Showing papers on "Diffraction published in 2006"

HKL-3000: the integration of data reduction and structure solution--from diffraction images to an initial model in minutes.

Abstract: A new approach that integrates data collection, data reduction, phasing and model building significantly accelerates the process of structure determination and on average minimizes the number of data sets and synchrotron time required for structure solution. Initial testing of the HKL-3000 system (the beta version was named HKL-2000_ph) with more than 140 novel structure determinations has proven its high value for MAD/SAD experiments. The heuristics for choosing the best computational strategy at different data resolution limits of phasing signal and crystal diffraction are being optimized. The typical end result is an interpretable electron-density map with a partially built structure and, in some cases, an almost complete refined model. The current development is oriented towards very fast structure solution in order to provide feedback during the diffraction experiment. Work is also proceeding towards improving the quality of phasing calculation and model building.

Ultrasonic metamaterials with negative modulus

Abstract: The emergence of artificially designed subwavelength electromagnetic materials, denoted metamaterials, has significantly broadened the range of material responses found in nature. However, the acoustic analogue to electromagnetic metamaterials has, so far, not been investigated. We report a new class of ultrasonic metamaterials consisting of an array of subwavelength Helmholtz resonators with designed acoustic inductance and capacitance. These materials have an effective dynamic modulus with negative values near the resonance frequency. As a result, these ultrasonic metamaterials can convey acoustic waves with a group velocity antiparallel to phase velocity, as observed experimentally. On the basis of homogenized-media theory, we calculated the dispersion and transmission, which agrees well with experiments near 30 kHz. As the negative dynamic modulus leads to a richness of surface states with very large wavevectors, this new class of acoustic metamaterials may offer interesting applications, such as acoustic negative refraction and superlensing below the diffraction limit.

Optical Hyperlens: Far-field imaging beyond the diffraction limit.

Abstract: We propose an approach to far-field optical imaging beyond the diffraction limit. The proposed system allows image magnification, is robust with respect to material losses and can be fabricated by adapting existing metamaterial technologies in a cylindrical geometry.

Femtosecond diffractive imaging with a soft-X-ray free-electron laser

Abstract: Theory predicts that with an ultrashort and extremely bright coherent X-ray pulse, a single diffraction pattern may be recorded from a large macromolecule, a virus, or a cell before the sample explodes and turns into a plasma. Here we report the first experimental demonstration of this principle using the FLASH soft X-ray free-electron laser. An intense 25 fs, 4 x 10{sup 13} W/cm{sup 2} pulse, containing 10{sup 12} photons at 32 nm wavelength, produced a coherent diffraction pattern from a nano-structured non-periodic object, before destroying it at 60,000 K. A novel X-ray camera assured single photon detection sensitivity by filtering out parasitic scattering and plasma radiation. The reconstructed image, obtained directly from the coherent pattern by phase retrieval through oversampling, shows no measurable damage, and extends to diffraction-limited resolution. A three-dimensional data set may be assembled from such images when copies of a reproducible sample are exposed to the beam one by one.

Integration of macromolecular diffraction data

Abstract: In this chapter the integration of macromolecular diffraction data from two-dimensional area detectors is described. Data integration refers to the process of obtaining estimates of diffracted intensities (and their standard deviations) from the raw images recorded by an X-ray detector. When collecting data, a decision has to be taken about the magnitude of the angular rotation of the crystal during the recording of each image: the rotation per image can be comparable to, or greater than, the angular reflection range of a typical reflection (coarse ϕ slicing), or it can be much less than the reflection width (fine ϕ slicing). The latter approach allows the use of three-dimensional profile fitting and, providing that the detector is relatively noise-free, improves the quality of the resulting data by minimizing the contribution of the X-ray background to the total measured intensity. Methods of integration are described and integration by simple summation and by profile fitting is discussed. Keywords: background; data integration; detector overloads; errors; integration of diffraction data; outliers; overloads; partially recorded reflections; profile fitting; standard profiles; summation integration

Far-field subdiffraction optical microscopy using metamaterial crystals: Theory and simulations

Abstract: Here we suggest and explore theoretically an idea for a far-field scanless optical microscopy with a subdiffraction resolution. We exploit the special dispersion characteristics of an anisotropic metamaterial crystal that is obliquely cut at its output plane, or has a curved output surface, in order to map the input field distribution onto the crystal's output surface with a compressed angular spectrum, resulting in a ``magnified'' image. This can provide a far-field imaging system with a resolution beyond the diffraction limits while no scanning is needed.

