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Deformation Behavior of Cross-Linked Supercrystalline Nanocomposites: An in Situ SAXS/WAXS Study during Uniaxial Compression

With the ever-expanding functional applications of supercrystalline nanocomposites (a relatively new category of materials consisting of organically functionalized nanoparticles arranged into periodic structures), it becomes necessary to ensure their structural stability and understand their deformation and failure mechanisms. Inducing the cross-linking of the functionalizing organic ligands, for instance, leads to a remarkable enhancement of the nanocomposites’ mechanical properties. It is however still unknown how the cross-linked organic phase redistributes applied loads, how the supercrystalline lattice accommodates the imposed deformations, and thus in general what phenomena govern the overall material’s mechanical response. This work elucidates these aspects for cross-linked supercrystalline nanocomposites through an in situ small- and wide-angle X-ray scattering study combined with uniaxial pressing. Because of this loading condition, it emerges that the cross-linked ligands effectively carry and distribute loads homogeneously throughout the nanocomposites, while the superlattice deforms via rotation, slip, and local defects generation.


Micropillars dimensions and stress-strain curves
shows scanning electron and optical microscope images of the tested pillars. The respective dimensions, compressive strengths and elastic moduli are given in Table S1. Figure S2. Samples and testing setup. A,B) Tested micropillars, seen from a side and from above, produced with a sequence of laser cutting and plasma focused ion beam by the Fraunhofer Institute for Microstructure of Materials and Systems (IMWS, Halle, Germany). The shape of the surrounding cavity was selected to allow ample access to pressing punch and X-ray beam, the latter before and after scattering through the pillars. C) Test setup seen from the side, with sample mounted on its support and tip with diamond flat punch during the alignment phase. D) Main pillar and punch seen from the front (viewing direction aligned with X-ray beam direction), with highlight of the impurity sitting on the top surface of the micropillar.  Fig. 1). Figure S4 shows the fracture surfaces of the pillars after compression. The nanocomposites' supercrystalline structure is visible in all samples, with varying orientations throughout the pillars, which in turn influence the shear deformation. Organic-rich areas or clusters are highlighted with dashed lines, located at the interface between the two supercrystalline grains of the main pillar (see Fig. 4), and in test pillar 2 in correspondence of the defect visible on the pillar's lateral surface already before the test (see Fig. 1). In some areas, a gradual change of orientation (a few degrees tilt) can be identified in the fracture surface's texture (see bottom-right micrographs).

Factors influencing elastic modulus and strength
Both elastic modulus and compressive strength of the tested pillars ( = 6.4 ± 0.2 GPa and = 239 ± 18 MPa) result in lower values than in cylindrical pillars tested ex situ ( = 47 ± 3 GPa and c = 1222 ± 127 MPa, unpublished results). The testing setup and pillars' sizes explain why this is the case.
For the elastic modulus, several experimental and numerical microcompression studies have revealed that its assessment is strongly dependent on the pillars' geometry (specifically their taper angle and aspect ratio) and alignment with respect to the compressing punch. 3,4 The taper of the prismatic pillars tested here is negligible, but the aspect ratio (height/cross-section characteristic length) is lower than the one that typically characterizes pillars for microcompression studies. The lower the aspect ratio, the stronger the influence of the bulk material surrounding the pillar's base. Even though the effect of the pillars' indentation into the bulk is considered via Sneddon-based estimation (see SI 2), it has been shown that an aspect ratio ~1 like in this case can lead to measured Young's moduli that underestimate the real values by up to 50%. 3 Such a strong effect was found e.g. for two different crystallographic directions of a Si single crystal, which is a result relevant for this study too, where micropillars have a mostly uniform supercrystalline orientation (quasi-single supercrystal). An even stronger apparent decrease in the Young's modulus can be due to misalignments between the pillar's upper surface and the pressing flat punch. Image analysis of pre-contact optical microscope pictures reveals, for the main pillar, a misalignment of ~1.5º. According to the literature, 4 this kind of value is enough to cause an underestimation of the measured elastic modulus up to ~70%. Assuming these two factors (aspect ratio and misalignment) add up, and based on a value of ~ 47 from ex situ tests, we find here an estimated elastic modulus of ~ 7 GPa, which is very close to the measured value. Additionally, the presence of an impurity on the top surface of the main pillar worsens the misalignment issue, and it is possible that the laser cutting and plasma-FIB processes lead to softening of the material surrounding the pillars' bases, thus providing additional factors leading to a decrease in the measured Young's modulus with respect to the ones measured in different contexts.
As for strength, the well-known size effect of materials' strength comes into play. Since both the present tests and ex situ tests on cylindrical micropillars show negligible plastic deformation, we assume that deterministic size effects play a negligible role here. For brittle materials, strength is known to decrease with increasing sample size, an effect due to flaw distributions within the tested samples that also affects compression tests of samples with free lateral surfaces, and that can be described through Weibull statistics. [5][6][7] The volume of the pillars tested here is ~2000x larger than in the case of the micropillars tested ex situ, the stress distribution is homogeneous, and we can assume one volume defect type to be dominating the failure behavior of the micropillars, namely the organic clusters visible in Fig. S4. Given a certain failure probability, then, we can express the relationship between strength ( c ) and sample volume ( ) as . [5][6][7] The smaller ex situ micropillars have ~ 100 µm 3  Finally, it is worth mentioning explicitly here that the ex situ tests have been conducted with loading rates spanning one order of magnitude, and this has resulted in negligible differences in the linear elastic behavior and strength of the supercrystalline nanocomposites, confirming that the present in situ tests are reliable even if the testing setup did not allow the application of a constant loading rate (the displacement steps were halted during X-ray scanning).
Even with these influencing factors in mind, priority was given in this experiment to testing large-size pillars, and to pillar aspect ratios minimizing the risks of pillar bending during testing.
The measured mechanical properties are still consistent with conventional ex situ tests, and valuable and otherwise inaccessible information on supercrystalline deformations during compression has been obtained.

