X-ray Intensity Fluctuation Spectroscopy Research Articles

Contribution of intermediate submicrometer structures to physical properties nearTcin Pb(Zn1/3Nb2/3)O3-9%PbTiO3

Complementary use of coherent x-ray diffraction (CXD), x-ray diffuse scattering, conventional x-ray diffraction techniques, and dielectric measurements has enabled us to investigate Pb(Zn${}_{1/3}$Nb${}_{2/3}$)-9%PbTiO${}_{3}$ with a multiple-length-scale approach from the macroscale (lattice constants, bulk averaged) and microscale to the nanoscale [polar nanoregions (PNRs)] and discuss the contribution of each scale to the dielectric permittivity. We estimate that diffuse scattering mainly originates from intra-PNR dynamics, which contributes to ``ionic'' polarization and results in high-frequency permittivity. Meanwhile, the appearance of intermediate submicrometer (sub-$\ensuremath{\mu}$m) structures observed by CXD is consistent with the appearance of low-frequency dielectric relaxation. The sub-$\ensuremath{\mu}$m structures exhibit large fluctuations at ${T}_{\mathrm{c}}$. This is also consistent with previously reported results obtained by x-ray intensity fluctuation spectroscopy and should give a lower limit for the low-frequency dielectric dispersion. We have suggested that the fluctuation is due to the competition between the growth of sub-$\ensuremath{\mu}$m structures and the appearance of the macroscopic tetragonal-ferroelectric phase. Since the present CXD mainly detected the strain field spreading throughout the crystal, we here demonstrate that the sub-$\ensuremath{\mu}$m structures are due to networks among PNRs connected by the strain field.

X-ray Intensity Fluctuation Spectroscopy Using Nanofocused Hard X-rays: Its Application to Study of Relaxor Ferroelectrics

The use of a combination of coherent X-rays from a third-generation synchrotron light source and ultraprecise Kirkpatrick-Baez mirrors enables us to apply nanofocused hard X-rays in solid-state physics. We developed an apparatus for X-ray intensity fluctuation spectroscopy using the nanofocused hard X-rays and applied it to the study of relaxor ferroelectrics. We have successfully detected a large and slow intensity fluctuation of scattered X-rays above cubic-to-tetragonal phase transition temperature with a characteristic time scale on the order of 10 s. We speculated that the intensity fluctuation originates from domain number fluctuation, which is directly related to the dielectric response, particularly the frequency dispersion.

A review of X-ray intensity fluctuation spectroscopy

This article reviews the literature on X-ray fluctuation intensity spectroscopy or, as it is often called, X-ray photon correlation spectroscopy. It highlights measurements using different types of diffuse scattering. To cite this article: M. Sutton, C. R. Physique 9 (2008).

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.

Structure and dynamics of a nanocolloidal silica gel dispersion

We studied the structure and the dynamics of a nanocolloidal silica gel dispersed in an organic solvent [octylcyanobiphenyl (8CB)] as a function of the silica density by x-ray intensity fluctuation spectroscopy (XIFS). The silica density of the dispersed aerosil gel samples ranged from 0.03 to 0.20 g cm-3 and the autocorrelation of the silica scattering was probed over the q range from 0.03 to 0.15 nm-1 (corresponding to length scales from 42 to 209 nm) at a constant room temperature at which 8CB is in the smectic-A phase. The gel structure has a fractal dimension in this density range of df approximately 2.15. The time autocorrelation functions of the gels show clear density-dependent and complex dynamics. The gel relaxation times are very long and become bimodal with nonergodic character for densities from 0.10 to 0.16 g cm-3. In this same density range, the fluctuation contrast (strength) is a minimum while the relaxation time becomes independent of wave vector. Together, these results indicate that there is a narrow silica density range for these gels in which the dynamics changes dramatically. This suggests a complex phase diagram for the dynamics of aerosil gels as a function of densification.

Dynamics of long-wavelength phason fluctuations in the i-Al–Pd–Mn quasicrystal

We report on the dynamics of phason modes in the i-Al–Pd–Mn icosahedral quasicrystal, measured between room temperature and 650°C, using the X-ray intensity fluctuation spectroscopy (XIFS) technique. Up to 500°C, the autocorrelation function, ℑ(q, t), displays almost no time evolution as expected for frozen-in phason fluctuations at low temperature. At higher temperatures, ℑ(q, t) follows a single exponential time decay from which the characteristic time τ c(q) is extracted. These results are compared to the expected shape of ℑ(q, t) as derived from the expressions of the eigenvalues and eigenvectors of the C ⊥ ⊥(q) phason dynamical matrix. In agreement with the hydrodynamic theory of quasicrystals, which predicts phasons with diffusive character, we find that τ c(q) varies linearly with q −2 at 650°C. The corresponding diffusion coefficient is 2.2(±0.5) × 10−18 m2 s−1 and the activation energy is estimated around 2.3(±1) eV.

