Using coherence to measure two-time correlation functions.

An introduction to x-ray intensity fluctuation spectroscopy is given by describing its relationship to speckle from coherent sources. Its use to measure two-time correlation functions is demonstrated using the equilibrium fluctuations of gold colloids in polystyrene and for non-equilibrium fluctuations in the unmixing below the miscibility gap in AlLi.

Kinetic evolution of unmixing in an AlLi alloy using x-ray intensity fluctuation spectroscopy.

Irreversible decomposition of an AlLi single crystal has been studied by x-ray photon correlation spectroscopy. The precipitate coarsening follows a universal behavior, as measured by the time-resolved average scattering. Using coherent scattering, two-time correlation functions have been measured. The time evolution of the speckle pattern gives new insight into the process of unmixing; at least two regimes govern this evaporation-condensation coarsening process. One is related to the overall arrangement of precipitates, and the characteristic time is linear with annealing time. The other is related to the motion of interfaces and is related to Porod's law.

X-ray intensity fluctuation spectroscopy by heterodyne detection.

A straightforward way of measuring X-ray intensity fluctuation spectroscopy in a small-angle X-ray scattering configuration is demonstrated using heterodyne techniques. Two examples are presented: the Brownian motion of latex spheres in glycerol, and a Doppler velocity experiment demonstrating the motion and the relaxation of carbon-black-filled elastomers after uniaxial stretching. In the latter case the effects of mechanical relaxation can be separated from those of aggregate diffusion. The results suggest that the dynamics of these filled elastomers are similar to the universal features observed in disordered jammed systems.

Coherent small-angle scattering on a bending-magnet beamline at the ESRF.

A coherent X-ray beam is obtained from the D2AM bending-magnet beamline (BM2) of the European Synchrotron Radiation Facility. As this line has permanent convergent optics, monochromated by an Si(111) double monochromator, coherence conditions are satisfied by selecting a part of the beam close to the focal point. Low intensity (10(6) X-rays s(-1)) is partially compensated by a high degree of coherence and by the use of a high-resolution direct-illumination CCD area detector. The stability of the small-angle set-up makes quantitative analysis possible. The calculated and measured degrees of coherence are compared. The distributions of speckle intensities are explained by a beam composed of two-thirds coherent and one-third incoherent parts. This incoherent component is caused by Kapton windows, which will be removed in future experiments.

X-ray diffraction from rectangular slits.

It is shown that for micrometre-sized beams the X-ray diffraction from slits is a source of strong parasitic background, even for slits of high quality. In order to illustrate this effect, the coherent diffraction from rectangular slits has been studied in detail. A large number of interference fringes with strong visibility have been observed using a single set of slits made of polished cylinders. For very small apertures, asymmetrical slits generate asymmetrical patterns. This pattern is calculated from the theory of electromagnetic field propagation and compared with experiment in the far-field regime. The use of guard slits to remove Fraunhofer diffraction from the beam-defining slits is treated theoretically. Numerical simulations yield the optimum aperture of the guard slits with respect to the distance to the primary slits. Diffraction theory is shown to be essential to understand how to reduce the background-to-signal ratio in high-resolution experiments.

Dynamics of phason fluctuations in the i-AlPdMn quasicrystal.

We report on the study of the dynamics of long wavelength phason fluctuations in the i-AlPdMn icosahedral phase using coherent x-ray scattering. When measured with a coherent x-ray beam, the diffuse intensity due to phasons presents strong fluctuations or speckles pattern. From room temperature to 500 degrees C the speckle pattern is time independent. At 650 degrees C the time correlation of the speckle pattern exhibits an exponential time decay, from which a characteristic time tau is extracted. We find that tau is proportional to the square of the phason wavelength, which demonstrates that phasons are collective diffusive modes in quasicrystals, in agreement with theoretical predictions.

Aging in a filled polymer: coherent small angle x-ray and light scattering

Measurements are described using small angle coherent x-ray scattering and small angle dynamic light scattering of motion in fumed silica aggregates suspended in a poly(dimethyl siloxane) melt. At rest, this system develops weakly bound superstructures that are disrupted by mechanical stirring or thermal treatment. The observed relaxation rates correspond to a combination of liquidlike diffusion and a structural relaxation (flocculation) whereby the diffusing silica aggregates recombine into larger agglomerates at long times. Both processes are diffusion controlled. Two samples are investigated. The first, in which the silica is hydrophilic, is a highly viscous liquid for which the respective rate coefficients are about 5x10(-14) cm(2) s(-1) and 2x10(-15) cm(2) s(-1). The second sample, in which the silica surface is hydrophobic, is a thixotropic paste. The same aging mechanism in the diffusion is also observed, but with much slower rate constants, 2x10(-15) cm(2) s(-1) and 9x10(-16) cm(2) s(-1), respectively.