Newly available x-ray nanobeams in synchrotron radiation facilities open new research avenues in the nanosciences. However, a significant challenge is to efficiently concentrate, particularly for high-energy x-rays, a large photon flux into a very small focal spot. Here, we demonstrate for the first time, to the best of our knowledge, a sub-13-nm (FWHM) diffraction-limited x-ray focus size with 6 billion photons per second formed using elliptically figured mirrors operating at 33.6 keV. This is the smallest and brightest focus spot in this high-energy range. We report the results of an x-ray ptychography experiment to characterize the wavefront at the focus position. This offers new opportunities in multidisciplinary fields for x-ray microscopy techniques in which the focal spot size limits the resolution.

Selective laser melting is a promising powder-bed-based additive manufacturing technique for titanium alloys: near net-shaped metallic components can be produced with high resource-efficiency and cost savings

Since its commercial introduction three-quarters of a century ago, fluid catalytic cracking has been one of the most important conversion processes in the petroleum industry. In this process, porous composites composed of zeolite and clay crack the heavy fractions in crude oil into transportation fuel and petrochemical feedstocks. Yet, over time the catalytic activity of these composite particles decreases. Here, we report on ptychographic tomography, diffraction, and fluorescence tomography, as well as electron microscopy measurements, which elucidate the structural changes that lead to catalyst deactivation. In combination, these measurements reveal zeolite amorphization and distinct structural changes on the particle exterior as the driving forces behind catalyst deactivation. Amorphization of zeolites, in particular, close to the particle exterior, results in a reduction of catalytic capacity. A concretion of the outermost particle layer into a dense amorphous silica–alumina shell further reduces the mass transport to the active sites within the composite.

Porosity in catalyst particles is essential because it enables reactants to reach the active sites and it enables products to leave the catalyst. The engineering of composite‐particle catalysts through the tuning of pore‐size distribution and connectivity is hampered by the inability to visualize structure and porosity at critical‐length scales. Herein, it is shown that the combination of phase‐contrast X‐ray microtomography and high‐resolution ptychographic X‐ray tomography allows the visualization and characterization of the interparticle pores at micro‐ and nanometer‐length scales. Furthermore, individual components in preshaped catalyst bodies used in fluid catalytic cracking, one of the most used catalysts, could be visualized and identified. The distribution of pore sizes, as well as enclosed pores, which cannot be probed by traditional methods, such as nitrogen physisorption and isotherm analysis, were determined.

Ptychographic imaging has gained popularity for its high resolving power and sensitivity as well as for its ability to map simultaneously the sample’s complex-valued refractive index and the illumination. Yet, despite significant progress that allows for reliable practical implementation, some of the technique’s fundamentals remain poorly understood, and oftentimes successful data acquisition is either overly conservative or relies more on experimenters experience than on rational data acquisition strategies. Here, we propose a theoretical framework of ptychography, which is based on Gabor’s notion of decomposition into elementary signals and the concept of frames. We demonstrate how this framework can straightforwardly be used to derive sampling requirements or to provide arguments on how to optimize the ptychographic scan. More generally, our theoretical framework can serve as a bridge between the experimental technique and the rich and well established mathematical disciplines of wavelets decomposition and spectrogram analysis.