Three-dimensional mapping of a deformation field inside a nanocrystal

Abstract: Synchrotron X-ray radiation, produced by electron accelerators at central facilities, can now be produced in extremely narrow coherent beams. When these X-rays illuminate a crystal of nanometre dimensions a diffraction pattern emerges that is highly resolved. This provides a powerful new tool for structural analysis, as the fine features of the diffraction pattern can be interpreted in terms of sub-atomic distortions within the crystal attributable to its contact with an external support. Coherent X-ray diffraction patterns derived from third-generation synchrotron radiation sources can lead to quantitative three-dimensional imaging of lattice strain on the nanometre scale. Coherent X-ray diffraction imaging is a rapidly advancing form of microscopy: diffraction patterns, measured using the latest third-generation synchrotron radiation sources, can be inverted to obtain full three-dimensional images of the interior density within nanocrystals1,2,3. Diffraction from an ideal crystal lattice results in an identical copy of this continuous diffraction pattern at every Bragg peak. This symmetry is broken by the presence of strain fields, which arise from the epitaxial contact forces that are inevitable whenever nanocrystals are prepared on a substrate4. When strain is present, the diffraction copies at different Bragg peaks are no longer identical and contain additional information, appearing as broken local inversion symmetry about each Bragg point. Here we show that one such pattern can nevertheless be inverted to obtain a ‘complex’ crystal density, whose phase encodes a projection of the lattice deformation. A lead nanocrystal was crystallized in ultrahigh vacuum from a droplet on a silica substrate and equilibrated close to its melting point. A three-dimensional image of the density, obtained by inversion of the coherent X-ray diffraction, shows the expected facetted morphology, but in addition reveals a real-space phase that is consistent with the three-dimensional evolution of a deformation field arising from interfacial contact forces. Quantitative three-dimensional imaging of lattice strain on the nanometre scale will have profound consequences for our fundamental understanding of grain interactions and defects in crystalline materials4. Our method of measuring and inverting diffraction patterns from nanocrystals represents a vital step towards the ultimate goal of atomic resolution single-molecule imaging that is a prominent justification for development of X-ray free-electron lasers5,6,7.

High-resolution ab initio three-dimensional x-ray diffraction microscopy

Abstract: Coherent x-ray diffraction microscopy is a method of imaging nonperiodic isolated objects at resolutions limited, in principle, by only the wavelength and largest scattering angles recorded. We demonstrate x-ray diffraction imaging with high resolution in all three dimensions, as determined by a quantitative analysis of the reconstructed volume images. These images are retrieved from the three-dimensional diffraction data using no a priori knowledge about the shape or composition of the object, which has never before been demonstrated on a nonperiodic object. We also construct two-dimensional images of thick objects with greatly increased depth of focus (without loss of transverse spatial resolution). These methods can be used to image biological and materials science samples at high resolution with x-ray undulator radiation and establishes the techniques to be used in atomic-resolution ultrafast imaging at x-ray free-electron laser sources.

Thermal radiation scanning tunnelling microscopy

Abstract: The resolution achievable by optical imaging is limited by the wavelength of the light used — the diffraction limit. Near-field scanning optical microscopy circumvents this limit by using a probe smaller than the wavelength of the incident light to map out the electromagnetic field at the sample surface, allowing a resolution well beyond the diffraction limit. Now a variant of this technique has been developed that does away with external illumination altogether. The new technique, called thermal radiation scanning tunnelling microscopy or TRSTM, makes use of the thermal infrared emissions from the sample itself. Think of it as a near-field equivalent of a night-vision camera. In standard near-field scanning optical microscopy (NSOM), a subwavelength probe acts as an optical ‘stethoscope’ to map the near field produced at the sample surface by external illumination1. This technique has been applied using visible1,2, infrared3, terahertz4 and gigahertz5,6 radiation to illuminate the sample, providing a resolution well beyond the diffraction limit. NSOM is well suited to study surface waves such as surface plasmons7 or surface-phonon polaritons8. Using an aperture NSOM with visible laser illumination, a near-field interference pattern around a corral structure has been observed9, whose features were similar to the scanning tunnelling microscope image of the electronic waves in a quantum corral10. Here we describe an infrared NSOM that operates without any external illumination: it is a near-field analogue of a night-vision camera, making use of the thermal infrared evanescent fields emitted by the surface, and behaves as an optical scanning tunnelling microscope11,12. We therefore term this instrument a ‘thermal radiation scanning tunnelling microscope’ (TRSTM). We show the first TRSTM images of thermally excited surface plasmons, and demonstrate spatial coherence effects in near-field thermal emission.

