Revealing Three-Dimensional Morphology in Nanoporous Gold Using Three-Dimensional X-Ray Fresnel Coherent Diffractive Imaging Tomography

Many important potential applications and intriguing fundamental aspects of nanoporous and bi-continuous metal structures have been discovered in recent years [1–3]. Dealloying is an effective method to fabricate these nanoporous and bi-continuous structures [4] with evolving methods including chemical and electrochemical dealloying [5–7], liquid metal dealloying [8–12], solid-state dealloying [13–15], vapor phase dealloying [16–18], and compound-decomposition dealloying [19]. Applications in energy storage and conversion have also been developed, including lithium ion batteries [20–24], sodium ion batteries [25,26], potassium ion batteries [27], fuel cells [28], super-capacitors [29], and catalysts [30–32].

Among the various nanoporous metallic materials, nanoporous gold (np-Au) prepared by dealloying has attracted great attention due to its range of potential applications [6,33,34]. These include bio-sensors [35–37], surface-chemistry-driven actuators [38], catalysis [39,40], super-capacitors [29], and Li-ion battery anodes [41]. The optical, electrochemical, and mechanical properties of (np-Au), and its performance in these applications, typically depend strongly on the degree of porosity and size of the gold ligaments. Dealloying by free corrosion is one of the simplest and most widely used methods for fabricating (np-Au). However, a major question raised is whether this approach can result in a homogeneous distribution of the pores. Coarsening of the pores as the dealloying front propagates through the sample can lead to growth of the ligament size, decrease in the porosity, or a combination of both.

Various methods have proven indispensable for studying the morphology of these materials and its relation to functionality including small angle X-ray scattering [42,43] and transmission electron microscopy [44,45]. Scanning electron microscopy (SEM) is generally used to characterize the ligament size and porosity at the surfaces of nanoporous metals. To quantify the ligament size and porosity distribution in bulk specimens of np-Au, an electron-dense, complex, sponge-like three-dimensional (3D) structure, characterization techniques with sufficient penetration and 3D imaging capability are required, in addition to complementary bulk analysis which provides spatially averaged information. Transmission X-ray microscopy (TXM) was used to study coarsening in a thick sample of np-Au in 3D by tomographic methods [46], propagation of the dealloying front during np-Au formation by in situ methods [47], and the dependence of dealloying velocity on alloy composition [48]. TXM was also applied to study processing-structure–property correlation in liquid metal dealloying for fabricating nanoporous materials with less noble elements [10,12]. X-ray Bragg coherent diffractive imaging (Bragg CDI) provides the capability to measure lattice displacement and strain filed, and to identify individual grain, and has been applied to study strain evolution in dealloying of nanoporous Au [49,50]. X-ray ptychography has also been applied to analyze np-Au [51,52]. X-ray Fresnel coherent diffractive imaging (FCDI) [53] is similarly well suited to study dense, thick specimens but with a higher spatial resolution than that of the X-ray lenses typically used in transmission X-ray microscopy. Prior work have demonstrated FCDI tomography using a glass capillary as a test object [54]. In this paper, we apply FCDI tomography to quantify the nanoscale porosity, ligament size distribution, and their homogeneity within the interior of a bulk sample of nanoporous gold formed by free corrosion dealloying.

We prepared the material used to fabricate the nanoporous gold sample by alloying silver and gold with an arc-melting technique into a Ag–30 at% Au alloy ingot, drew the alloy in to a wire of 50 µm diameter, cast it within a glass tube, and then thinned an exposed tip of the wire to 0.5–1 µm diameter by focused ion beam milling. We dealloyed the thinned tip to fabricate the nanoporous structure by submerging it in nitric acid (11.7M, 75 vol%, 68–70% assay, in de-ionized water) for 30 min. A SEM image of the resulting nanoporous gold sample is shown in Fig. 1(a).

