In this study, we apply scale-bridging non-destructive tomography techniques to capture topological and surface morphological features of npg with a characteristic size ranging from tens to hundreds of nanometers. In situ mechanical compression tests are performed on npg and combined with tomography studies before and after deformation, enabling quantitative deformation mapping using digital volume correlation (DVC). Experimentally-derived 3D microstructural data are used as input structures for cross-scale atomistic and continuum modelling. Large-scale molecular dynamics (MD) simulations are performed on the small-scale (sub-ten to tens of nanometers characteristic length scale) experimentally-informed npg to accurately capture the atomic origins of deformation mechanisms. The simulation results are correlated with high-resolution TEM observations of defect structures, providing insight into the effect of strain gradients on dislocation-based deformation mechanisms. Finite element (FE) simulations are performed on the large-scale (with a characteristic length scale of hundreds of nanometers) experimentally informed npg. By comparing the dislocation structures revealed by TEM with the deformation gradients, obtained using both DVC and FE methods, we can clearly identify different mechanisms at work for the different sizes. Based on this, different material models have to be applied and are evaluated in simulations to represent the mechanical response of realistic nanoporous network structures.
The correlative workflow combining in situ micromechanical testing with non-destructive tomographic techniques on micropillars before and after compression is illustrated in Fig. 1. Npg is synthesized by chemical dealloying of an Au-Ag solid solution featuring a mean ligament size of L ~30 nm (SI Fig. 1a-d). For scale-bridging analyses, one batch of the as-prepared material is additionally coarsened by a post-annealing treatment to achieve a mean ligament size of L ~300 nm (SI Fig. 1d-e). Details about the synthesis route can be found in the experimental description. A ligament size distribution is obtained on both length scales, which is broadened upon annealing by a factor of about two (SI Fig. 1f). Regarding the dependency of yield strength on the ligament size, nanoscale sponges are obtained featuring an intrinsic distribution of mechanical strength by its differently sized interconnected nano-struts. Upon mechanical loading (see the section below), complex stress fields are additionally superimposed, as triggered by the 3D mesoscale sponge topology and surface morphology. Npg pillar samples are site-specifically fabricated (from a single grain in npg) by advanced FIB lift-out techniques on top of tomography tips on both respective length scales (SI Fig. 2, SI Fig. 3). To analyze the crystal structure and pillar orientation after FIB preparation, selected area electron diffraction (SAED) is performed in case of the small-scale sample, while electron backscattered diffraction (EBSD) is employed for the large-scale sample. Both diffraction techniques demonstrate the single crystalline nature of each pillar on its respective length-scale. Only a small defect-enriched layer is identified by SAED in the outer shell of the small-scale sample as a result of FIB damage (SI Fig. 4). Furthermore, residual Ag content of ~6 at.-% is still present in the samples, which is concentrated in the as-dealloyed material in local Ag-rich clusters with a size of about 20 nm and up to 25 at.-% Ag as shown in the chemical mapping derived from energy dispersive x-ray spectroscopy (EDXS) in TEM (SI Fig. 5). This agrees well with earlier observations of residual Ag content in npg of ~6 at.-%. Both obtained pillar samples, as well as the respective 3D network structures derived from non-destructive tomography methods, are presented in Fig. 2a, b, respectively. The corresponding tomographic tilt-series and animations of the 3D reconstructions are shown in Supplementary Movies 1-4. On the small length-scale, a pillar with a ligament size of L ~30 nm, a pillar diameter of Ø ~400 nm and a pillar orientation along <137> is prepared, while on the larger scale a pillar with a ligament size of L ~300 nm, a pillar diameter of Ø ~4 µm and a pillar orientation along <013> is obtained. The derived 3D structural information is used to evaluate the comparability of both network geometries, by 3D analyses of topology and surface morphology, i.e., local thickness distribution of ligaments, relative density, scaled genus density and interface shape distribution function (ISD). The following results are hereby obtained: During annealing the average local thickness of the ligaments increases from ~28 nm in the small-scale sample to ~260 nm in the large-scale sample (SI Fig. 6a, b). The calculated relative density of the large-scale sample (~39%) is slightly higher compared to the small-scale sample (~35%), which might result from a slight densification of the sponge network upon annealing. The average connectivity of the network structure, which is indicated by the scaled genus density (defined by Eqs. 9-11) stays nearly constant, yielding 0.076 (small-scale sample) and 0.074 (large-scale sample) and is in close agreement with previous literature data on npg and very different from artificial networks based on e.g. spinodal or gyroid structures (c.f. SI Fig. 7). Last to mention is the observation of a shift of the ISD pattern (surface morphological characterization) along the minimal surface () after annealing (SI Fig. 8), which happens since the coarsening process is driven by the minimization of surface free energy.
