3D object reconstruction from random orientations

The featured item this time is “Structure from Fleeting Illumination of Faint Spinning Objects in Flight with Application to Single Molecules” by Russell Fung and co-authors at U Wisconsin Milwaukee.

The promise of solving atomic-resolution 3D structure of biological proteins with X-ray Free Electron Lasers has several obstacles. First one is to have fast enough x-ray pulse to image molecules before it starts to undergo “Coulomb explosion”. But even that is not sufficient to produce atomic-scale structure due to low scattering cross-section of hard x-rays – so the experiment will need to be repeated many (thousands?) times to improve statistics. Luckily, protein molecules are identical, so the fundamental 3D structure of the sample could be considered the same – however, the orientation of protein molecule is going to be different each time.

There are two ways to solve the “random orientation” problem – one is to try to align the molecule, for example with a laser beam. However this has to be done with a very high precision and is difficult to achieve in practice. Another approach is to do experiment thousands of times with random orientations of molecules, catalogue all resulting projections, and then use mathematical algorithms to “fold” the projections into a unique 3D object that is consistent with all resulting projections.

Russel Fung et al. provide an algorithm that does just that – by simulating realistic conditions of 4th generation synchrotron source, X-ray Free Electron Laser, with collection of 100,000 photons, 72,000 repeated diffraction patterns from single shot experiments and scattering rates as low as 0.01 photons per pixel at large wavevectors corresponding to 1.8 Angstrom.

The result of folding using Generative Topographic Mapping for protein chignolin in random orientations is shown in figure above, for 3D movie of this reconstructed molecule see Abbas Ourmazd’s webpage at UW Milwaukee.

sub-picosecond movies of nucleation dynamics

A shortlived SPPS facility is still producing papers – this week it’s the PRL paper by Aaron Lindenberg and some 28 co-authors ” X-Ray Diffuse Scattering Measurements of Nucleation Dynamics at Femtosecond Resolution” Phys. Rev. Lett. 100, 135502 (2008).

This is yet another pump-probe experiment, where pump is a femtosecond laser which ablates/melts a crystal, and a probe is a sub-picosecond x-ray pulse from SPPS. X-ray probe pulse length is still a limiting parameter in overall time resolution of such pump-probe setups. This experiment had a time resolution of 700 fs, but in the near future at XFEL facilities such as LCLS the time resolution will approach tens of femtosecond.

Lindenberg and coworkers were able to look at both high-angle and small-angle diffuse scattering resulting in ablation process in this time-resolved mode. Their data indicates presence of short-lived nanoscale voids (shown in green in the figure on the right) in the liquid state caused by the laser pulse, and these voids merge together to form larger voids over the timescale of 20 ps or so – claims supported by molecular dynamics simulations. While their data was taken in reciprocal space, by recording ensemble-averaged structure factor S(q) at various time delays from the laser pulse, in the future one could envision fully inverting the speckle patterns shown in the figure above, to obtain a real-space images of the nanoscale voids.

Droplet Coalescence

Two recent PRLs are addressing the issue of how two droplets merge into one.

Kamel Fezzaa and Yujie Wang from Argonne use ultrafast x-ray phase-contrast imaging to take sub-microsecond exposures of droplet coalescence, which is complete in just under a milisecond.

Phys. Rev. Lett. 100, 104501 (2008)

The studied liquid droplets are ~1mm (bar size in the image on the left) in size, and can be seen with <5 micron resolution using phase contrast (as opposed to adsorption contrast) using high energy 13keV x-rays. Fezzaa and Wang cleverly used the hybrid filling pattern of Advanced Photon Source, where each electron bunch produces a short x-ray pulse 472 nanoseconds long used for imaging, with each pulse separated from the next one by 3.6 microseconds. The result is a sub-microsecond “shutter time” defined by the length of each pulse, with consecutive images taken 3.6 microseconds apart.

Of particular interest in this study is the stability of torroidal air bubble formed due to air trapped by the two rapidly coalescing droplet menisci. Fezzaa and Wang show for the first time that the torroidal bubble remains trapped until some 400 microsecond after the droplets start merging.

The second recent paper on this topic of droplet coalescence is by Sara Case and Sid Nagel at University of Chicago. PRL 100, 084503 (2008)

Case and Nagel abandon the visual approach to studies of ultrafast coalescence process, and instead adopt a technique which measures the changes in conductivity across the connection between the two droplets as a function of time. When the droplets begin to coalesce, the effective resistivity is high, since it is defined primarily by the width of the narrow region where the two droplets touch each other. As they coalesce, this resistivity will drop. This technique proves to be especially useful in the timescale range from sub-microsecond to hundreds of microsecond. Case and Nagel observe a cross-over in power-law behavior for R(t) from 1/t for small t to 1/√t at large t, but do not see time-dependent fluctuations in R(t) which would be the signature of the connected menisci repeatedly disconnecting and reconnecting again.

Xraying Nanoparticles in Ball-Lightning and Fuel Injection jets

Observations of ball-lightning – long-lived (2 to 50 seconds) bright fireballs size of baseball to beach ball – have been observed for centuries. Previous theoretical work ascribes the longevity of the ball lightnings to the slow oxidation process of silicon, forming nanoparticle networks. Now, Mitchell et al. Phys. Rev. Lett. 100, 065001 (2008) have created artificial ball-lightning using localized microwaves and have studied them in-situ with synchrotron radiation (using small-angle x-ray scattering), proving that the fireballs do indeed contain nanoparticles with sizes of the order 50 nm.