We imaged the sample by X-ray FCDI at the 2-ID-B beamline [55] at the Advanced Photon Source, Argonne National Laboratory. A coherent X-ray beam with an energy of 2.5 keV (above the Au M5 absorption edge at 2.2 keV) was used to optimize the sample contrast. The sample was placed ∼0.6 mm downstream of the focus of a Fresnel zone plate lens with a 50 nm outmost zone width and 16.36 mm focal length. Fresnel coherent diffraction patterns were measured 332 mm downstream of the focus with a charge-coupled device (CCD) camera (2048 × 2048 pixels with a size of 13.5 × 13.5 µm). Further discussion on the FCDI method can be found in prior work [56].

Diffraction patterns were measured at every 5 deg over a 180 deg range of sample projections to collect a tomographic dataset (Figs. 1(b) and 1(c)). The exact sample distance to the zone plate was determined by fitting a circular pattern to the focus distance from an initial estimate of the reconstruction (from the central holographic region of the diffraction data). Two sets of 100 frames of data were taken at each projection angle. One set was taken with a shorter exposure time (2–2.5 s) to measure the signal at small momentum transfer. The other set was taken with a longer exposure time (7–7.5 s) to measure the higher resolution signal at large momentum transfer. A Kapton attenuator was used for the latter measurement in order to avoid saturating the center of the CCD. A distinctive ring was present around the center of the diffraction patterns, indicating that the sample had a characteristic length. The highest resolution data extend to 0.4 nm⁻¹ in reciprocal space. So-called “white-field” data (with the sample removed to measure the incident illumination) and “black-field” data (with the X-ray beam shuttered to measure the CCD background signal) were also collected.

Reconstruction of tomographic projections from the Fresnel coherent diffraction patterns involved two steps. First, the complex amplitude of the incident illumination was recovered from the white-field data. Second, phase retrieval of the sample diffraction data was performed to recover the complex transmission function of the nanoporous gold sample, using the algorithm developed by Williams et al. [57]. Using a tight support based on the approximate sample shape as a constraint significantly decreased the number of iterations needed and improved the reproducibility of the reconstructions.

The projections were aligned manually defining a box (∼1 µm × 1 µm) centering the tip of the nanoporous gold sample and then shifting the projections pixel by pixel to maximize the correlation coefficient between projections. A standard filtered back-projection algorithm [58] was then applied to the aligned projections to obtain a 3D reconstruction. Segmentation of the reconstructed images was conducted by thresholding and was then applied to a sub-volume (∼300 nm × 300 nm × 900 nm) taken from the center of the tomography reconstructed dataset. Cropping into a sub-volume can avoid the surface region that has been slightly damaged by the ion beam during the sample preparation process, as seen in the SEM image (Fig. 1(a)). Within ±8% of theoretical average porosity (70%), different threshold values were chosen. The porosity and the pore size distribution were calculated as a function of position from this volume. The effects of choosing different threshold values to the porosity and pore size will also be discussed in Sec. 3.

The porosity was calculated along the long axis (axial direction) of the sample from the fraction of the occupied volume within the overall sample volume. The pore size was represented by reciprocal of area density (Sv⁻¹), calculated from a triangulated mesh used to approximate the surface. The gold volume fraction (1-porosity) was calculated along the radial direction of the sample.

The reconstructed sample absorption for three representative projection angles through the nanoporous gold sample with a voxel size of 5.9 nm is shown in Figs. 2(a)–2(c). They were calculated from the reconstructed magnitude and phase of the reconstructed transmission function. The tabulated value of δ = 3.211 × 10⁻⁴ was used. The value δ is defined as the real part of the refractive index of the sample for X-rays. The effective field of view is changing as a function of angle due to the fact that the center of the sample tip was not perfectly aligned to the center of rotation, and therefore the region of illumination was changing while rotating the sample. A zoom-in view of Fig. 2(a) was shown in Fig. 2(d). As the method is based on phase retrieval, Fresnel CDI can also provide better phase-contrast image, which can be applied in the future for materials with low absorption contrast.

A cross section of the reconstructed 3D volume of the sample is shown in Fig. 3(a). The porous nature of the structure is clearly visible (Fig. 3(b)). Figure 3(c) shows the details of the structure after segmentation.

