Sparse ab initio x-ray transmission spectrotomography for nanoscopic compositional analysis of functional materials

HomeTechnology

Sparse ab initio x-ray transmission spectrotomography for nanoscopic compositional analysis of functional materials

AbstractThe performance of functional materials is either driven or limited by nanoscopic heterogeneities distributed throughout the material’s volume

Persona 5 Strikers’ Menus Are As Vibrantly Alive As Its Cast
Coal investments ‘must stop now’: Australia isolated as world’s largest economies ditch coal
Why Lenovo’s attractive P11 Pro tablet could be similar to what ‘Coachz’ will become

Abstract

The performance of functional materials is either driven or limited by nanoscopic heterogeneities distributed throughout the material’s volume. To better our understanding of these materials, we need characterization tools that allow us to determine the nature and distribution of these heterogeneities in their native geometry in 3D. Here, we introduce a method based on x-ray near-edge spectroscopy, ptychographic x-ray computed nanotomography, and sparsity techniques. The method allows the acquisition of quantitative multimodal tomograms of representative sample volumes at sub–30 nm half-period spatial resolution within practical acquisition times, which enables local structure refinements in complex geometries. To demonstrate the method’s capabilities, we investigated the transformation of vanadium phosphorus oxide catalysts with industrial use. We observe changes from the micrometer to the atomic level and the formation of a location-specific defect so far only theorized. These results led to a reevaluation of these catalysts used in the production of plastics.

INTRODUCTION

Composition and structure define a material’s functionality (1). While we can determine and sometimes predict the relationship between structure and emergent functionality for simple single-component materials with some effort, we frequently face difficulties when dealing with structurally and compositionally more complex materials such as heterogeneous catalysts, energy storage materials, or biominerals (24). Here, functionality is often defined by local heterogeneities in structure and/or composition such as interfaces between two components or selected crystallographic defects, distributed in a larger volume (5, 6). The distribution of these heterogeneities within frequently hierarchically structured assemblies, spanning multiple length scales, and their interaction with the local environment further guide the material’s functionality or device performance. Hence, we face the challenge to provide characterization tools that allow us to determine the nature and distribution of these heterogeneities in their native geometry in three dimensions (3D). This is to better our understanding of current materials and aid the design of next-generation materials.

X-ray absorption near-edge spectroscopy (XANES), the measurement of x-ray excitation characteristics of a chemical element in response to variation in incident energy, has become the dominant method for chemical speciation and component identification in various research fields (7, 8). While initially limited to bulk analysis, the increasing importance of advanced composite materials (3, 4, 6, 911) has led to the development of XANES imaging and, eventually, to XANES tomography (1218), adding a structural characterization element and aiming to identify and localize local heterogeneities in a system-representative sample volume, i.e., providing the desired characterization tool. These techniques are especially of interest when aiming for nanoscale resolution to reveal features at the scale in which different chemical phases intertwine in these materials (3, 4, 6, 911). However, current XANES tomography implementations (1218) suffer from two particular difficulties when in pursuit of nanoscopic features in representative sample volumes: Access to local quantitative density or elemental concentrations requires effort in calibration and normalization that is often overlooked, and lengthy acquisition times (19). Until now, spectral tomogram synthesis involved the acquisition of one tomogram per energy to generate the hyperspectral dataset. The required number of projections per tomogram scales with the sought spatial resolution and the diameter of the sample following the Crowther criterion (20). Iterative reconstruction methods, such as the simultaneous algebraic reconstruction technique (SART) (21), were introduced to relax the number of projections while preserving the quality of the tomographic reconstruction.

Here, we introduce a novel acquisition scheme and iterative reconstruction technique that leverages the sparsity of information in a hyperspectral tomogram to relax the required number of projections further, thereby substantially reducing XANES tomogram acquisition times (19). Specifically, using the introduced reconstruction technique, we were able to reduce the number of projections to 11% of the Crowther criterion at no noticeable cost of spectral or spatial resolution. Such a reduction is possible, as signal variation across the spectra is heavily correlated and can be reduced to spatially localized and consistent gray-level changes; our reconstruction leverages this correlation to relax the required measurements.