Neutron and x-ray diffraction studies of liquids and glasses

Abstract: The techniques of neutron diffraction and x-ray diffraction, as applied to structural studies of liquids and glasses, are reviewed. Emphasis is placed on the explanation and discussion of the experimental techniques and data analysis methods, as illustrated by the results of representative experiments. The disordered, isotropic nature of the structure of liquids and glasses leads to special considerations and certain difficulties when neutron and x-ray diffraction techniques are applied, especially when used in combination on the same system. Recent progress in experimental technique, as well as in data analysis and computer simulation, has motivated the writing of this review.

Single-particle diffraction and interference at a macroscopic scale.

Abstract: A droplet bouncing on a vertically vibrated bath can become coupled to the surface wave it generates. It thus becomes a "walker" moving at constant velocity on the interface. Here the motion of these walkers is investigated when they pass through one or two slits limiting the transverse extent of their wave. In both cases a given single walker seems randomly scattered. However, diffraction or interference patterns are recovered in the histogram of the deviations of many successive walkers. The similarities and differences of these results with those obtained with single particles at the quantum scale are discussed.

High efficiency Silicon-on-Insulator grating coupler based on a poly-Silicon overlay

Abstract: A high efficiency broadband grating coupler for Silicon-On-Insulator waveguides was designed. The grating coupler is defined by locally adding a poly-Silicon layer on top of the existing waveguide layer structure prior to grating etching. Adding this poly-Silicon layer reshapes the grating structure which changes its diffraction properties. Coupling efficiencies as high as 78% at a wavelength of 1.55 mum are calculated and the optical 3dB bandwidth of the device is about 85 nm. The device layout is compatible with standard CMOS technology processing.

Rapid synthesis of ZnO nano-rods by one-step, room-temperature, solid-state reaction and their gas-sensing properties

Abstract: ZnO nano-rods are prepared by one-step solid-state reaction of zinc acetate dihydrate, sodium hydroxide and cetyltrimethylammonium bromide (CTAB) at room temperature. The samples are characterized by x-ray diffraction (XRD), scanning electron microscopy (SEM) and transmission electron microscopy (TEM). The gas-sensing properties of the prepared material have been investigated. The results indicate that the as-prepared ZnO nano-rods are uniform with diameters of 10?30?nm and lengths of about 150?250?nm. The relatively high sensor signal and stability of sensors made from ZnO nano-rods demonstrate the potential for developing a new class of sensitive sensors.

Overcoming the rayleigh criterion limit with optical vortices.

Abstract: We experimentally and numerically tested the separability of two independent equally luminous monochromatic and white light sources at the diffraction limit, using optical vortices (OV). The diffraction pattern of one of the two sources crosses a fork hologram on its center generating the Laguerre-Gaussian (LG) transform of an Airy disk. The second source, crossing the fork hologram in positions different from the optical center, generates nonsymmetric LG patterns. We formulated a criterion, based on the asymmetric intensity distribution of the superposed LG patterns so created, to resolve the two sources at angular distances much below the Rayleigh criterion. Analogous experiments in white light allow angular resolutions which are still one order of magnitude below the Rayleigh criterion. The use of OVs might offer new applications for stellar separation in future space experiments.

Nanometer linear focusing of hard x rays by a multilayer Laue lens.

Abstract: We report on a type of linear zone plate for nanometer-scale focusing of hard x rays, a multilayer Laue lens (MLL), produced by sectioning a multilayer and illuminating it in Laue diffraction geometry. Because of its large optical depth, a MLL spans the diffraction regimes applicable to a thin Fresnel zone plate and a crystal. Coupled wave theory calculations indicate that focusing to 5 nm or smaller with high efficiency should be possible. Partial MLL structures with outermost zone widths as small as 10 nm have been fabricated and tested with 19.5 keV synchrotron radiation. Focal sizes as small as 30 nm with efficiencies up to 44% are measured.

