While high-angle annular dark field scanning transmission electron microscopy ͑HAADF-STEM͒ has been successfully used for the analysis of heavy atoms in a lighter matrix, the detection of light atoms in a heavy matrix remains challenging. In this paper, we show that the combination of first-principles total-energy calculations with aberration-corrected HAADF-STEM experimental and simulated images can be used to overcome this problem. The application of this methodology to the analysis of dilute nitrides of GaAs points to the existence of a major proportion of ͑2N As ͒ nn in the alloy, which is a relatively stable configuration in GaAsN as revealed by our energetic calculations. Our study has allowed us to shed light in the effect of the local distortion of the lattice due to different configuration of atoms in HAADF-STEM imaging.

First-principles calculations using the Vienna Ab Initio Simulation Package (VASP) have been performed in order to scrutinize the hydrogen-graphene interaction. Emphasis has been placed on how surface relaxation and the prior chemisorption of one, two and three hydrogen atoms on graphene affect the adsorption properties of an encroaching gas phase hydrogen atom. Chemisorption at the para site was found to be barrierless, while it has been shown that a stable ortho adsorbate can form directly from the gas phase. Adsorption of the third and fourth H atoms was found in all cases to have a significant barrier. The resultant minimum energy structures show a reasonable agreement with scanning tunneling microscopy images obtained by Hornekaer et al (2007 Chem. Phys. Lett. 446 237).

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Diffractive imaging algorithms enable high resolution structural determination of non-periodic objects, be they proteins or inorganic nanostuctures, using radiation sources for which lenses are either unavailable or subject to significant aberrations. These iterative algorithms solve the phase problem for Fraunhofer diffraction patterns from such objects, and have been proven successful at reconstructing images at femtosecond time resolution [1]. This class of algorithms has the potential to enable ultrafast, high resolution, diffractive imaging using both X-ray free electron lasers and Dynamic Transmission Electron Microscopy [2].While iterative phase retrieval algorithms have lead to some stark successes, their tendency to stagnate in local minima in hyper-dimensional search spaces has hindered their ability to be applied to a wider range of problems [3]. By incorporating the use of Particle Swarm Optimization (PSO) with well established diffractive imaging algorithms these limitations can be overcome.PSO algorithms are a class of global search algorithms that seek out global minima by emulating social behavior such as bird flocking or fish schooling. This new algorithm, called Swarm Optimized Phase Retrieval (SOPR), initializes the particles as a random set of phases for the known modulus of the diffraction pattern. Each particle is then run through a series of iterative phase retrieval algorithms, specifically the Hybrid Input Output (HIO) algorithm and the Error Reduction (ER) algorithm [4][5][6]. The error metrics for these algorithms can then be used to choose a personal best solution for each particle and global best solution from all of the particles. These solutions drive a velocity equation that shifts the position of each particle in the search space [7]. This final step allows particles to escape local minima in the search space and thereby avoid the stagnation problems common to HIO and ER. Initial results indicate that the particle swarm's ability to seek out global minima, effectively overcomes the stagnation problems of the HIO and ER algorithms.

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