Although the developed reconstruction technique is applicable to a wide range of tomography techniques, we here selected ptychographic x-ray computed tomography (PXCT) (22) as the vehicle of choice to provide an easier or more direct access to quantitative values (19). PXCT readily provides quantitative tomograms of the complex-valued refractive index distribution, i.e., phase and absorption. As a lensless imaging technique, its spatial resolution is not limited by aberrations or technical limitations in the fabrication of optics, which is a substantial challenge for x-ray wavelengths; this makes PXCT prolific in terms of signal-to-noise ratio (SNR) and with outstanding resolving power. The combination of PXCT’s high resolution and quantitativeness with our sparse reconstruction method for spectral tomography, termed sparse x-ray transmission near-edge spectrotomography (XTNES), enables the acquisition of a 3D picture of representative volumes with nanometer resolution, which reconstructs into quantitative values of electron density, absorption, elemental concentration, and oxidation state. This ultimately allows a local, quantitative characterization of structure, chemical composition, and coordination geometry.

In this first application, we examined a pristine and industrially used vanadium phosphorus oxide (VPO) catalyst. These oxides are used to catalyze the selective oxidation of n-butane (C4H10) to maleic anhydride (MA) (C4H2O3). MA is a precursor in the production of plastics, with a steadily increasing production quantity of currently 2 million tons per year (23, 24). In consideration of the reaction by-products, carbon monoxide and carbon dioxide, a financial and environmental incentive is present to increase the productivity of these catalysts. State-of-the-art catalysts are a composite of hierarchical porosity, and one of the factors that hinder catalyst improvement is that the composition and spatial distribution of its vanadium phosphate phases (table S1) are not precisely known. Another factor is that, during reactor operation, the catalyst undergoes a series of structural and compositional changes that culminate in a gradual loss of catalyst productivity. Because of the compositional uncertainty, the aforementioned changes are yet to be fully understood, leading to an active discussion regarding the best catalyst design, the most desirable active phase, and the nature of active sites in general (2529). Historically, V═O bonds or V5+/V4+ redox pairs on the catalyst’s surface are considered to be the active sites in the initial hydrogen transfer reaction to activate n-butane on the catalyst surface. The former, i.e., the cleaving of alkane C─H bonds, is suggested to be the rate-limiting step (24, 26, 2831). More recently, P═O bonds were theoretically suggested to play an equally important role (32, 33). Naturally, materials of increased structural disorder, exhibiting more of these bonds at their surfaces, find use in industrial VPO catalysts (34, 35), for example, defect-rich nanoparticles and amorphous phases. Please see the Supplementary Materials and fig. S1 for further details regarding VPO catalysts and their industrial use.

The XTNES tomography measurements presented here provide answers to some of these uncertainties, explicitly those surrounding catalyst structure, composition, active sites, and productivity. The multimodal hyperspectral tomograms revealed a structural and chemical transformation following 4 years of industrial reactor utilization, that is, from a mesoporous catalyst of high surface area composed of a series of amorphous and nanocrystalline vanadium phosphate phases to a macroporous catalyst composed of micrometer-sized and defect-rich vanadyl pyrophosphate crystals. When evaluated against catalytic performance, this transformation directly implies the used catalyst to be more productive on a surface area–specific basis than the pristine and equilibrated catalyst. By using the quantitativeness of XTNES to perform local structure optimizations on vanadyl pyrophosphate crystals that were in contact with the reactive medium, we were able to correlate this increased productivity of the used catalyst to vanadyl defects, which create unsaturated P═O bonds that are accessible from {200}-terminated facets. Hence, catalysts of highest activity might not be derivable from amorphous surface deposits enriched in V5+ or the interaction of nanometer-sized V5+ and V4+ components as previously targeted but rather through defect engineering of highly crystalline vanadyl pyrophosphate crystals (30, 31). These observations currently aid the design of improved VPO catalysts and hopefully highlight the prowess of XTNES tomography including local defect and potential active site characterization.

RESULTS

X-ray transmission near-edge spectrotomography

Clariant AG provided the pristine and used VPO catalyst bodies, i.e. pellets (36). The latter were sourced from an industrial fixed-bed reactor after 4 years of known operation history. The reactor coolant temperature was gradually increased from 400° to ~420°C following the first year of operation to ensure steady reactor performance. From performance profiles (fig. S2), we can estimate that a catalyst equilibrium state and structure was reached after ~1.5 years of operation. Bulk examination revealed the used catalyst to exhibit a 70% decrease in specific surface area and a ~10% reduction in productivity after 4 years of operation (table S2). As shown in Fig. 1A, samples intended for tomographic examination were extracted from the central region of randomly selected catalyst pellets and shaped into cylinders roughly 12 μm in diameter.

Fig. 1 Illustration of sparse XTNES acquisition.