Lattice of double wells for manipulating pairs of cold atoms

Abstract: We describe the design and implementation of a two-dimensional optical lattice of double wells suitable for isolating and manipulating an array of individual pairs of atoms in an optical lattice. Atoms in the square lattice can be placed in a double well with any of their four nearest neighbors. The properties of the double well (the barrier height and relative energy offset of the paired sites) can be dynamically controlled. The topology of the lattice is phase stable against phase noise imparted by vibrational noise on mirrors. We demonstrate the dynamic control of the lattice by showing the coherent splitting of atoms from single wells into double wells and observing the resulting double-slit atom diffraction pattern. This lattice can be used to test controlled neutral atom motion among lattice sites and should allow for testing controlled two-qubit gates.

Fast-Fourier-transform based numerical integration method for the Rayleigh-Sommerfeld diffraction formula

Abstract: The numerical calculation of the Rayleigh-Sommerfeld diffraction integral is investigated. The implementation of a fast-Fourier-transform (FFT) based direct integration (FFT-DI) method is presented, and Simpson's rule is used to improve the calculation accuracy. The sampling interval, the size of the computation window, and their influence on numerical accuracy and on computational complexity are discussed for the FFT-DI and the FFT-based angular spectrum (FFT-AS) methods. The performance of the FFT-DI method is verified by numerical simulation and compared with that of the FFT-AS method.

The optical response of nanostructured surfaces and the composite diffracted evanescent wave model

Abstract: Investigations of the optical response of subwavelength-structure arrays milled into thin metal films have revealed surprising phenomena, including reports of unexpectedly high transmission of light. Many studies have interpreted the optical coupling to the surface in terms of the resonant excitation of surface plasmon polaritons (SPPs), but other approaches involving composite diffraction of surface evanescent waves (CDEW) have also been proposed. Here we present a series of measurements on very simple one-dimensional subwavelength structures to test the key properties of the surface waves, and compare them to the CDEW and SPP models. We find that the optical response of the silver metal surface proceeds in two steps: a diffractive perturbation in the immediate vicinity (2–3µ m) of the structure, followed by excitation of a persistent surface wave that propagates over tens of micrometres. The measured wavelength and phase of this persistent wave are significantly shifted from those expected for resonance excitation of a conventional SPP on a pure silver surface.

SHADE web server for estimation of hydrogen anisotropic displacement parameters

Abstract: The SHADE web server estimates anisotropic displacement parameters for hydrogen atoms by combining a rigid-body analysis of the non-hydrogen-atom anisotropic displacement parameters (ADPs) with a contribution from internal atomic motion. The contributions from internal mean square displacements are based on a previously compiled database derived from analysis of neutron diffraction experiments. The estimated hydrogen-atom ADPs can be used as fixed parameters in advanced applications of high-resolution X-ray diffraction, such as electron density studies using multipole modelling. The resulting electron density models have been shown to be in excellent agreement with reference models based on atomic motion derived from neutron diffraction experiments.

Photonic-crystal slabs with a triangular lattice of triangular holes investigated using a guided-mode expansion method

Abstract: According to a recent proposal [S. Takayama et al., Appl. Phys. Lett. 87, 061107 (2005)], the triangular lattice of triangular air holes may allow us to achieve a complete photonic band gap in two-dimensional photonic crystal slabs. In this work we present a systematic theoretical study of this photonic lattice in a high-index membrane, and a comparison with the conventional triangular lattice of circular holes, by means of the guided-mode expansion method whose detailed formulation is described here. Photonic mode dispersion below and above the light line, gap maps, and intrinsic diffraction losses of quasiguided modes are calculated for the periodic lattice as well as for line and point defects defined therein. The main results are summarized as follows: (i) The triangular lattice of triangular holes does indeed have a complete photonic band gap for the fundamental guided mode, but the useful region is generally limited by the presence of second-order waveguide modes; (ii) the lattice may support the usual photonic band gap for even modes (quasi-TE polarization) and several band gaps for odd modes (quasi-TM polarization), which could be tuned in order to achieve doubly resonant frequency conversion between an even mode at the fundamental frequency and an odd mode at the second-harmonic frequency; (iii) diffraction losses of quasiguided modes in the triangular lattices with circular and triangular holes, and in line-defect waveguides or point-defect cavities based on these geometries, are comparable. The results point to the interest of the triangular lattice of triangular holes for nonlinear optics, and show the usefulness of the guided-mode expansion method for calculating photonic band dispersion and diffraction losses, especially for higher-lying photonic modes.