Figure 2c shows the results of in situ compression testing in TEM (Supplementary Movie 5) and SEM (Supplementary Movie 6) up to an engineering strain of 16% on both length scales. Unloading segments are performed in regular strain-intervals to calculate the sponge's Young's modulus, and to evaluate plasticity and densification. The mechanical behavior is described in both cases by an initial 'elastic'-like loading of the entire network structure, characterized by a constant slope up to a strain of ~5% at which a drastic change of slope occurs. This point is defined as the global yield point. The corresponding stress describes the strength of the nanoporous network and amounts to MPa (small-scale sample) and MPa (large-scale sample). These values are used to calculate the yield strength of the solid (yield strength of ligaments) by using the macroscopic foam scaling laws derived from Gibson and Ashby for comparison with former literature studies. The scaling laws are further used to re-calculate the solid Young's modulus (Young's modulus of ligaments) from the sponge Young's modulus, which is GPa and GPa. Please refer to the Supplementary information on pages 10-12 (SI, Fig. 9 and SI note 1) for further details on the applicability of the Gibson and Ashby scaling equations. Furthermore, all mechanical properties of npg samples under in situ compression tests are summarized in Table S1 in the Supplementary information.
After the global yield point the stress increases, which is attributed to strain hardening (and slight densification effects, i.e., vanishing pore space/touching ligaments, since the sponge elastic modulus is slightly increasing). However, severe plasticity takes place nearly immediately after loading (before the global yield point), which is indicated by the remanent plastic strain in early unloading segments (before ~5% strain). This early plasticity concentrates at local weak spots of the network structure and can be visualized by applying digital image correlation analysis (DIC) to in situ compression series in the SEM (SI, Fig. 10). The DIC further reveals that plasticity occurs very inhomogeneously and localized in npg, which leads to the evolution of local strain gradients during deformation (SI, Fig. 10, Supplementary Movie 7). Therefore, weak spots in the network structure can easily affect the overall network stability and trigger, e.g., buckling of the struts during micropillar compression (SI, Figs. 10-11, Supplementary Movies 8-9). In the large-scale sample, early plasticity and inhomogeneous deformation occur primarily in the upper part of the pillar (see SI, Fig. 12, Fig. 5b), while plasticity in the small-scale sample evolves in a slightly more homogeneous manner (Supplementary Movies 5-6, Fig. 2c). This difference influences the subsequent densification behavior. In the large-scale sponge, densification begins in a highly localized manner near the indenter contact in the upper pillar region at a strain of 0.09. At this point, some ligaments start to come in contact with each other (see white arrow in SI Fig. 12). This contributes to hardening and is also evident in the stress-strain plot in Fig. 5, where a steeper stress increase occurs after the 6th loading cycle (strain of 0.09). However, due to its localized nature and the limited compression applied in this study (strain of 0.16), the overall impact of densification remains relatively minor. For higher compression levels beyond a strain of 0.16, its influence is expected to be significantly more pronounced. For the small-scale sponge, densification does not play a role up to the maximum experimental strain of 0.16, as plastic deformation is more uniformly distributed. Please also refer to the Supplementary information on pages 15-18 (SI note 2) for a more detailed discussion on what triggers strain localization, inhomogeneous deformation, and the role of local densification in the mechanical response of the small-scale and large-scale sample.
