Spatial Mapping of Bulk Elastic Strain in De-alloyed Nanoporous Gold using Four-dimensional Scanning Transmission Electron Microscopy

There is a growing interest in nanoporous gold (NPG) as a promising material for next generation biosensors, actuators, and catalysts. Formed by scalable top-down methods, the dealloying of Ag-Au precursors yields a mechanically stable, noble metal nanostructure (see Fig. 1) with active mass-specific surface areas on the order of several m2/g. This property is readily exploited for the abundance of binding sites in many useful applications. Throughout the porous layer, the predominance of surface atoms relative to the master alloy, coupled with the local curvature at the solid-pore interface, changes the strain state in the bulk of the solid phase [1]. The strain alters the macroscopic deformation of the material and is impacted by the adsorption and desorption of reactants [2]. Understanding and harnessing these strain effects are pivotal in advancing the design and optimization of NPG-based functional materials for enhanced performance in actuation and sensing applications. Among the techniques used for nanoscale strain resolution, four-dimensional scanning transmission electron microscopy (4D-STEM) stands out for its ability to quantify and spatially resolve lattice strain at varying magnifications [3]. In this work, 4D-STEM was used to map strain at multiple length scales, spanning the entire nanoporous layer and at the level of individual NPG ligaments. At the nanoscale, the magnitude and direction of elastic strain are known to depend on both the size and orientation of NPG features [4]. Using a relatively large spot size on the order of tens of nanometers, these localized effects were deconvolved from the broader strain distribution resulting from the corrosion process. Hence, this work presents a novel approach for the analysis of bulk strain in finely structured 3D nanomaterials. Additionally, for the first time, 4D-STEM was performed on de-alloyed Ag-Au-Pt (NPG-Pt), revealing the role of Pt on the strain distribution within individual nanoligaments. It is understood that Pt refines the initial structure, and furthermore segregates to ligament surfaces during high temperature treatment [5]. These effects are expected to influence the surface-induced strain, but the nanoscale mechanism has not yet been explored in detail in NPG-Pt. Ag77Au23 and Ag77Au21Pt2 alloys were de-alloyed electrochemically, producing NPG and NPG-Pt, respectively. For analyses at the ligament scale, nanoporous samples were also coarsened at high temperatures (400 – 600 °C), yielding larger feature sizes. All electron transparent cross-sections were made from a standard focused ion beam (FIB) lift-out procedure using a Hitachi NB5000 Dual-Beam FIB. 4D-STEM data were collected using a Hitachi HF-3300 TEM/STEM operated at 300 kV, where the acquisition protocol was controlled using Gatan DigitalMicrograph™ scripts written by D. R. G. Mitchell [6]. For low-magnification scans spanning the full porous layer, the probe diameter was estimated to be 20 nm. High-magnification scans of coarsened nanoligaments utilized a probe with an estimated diameter of 9 nm. Among other constraints, these lens configurations were chosen to maintain near-parallel beam illumination conditions for improved diffraction disk detection in the processing stage. This work also focuses on the influence and mitigation of optical distortions (e.g. elliptical and parabolic distortions [7]) which vary between the acquisition schemes. All 4D-STEM datasets were processed using py4DSTEM [8], an open-source Python package containing methods for the calibration and analysis of serial electron diffraction data. Results of analyses across the porous layer in NPG-Pt are shown in Fig 2. A spatial gradient of bulk strain was observed (Fig. 2C-D), which is explained by a decline in surface-stress-induced strain as nanoscopic features coarsened in solution. Regional ligament sizes estimated from high-angle annular dark-field (HAADF)-STEM images correlate well with the strain distribution (Fig. 2E), supporting the evidence for coarsening-induced strain relaxation. These results also coincide with in-situ X-ray diffraction studies of porosity evolution in NPG [9], although the evidence for regional variation in strain is a unique advantage of the spatially resolved approach used in the present work. Increasing the scan magnification to the scale of (coarsened) nanoscopic features, anisotropic distributions of strain were revealed at the interiors of ligaments (Fig. 3A-D). Relative to the nodes or connecting points in the microstructure (Fig. 3E), the crystals at ligament interiors were found to be compressed in the axial direction and expanded in the radial direction. This observation coincides with continuum mechanics models that predict anisotropic bulk strain coupled to surface stress for cylindrical solid geometries [4]. Additionally, deformation in coarsened NPG-Pt was measured larger than that of NPG, implying a more tensile in-plane stress at the solid-pore interface, concomitant with the presence of co-segregated Pt. These insights are important for the design of functional nanoporous metals in several potential applications. For example, surface-stress driven sensors and actuators with vastly improved sensitivity have been demonstrated as viable uses for NPG [2]. The findings suggest that alloying small fractions of Pt with Ag-Au leads to a stronger surface stress and corresponding bulk strain that may be harnessed in these applications. Stress and strain in the bulk of NPG(-Pt) is also critical to the plastic deformations that occur during mechanical failure, which must be considered in any practical scenario. Moreover, the advantages and limitations of extracting spatially resolved strain maps from TEM foils with finite thickness were explored in detail [10]. HAADF-STEM micrograph showing the morphology of NPG. Bulk strain analysis across complete porous layer in de-alloyed Ag-Au-Pt. (A) Secondary electron STEM image showing thinned NPG-Pt foil. The red box indicates the 4D-STEM scan region. (B) Bright-field TEM image at high magnification showing single feature with ligament width, L⁠. (C-D) Strain maps in (C) [111] crystal direction and (D) perpendicular direction. Lattice directions with respect to the scan orientation are indicated to the right of maps. (E) Average strain plotted as a function of (inverse) ligament width, L⁠. The dashed line indicates the best fitting trend. Strain distribution at the interior of a single NPG-Pt ligament coarsened at 600°C. (A-D) Maps depicting four strain tensor components, with overlays in the bottom left indicating directions with respect to the scan. (A) and (B) show radial and axial strains, respectively, showing anisotropy in elastic deformation. (C) and (D) show the shear and rotational strains, respectively. (E) The fit error, describing the variance in diffraction disk locations in the corresponding patterns at each scan point. The red box indicates the reference region from which the lattice of zero strain is calculated.

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