SPEDEN: Reconstructing single particles from their diffraction patterns

Speden is a computer program that reconstructs the electron density of single particles from their x-ray diffraction patterns, using a single-particle adaptation of the Holographic Method in crystallography. (Szoke, A., Szoke, H., and Somoza, J.R., 1997. Acta Cryst. A53, 291-313.) The method, like its parent, is unique that it does not rely on ``back'' transformation from the diffraction pattern into real space and on interpolation within measured data. It is designed to deal successfully with sparse, irregular, incomplete and noisy data. It is also designed to use prior information for ensuring sensible results and for reliable convergence. This article describes the theoretical basis for the reconstruction algorithm, its implementation and quantitative results of tests on synthetic and experimentally obtained data. The program could be used for determining the structure of radiation tolerant samples and, eventually, of large biological molecular structures without the need for crystallization.Comment: 12 pages, 10 figure

Progress in Three-Dimensional Coherent X-Ray Diffraction Imaging

The Fourier inversion of phased coherent diffraction patterns offers images without the resolution and depth-of-focus limitations of lens-based tomographic systems. We report on our recent experimental images inverted using recent developments in phase retrieval algorithms, and summarize efforts that led to these accomplishments. These include ab-initio reconstruction of a two-dimensional test pattern, infinite depth of focus image of a thick object, and its high-resolution (~10 nm resolution) three-dimensional image. Developments on the structural imaging of low density aerogel samples are discussed.Comment: 5 pages, X-Ray Microscopy 2005, Himeji, Japa

Coherent X-ray Diffractive Imaging; applications and limitations

The inversion of a diffraction pattern offers aberration-free diffraction-limited 3D images without the resolution and depth-of-field limitations of lens-based tomographic systems, the only limitation being radiation damage. We review our experimental results, discuss the fundamental limits of this technique and future plans.Comment: 7 pages, 8 figure

Three-dimensional coherent X-ray diffraction imaging of a ceramic nanofoam: determination of structural deformation mechanisms

Ultra-low density polymers, metals, and ceramic nanofoams are valued for their high strength-to-weight ratio, high surface area and insulating properties ascribed to their structural geometry. We obtain the labrynthine internal structure of a tantalum oxide nanofoam by X-ray diffractive imaging. Finite element analysis from the structure reveals mechanical properties consistent with bulk samples and with a diffusion limited cluster aggregation model, while excess mass on the nodes discounts the dangling fragments hypothesis of percolation theory.Comment: 8 pages, 5 figures, 30 reference

X-ray image reconstruction from a diffraction pattern alone

A solution to the inversion problem of scattering would offer aberration-free diffraction-limited 3D images without the resolution and depth-of-field limitations of lens-based tomographic systems. Powerful algorithms are increasingly being used to act as lenses to form such images. Current image reconstruction methods, however, require the knowledge of the shape of the object and the low spatial frequencies unavoidably lost in experiments. Diffractive imaging has thus previously been used to increase the resolution of images obtained by other means. We demonstrate experimentally here a new inversion method, which reconstructs the image of the object without the need for any such prior knowledge.Comment: 5 pages, 3 figures, improved figures and captions, changed titl

Electromigration-induced plasticity and texture in Cu interconnects

Plastic deformation has been observed in damascene Cu interconnect test structures during an in-situ electromigration experiment and before the onset of visible microstructural damage (ie. voiding) using a synchrotron technique of white beam X-ray microdiffraction. We show here that the extent of this electromigration-induced plasticity is dependent on the texture of the Cu grains in the line. In lines with strong <111> textures, the extent of plastic deformation is found to be relatively large compared to our plasticity results in the previous study [1] using another set of Cu lines with weaker textures. This is consistent with our earlier observation that the occurrence of plastic deformation in a given grain can be strongly correlated with the availability of a <112> direction of the crystal in the proximity of the direction of the electron flow in the line (within an angle of 10{sup o}). In <111> out-of-plane oriented grains in a damascene interconnect scheme, the crystal plane facing the sidewall tends to be a {l_brace}110{r_brace} plane,[2-4] so as to minimize interfacial energy. Therefore, it is deterministic rather than probabilistic that the <111> grains will have a <112> direction nearly parallel to the direction of electron flow. Thus, strong <111> textures lead to more plasticity, as we observe

Sub-nanometer-scale measurements of the interaction of ultrafast soft x-ray free-electron-laser pulses with matter

Femtosecond pulses from soft-x-ray free-electron lasers (FELs) [1] are ideal for directly probing matter at atomic length scales and timescales of atomic motion. An important component of understanding ultrafast phenomena of light-matter interactions is concerned with the onset of atomic motion which is impeded by the atoms inertia. This delay of structural changes will enable atomic-resolution flash-imaging [2-3] to be performed at upcoming x-ray FELs [4-5] with pulses intense enough to record the x-ray scattering from single molecules [6]. We explored this ultrafast high-intensity regime with the FLASH soft-x-ray FEL [7-8] by measuring the reflectance of nanostructured multilayer mirrors using pulses with fluences far in excess of the mirrors damage threshold. Even though the nanostructures were ultimately completely destroyed, we found that they maintained their integrity and reflectance characteristics during the 25-fs-long pulse, with no evidence for any structural changes during that time over lengths greater than 3 {angstrom}. In the recently built FLASH FEL [7], x-rays are produced from short electron pulses oscillating in a periodic magnet array, called an undulator, by the principle of self-amplification of spontaneous emission [9-10]. The laser quality of the x-ray pulses can be quantified by the peak spectral brilliance of the source, which is 10{sup 28} photons/(s mm2 mrad2 0.1% bandwidth) [8]; this is up to seven orders of magnitude higher than modern third-generation synchrotron sources. For our studies, the machine operated with pulses of 25 fs duration at a wavelength of 32.5 nm and energies up to 21 {micro}J. We focused these pulses to 3 x 10{sup 14} W/cm{sup 2} onto our nanostructured samples, resulting in an the unprecedented heating rate of 5 x 10{sup 18} K/s, while probing the irradiated structures at the nanometer length scale. The x-ray reflectivity of periodic nanometer-scale multilayers [11] is very sensitive to changes in the atomic positions and the refractive indices of the constituent materials, making them an ideal choice to study structural changes induced by ultrashort FEL pulses. The large multilayer reflectivity results from the cooperative interaction of the x-ray field with many layers of precisely fabricated thicknesses, each less than the x-ray wavelength. This Bragg or resonant reflection from the periodic structure is easily disrupted by any imperfection of the layers. The characteristics of the structure, such as periodicity or layer intermixing, can be precisely determined from the measurement of the Bragg reflectivity as a function of incidence angle. These parameters can be easily measured to a small fraction of the probe wavelength, as is well known in x-ray crystallography where average atomic positions of minerals or proteins are found to less than 0.01{angstrom}. Thus, we can explore ultrafast phenomena at length scales less than the wavelength, and investigate the conditions to overcome the effects of radiation damage by using ultrafast pulses

Ultrafast Coherent Diffraction Imaging with X-ray Free-Electron Lasers

The ultrafast pulses from X-ray free-electron lasers will enable imaging of non-periodic objects at near-atomic resolution [1, Neutze]. These objects could include single molecules, protein complexes, or virus particles. The specimen would be completely destroyed by the pulse in a Coulomb explosion, but that destruction will only happen after the pulse. The scattering from the sample will give structural information about the undamaged object. There are many technical challenges that must be addressed before carrying out such experiments at an XFEL, which we are doing so with experiments at FLASH, the soft-X-ray FEL at DESY