Mapping Short-Range Order at the Nanoscale in Metal–Organic Framework and Inorganic Glass Composites

Characterization of nanoscale changes in the atomic structure of amorphous materials is a profound challenge. Established X-ray and neutron total scattering methods typically provide sufficient signal quality only over macroscopic volumes. Pair distribution function analysis using electron scattering (ePDF) in the scanning transmission electron microscope (STEM) has emerged as a method of probing nanovolumes of these materials, but inorganic glasses as well as metal-organic frameworks (MOFs) and many other materials containing organic components are characteristically prone to irreversible changes after limited electron beam exposures. This beam sensitivity requires 'low-dose' data acquisition to probe inorganic glasses, amorphous and glassy MOFs, and MOF composites. Here, we use STEM-ePDF applied at low electron fluences (10 e- Å-2) combined with unsupervised machine learning methods to map changes in the short-range order with ca. 5 nm spatial resolution in a composite material consisting of a zeolitic imidazolate framework glass agZIF-62 and a 0.67([Na2O]0.9[P2O5])-0.33([AlO3/2][AlF3]1.5) inorganic glass. STEM-ePDF enables separation of MOF and inorganic glass domains from atomic structure differences alone, showing abrupt changes in atomic structure at interfaces with interatomic correlation distances seen in X-ray PDF preserved at the nanoscale. These findings underline that the average bulk amorphous structure is retained at the nanoscale in the growing family of MOF glasses and composites, a previously untested assumption in PDF analyses crucial for future non-crystalline nanostructure engineering.


SED data pre-processing and calibration
SED data were acquired using a Merlin-Medipix3 hybrid counting-type direct electron detector.
The data were acquired with either a 512×512 pixel quad Medipix3 detector or a single 256×256 pixel Medipix3.
Calibration of the scan step size and diffraction pattern pixel size was performed using a standard 500 nm gold diffraction grating replica with latex spheres (Ted Pella). The gold diffraction data was also used to determine residual elliptical distortions in the diffraction plane due to postspecimen optics.
The SED data was pre-processed in Pyxem as follows: 1. Centering the direct beam in each diffraction pattern using a cross-correlation routine.
2. Applying an affine transformation to correct for elliptical distortion.
3. Integrating each diffraction pattern azimuthally around the center of the direct beam to acquire a 1D scattering profile.

X-ray scattering acquisition
X-ray data were collected at the I15-1 beamline at Diamond Light Source, UK (λ = 0.161669 Å, 76.7 keV). Samples were loaded in borosilicate capillaries of 1.17 mm inner diameter. Data were collected in the region of ~0.4 < Q < ~22 Å -1 . Correction for the background, multiple scattering, container scattering, Compton scattering, fluorescence and absorption were performed using the GudrunX program 1 .

Relative Electron and X-ray Scattering factors
The relative scattering factors by element differ between X-ray and electron scattering. The pair partial scattering factors are given by 2 where is the sum over all elements in the sample and a is the scattering factor for element . Note that due to the division by the total sum, the relative contribution of a pair can increase with increasing , even though is a decreasing function. The factors 3 and their ( ) relative ratios are plotted below for ZIF-62 in Figures S1 and S2 respectively. In particular, the significant relative increase in IX-H correlations at high is notable (Fig. S2), primarily due to the extremely low scattering cross-section of H by X-rays. In electron scattering in absolute rather than relative terms (Fig. S1b), the H contribution is relatively weak, but it is non-negligible The relative scattering factors for the inorganic glass are given in Figures    8 Figure S4. The natural logarithm of the electron/X-ray pair partial ratio for inorganic glass as a function of for the partials given in Figure S1 for Å -1 . The overall scale of difference is 0 < < 3 much smaller than in the ZIF-62.

Crystalline ZIF-62 PDF fitted with electron and X-ray scattering factors
A simplified ZIF-62 crystal structure was used to calculate partial atomic pair distribution functions, which were then turned into partial reduced intensities and multiplied by the partial scattering factor distributions given above in Figures S1.
The ZIF-62 crystal structure retrieved from the Cambridge Structural Database (CSD, CCDC number 671070) incorporates disorder in the benzimidazolate (bIm) position as well as solvent molecules 4 . For ZIF-62 PDF calculations, a lowered symmetry structure was adapted from the same lattice parameters and derived from the fractional coordinates of the reported ZIF-62 structure, with partial occupancies and solvent molecules removed (Table S1). This approach is similar to that used by Thorne et al. 5 though here we retain all hydrogen atoms in the structure.
The same data processing pipeline as for the respective X-ray and electron data was followed, and are presented in Figure S5a-b. The differences in the simulated electron and X-ray PDFs are very consistent with the observed differences, with the relative intensities of the 5 and 6 Å peaks accurately represented. The inaccuracies in peak intensities between simulated and observed PDFs is likely due to the lack of bImlinkers in the unit cell.
In addition, Figure S5c-f contain simulated electron and X-ray PDFs for a range of values. The same processing was applied to each PDF, to ensure any differences are due to different scattering factors. The partial structure factors were obtained, weighted, and damped by a Lorch function before being transformed into reduced PDF. Relative peak intensities differ throughout, but in a consistent manner. Peaks around 1.0, 1.5 Å and 5 Å are stronger in ePDF, while peaks are 2.6, 3.1, 4.9, and 6.4 Å are stronger in XPDF. Many of the distances stronger in the ePDF are associated with H, such as C-H and Zn-H partial 6 . This suggests the difference in the electron and X-ray PDFs observed in Figure 2 are real features that are differentially weighted in electron and X-ray scattering.

