reaction at 140 °C. a In situ timeresolved background-subtracted I(q) data. b In situ time-resolved PDFs. The heating steps in a and b involve the heating from room temperature to 60 °C, 5 min at 60 °C, and the heating from 60 to 140 °C. c PDFs at the local ordering region for selected reaction times of the in situ data.
Supplementary Figure 19. Additional refined PDF parameters. a-g Refinement results for the in situ reaction at 140 °C. Evolution of a lattice parameter a, b scale factor, c the quadratic atomic correlation factor δ2, d isotropic atomic displacement parameter uCo for cobalt, e isotropic atomic displacement parameter uO for oxygen, f sp-diameter, and g Rw, as a function of the reaction time. The data were obtained from the sequential refinement of time-resolved PDFs. h Changes in the shortest Co-O bond over the reaction course at 140 °C.

Supplementary Notes 6. SAXS data analysis
Homogeneous spherical model: The low q regime of the SAXS data was analyzed with a model form factor intensity describing homogeneous spherical particles. The form factor is related to the particle diameter D = 2R by The scattering intensity of a particle in a solvent with scattering contrast particle − solvent is 3 is the volume of the particle and c is the volume fraction of the particles, which can be determined in absolute units if the instrumental scaling constant (const) and the scattering contrast are determined e.g. by calibration measurements of standard substances.
The model is included in the SasView software package, version 4.2.2. We used the population-based DREAM algorithm with 10 4 samples for fitting. Radii were drawn from a Schulz-Zimm polydispersity distribution. 16 The fitted data range is shown as a solid curve in Figure 6. Resulting particle diameter values are given in Supplementary Table 4. To quantify the concentration of assemblies obtained at the beginning and end of assembly formation, we recorded SAXS data of aliquots extracted at 20 and 90 min reaction time with our laboratory SAXS setup at LMU. Here, we obtain the scattering intensity on absolute scale (cm -1 ), by using a high dynamic range, photon counting detector, and normalizing the intensity as We assume the reaction product to be composed of CoO assemblies ( particle = 51.5 • 10 −6 Å −2 ) in benzyl alcohol ( solvent = 9.47 • 10 −6 Å −2 ) and use the above equation for I(q) for fitting. In the case of absolute scale data and scattering contrast the volume fraction of assemblies is obtained from the model fit. Assuming a mass density of CoO of 6.45 g/cm 3 and a molecular weight of 74.933 g/mol we calculate the final and initial concentration of CoO. The resulting values are given in Supplementary Table 5. Given an initial concentration of Co of 0.1 mol/l, the final concentration of 2.2 • 10 −2 mol/l corresponds to a yield of 22%. The main uncertainty of the concentration measurement is the fit uncertainty of the model, since the data range does not reach the intensity plateau needed to unambiguously determine the particle size distribution. We estimate this uncertainty as 20%, based on a variation of the fitting range.

Supplementary Notes 7. PXRD data analysis
In order to probe for crystallinity, powder X-ray diffraction patterns were recorded on the same samples as the SAXS data (Supplementary Figure 21). The sample at 20 min reaction time shows some very sharp reflections, which presumably come from a crystallized reaction intermediate, and are not observed in the in situ total scattering experiment ( Figure 4 and Supplementary Figure 12). A crystalline PXRD signal related to CoO was not observed at this reaction time. Starting from 40 min reaction time, Bragg reflections of cubic CoO were seen. A Scherrer analysis of the widths of the reflections yields crystallite sizes of (4.9 ± 2.8) nm, (5.8 ± 1.0) nm, and (6.0 ± 1.2) nm for 40, 60 and 90 min reaction time, respectively. Details of the Scherrer analysis are given below.
The PXRD reflections of CoO were fitted with a sum of Lorentzian functions of the scattering angle 2θ. The widths were then analyzed using the Scherrer equation for the crystallite size d: 17,18 = cos K=1 is a numerical shape factor, λ = 0.71 Å is the X-ray wavelength. is the Bragg angle in radians of a reflection of width . For , we use the full width at half maximum (FWHM) B of the fitted reflection, corrected by the instrumental resolution B1 ≈ 3.3 mrad. B1 is the measured angle-dependent FWHM of a LaB6 powder standard.
In case of a strong, Lorentzian broadening B2 = due to particle size, and a weak, Gaussian instrumental broadening B1, the following approximation holds: 19 2 ≈ 1 − 2 ( 1 ) 2 We solve for B2 = and obtain In Supplementary Table 6, we report the mean and standard deviation of d obtained from 5 reflections (3 for the 40 min data set). The estimate of the number of crystallites is calculated as = 0.74 • 3 3 , with the pre-factor assuming dense packing of spherical crystallites in a spherical particle. This number shows an increasing trend as the values obtained from the combination of assembly sizes from SAXS with crystallite sizes from PDF.