(A) Examined VPO catalyst pellet as retrieved from the reactor (top left). Preshaped sample mounted on a tomography pin (top right, black arrow) and focused ion beam milled sample cylinder (bottom). Scale bars are 5 mm, 1 mm and 10 μm. The white circle indicates the region from which the sample cylinder was extracted. The blue rectangle indicates roughly the field of view during XTNES tomogram acquisition. Photo credit: Zirui Gao, PSI, ETHZ. (B) Spectral tomograms were assembled by acquiring a series of angularly sparse ptychographic tomograms across the vanadium K-edge. (C) Graphical illustration of the acquisition scheme of tomography angular orientations versus x-ray photon energy. For each energy, the Crowther criterion is indicated by small dots, while larger dots indicate angularly sparse measured projections. At each energy, an offset to the angle based on a golden ratio is added to each projection to maximize the available information diversity.

” data-hide-link-title=”0″ data-icon-position=”” href=”https://advances.sciencemag.org/content/advances/7/24/eabf6971/F1.large.jpg?width=800&height=600&carousel=1″ rel=”gallery-fragment-images-33549473″ title=”Illustration of sparse XTNES acquisition. (A) Examined VPO catalyst pellet as retrieved from the reactor (top left). Preshaped sample mounted on a tomography pin (top right, black arrow) and focused ion beam milled sample cylinder (bottom). Scale bars are 5 mm, 1 mm and 10 μm. The white circle indicates the region from which the sample cylinder was extracted. The blue rectangle indicates roughly the field of view during XTNES tomogram acquisition. Photo credit: Zirui Gao, PSI, ETHZ. (B) Spectral tomograms were assembled by acquiring a series of angularly sparse ptychographic tomograms across the vanadium K-edge. (C) Graphical illustration of the acquisition scheme of tomography angular orientations versus x-ray photon energy. For each energy, the Crowther criterion is indicated by small dots, while larger dots indicate angularly sparse measured projections. At each energy, an offset to the angle based on a golden ratio is added to each projection to maximize the available information diversity.”>

Fig. 1 Illustration of sparse XTNES acquisition.

(A) Examined VPO catalyst pellet as retrieved from the reactor (top left). Preshaped sample mounted on a tomography pin (top right, black arrow) and focused ion beam milled sample cylinder (bottom). Scale bars are 5 mm, 1 mm and 10 μm. The white circle indicates the region from which the sample cylinder was extracted. The blue rectangle indicates roughly the field of view during XTNES tomogram acquisition. Photo credit: Zirui Gao, PSI, ETHZ. (B) Spectral tomograms were assembled by acquiring a series of angularly sparse ptychographic tomograms across the vanadium K-edge. (C) Graphical illustration of the acquisition scheme of tomography angular orientations versus x-ray photon energy. For each energy, the Crowther criterion is indicated by small dots, while larger dots indicate angularly sparse measured projections. At each energy, an offset to the angle based on a golden ratio is added to each projection to maximize the available information diversity.

High-resolution tomographic projections (fig. S3) were acquired at 60 x-ray photon energies across the vanadium K-edge, between 5.443 and 5.530 keV. For a target spatial resolution of 25 nm, a conventional spectrotomography measurement using analytical reconstruction technique, i.e., satisfying the Crowther sampling criteria, would require the acquisition of 628 projections at each energy. Following our sparse sampling approach, we measured, at each energy, only 68 projections, resulting in a reduction in acquisition time per XTNES tomogram from more than 1 week to less than 20 hours. To retain information from a high diversity of incident angles, which aids the sparse synthesis, we further introduced a unique offset to the first projection angle of each single-energy tomogram (37). Figure 1 (B and C) illustrates the acquisition strategy. Similar angle interleaved acquisition strategies found previous application within the field of time-resolved x-ray tomography (37, 38).

At these photon energies, the phase of the complex-valued projections provides a better SNR and spatial resolution compared to the amplitude. Therefore, high-resolution processing was conducted using the phase, while the amplitude or absorption signal was used as a low-resolution reference.

The reconstruction of the sparse XTNES tomograms was carried out using a novel iterative algorithm based on principal components analysis (PCA) (39) and SART (21). The reconstruction process involves a noncentered PCA decomposition of a downsized hyperspectral tomogram to extract a set of spectral modes with their corresponding component tomograms to be used as initial guess. The initial guess is then iteratively refined using all the high-resolution projections at all energies. This process results in a set of spectral modes and their corresponding tomograms at the highest resolution, from which we can calculate the XTNES tomogram. The half-period spatial resolution of the obtained XTNES tomograms was determined using 4D Fourier shell correlation and found to be limited by the voxel size, here 26.50 nm. The corresponding full-period resolution is 53.0 nm. Please see Materials and Methods for a detailed explanation of the reconstruction procedure and fig. S4 for details regarding resolution estimates. Furthermore, the reader is referred to fig. S5, which provides a comparison of different analytical and iterative tomogram reconstruction methods to showcase the benefit of the introduced sparse spectral tomogram reconstruction method.