ZIF-62 PDF as a function of maximum scattering vector
The area-averaged PDFs from the a g ZIF-62 were fitted with varying strength of damping factor for the term to investigate whether the feature around 5 Å is a result differing scattering factors. The resulting PDFs are shown in Figures S1. The feature was present until a high damping factor, like features around 7 Å and the major peaks around 2-3 Å. It changes faster than peaks at low but similarly to the features around it. A fit similar fit was performed with just changing and , shown in Figure S6. Little changes were observed. While it is not possible to conclusively rule out the feature as a result of a truncation effect, its lack of change suggests it may be a structural feature.  Increasing .

Principal Component Analysis Variance ratios
For each PCA decomposition, the component-variance ratios were used to choose the number of signal components for the subsequent ICA decomposition. Two significant components were chosen for the decompositions in both Figure 3 and Figure 5. The variance ratios by component are presented below. Figure S8a. Fraction of the variance explained by the most significant 25 principal components.
The PCA decomposition was performed on the pixel-by-pixel ePDFs for the 512×512 data set shown in Figure 3. Two components are strongly above the baseline and were used for the subsequent ICA decomposition. Figure S8b. Fraction of the variance explained by the most significant 25 principal components.
The PCA decomposition was performed on the pixel-by-pixel ePDFs for the 256×256 data set shown in Figure 5. Three components were above the baseline, but the largest two that were significantly higher were used for the subsequent ICA decomposition. The third was not found to contain meaningful spatial variation information and reduced the accuracy of the two PDFs compared to the higher fidelity 512×512 data set.

PDF as a function of background composition
The area-averaged PDFs from the a g ZIF-62 and inorganic glass were fitted with varying background compositions. The fits are shown in Figures S9a and S9b. The effect of an incorrect composition was primarily to increase peak heights in the a g ZIF-62 and decrease peak heights in the inorganic glass. This can be attributed to the different scattering profile being fit as a function of composition, combined with incorrect fitting at low s as a result of inelastic scattering. Peak positions were virtually unchanged, meaning incorrect background fitting should have little to no effect on the ICA decomposition being able to distinguish the signals from one another. Figure S9a. Area-averaged ePDF as a function of background composition for the a g ZIF-62, from 100% a g ZIF-62 and 0% inorganic glass to 0% a g ZIF-62 and 100% inorganic glass. Figure S9b. Area-averaged ePDF as a function of background composition for the inorganic AlF 3 -NaPO 3 glass, from 100% inorganic glass and 0% a g ZIF-62 and to 0% inorganic glass and 100% a g ZIF-62.

PDF of carbon film
An ePDF was acquired from the carbon film to compare to references. The reduced intensity and PDF profiles are plotted below in Fig S3a and S3b. The ePDF agrees well with previous works 7 , with peak positions at 1.4 Å and 2.5 Å accurately reflected. In general, the carbon signal is very weak in comparison to the nanoparticles. Notably, the ICA in Figure 3 showed incomplete separation of the ePDFs at approximately 2.5 Å which may be related to the amorphous carbon contributions from the support film. Figure S10a. Reduced intensity measured in the carbon film, averaged from a 50×50-pixel real space region. Figure S10b. STEM-ePDF of the amorphous carbon film, from the reduced intensity in Fig S3a. The data was summed from a 50×50-pixel real space region.

PDF variation across thickness
The variation of the acquired ePDFs as a function of thickness was investigated for both the a g ZIF-62 and the inorganic glass ( Figure S1). The average peak height decreased with increasing thickness, but the peak positions remained consistent as expected 8 . Minor peak shifts were observed for the inorganic glass, likely due to its greater density and scattering power, resulting in fast changes with increased thickness relative to a g ZIF-62. The consistency in peak position and profile shape is important for the PCA/ICA decomposition as it should primarily affect the total weight of each phase assigned to each pixel, but not result in pixels being misclassified as one phase over the other. At large thicknesses, particularly in the inorganic glass, this assumption is no longer satisfied, but the primary peak positions are still well defined.  glass from the area shown in Figure S11a, overlaid with the area-averaged ('full') ePDF shown in Figure 2. Color coding follows Figure S11a. With increasing thickness (more yellow), the peaks become weaker and more blurred, with notable slight shifting and blurring of the peaks around 3.8 Å and 5 Å. The area-averaged PDF sits roughly in the middle of this thickness range Figure S11c. A series of ePDFs acquired at different thicknesses of the a g ZIF-62 particle from the area shown in Figure S11a, overlaid with the area-averaged ('full') ePDF shown in Figure 2. Color coding follows Figure S11a. With increasing thickness (lighter blue), the peaks also become weaker and more blurred, although less so than the inorganic glass. The area-averaged PDF reflects the PDF from the thin areas more accurately.

PDF at interfacial region
A PDF was acquired from the area at the interface outlined in purple in Figure S13 by summing the diffracted intensity and then performing the ePDF acquisition procedure detailed in the Methods. The acquired ePDF was compared to ones acquired from single-domain regions. These PDFs are show in Figure S13b. The interface PDF shows small differences to a best fit of a sum of the component PDFs, shown in Figure S13c. Small differences are present in relative peak intensities, but it was not possible to distinguish signal from noise in this interface signal.   difference is plotted at the bottom.

ICA decomposition of the reduced intensities
The PCA-ICA decomposition was also applied on the reduced intensities in the data set. This revealed two main components, but those components, particularly the inorganic glass, were significantly affected by thickness, as shown in Figure S14. A third component was observed above the noise floor, but not found to correspond to a physical signal and was instead partially correlated to thickness. Hence 2 components were used for the subsequent ICA decomposition.
This thickness-dependent variation is a slow oscillation that manifests itself differently in the PDF, in a way that ICA was able to resolve, and as such ICA was directly applied to the PDF signals.