Friday 12th August 2022

Sparse ab initio x-ray transmission spectrotomography for nanoscopic compositional

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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…

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