An experimental 3D structure derived from the small ligament size (L ~30 nm) npg using 360°-ET is used as an input for reconstructing atomistic configurations for large-scale atomistic simulations (Fig. 1). This experimentally informed (ExIn) approach allows a one-to-one comparison of experimental and simulated mechanical response. The correlation of local stress fields and associated crystal defects provides the explanation of the fundamental defect mechanisms observed in the experiment. To investigate the topology-dependent deformation behavior of npg at the atomic scale, analogous simulations are performed on a geometrically constructed (GeCo) npg sample (gyroid structure) with an average L and close to the ExIn sample. The configurations of undeformed and deformed (at 0.27 strain) simulated npg samples and the corresponding engineering stress-strain response (engineering stress, , as defined in Eq. 7) are shown in Fig. 3a-c. The GeCo sample shows roughly two times higher Young's modulus (fitted in the elastic regime of engineering stress-strain curves, = 14.0 GPa) and engineering compressive strength (defined as at the global yield point, = 153 MPa) than the ExIn sample ( = 7.6 GPa, = 72 MPa). The effective Young's modulus of the ExIn sample unloaded at 0.16 strain calculated from the unloading curve amounts to 9.2 GPa, which is 4.2 times higher than the value of the experimental small-scale sample ( = 2.2 GPa). The deviation in experimentally measured modulus from the simulation value arises primarily from differences in sampled volume, due to computational constraints affecting structural representativeness, and from the lack of rigid substrate support in experiments, which introduces additional compliance not accounted for in simulations. Both the simulated ExIn and experimental small-scale samples show strain hardening behavior during the compression, as evidenced by the steady increase in sessile dislocation density resulting from dislocation interactions (see SI, Fig. 13). The simulated ExIn sample shows densification behavior after 0.20 strain as indicated by the reduction of surface area (SI, Fig. 13), and neighboring ligaments are in contact at a strain of 0.27 as shown in Fig. 3a. However, no densification is observed in the simulated GeCo sample at the same strain level. The mechanical responses of atomic samples agree well with previous FE simulations on realistic npg structures obtained from FIB tomography and the GeCo gyroid structure where npg shows topology-dependent mechanical properties. The topology and surface morphology of simulated samples are characterized via average local thickness, nodal connectivity, scaled genus density and ISD, see SI Figs. 6-8. The ExIn and GeCo samples show distinct topologies and surface morphologies. Interestingly, the ExIn sample shows a similar flow behavior compared to the in situ mechanical testing on the small-scale sample. In particular, the strain at yielding and the flow stress are comparable in the experiment and the simulation.
True stress (, as defined in Equation 8) measures the average internal material interaction without the sudden jump of stress in caused the virtual indenters to partially lose contact with the ligaments. The evolution of and percentage of HCP (hexagonally closed packed) atoms of simulated npg samples during the simulated compression tests are studied (Fig. 3d). The rise of HCP atoms correlates with the initiation of plasticity since atoms within an HCP environment are considered to represent planar faults of the FCC (face centered cubic) lattice, e.g. stacking faults and twin boundaries, which occur when partial dislocations are present. Similar to the experimental observations (see SI, Fig. 10), the ExIn sample exhibits an early yielding before it reaches the true compressive strength ( = 190 MPa, defined as the true stress at the global yield point) due to the localized stress concentration originating from the realistic network connectivity and inhomogeneous distribution of ligament size (see SI Fig. 6 and SI Fig. 7). In contrast, the GeCo sample reaches the true compressive strength = 423 MPa right after the initiation of plasticity since the stress state and activation criteria of nucleation sites in each unit cell of a periodic gyroid structure are identical (SI, Fig. 14). Furthermore, the first stress drop of the ExIn sample is less abrupt than the one for the GeCo sample, see Fig. 3c, d. The stress is released by the nucleation and propagation of dislocations. The higher rate of the increase of HCP atoms in the GeCo sample indicates that more dislocations are simultaneously activated after the initiation of plasticity. An abrupt transition in the increase of HCP atoms is observed in the GeCo sample after the pronounced stress drop. The mechanical properties of the simulated npg samples are summarized in Table S2 in the Supplementary information.
