Imaging of Chemical Structure from Low-signal-to-noise EELS Enabled by Diffusion Mapping

Electron energy loss spectroscopy (EELS) performed in a scanning transmission electron microscopy (STEM) is a powerful spectroscopic technique which can uniquely achieve both atomic-scale mapping of a material's elemental structure while also containing high energy-resolution information of the local bonding and valence states [1]. Such measurements often exhibit low signal-to-noise ratios (SNRs) due to the fast scan times required for atomic-resolution chemical imaging and especially when low doses are required for radiation sensitive materials [2, 3]. Recently developed direct electron detectors (DEDs) can reduce readout noise and dead time, maximizing the information obtained from each inelastic scattering event [2]. Still, as we push for faster acquisitions and lower currents needed for challenging conditions brought on by cryogenic and other in-situ STEM experiments, low SNR EELS data is unavoidable and can be exceptionally difficult to analyze. Linear dimensionality reduction techniques such as principal component analysis are commonly employed tools used for both denoising and classification of EELS data [4]. While these techniques offer simplicity and speed, they are inherently limited by the constraint of orthogonalization [5]. This is particularly true in low-signal data in which the noise variance is higher than the variance in real spectral signals [6]. Here, we introduce diffusion mapping, a robust non-linear dimensionality reduction technique that can accurately capture the geometry of a complex hyperspectral dataset while retaining accuracy in cases of high levels of noise [7, 8]. We first validate its performance by extracting the local valence states at atomic resolution in a simulated charge ordered oxide system, and then apply it to spectroscopically map anion exchange ionomer at ultra-low dose in a polymer electrolyte fuel cell. Interactions between electrons and the atomic lattice can give rise to charge ordering, which is found in a broad range of strongly-correlated systems including 2D transition metal dichalcogenides and oxides such as the cuprates and manganites [9]. In the half-doped manganites, a site-centered charge modulation localized on the manganese sites is expected to form a checkerboard valence pattern that doubles the unit cell [10]. To demonstrate the efficacy of diffusion mapping for extracting minute changes in noisy EELS data at atomic resolution, we benchmark its performance on simulated data modeling charge order in Nd0.5Sr0.5MnO3 (Fig. 1a). A spectral image (SI) with alternating Mn3.25+ and Mn3.75+ sites and Poissonian noise was generated to emulate low dose spectral data acquired via a DED (Fig. 1b,c). With a low average SNR of 0.9, the alternating manganese valences cannot be distinguished either by projecting the spectra along a single row of Mn sites (Fig. 1e) or by directly summing individual columns (Fig. 1d). Consequently, a dimensionality reduction technique that can integrate information from the entire SI is needed. In Fig. 1f we see a manifold constructed via diffusion mapping which shows elongation along the first diffusion coordinate. Clustering via fuzzy C-means (FCM) and mapping these clusters back to real space reveals the checkerboard pattern of the Mn valence ordering (Fig. 1g) [11]. Figure 1h shows average spectra of each cluster which closely resembles the original ground truth spectra used to generate the SI. This shows that diffusion mapping can extract meaningful results even when the spectral changes are minor and the data are noisy. Next, we demonstrate diffusion mapping with real experimental data on soft polymeric material. The ionomer is a crucial element of the catalyst layers in anion exchange membrane fuel cells (AEMFCs) which heavily influences the ionic conductivity, gas transport, and overall performance of the fuel cell [12, 13]. Ionomer can be exceptionally difficult to map in TEM due to its high radiation sensitivity and nanometer-thin dispersion throughout the carbon-based catalyst support structure. Figure 2a shows a cryo-ADF-STEM image of AEMFC catalyst ink consisting of a dispersion of platinum-loaded carbon black and the commercial ionomer QAPPT, drop-casted onto a quantifoil TEM grid [14]. Due to the chemical composition of QAPPT, consisting of mostly carbon with a single nitrogen atom in the cationic group, it is impractical to elementally distinguish the ionomer from carbon black. Still, given the higher concentration of carbon-hydrogen bonds in QAPPT, we expect to see a change in the fine structure of the carbon-K edge. EELS data acquired over the ionomer/QAPPT interface using the Gatan K2 Summit DED was limited to a total dose of 500 e/Å2 due to the extreme dose sensitivity of the ionomer. Analysis of the carbon-K edge shows no discernible features differentiating between regions of expected high ionomer concentration and high carbon black concentration (Fig. 2b,c). Nonetheless, after applying dimensionality reduction via diffusion mapping to the background subtracted C-K edge, we can identify two primary diffusion coordinates which characterize the carbon features (Fig. d). Firstly, two clusters appear separated along the first diffusion coordinate which are clearly distinguishing regions of vacuum and regions of carbon. The cluster on the right side of the scatterplot is elongated over the second diffusion coordinate, and segmenting this cluster further via FCM reveals changes in the bonding environment of carbon along this axis. We see a clear suppression in the σC−H peak between the green and cyan clusters (Fig. 2f), correlating to the expected decrease in C-H bonding in the carbon black structure relative to QAPPT. Mapping each of clusters back to real space reveals the ionomer/catalyst distribution. Our results demonstrate the strong capabilities of diffusion mapping in extracting information even from extremely low-signal data [15]. a) Crystal structure of Nd0.5Sr0.5MnO3 with site-centered charge ordering adapted from [11]. b) Modeled L2,3 EELS edges of Mn3.75+ and Mn3.25+ valence. c) Simulated SI using Poissonian noise to emulate a direct electron detector with a background intensity of 20 e−/channel at 635eV and a SNR of 0.9. d) A 25-pixel average in Mn3.75+ and Mn3.25+ columns outlined in c). e) Spectral profile along center of the Mn column shown in c) demonstrating the low SNR. f) After diffusion mapping, the simulated SI dataset is separated along the ψ0 diffusion coordinate. The dimension reduced dataset is clustered using fuzzy c-means. g) Real space map of clusters labeled in f). h) Mean spectra of each diffusion cluster, where the features of Mn3.75+ and Mn3.25+ are recovered in C1 and C2, respectively. a) Cryo-ADF-STEM image of catalyst-ionomer composite. b) Carbon concentration map via EELS SI acquired in region highlighted in a). c) Single pixel carbon spectra from points shown in b). Below shows the mean carbon spectra outlined by one standard deviation shown in gray. d) Diffusion map of background subtracted carbon-K edge. The reduced dataset is then clustered via FCM into 4 regions. e) Clusters in d) are mapped back into real space, revealing the distribution of the ionomer identified by the green cluster. f) The mean spectra of each cluster shown in d,e) where the principal modulation is highlighted by the change in C-H σ bonds. The vacuum cluster is shown in black.