Small Angle X-ray Scattering, or SAXS, has been used to all kinds of samples – liquid, vapor or solid, but this may be the first time this technique was applied to plasma.

Meanwhile, Wang et al. (Nature Physics, advanced publication) performed an ultra-fast time resolved study of morphology of optically dense jets from fuel injector nozzle. The achieved microsecond temportal resolution is due to application of time-resolved full-field phase contrast imaging. Unlike typical radiography (such as used at the dentist’s office) that is sensitive to the mass density (adsorption) of material through intensity measurements, phase contrast measurements rely on phase changes.

For more details on phase contrast imaging see Wilkins et al., Nature 384, 335 – 338 (28 November 1996)

Techniques using visible light scattering are suffering from problems due to multiple scattering from various interfaces of jet droplets – ironically, these interfaces are precisely what serves as a contrast mechanism in the x-ray phase contrast imaging technique used by Wang et. al in this study.

Metal-Insulator transition in VO2

There were a number of papers in the past month or so on Metal-Insulator transition in vanadium dioxide. The first work is the near-scanning infrared microscopy measurements done by Mumtaz Qazilbash et al. from Basov group at UCSD published last week in Science revealing nucleation and growth of metallic domains in vanadium dioxide films with nanoscale resolution.

M. M. Qazilbash et al., “Mott Transition in VO₂ Revealed by Infrared Spectroscopy and Nano-Imaging” Science 14 December 2007: 1750-1753

Last month there was another Science paper by Peter Baum et al. from Zewail group at Caltech looking at “4D” visualization of metal-insulator transition in vanadium dioxide – involving a combination of 3D observations of Bragg peaks with electron diffraction, resolved on the femtosecond scale.

Also see this PNAS article by Baum and Zewail (PNAS | November 20, 2007 | vol. 104 | no. 47 | 18409-18414, Open access), as well as a Science perspective by Cavalleri.

Baum et al., Science 318 (5851), 788. [DOI: 10.1126/science.1147724]

And in September, there was a PRL by Kubler et al. on light-induced femtosecond MIT transition in VO2, followed by another PRL by Hilton et al. in late November on a similar topic.

XFEL trifecta in Science, Nature

Last week was the “perfect storm” of XFEL ultrafast science, with four papers in Nature and Science:

Nature featured a paper by Henry Chapman et al. on Femtosecond time-delay X-ray Holography. By recording an interference pattern of a particle and it’s mirror image it is possible to record an ultrafast “explosive” motion of the particle due to exposure of the x-ray beam. It’s the ultimate pump-probe experiment where both pump and probe are one and the same.
This paper is accompanied by News and Views article “Femtophysics: Double vision” by Andrea Cavalleri.

Science has two review papers out – one is “Harnessing Attosecond Science in the Quest for Coherent X-rays” by Kaptey et. al from Margaret Murnane’s group at Colorado Boulder.

There is also a Review paper by Phil Bucksbaum on “The Future of Attosecond Spectroscopy”.

Thee two papers are part of the special section on attosecond spectroscopy, also featured as a cover story.

Ultrafast work at SPPS

This week’s item is inspired by my recent visit to Stanford, in anticipation of the world’s first x-ray free electron laser – LCLS, which will open in 2009. LCLS is a facility that will feature ultrashort (200 fs) x-ray pulses that are fully coherent in transverse directions, and will be using one third of a 3-km linear accelerator as the source of electrons that will be used for “lasing” in a total of about 100m of undulator. In comparison, current third generation hard x-ray sources like APS, ESRF or SPRING-8 use undulators that are only a couple of meters long, and pulses that are about 1,000 times longer – on the order of 100 ps.

In preparation to LCLS, scientists built a temporary facility called Sub-Picosecond Pulse Source (SPPS). It used SLAC’s LINAC electron beam outfitted with a relatively short undulator. The total flux was nowhere near projected LCLS values or even sources like APS – in fact (as reported here previously) when LCLS becomes operational it will produce more x-rays in the first 10 seconds than SPPS produced in its entire 3-year lifetime. But SPPS was a unique source of sub-ps x-rays, and produced some really interesting science. One such result was featured in Science earlier this year: a report by D. Fritz et al., includes almost 40 collaborators from 20 different institutions.

The basic idea of experiment is pump-probe – hitting Bi crystal with a ultrafast powerful laser and use x-rays to probe the lattice structure some short time later. Because both laser and x-ray pulses are sub-ps, one can in principle shoot a movie of structural lattice dynamics in response to the initial laser pulse, with sub-ps time resolution – something other x-ray sources currently cannot do. But in order to do this, one has to be able to vary the delay between laser and x-ray pulse – which was problematic at SPPS due to jitter, which results in random delay between the two pulses. However, using a clever time-tagging technique, the jitter was used to the experiment’s advantage – by figuring out the time delay between the two pulses that resulted from jitter for each pulse, scientists were able to use jitter to scan the time delay – even though the time of arrival is highly random, this randomness provides a way for varying the delay.