During the dealloying process, the silver atoms that occupied 70% of the sample volume were dissolved into the nitric acid solution, leaving a nanoporous gold structure with ∼70% overall porosity. However, the porosity may have varied within the sample as a result of heterogeneous pore formation. The porosity was calculated from a total of ∼160 thin slabs (300 nm × 300 nm × 5.9 nm), with the x–y plane perpendicular to the sample axis (z) and plotted as a function of the distance between the cross-sectional planes to the sample tip (d). The result is shown in Fig. 4 for three different thresholds, which yield an average porosity ranging from 62.3% to 74.0%. Although the average porosity value depends on the threshold value used for segmentation, the overall trend in the porosity distribution as a function of the position remains unchanged. The insets in Fig. 4 show the nanoporous gold morphology at corresponding sample locations.

The ligament size is an important parameter determining the properties of nanoporous gold, but this can be difficult to define because the porous structure forms an open network. Here, we used the characteristic feature size or area density, S_V, defined to be the gold surface area per sample volume. The reciprocal of the area density, Sv⁻¹, is a good representation of the feature size [46]. We calculated Sv⁻¹ as a function of d with a volume of ∼300 nm × 300 nm × 30 nm at each position d. The result is plotted in Fig. 5. A slight decreasing trend was observed in the features size distribution, potentially due to the simultaneous coarsening occurred during the dealloying. However, the variation is small, and the feature size distribution remains relatively homogeneous. The same threshold values were used here as in the porosity calculation. The threshold which results in a higher porosity also gives a higher Sv⁻¹. The insets in Fig. 5 show the sample surface at the positions corresponding to the maximum and minimum characteristic feature sizes, Sv⁻¹, respectively.

The average threshold value, porosity, and the pore size are summarized in Table 1. Regardless of how the porosity and ligament size depend on the threshold value, the standard deviations of their values from the average as a function of axial position remains small, 3.3–3.5% for the porosity and 0.8–1.9 nm for the ligament size. This result shows that, independent of any rearrangement of the gold atoms and coarsening during the dealloying process, the porosity and the ligament size distributions are nearly homogeneous throughout the sample with only slight variation. Analysis on sample with larger size could be conducted in the future to further understand if there is limitation of long-range mass transport in the dealloying process that could lead to morphological heterogeneity.

We used Fresnel CDI to image a nanoporous gold sample with diameter ∼500 nm and height ∼1.5 µm. Diffraction patterns collected at every 5 deg were reconstructed into projections of the sample absorption, which were then reconstructed into a 3D volume by tomographic methods. We calculated the porosity and ligament size distribution as a function of axial sample position from thin slabs extracted from the reconstructed 3D sample volume. Small variations in these parameters indicate that the free corrosion can be used to fabricate nanoporous gold with a nearly homogeneous pore distribution. This analysis provides valuable insight for developing devices including sensors and actuators and for energy-related applications such as catalysts, super-capacitors, and battery supports based on this material. In the future, Fresnel CDI with smaller angular step size for higher resolution characterization would be important to provide better 3D analysis. Future work can also utilize ptychographic tomography to further investigate the 3D morphology of materials fabricated by dealloying for energy-related applications.

The authors are grateful to Dr. Qun Shen and Professor David Dunand for encouraging this project. Enju Lima is acknowledged for her efforts in the experiment. The authors acknowledge the support of the Australian Research Council and the Australian Synchrotron Research Program. Work at the Advanced Photon Source and Center for Nanoscale Materials was supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences (Contract No. DE-AC02-06CH11357). Karen Chen-Wiegart also acknowledges the support from the Department of Materials Science and Chemical Engineering, the College of Engineering and Applied Sciences, and the State University of New York at Stony Brook, as well as from the Brookhaven National Laboratory. This material is based on work supported by the National Science Foundation (Grant No. DMR-1752839). Karen Chen-Wiegart acknowledges the support provided via the Faculty Early Career Development Program (CAREER) and Metals and Metallic Nanostructures Program of National Science Foundation. This research used resources of the National Synchrotron Light Source II, a U.S. Department of Energy (DOE) Office of Science User Facility operated for the DOE Office of Science by Brookhaven National Laboratory (Contract No. DE-SC0012704). Chonghang Zhao is grateful for the support of a student fellowship by the Joint Photon Science Institute at Stony Brook University.