Forward modeling method for microstructure reconstruction using x-ray diffraction microscopy: Single-crystal verification

Abstract: We describe and illustrate a forward modeling method for quantitatively reconstructing the geometry and orientation of microstructural features inside of bulk samples from high-energy x-ray diffraction microscopy data. Data sets comprise charge-coupled device images of Bragg diffracted beams originating from individual grains in a thin planar section of sample. Our analysis approach first reduces the raw images to a binary data set in which peaks have been thresholded at a fraction of their height after noise reduction processing. We then use a computer simulation of the measurement and the sample microstructure to generate calculated diffraction patterns over the same range of sample orientations used in the experiment. The crystallographic orientation at each of an array of area elements in the sample space is adjusted to optimize overlap between experimental and simulated scattering. In the present verification exercise, data are collected at the Advanced Photon Source beamline 1-ID using microfocused ...

Ultrafast Time-Resolved Electron Diffraction with Megavolt Electron Beams

Abstract: A rf photocathode electron gun is used as an electron source for ultrafast time-resolved pump-probe electron diffraction. The authors observed single-shot diffraction patterns from a 160nm Al foil using the 5.4MeV electron beam from the Gun Test Facility at the Stanford Linear Accelerator. Excellent agreement with simulations suggests that single-shot diffraction experiments with a time resolution approaching 100fs are possible.

Coherent imaging with pseudo-thermal incoherent light

Abstract: We investigate experimentally fundamental properties of coherent ghost imaging using spatially incoherent beams generated from a pseudo-thermal source. A complementarity between the coherence of the beams and the correlation between them is demonstrated by showing a complementarity between ghost diffraction and ordinary diffraction patterns. In order for the ghost imaging scheme to work it is therefore crucial to have incoherent beams. The visibility of the information is shown for the ghost image to become better as the object size relative to the speckle size is decreased, and therefore a remarkable tradeoff between resolution and visibility exists. The experimental conclusions are backed up by both theory and numerical simulations.

Complex zeolite structure solved by combining powder diffraction and electron microscopy

Abstract: Many industrially important materials are polycrystalline and so most conventional methods to solve crystal structures, which require single crystals, are ineffective. Of the alternatives, transmission electron microscopy has so far solved only simple structures; and in powder diffraction the overlap of peaks with similar diffraction angles causes ambiguities in the intensities. Now, powder diffraction data applied to an algorithm incorporating phase information from high-resolution transmission electron micrographs has provided a way of solving zeolite structures using polycrystalline samples. The new technique has successfully solved the structure of zeolite TNU-9, the most complex zeolite known. Many industrially important materials, ranging from ceramics to catalysts to pharmaceuticals, are polycrystalline and cannot be grown as single crystals. This means that non-conventional methods of structure analysis must be applied to obtain the structural information that is fundamental to the understanding of the properties of these materials. Electron microscopy might appear to be a natural approach, but only relatively simple structures have been solved by this route. Powder diffraction is another obvious option, but the overlap of reflections with similar diffraction angles causes an ambiguity in the relative intensities of those reflections. Various ways of overcoming or circumventing this problem have been developed1,2, and several of these involve incorporating chemical information into the structure determination process3,4,5,6,7. For complex zeolite structures, the FOCUS algorithm8,9 has proved to be effective. Because it operates in both real and reciprocal space, phase information obtained from high-resolution transmission electron microscopy images can be incorporated directly into this algorithm in a simple way. Here we show that by doing so, the complexity limit can be extended much further. The power of this approach has been demonstrated with the solution of the structure of the zeolite TNU-9 (|H9.3|[Al9.3Si182.7O384]; ref. 10) with 24 topologically distinct (Si,Al) atoms and 52 such O atoms. For comparison, ITQ-22 (ref. 11), the most complex zeolite known to date, has 16 topologically distinct (Si,Ge) atoms.

Fast focus field calculations.