The size-dependent deformation behavior of npg below L = 30 nm is investigated by comparison of MD compression tests on real-size (L = 30 nm) and scaled-down (L = 5, 7.5 and 10 nm) samples (Fig. 4). The true stress-strain response of atomistic simulated npg with different ligament sizes is shown in Fig. 4a and SI, Fig. 15a. The stresses at first plastic event (, defined as the true stress at the onset of plasticity) of simulated npg samples with different ligament sizes are normalized by the values of samples with L = 30 nm, see Fig. 4b. In both simulated npg samples, decreases with decreasing ligament size. A similar trend is observed with the deformation of gold nanowires with their axis along the [137] crystallographic orientation, identical to the compression axis of the npg samples, see Fig. 4b. This abnormal "smaller is weaker" trend can be explained by the effect of surface-induced stress on surface dislocation nucleation. SI, Fig. 15c shows the resolved shear stress state along the Burgers vector on the slip plane (b) in a representative junction in the GeCo samples with different ligament sizes before compression. The partial dislocation is first activated in the further compression tests, therefore the stress state before mechanical loading reflects the effect of surface-induced stress on the dislocation activation. The stress level is significantly higher in the smaller samples, since the effect of surface-induced stress is more pronounced in the samples with a higher surface-to-volume ratio. Surface-induced stress assists surface dislocation nucleation by reducing the applied stress needed to overcome the activation barrier for nucleation. After yielding, a stress drop is only observed in the real-size samples (see Fig. 4a and SI, Fig. 15a). This is caused by the nucleation of many dislocations and can be explained by the much larger number of surface dislocation nucleation sites than are present in the scaled-down samples.
In the simulations as well as in the corresponding experiment the strain rate is constant. For the present case where dislocations are nucleated and then move successively very quickly over a distance before being annihilated at the surface or immobilized, the Orowan equation can be written as:
with being the dislocation density. To understand the size-dependence of the true flow stress (see Fig. 4a and SI, Fig. 15a) can be determined from the simulations, see Fig. 4d and SI, Fig. 15b. There, is normalized by multiplying it with the mean ligament size . The rationale is that in order to maintain the same plastic strain gradient, the number of geometrically necessary dislocations (GNDs) N, needs to scale in proportion to , see Fig. 4d. From Fig. 4c one can see that the large-scale sample has more dislocations than would be required to maintain the same strain gradient than in the smaller samples. Given a constant and , the (initially) larger for the large-scale sample compared to the small-scale samples, it immediately follows from Eq. 1 that , with the later term probably being , i.e., in the large-scale sample the dislocations glide not so far compared to the ligament size than in the small-scale samples, where many can just escape via the surface. Only after longer deformation and at larger strains, also in the small-scale samples the dislocations accumulate inside the ligaments at the same rate as in the large-scale sample. Assuming similar deformation and strain gradients independent of size, the additional dislocation density in the large-scale sample is not geometrically necessary but rather statistically stored, and as such can contribute to the deformation, requiring less stress for the same strain increment than the small-scale sample with fewer dislocations. Our observations show that in the real-size npg (L = 30 nm), dislocation-dislocation interactions are common (SI, Fig. 16). In the simulated npg with ligament sizes ranging from 5 nm to 10 nm, plasticity is governed by the dislocation nucleation, where dislocations can easily nucleate and annihilate at the free surfaces without interacting and forming immobile dislocations. Their flow stress is therefore mostly dominated by the nucleation stress to generate dislocations at the surface.
The deformation behavior of npg on larger length scale ( = 300 nm) is studied via experimentally informed FE simulations using the meshed reconstruction from nano X-ray computed tomography (nano-CT) (see Fig. 2a). The FE simulations with the von Mises model are parameterized with small-scale data from compression experiments on gold nanopillars with a comparable characteristic length ( = 400 nm) and bulk gold data. The stress-strain response obtained from the FE simulation using small-scale data fits well to the in situ compression experiment on the correlative npg ( = 300 nm), see Fig. 5b and Table S1 and S2. In contrast, the stress level of the FE simulation using bulk-scale data deviates far from the experiment. Regarding the elastic properties, the sponge's Young's modulus from experiments and simulations are in very good agreement, as shown in Table S1 and S2 in the Supplementary information. Since the macroscopic modulus in the related crystal orientation is used in the modelling, no anomalous low compliance of npg is reported here. Furthermore, the modelling results highlight the good representation of the network geometry by nano-CT and demonstrate the size effect in mechanical strength independent of the Gibson and Ashby scaling law. As reported by the MD simulations on the small-scale npg ( = 30 nm) in Fig. 3d, early yielding is also observed in the FE simulations on the large-scale npg ( = 300 nm). Here, the simulated nodes reach the plastic limit at the early stage of the deformation process before global yielding (c.f. Fig. 5a, b). Although the applied von Mises model is a macro-scale material model, by parameterizing with small-scale data it represents well the elastic and plastic behavior of the complex nanosponge structure.
