Many metal clusters in the 1-nm size range are catalytically active, and their enhanced reactivity is often attributed to their size, structure, morphology, and details of alloying. Synchrotron sources provide a wide range of opportunities for studying catalysis. Among them, extended X-ray absorption fine-structure (EXAFS) spectroscopy is the premier method for investigating structure and composition of nanocatalysts. In this review, we summarize common methods of EXAFS analysis for geometric and compositional characterization of nanoparticles. We discuss several aspects of the experiments and analyses that are critical for reliably modeling EXAFS data. The most important are sample homogeneity, the width of the size and compositional distribution functions, and accounting for multiple-scattering contributions to EXAFS. We focus on the contribution of structural disorder and structural/compositional heterogeneity to the accuracy of three-dimensional modeling.

Small ͑1-5 nm͒ metal clusters may undergo significant surface relaxation under the influence of ligands, adsorbates, and substrate-induced stress. As a result, the nearest-neighbor distance between surface atoms can be reduced by up to 10% relative to those in the cluster core, enhancing the disorder in the interatomic distances. Accordingly, the pair distribution function extracted from EXAFS data under the standard assumption that the distribution function of nearest-neighbor bonds is quasi-Gaussian yields systematic errors. Here we analyze the surface disorder effects with emphasis on their impact on the accuracy of the size and shape determination of nanocatalysts.

Holograms of colloidal dispersions encode comprehensive information about individual particles' three-dimensional positions, sizes and optical properties. Extracting that information typically is computationally intensive, and thus slow. Here, we demonstrate that machine-learning techniques based on support vector machines (SVMs) can analyze holographic video microscopy data in real time on low-power computers. The resulting stream of precise particle-resolved tracking and characterization data provides unparalleled insights into the composition and dynamics of colloidal dispersions and enables applications ranging from basic research to process control and quality assurance.

A tractor beam is a travelling wave that transports illuminated objects back to its source, opposite to the wave's direction of propagation, along its entire length. The requisite retrograde force arises when an object scatters the wave's momentum density downstream into the direction of propagation, and then recoils upstream by conservation of momentum. Achieving this condition imposes constraints on the structure of the wave, which we elucidate in the Rayleigh limit, when the wavelength exceeds the size of the object. Continuously propagation-invariant modes such Bessel beams do not satisfy these conditions at dipole order in the multipole expansion, and so cannot serve as general-purpose long-ranged tractor beams. Modes with discrete propagation invariance, however, can act as first-order tractor beams. We demonstrate this by introducing a class of minimal solenoidal waves together with a set of design criteria that distinguish tractor beams that pull objects from repulsor beams that push them.

The theory of photokinetic effects expresses the forces and torques exerted by a beam of light in terms of experimentally accessible amplitude and phase profiles. We use this formalism to develop an intuitive explanation for the performance of optical tweezers operating in the Rayleigh regime, including effects arising from the influence of light's angular momentum. First-order dipole contributions reveal how a focused beam can trap small objects, and what features limit the trap's stability. The first-order force separates naturally into a conservative intensity-gradient term that forms a trap and a non-conservative solenoidal term that drives the system out of thermodynamic equilibrium. Neither term depends on the light's polarization; light's spin angular momentum plays no role at dipole order. Polarization-dependent effects, such as trap-strength anisotropy and spin-curl forces, are captured by the second-order dipole-interference contribution to the photokinetic force. The photokinetic expansion thus illuminates how light's angular momentum can be harnessed for optical micromanipulation, even in the most basic optical traps.This article is part of the themed issue 'Optical orbital angular momentum'.