The phase and absorption spectra of two voxels extracted from the pristine catalyst are shown in Fig. 2A. The provided absorption spectra were obtained using a Kramers-Kronig transformation (KKT) of the phase spectra (40). Given that this is the method’s first application, we transformed the phase signal to absorption via a KKT to allow an easier analysis and validation of the reconstructed spectra owing to the established analysis routines for XANES spectroscopy and the availability of reference spectra (41). For example, a comparison of one of the provided voxel-level absorption spectra with spectra from the literature, as shown in fig. S6, confirms that the voxel consists mainly of vanadyl pyrophosphate. The typical approach for the analysis of XANES spectra, as well as XANES tomography, is to compare the measured spectra to those of a list of reference components. A particular match with one, or a linear combination of multiple reference spectra, allows the identification of a single or fractional quantification of multiple components (7, 13, 42). The quantitativeness of ptychography-based XTNES tomography affords us with a different analysis approach to reach the same goal. This approach is based on the extraction of a set of key quantities directly from the acquired phase or absorption spectra of each voxel. The quantities extracted in the present case include (i) local electron densities obtained from the phase signal away from the resonant edge, (ii) local vanadium concentrations retrieved from the edge jump magnitude, (iii) local vanadium oxidation states determined by the position of the absorption edge, and (iv) local vanadium coordination geometry inferred from pre-edge peak intensity variations. Please see Fig. 2A for a graphical illustration and Materials and Methods for further details about how these quantities are obtained. Instead of a comparison of spectra, we compare the extracted set of quantities with those of a list of possible, or considered, reference components (shown in table S1). If a match of the measured set with those of a single reference component is not possible, a linear combination of multiple reference components can be explored to best describe the measured set of quantities. While the typical spectrum comparison–based analysis is reliant on the availability of reference spectra or reference materials from which spectra can be collected, the quantity-based analysis is largely free of this constraint. In this study, a selected number of reference spectra of components with known oxidation state are used to convert measured edge energies to oxidation state. However, the quantities used here for component identification are also readily available in the literature for a vast amount of materials. This makes the presented approach well suited for the examination of materials where reference spectra are hard to come by, as is often the case for industrial materials. For cases in which reference spectra are available, this approach could, of course, leverage this extra information to add additional constrains for a refined material characterization.

Fig. 2 Local vanadium K-edge spectra and XTNES tomograms of industrial VPO catalysts.

(A) Example of two voxel-level phase and KKT-obtained absorption spectra. From these spectra, we obtain quantitative values for (i) the electron density, (ii) vanadium concentration, (iii) vanadium oxidation state, and (iv) pre-peak intensity. (B) Hue saturation value 3D color map used for the combined visualization of electron density, vanadium concentration, and vanadium oxidation state. (C) 3D volume rendering of the pristine catalyst based on the color map presented in (B) and axial virtual slices taken from the middle of the catalyst sample highlighting the individual quantities. (D) 3D volume rendering and virtual slices of the used catalyst based on the color map in (B). Scale bars, 2 μm. The positions of the voxels discussed in (A) are marked in (C) using a cross and a circle, respectively.

” data-hide-link-title=”0″ data-icon-position=”” href=”https://advances.sciencemag.org/content/advances/7/24/eabf6971/F2.large.jpg?width=800&height=600&carousel=1″ rel=”gallery-fragment-images-33549473″ title=”Local vanadium K-edge spectra and XTNES tomograms of industrial VPO catalysts. (A) Example of two voxel-level phase and KKT-obtained absorption spectra. From these spectra, we obtain quantitative values for (i) the electron density, (ii) vanadium concentration, (iii) vanadium oxidation state, and (iv) pre-peak intensity. (B) Hue saturation value 3D color map used for the combined visualization of electron density, vanadium concentration, and vanadium oxidation state. (C) 3D volume rendering of the pristine catalyst based on the color map presented in (B) and axial virtual slices taken from the middle of the catalyst sample highlighting the individual quantities. (D) 3D volume rendering and virtual slices of the used catalyst based on the color map in (B). Scale bars, 2 μm. The positions of the voxels discussed in (A) are marked in (C) using a cross and a circle, respectively.”>

Fig. 2 Local vanadium K-edge spectra and XTNES tomograms of industrial VPO catalysts.

