two PRLs on x-ray phasing

Two new PRLs are dealing with x-ray phasing.

The first paper is de Jonge et al., “Quantitative Phase Imaging with a Scanning Transmission X-Ray Microscope” Phys. Rev. Lett. 100, 163902 (2008). Typically the differential phase contrast measurements become non-trivial for thick specimens, when the adsorption and phase-wrapping effects become significant. This paper resolves this problems when differential phase contrast measurements are done in scanning transmission x-ray microscopy mode (STXM), since the solution is overconstrained, allowing to arrive at unique phase and adsorption values.

The second paper is Johnson et al., “Coherent Diffractive Imaging Using Phase Front Modifications” Phys. Rev. Lett. 100, 155503 (2008).

Since phase is lost during the measurements, it is impossible to simply fourier-transform the coherent x-ray diffraction pattern to obtain a real-space image of an object with nanoscale resolution. There are numerous numerical approaches of phase-retrieval based on oversampling the diffraction pattern. This paper presents an alternative approach of introducing a phase plate, and deconvolving the set of phases resulting from the sample by scanning the phase object around, making the contribution from the phase plate known, and providing information on un-altered phases that would be observed if no phase plate was present. This technique is similar to ptychography, as it provides additional constraints that help arriving at unique solution in a rapidly convergent manner, except it scans the known phase plate, rather than the object being imaged.

Keyhole Imaging, Relaxation in Nanoparticles, CDW correlations

In advanced publication of Nature Physics, Brian Abbey and colleagues present a new technique, called “Keyhole Coherent Diffractive Imaging”, which enables them to study extended objects (in similar fashion as ptychography, but based on a somewhat different geometry). The basic idea of KCDI is to combine Fresnel and Fraunhoffer imaging in a divergent (curved) wavefront by placing an imaged object behind the focal spot of a lens and use this additional information to reconstruct the wavefront. It is somewhat counter-intuitive to understand why curved wavefronts should provide a faster phase-retrieval algorithm convergence than flat wavefronts, but it’s a bit like mixing near-field and far-field techniques.

In advanced publication of Nature Materials, Urbana group lead by Jim Zuo show how application of coherent electron diffraction imaging (very similar to x-ray techniques) can reveal the relationship between the coordination number of Au atoms within a ~4 nm nanoparticle and the out-of-plane bond length. Electrons interact much stronger with matter than x-rays and one could argue that electrons are better for imaging of small nanosized objects, while x-rays are better for imaging extended micron-sized objects. Surface relaxation is a well-known phenomenon in surface science – due to reduced number of near-neighbors, atoms in the near-surface region end up with “dangling bonds” effect – and by turning these bonds inward the atoms can reduce out-of-plane atomic distance. Zuo and his group provide a very detailed analysis of surface relaxation for various facets of Au nanoparticles, as a function of near-neighbor coordination number.

And in a recent issue of Physical Review Letters, David LeBolloch’ and colleagues show that charge density wave condensate in blue bronze compound can spontaneously develop long-range correlations (up to micron-size) when the charge density waves is depinned due to applied current and is in a sliding state (imagine a particle on a washboard potential which is getting tilted).

X-ray lens-less imaging of buried nanostructures

Coherent X-ray Diffraction allows reconstruction of small particles with ~15 nanometer resolution. However, High Resolution Transmission Electron Microscopy (see current issue of MRS Bulletin for review) can achieve an atomic-scale resolution for crystalline nanoscale objects.

But since electrons interact very strongly with positively charged ions in the lattice, electron microscopy cannot see deep inside of materials. X-rays have deep penetrating power, and can provide detailed structural information about deeply buried structures. In small-angle scattering regime all of the material in the path of the x-rays will contribute to the coherent speckle. However, using the energy tunability feature of synchrotron sources, one could scan the energy across the resonant edge of a specific element, changing the effective electron density of specific atomic species. The difference between density maps will reveal the specific elemental distribution of this atomic species, since all other elements will subtract off. Changyong Song from John Miao’s Coherent X-ray Imaging group at UCLA and co-workers have demonstrated this by imaging a Bi nanostructure buried deep within Si matrix (Phys. Rev. Lett. 100, 025504 (2008) ). This microscopy technique, which combines lens-less imaging based on phase-retrieval of coherent x-ray diffraction pattern and the resonant measurements could be extended to samples containing multiple elements – repeating these measurements at various adsorption edges of different elements will produce detailed elemental maps of deeply buried structures (microns or more beneath the surface).