After deformation, the small- and large-scale samples are studied again by means of non-destructive tomography (Supplementary Movies 10-11, Supplementary Movies 3-4) to identify 3D regions of interest (ROIs) at which plasticity localizes. From such a region, a FIB-lift out sample is prepared in <110> orientation (in lamella normal determined by correlative SAED analysis) and investigated by TEM to analyze the corresponding crystal defects. Figure 6 summarizes the results on the small-scale sample analyzed by means of 360°-ET and high-resolution TEM (HRTEM). Figure 6a shows the high-quality 3D reconstructions (without missing-wedge artefacts) of the undeformed and deformed network in the same outer view and in the middle section of the FIB lift-out. The defects are analyzed at the regions where the strain is localized in single ligaments and ligament junctions (Fig. 6b) and are identified as dominantly micro-twins, stacking fault tetrahedra (SFTs) and small-angle grain boundaries (SAGB). As an example, one ligament is shown in Fig. 6 (marked by black arrow), which is located at the outer rim of the pillar, initially parallel to the loading direction (<137>) and exhibiting a size of ~30 nm. Upon compression, this specific ligament is dominantly deformed by bending/buckling in its middle section, which is enabled on the atomic scale by GNDs forming a SAGB. SAGBs are also observed in larger ligaments enabling the geometric adaption of the network structure (by lattice rotations of up to ~10°). In specific cases, also extended SAGB networks are observed in between neighboring larger ligaments (SI, Fig. 17). Contrarily, no SAGBs but stacking faults/micro-twins are observed in smaller ligaments (SI, Fig. 18). Specifically, a higher dislocation density is often present at ligament junctions, with full and partial dislocations, dislocation locks or complex fault structures, e.g. SFTs (Fig. 6, SI, Fig. 18). This effect can be attributed to local stress concentrations at ligament junctions (as shown in Fig. 6b) causing dislocation nucleation, but may also result from statistical storage of dislocations, whereby dislocations from different ligaments meet and interact with each other. In many cases, micro-twins are identified accompanying plastic deformation, while only a few are identified in the undeformed material (SI, Fig. 19). In general, more defects and structural disorder evolve with increasing local strain leading to the steady formation of new sub-grains and a polycrystalline nature within npg (SI, Fig. 19). As mentioned before, weak spots can easily trigger local plastic deformation. Npg exhibits locally intrinsic flaws, which can be caused by inhomogeneous dealloying along grain boundaries or inside of grains. These defects can trigger strain localization but are often not directly visible by a pure 2D analysis. SI, Fig. 20 and Supplementary Movie 12 illustrate this case and emphasize the importance of 3D analysis for understanding the local deformation in npg.
Since the ExIn simulations are performed on the geometric network structure derived from the experiment, the topology-dependent deformation behavior of npg can be analyzed in a correlative manner by comparison of defect distributions in an identical ROI from experiment and simulation. As shown in the TEM image of the deformed small-scale sample in Fig. 7a, defects are mainly localized near the junctions of the network structures. The defect distribution of the deformed ExIn sample ( = 30 nm) from MD simulations in Fig. 7b correlates well with the identical area as observed by TEM. Furthermore, the characteristic defects in the deformed small-scale sample, e.g. micro-twins, SAGBs and SFTs, are also widely observed in the simulated npg sample ( = 30 nm) after unloading from 0.16 strain.