X-ray intensity fluctuation spectroscopy studies of ordering kinetics in a Cu-Pd alloy

X-ray intensity fluctuation spectroscopy has been used to examine the coarsening kinetics in the classic long-period superlattice Cu-Pd alloy. The evolution of the speckle intensity was examined near the centers of both a superlattice peak (associated with local $L{1}_{2}$ order) and a satellite peak (associated with one-dimensional antiphase correlations). The decay of the two-time correlation function $C({t}_{1},{t}_{2},q)$ was independent of the direction examined and was similar for the superlattice and satellite peaks. In agreement with published Langevin theory and simulations, the decay time $\ensuremath{\tau}$ of the two-time correlation function increases linearly with average time ${t}_{m}=({t}_{1}+{t}_{2})∕2$. It is relatively independent of the wave vector near the peak centers. However, $\ensuremath{\tau}$ increases much more slowly with increasing ${t}_{m}$ than is expected.

X-Ray Intensity Fluctuation Spectroscopy Studies on Phase-Ordering Systems

The order-disorder phase transition in Cu3Au has been studied by x-ray intensity fluctuation spectroscopy. Following a quench from the high-temperature, disordered phase, the ordering kinetics is well described by a universal scaling form that can be measured by time-resolved (incoherent) x-ray scattering. By using coherent scattering, we have measured the fluctuations about this universal scaling form. In the late stages of the ordering process, these fluctuations give a two-time correlation function C(q,t1,t2) which has a scaling form with natural variables deltat=/t1-t2/ and t =(t1+t2) / 2. The scaling form crosses over from linear in t to t1/2. These present the first such results for a nonconserved system.

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.

X-ray intensity fluctuation spectroscopy measurements of the charge density wave phases of NbSe3

An introduction to X-ray Intensity Fluctuation Spectroscopy (XIFS) is given by describing its relationship to speckle from coherent sources. A brief description of the relationship of XIFS measurements to the underlying equations of motion is given. Preliminary results for the charge density wave (CDW) system NbSe3 are then presented. Static speckle patterns are shown for the $\overrightarrow {Q}_1 = (0 .76$ 0) CDW peak showing that XIFS experiments are possible in this systom provided time constants are long enough. For electrical currents below threshold, a static speckle pattern is observed but for currents above threshold the speckles are smeared out showing movement of the CDW. It is also shown that above threshold, the longitudinal correlation length decreases.

Elastic coupling of silica gel dynamics in a liquid-crystal-aerosil dispersion.

The dynamics of a thixotropic silica aerosil gel dispersed in an octylcyanobiphenyl liquid crystal were directly probed by x-ray intensity fluctuation spectroscopy. For all samples, the time-autocorrelation function of the gel was well described by a modified-exponential function over the q range studied. Compared to a pure gel sample, a dilute (0.06 g cm(-3)) gel embedded within the liquid crystal displayed more complex and temperature dependent dynamics. Near the second-order smectic-A-to-nematic phase transition of the liquid crystal the gel relaxation became significantly more complex and slower (tau approximately 2150 s) compared to relaxations observed well within either phase. This clearly demonstrates coupling between the dynamics of the gel and the host liquid crystal, consistent with critical slowing down of smectic and director fluctuations. A random dampening field, elastically coupled to the liquid crystal, would explain the earlier observed crossover of this transition towards 3d-XY behavior.

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.

Dynamics of concentrated colloidal suspensions probed by x-ray correlation spectroscopy

We report x-ray intensity fluctuation spectroscopy (XIFS) measurements of the equilibrium dynamics of colloidal suspensions of charge-stabilized ${\mathrm{Sb}}_{2}{\mathrm{O}}_{5}$ spheres of radius $250\ifmmode\pm\else\textpm\fi{}40 \mathrm{\AA{}}$ in glycerol. The dynamics were investigated for times between 4 and several thousand seconds, and for wave vectors, $Q$, from 0.003 to 0.012 ${\mathrm{\AA{}}}^{\mathrm{\ensuremath{-}}1}$, well beyond wave vectors that can be studied with visible light. The unique advantages of XIFS for studies of concentrated suspensions composed of refractive-index-mismatched components have not previously been explored. Here, we study a dilute sample (sample I) and a concentrated sample (sample II). For sample I, the diffusion coefficient is independent of $Q$, with a value consistent with the Stokes-Einstein relation. For sample II (effective hard-sphere volume fraction, $\ensuremath{\varphi}=0.18)$, the diffusion coefficient exhibits a minimum at the peak of the structure factor, indicating modifications to Brownian behavior due to interparticle interactions.

Dynamics of Block Copolymer Micelles Revealed by X-Ray Intensity Fluctuation Spectroscopy

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 $0.015{\AA{}}^{\ensuremath{-}1}$, far beyond wave vectors that can be studied with visible light. A wave-vector-dependent diffusion coefficient is found.