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Gradient‐type iterative methods for solving Hermitian eigenvalue problems can be accelerated by using preconditioning and deflation techniques. A preconditioned steepest descent iteration with implicit deflation (PSD‐id) is one of such methods. The convergence behavior of the PSD‐id is recently investigated based on the pioneering work of Samokish on the preconditioned steepest descent method (PSD). The resulting non‐asymptotic estimates indicate a superlinear convergence of the PSD‐id under strong assumptions on the initial guess. The present paper utilizes an alternative convergence analysis of the PSD by Neymeyr under much weaker assumptions. We embed Neymeyr's approach into the analysis of the PSD‐id using a restricted formulation of the PSD‐id. More importantly, we extend the new convergence analysis of the PSD‐id to a practically preferred block version of the PSD‐id, or BPSD‐id, and show the cluster robustness of the BPSD‐id. Numerical examples are provided to validate the theoretical estimates.

 

This study demonstrates an atomic composition manipulation on Pt–Ni nano-octahedra to enhance their electrocatalytic performance. By selectively extracting Ni atoms from the {111} facets of the Pt–Ni nano-octahedra using gaseous carbon monoxide at an elevated temperature, a Pt-rich shell is formed, resulting in an ∼2 atomic layer Pt-skin. The surface-engineered octahedral nanocatalyst exhibits a significant enhancement in both mass activity (∼1.8-fold) and specific activity (∼2.2-fold) toward the oxygen reduction reaction compared with its unmodified counterpart. After 20,000 potential cycles of durability tests, the surface-etched Pt–Ni nano-octahedral sample shows a mass activity of 1.50 A/mgPt, exceeding the initial mass activity of the unetched counterpart (1.40 A/mgPt) and outperforming the benchmark Pt/C (0.18 A/mgPt) by a factor of 8. DFT calculations predict this improvement with the Pt surface layers and support these experimental observations. This surface-engineering protocol provides a promising strategy for developing novel electrocatalysts with improved catalytic features. 

Combining different precious metals to generate alloy nanocrystals with desirable shapes and compositions remains a challenge because of the low miscibility between these metals and/or the different reduction potentials of their salt precursors. Specifically, Rh and Pd are considered to be immiscible in the bulk solid over the entire composition range. Here we demonstrate that Rh−Pd alloy nanorods with well‐distributed and tunable compositions can be synthesized using a one‐pot polyol method. The success of our synthesis relies on the introduction of bromide as a coordination ligand to tune the redox potentials of Rh(III) and Pd(II) ions for the achievement of co‐reduction. The atomic ratio of the Rh−Pd alloy nanorods can be facilely tuned by changing the molar feeding ratio between the two precursors. We also systematically investigate the effects of water on the morphology of the Rh−Pd alloy nanocrystals. In an attempt to promote future use of these alloy nanorods, we successfully scale up their synthesis in a continuous‐flow reactor with no degradation to the product quality.

 

There is a long history of using angle sensors to measure wavefront. The best example is the Shack-Hartmann sensor. Compared to other methods of wavefront sensing, angle-based approach is more broadly used in industrial applications and scientific research. Its wide adoption is attributed to its fully integrated setup, robustness, and fast speed. However, there is a long-standing issue in its low spatial resolution, which is limited by the size of the angle sensor. Here we report a angle-based wavefront sensor to overcome this challenge. It uses ultra-compact angle sensor built from flat optics. It is directly integrated on focal plane array. This wavefront sensor inherits all the benefits of the angle-based method. Moreover, it improves the spatial sampling density by over two orders of magnitude. The drastically improved resolution allows angle-based sensors to be used for quantitative phase imaging, enabling capabilities such as video-frame recording of high-resolution surface topography.

 

Palladium (Pd)‐based electrocatalysts have recently emerged as one class of the foremost promising candidates for the oxygen reduction reaction (ORR) in alkaline media due to their excellent ORR activity and durability and lower costs compared with platinum. Insightful design of Pd‐based nano‐architectures with optimized active surface sites and maximal intrinsic performance is central to promoting the ORR applications. To further accelerate the sluggish ORR kinetics at the cathode of fuel cells and substantially decrease the overall cost of the electrocatalysts, various strategies, including controlled sizes and shapes with selected crystallographic facets, crystal‐phase engineering, heteroatom doping, tailored surface strains, and surface engineering by de‐alloying, have been extensively developed in the past decade. In this review, a brief introduction to the fundamental ORR mechanisms of Pd‐based electrocatalysts in alkaline media is presented, followed by a thorough discussion on various strategies for delicately designing high‐performance Pd‐based catalysts with corresponding examples. Thereafter, the perspectives and new insights into the challenges are outlined, and some emerging research directions related to the rational design and controlled synthesis of Pd‐based ORR electrocatalysts are also proposed.