The formation of SFT and SAGB shows a strong size dependency in MD simulations within the studied size range ( = 5-30 nm). SFT and SAGB are characteristic defects in the deformed real-size npg samples ( = 30 nm), but very few of those defects are observed in the deformed scaled-down samples ( < 10 nm), see SI, Fig. 16. SI, Fig. 21 and 22 show the mechanism of formation of deformation-induced SFT and SAGB in the ExIn sample ( = 30 nm) during the compression test. A complex local stress state (see SI, Fig. 23) combined with interaction and cross-slip of full dislocations is necessary for the formation of SFT. This is different to the mechanism of vacancy-induced SFT reported in a previous study of npg. The formation of SAGB is due to the interaction between an array of full dislocations and partial dislocations, which leads to the formation of extended dislocation nodes. A more detailed description of the formation of SFT and SAGB can be found in the SI. A simple line-tension-based model with the incorporation of the crystallographic orientation dependency by including the Schmid factors for the full and leading partial dislocations estimates the critical size for nucleation of full dislocation and partial dislocation:
where 0.5 and 1.5 for edge and screw dislocations, respectively. is the shear modulus, and is the stacking fault energy. and are the magnitudes of Burgers vectors of the full and the partial dislocations, respectively. and are the largest Schmid factors of the full and the leading partial dislocations. Here, taking 1, 0.498 (for the slip system, see Table S3), 0.431 (for the or slip system), and other parameters calculated using the used interatomic potential, is around 24 nm. The resolved shear stresses of leading partial dislocations in the simulated npg samples showed anisotropic plasticity that correlated well with the Schmid factors (see SI, Fig. 24), which agree well with a previous crystal plasticity study on single-crystalline stochastic honeycombs. Therefore, the crystallographic orientation of the single-crystalline npg was taken into account in the estimation. The critical size with this orientation information is 24 nm which is about 2/3 of the one without considering the orientation dependency (i.e., when = 1, 35 nm). The mean ligament size of the real-size simulated samples is around 30 nm, which is higher than the estimated . Therefore, the nucleation of full dislocations is expected to occur mainly in the real-size sample and less in the scaled-down samples. For the simulated real-size ExIn sample ( = 30 nm) with a normalized dislocation density = 0.062 nm after global yielding (3.3% strain), 132 (~42%) full dislocations were detected out of 315 dislocations. For the corresponding scaled-down ExIn sample (= 10 nm) at a similar level of normalized dislocation density (~0.082 nm), only 46 (~29%) full dislocations were found out of 161 dislocations. Except for the size-dependent preference of dislocation nucleation, dislocations in the smaller samples have a greater probability of escaping at the free surfaces than of interacting with one another as shown in the evolution of normalized dislocation density in Fig. 4c. The size-dependent dislocation nucleation and interaction explain the formations of SFT and SAGB observed in the real-size npg samples.
The observed agreement in flow stress between MD simulations and experiments on the npg samples ( = 30 nm), despite the orders-of-magnitude difference in strain rates, requires consideration beyond surface dislocation nucleation. Structural heterogeneity and surface conditions must be taken into account. The activation volume associated with surface dislocation nucleation typically falls within the range of 1-10b, leading to a strong dependence of nucleation stress on both strain rate and temperature. In npg, structural heterogeneity and variations in surface conditions give rise to a broad distribution of nucleation stresses, contributing to the pronounced stochastic nature of surface dislocation nucleation similar to thermal activation processes. This heterogeneity can mitigate strain rate effects by enabling localized plasticity initiation at lower applied stresses. Experimental investigations on nanoporous gold (L = 55 nm) using strain rate jump compression tests (strain rate ranging from 10 to 10/s) have demonstrated exceptionally low strain rate sensitivity in the early stages of plastic deformation (below 0.2 strain), where dislocation nucleation governs plasticity. A similar conclusion was drawn from in situ TEM tensile experiments on Pd nanowires (30 to 100 nm diameters), which exhibited weak strain rate dependence over a comparable experimental strain rate range (10 to 10/s) but a pronounced sensitivity to temperature. Furthermore, MD simulations of nanoporous gold (L = 6.4 nm) at 300 K, performed over strain rates ranging from 10 to 10/s, demonstrated that strain rate effects on flow stress were minor below ~10/s. These findings suggest that the apparent consistency in flow stress between MD simulations and experiments may arise from compensating effects between strain rate sensitivity and local stress heterogeneities. Additionally, differences in experimental and simulation conditions, such as the presence of Ag solutes and pre-existing defects in experimental samples, as well as the limited system size in simulations, must be taken into account.