Strains in the organic phase
If one considers a simplified model consisting of a layer of organic ligand molecules sandwiched between two layers of NPs, the supercrystalline strain can be approximated as the final distance between the NP centers , minus the initial one , all divided by . In general, is ℎ ℎ 0 ℎ 0 ℎ the sum of the thickness of the organic layer, or inter-NP distance , and the NP diameter, .  . Scheme to estimate compression strains of the organic phase at inter-NP contacts. Note that the organic ligands' depiction is a simplified representation.

Stress distributions within NPs
Through multiscale finite-element (FE) simulations 2   absolute stress values. Due to its high confinement in an ultra-thin interface, anchoring to the NP surfaces, and crosslinking, we assume the applicability to the organic phase of the continuum approach that FE method entails. A previous study of this same group has shown excellent matching of FE-based outcomes with both experiments and theoretical considerations, reinforcing this assumption. 2 Nevertheless, the choice of modeling the behavior of the organic phase with continuum or discrete (atomistic) methods does not influence the conclusions drawn here on the stress distributions within the NPs -it might only alter the calculated absolute values.

Superlattice strains via SAXS
The strains within the superlattice vary depending on the scanned position. Six sample positions were selected throughout the pillar and the corresponding strains evaluated as shown in Table S2. The strains are here defined as the change in inter-planar spacing ( ) due to the applied load. The applied pressure of 101.3 MPa (0.35 N) was considered, because immediately prior to the onset of block slip. The negative values are assumed to be due to organic material being squeezed inside the superlattice, or to a local superlattice orientation leading to marked lateral expansion. The right portion of the pillar experienced higher loads in the first compression stages (see Fig. 3), which finds here agreement with the on average higher strains of points 4-6.  Figure S8 below shows changes in the SAXS spectra of two sample regions upon loading. Peak broadening and splitting can be observed, which are typically associated with gradual and localized superlattice rotation, respectively. In the bottom-right panel of the figure, a specific peak splitting configuration can be observed at the order of the {111} family reflections, with an additional reflection appearing halfway between two of the pre-loading reflections (marked with an arrow). We consider this effect as an indication of twinning. 8 Figure S8. SAXS spectra relative to two micropillar locations (above, top left of the pillar; below, bottom right) at contact and at 146.7 MPa (0.50 N) loading stages. The color scale represents the spectra intensity in arbitrary units. The arrow indicates the peak splitting associated with twinning.

Sample preparation
The supercrystalline nanocomposites' building blocks are iron oxide (magnetite, Fe 3 O 4 ) nanoparticles with inorganic core radius of 7.9 ± 1.

In situ compression tests
The in situ microcompression tests were conducted in a self-developed indenting setup. 9 The prepared samples (micro-structured 0.5 mm-thick slices) were deposited on 0. SAXS-WAXS parameters X-ray scattering experiments were performed at the Nanofocus Endstation (NFE) of P03 beamline at the PETRA III Synchrotron in DESY (Hamburg, Germany). 10 The photon energy was selected by large-offset fixed-exit monochromator and set equal to 13.7 keV (λ=0.905Å).
The beam was focused by systems of KB mirrors (JTEC, Japan) down to 1.7 x 2.4 µm 2 (horizontal x vertical) size, with focal distance of ~10 cm. Scattering signals in small-and wide-angle X-ray scattering configuration were recorded by detectors placed at a distance of 2241 mm and 238 mm respectively. A Pilatus 1M detector (with 981 x 1043 pixels 2 of 172 x 172 µm 2 size) was used for the SAXS signal and a Pilatus 300k detector (with 487 x 619 pixels 2 of similar size) for WAXS. Exact wavelengths and sample-detector distances were defined through standard material (LaB6 for WAXS and AgC22H43O2 for SAXS) measurements. Data analysis was performed with DPDAK (calibration, integration) 11 and self-developed MATLAB codes (fitting, plotting, presentation).