Abstract: We present a fast calculation of the electromagnetic field near the focus of an objective with a high numerical aperture (NA). Instead of direct integration, the vectorial Debye diffraction integral is evaluated with the fast Fourier transform for calculating the electromagnetic field in the entire focal region. We generalize this concept with the chirp z transform for obtaining a flexible sampling grid and an additional gain in computation speed. Under the conditions for the validity of the Debye integral representation, our method yields the amplitude, phase and polarization of the focus field for an arbitrary paraxial input field on the objective. We present two case studies by calculating the focus fields of a 40×1.20 NA water immersion objective for different amplitude distributions of the input field, and a 100×1.45 NA oil immersion objective containing evanescent field contributions for both linearly and radially polarized input fields.

Hydrogen adsorption in an interpenetrated dynamic metal-organic framework.

Abstract: A metal−organic framework Zn(NDC)(4,4‘-Bpe)0.5·xG [NDC = 2,6-naphthalenedicarboxylate; 4,4‘-Bpe = 4,4‘-trans-bis(4-pyridyl)ethylene; G = guest molecules] has been synthesized, structurally characterized, and rationalized to be a two-interpenetrated elongated primitive cubic net. Powder X-ray diffraction and adsorption studies reveal the dynamic feature of the framework, which can take up hydrogen of about 2.0 wt % at 77 K and 40 bar and 0.3 wt % at 298 K and 65 bar.

Femtosecond electron diffraction: 'making the molecular movie'.

Abstract: Femtosecond electron diffraction (FED) has the potential to directly observe transition state processes. The relevant motions for this barrier-crossing event occur on the hundred femtosecond time-scale. Recent advances in the development of high-flux electron pulse sources with the required time resolution and sensitivity to capture barrier-crossing processes are described in the context of attaining atomic level details of such structural dynamics-seeing chemical events as they occur. Initial work focused on the ordered-to-disordered phase transition of Al under strong driving conditions for which melting takes on nm or molecular scale dimensions. This work has been extended to Au, which clearly shows a separation in time-scales for lattice heating and melting. It also demonstrates that superheated face-centred cubic (FCC) metals melt through thermal mechanisms involving homogeneous nucleation to propagate the disordering process. A new concept exploiting electron-electron correlation is introduced for pulse characterization and determination of t=0 to within 100fs as well as for spatial manipulation of the electron beam. Laser-based methods are shown to provide further improvements in time resolution with respect to pulse characterization, absolute t=0 determination, and the potential for electron acceleration to energies optimal for time-resolved diffraction.

Extended high-frame rate imaging method with limited-diffraction beams

Abstract: Fast three-dimensional (3-D) ultrasound imaging is a technical challenge. Previously, a high-frame rate (HFR) imaging theory was developed in which a pulsed plane wave was used in transmission, and limited-diffraction array beam weightings were applied to received echo signals to produce a spatial Fourier transform of object function for 3-D image reconstruction. In this paper, the theory is extended to include explicitly various transmission schemes such as multiple limited-diffraction array beams and steered plane waves. A relationship between the limited-diffraction array beam weighting of received echo signals and a 2-D Fourier transform of the same signals over a transducer aperture is established. To verify the extended theory, computer simulations, in vitro experiments on phantoms, and in vivo experiments on the human kidney and heart were performed. Results show that image resolution and contrast are increased over a large field of view as more and more limited-diffraction array beams with different parameters or plane waves steered at different angles are used in transmissions. Thus, the method provides a continuous compromise between image quality and image frame rate that is inversely proportional to the number of transmissions used to obtain a single frame of image. From both simulations and experiments, the extended theory holds a great promise for future HFR 3-D imaging

Ab initio determination of solid-state nanostructure

Abstract: Advances in materials science and molecular biology followed rapidly from the ability to characterize atomic structure using single crystals. Structure determination is more difficult if single crystals are not available. Many complex inorganic materials that are of interest in nanotechnology have no periodic long-range order and so their structures cannot be solved using crystallographic methods. Here we demonstrate that ab initio structure solution of these nanostructured materials is feasible using diffraction data in combination with distance geometry methods. Precise, sub-angstrom resolution distance data are experimentally available from the atomic pair distribution function (PDF). Current PDF analysis consists of structure refinement from reasonable initial structure guesses and it is not clear, a priori, that sufficient information exists in the PDF to obtain a unique structural solution. Here we present and validate two algorithms for structure reconstruction from precise unassigned interatomic distances for a range of clusters. We then apply the algorithms to find a unique, ab initio, structural solution for C60 from PDF data alone. This opens the door to sub-angstrom resolution structure solution of nanomaterials, even when crystallographic methods fail.