Figure 8 shows the 3D analysis of the large-scale sample after deformation and the deformation microstructure. For local 3D strain analysis, the 3D reconstructions of the undeformed and deformed network obtained by high-resolution nano-CT (without missing-wedge artefacts) are correlated. Figure 8a shows the reconstructions in the same external view and middle section. The high-quality 3D data of the network structure before and after deformation allows the calculation of the local displacement field in 3D evolving upon compression by methods of digital volume correlation (DVC), shown in Fig. 8d. This method gives the unique possibility to compare the experimentally derived displacement field (Fig. 8d) with the one observed in the experimentally informed FE simulation (Fig. 8e), performed on the same structure. A qualitatively good agreement between both displacement fields and therefore both methods is found, which corroborates the parameterization using the small-scale data used in the FE simulation. For the analysis of crystal defects, a TEM lamella is prepared along a <100> orientation by performing a FIB lift-out from the central region of the deformed large-scale sample, but slightly angled with respect to the pillar axis. The targeted crystal orientation with respect to the npg network is identified by correlative EBSD and 3D analyses of the reconstruction (in the deformed state). Figure 8b shows the as-prepared lamella in the TEM and reveals a bulk-like deformation microstructure in locally yield regions, with extended networks of full dislocations and dislocation walls. This observation is in strong contrast to the observed defects in the small-scale study but is consistent with the change in deformation mechanisms predicted by above line-tension-based model, i.e. the occurrence of full dislocations at larger length scale and partial dislocations at smaller length scale. By analyzing the equivalent plastic strain (PEEQ) in the corresponding experimentally informed FE simulation (Fig. 8c) 'hot spots' are identified, i.e., ROIs at which strain localizes. The strain localization often occurs at ligament junctions, which act as plastic hinges that experience high bending moments. By correlating both, TEM defect and FE strain analysis, a good agreement between the local occurrence of high dislocation densities and plastic strain concentrations is observed.
By the comprehensive linkage of correlated microscopy techniques and simulation methods, a scale-bridging deformation mechanism landscape is derived (SI, Fig. 25), showcasing size effects on dislocation nucleation and interaction in complex nanosponges, as exemplarily shown for npg. In the smallest size regime with a characteristic ligament size of around ten nanometers, corresponding to the scaled-down samples studied by MD simulations in the present work and typical for most atomistic studies, the influence of surface-induced stress on surface dislocation nucleation is very pronounced. The surface-induced stress can either assist or hinder the surface dislocation nucleation depending on the relative orientation between applied strain and crystallography. The nucleation of partial dislocations is strongly preferred at this length scale, as well as the formation of deformation twins results from continuous nucleation of leading partial dislocations on adjacent slip planes. Dislocations are unable to be stored in such small dimensions. Therefore, the effect of dislocation-interaction-related hardening mechanisms is limited. In the intermediate size regime with a characteristic length of a few tens of nanometers, represented by the small-scale experimental sample (L ~30 nm) in the present work and studied by in situ nanomechanics in TEM, 360°-ET, HRTEM and MD simulations, the nucleation of full dislocation is preferred. Furthermore, the ligament size is large enough for dislocation interactions to take place. Therefore, the dislocation density multiplied by L is higher at that scale than for smaller systems. Furthermore, the formation of SAGB, SFT and other defects resulting from the interactions of full dislocations are the expected mechanisms on this length scale. In the size regime of hundreds of nanometers, represented by the large-scale experimental sample (L ~300 nm) in the present work and studied by in situ micromechanics in SEM, nano-CT, (HR)TEM and FE simulations, the deformation is governed by dislocation-dislocation interactions and classical dislocation sources inside the ligaments. This leads to a bulk-type deformation behavior, which can be successfully modeled by von Mises type isotropic plasticity model. The size dependence of the yield and flow stress needs, however, to be taken into account. The underlying reason for this size dependence is most probably the truncation of dislocation sources.