(A) Example of two voxel-level phase and KKT-obtained absorption spectra. From these spectra, we obtain quantitative values for (i) the electron density, (ii) vanadium concentration, (iii) vanadium oxidation state, and (iv) pre-peak intensity. (B) Hue saturation value 3D color map used for the combined visualization of electron density, vanadium concentration, and vanadium oxidation state. (C) 3D volume rendering of the pristine catalyst based on the color map presented in (B) and axial virtual slices taken from the middle of the catalyst sample highlighting the individual quantities. (D) 3D volume rendering and virtual slices of the used catalyst based on the color map in (B). Scale bars, 2 μm. The positions of the voxels discussed in (A) are marked in (C) using a cross and a circle, respectively.

XTNES tomograms of pristine and deactivated VPO catalysts

Figure 2 (B to D) shows compound volume renderings of the tomogram extracted quantities (i), (ii), and (iii) for both the pristine and used VPO catalyst together with orthoslices of the individual quantities. Please refer to movies S1 and S2 for an animated representation. Associated histograms and correlations of these quantities are shown in fig. S7.

It is evident from a structural comparison of the electron density tomograms, i.e., the outcome of a conventional PXCT measurement, that the catalyst undergoes a structural reorganization during reactor operation. The catalyst’s nanoporosity and fine structure are lost, leaving behind a mesoporous structure composed of micrometer-sized domains. Accordingly, a decrease in surface area and widening of the pore network is registered, as shown in fig. S8 and table S2. An increase in average electron density (±σ) from 0.66 (± 0.007) to 0.86 (± 0.006) neÅ−3 further suggests that the observed changes in structure are a product of phase transformation processes. Last, on the basis of electron density distribution, as shown in Fig. 2 (C and D) and fig. S7, there appears to be little compositional variance within the pristine and used catalyst. While this may appear to conflict with the reported ill-defined nature of VPO catalysts (2529), in reality, we find numerous industrial VPO catalyst components to have comparable electron densities. The situation is similar for vanadium concentration and vanadium oxidation state (table S1). This renders schemes based on a single value for component identification insufficient. For example, an electron density of 0.86 neÅ−3 as dominantly observed in the used catalyst could equally be interpreted, among others, as nanocrystalline (VO)2P2O7, V(PO3)3, and VO(HPO4)·0.5H2O, all known to be possible catalyst components (26, 28, 34, 35).

An identification of components becomes possible, when electron density, vanadium concentration, and vanadium oxidation state are considered together, as demonstrated in fig. S7. On the basis of this correlative identification approach, we identified three distinct components in the pristine catalyst. Identification was limited to materials reported in the literature to be present in VPO catalysts, as shown in table S1 (26, 28, 34, 35). These are amorphous vanadium-rich metaphosphate, nanocrystalline vanadyl pyrophosphate [(VO)2P2O7)], and vanadium hydrogen phosphate [~(VO)PO4·2H2O]. While the latter is present in the form of isolated, micrometer-sized objects, the former two, which account for the majority of the sample volume, are found in nano-sized domains. Notably, domains of these two components are spatially intertwined, with the minor metaphosphate phase preferentially facing the pore space or reaction environment, thereby increasing the vanadium concentration and oxidation state at the catalyst surface. The catalyst composition changes with reactor operation. In the used catalyst, we identified only two components, namely, small islands of VOPO4 (<10 volume %) and a dominantly defect-rich vanadyl pyrophosphate. The latter appears throughout the entire catalyst in micrometer-sized domains that exhibit a variance in vanadium concentration and oxidation state, which are known to occur in solid-state transformation processes. See figs. S9 to S12 for electron microscopy, x-ray fluorescence, and x-ray diffraction measurements. Each measurement confirms a selected general aspect of the XTNES tomogram analysis, such as changes in pore and fine structure, the loss/absence of amorphous material, variation in vanadium concentration, and the general presence of identified components.

Intensity variations of the vanadium pre-edge peak (iv) are discussed separately and shown in Fig. 3 (A and B). These variations provide a first glance at the microstructure of the catalysts, e.g., allowing the detection of crystalline and amorphous domains (43). This is made possible by the combination of using a linearly polarized illumination and the net anisotropy of most crystalline materials (44, 45). Notably, it is the spatial extent of regions with increased pre-peak inte

COMMENTS

WORDPRESS: 0
DISQUS: