We have carried out intensity fluctuation spectroscopy measurements using coherent x rays to study the dynamics of critical fluctuations in a binary alloy at equilibrium.An intense coherent hard x-ray beam, produced from an undulator source, was scattered from a single crystal of Fe3Al held at l l l temperatures near the B2 DO& order--disorder transition. A speckle pattern was observed at the (; -, -, ) superlattice reAection. Below T, it was essentially static, while above T, it Auctuated in time. The behavior of the normalized time correlation function is consistent with predictions of theory.

A simple approach for producing a high-coherent-flux X-ray beam for small-angle-scattering studies used at the Troika beamline of the European Synchrotron Radiation Facility is reported. For such small-angle studies it is permissible to reduce the longitudinal coherence .length of the beam, thus increasing the energy bandpass and intensity of the beam, because there is only a small optical pathlength difference. By using mirrors and filters to cut unwanted energies from the undulator harmonic structure, a high-flux beam of >109 photons s -~ through a 5 ~tm-diameter pinhole at 8.2 keV with a bandpass of 1.3% can be produced. The coherent properties of this beam have been measured by analyzing a static speckle pattern from an aerogel sample imaged by a directly illuminated CCD camera. The speckle size and contrast are compared with the expected values based on a statistical analysis of the intensity distribution of speckle patterns obtained using partially coherent conditions. The expected widths of the spatial autocorrelation are found, but there is an apparent incoherent fraction of the beam which reduces the measured contrast. The method presented is to be used as a tool to optimize conditions for diffraction experiments using coherent X-rays.

We report x-ray intensity fluctuation spectroscopy measurements of the equilibrium dynamics of polymer micelle liquids, composed of polystyrene-polyisoprene block copolymer micelles within a polystyrene homopolymer matrix. The equilibrium dynamics were investigated for times between one and several hundred seconds, and for wave vectors from 0.003 to 0.015 Å 21 , far beyond wave vectors that can be studied with visible light. A wave-vector-dependent diffusion coefficient is found.[S0031-9007 (97)02392-2] PACS numbers: 61.41. + e, 61.10.YhBlock copolymers show a variety of microstructures as a result of their amphiphilic molecular architectures [1], motivating continuing investigations of their structure, thermodynamics, and rheology. However, it has not generally been possible to study the molecular-scale dynamics of block copolymer melts, because the length scale of the microstructure is several tens of nanometers-determined by the size of the polymers-and is thus inaccessible to light scattering techniques; while the relevant time scales are slower than can be easily studied by neutron scattering [2].The introduction of high-brilliance synchrotron sources now allows for intensity fluctuation spectroscopy measurements using coherent x rays (XIFS), enabling investigations of molecular-scale dynamics [3][4][5][6]. XIFS was recently demonstrated in small-angle scattering studies of the diffusion of dilute gold [5] and palladium [6] colloidal particles, suspended in glycerol. In the present paper, we report an XIFS study of the dynamics of mixtures of polystyrene-polyisoprene block copolymers with polystyrene homopolymer. The mixtures lie in a micellar region of the phase diagram, forming either spherical or wormlike micelles [7][8][9]. There are correlations among the micelles, which give rise to a peak in the static scattering function at ϳ0.012 Å 21 , corresponding to liquidlike micellar order. The glass transition of the homopolymer matrix occurs at ϳ360 K. It follows that the micelles are mobile only above ϳ360 K. We have investigated the dynamics of these polymer micelle liquids for times between one and several hundred seconds, and for wave vectors from 0.003 to 0.015 Å 21 , extending far above what can be achieved with visible light and including the peak in the static structure factor.Copolymer synthesis was performed via anionic polymerization under inert gas, yielding P (S-b-I) with a styrene number fraction of f s 0.5,M w 89.1k, andM w M n 1.02. (M w andM n are the weight-and numberaveraged molecular weights, respectively.) The mixtures were prepared by dissolution in toluene, followed by methanol precipitation. After drying, samples were hot pressed into 1 mm diameter, 0.5 mm thick Al sample holders and vacuum annealed at 150 ± C. For the x-ray studies, the samples were held under vacuum, and at constant temperature to within 60.1 ± C. The XIFS experiments were carried out at beam line ID10A (TROIKA) at the European Synchrotron Radiation Facility (ESRF) and employed undulator radiation with an energy of ...

Perfect crystals in the asymmetric Bragg geometry are evaluated as optical elements for manipulating coherent X-ray beams. Such optics can be used to modify the transverse coherence length of a synchrotron X-ray beam, with the intention of increasing the usable coherent flux. The wavelength range, angular divergence and flux of X-rays passing through a pinhole aperture are examined in detail, as functions of source and pinhole size, crystal-to-pinhole separation and the asymmetry factor. In developing this analysis, the behavior of asymmetrically cut crystals is explained in reciprocal space, with reference to the crystal truncation rod associated with the reflection. The results show that, for synchrotron beams that are collimated to a small fraction of the incident Darwin width, the wavelength range accepted by the crystal is typically dispersed into an angular spread in the exit beam. This chromatic aberration greatly reduces the transverse coherence length in a manner that does not conserve the coherent flux. The calculations are in agreement with measurements of the divergence and flux through a micrometer-sized pinhole using a synchrotron wiggler X-ray source.

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