Evolution of speckle during spinodal decomposition

Phase Transition Dynamics in a Complex Oxide Heterostructure

Understanding the behavior of defects in the complex oxides is key to controlling myriad ionic and electronic properties in these multifunctional materials. The observation of defect dynamics, however, requires a unique probe-one sensitive to the configuration of defects as well as its time evolution. Here, we present measurements of oxygen vacancy ordering in epitaxial thin films of SrCoO_{x} and the brownmillerite-perovskite phase transition employing x-ray photon correlation spectroscopy. These and associated synchrotron measurements and theory calculations reveal the close interaction between the kinetics and the dynamics of the phase transition, showing how spatial and temporal fluctuations of heterointerface evolve during the transformation process. The energetics of the transition are correlated with the behavior of oxygen vacancies, and the dimensionality of the transformation is shown to depend strongly on whether the phase is undergoing oxidation or reduction. The experimental and theoretical methods described here are broadly applicable to in situ measurements of dynamic phase behavior and demonstrate how coherence may be employed for novel studies of the complex oxides as enabled by the arrival of fourth-generation hard x-ray coherent light sources.

Interplay between Kinetics and Dynamics of Liquid-Liquid Phase Separation in a Protein Solution Revealed by Coherent X-ray Spectroscopy

Microscopic dynamics of complex fluids in the early stage of spinodal decomposition (SD) is strongly intertwined with the kinetics of structural evolution, which makes a quantitative characterization challenging. In this work, we use X-ray photon correlation spectroscopy to study the dynamics and kinetics of a protein solution undergoing liquid-liquid phase separation (LLPS). We demonstrate that in the early stage of SD, the kinetics relaxation is up to 40 times slower than the dynamics and thus can be decoupled. The microscopic dynamics can be well described by hyper-diffusive ballistic motions with a relaxation time exponentially growing with time in the early stage followed by a power-law increase with fluctuations. These experimental results are further supported by simulations based on the Cahn-Hilliard equation. The established framework is applicable to other condensed matter and biological systems undergoing phase transitions and may also inspire further theoretical work.

de Gennes Narrowing and Relationship between Structure and Dynamics in Self-Organized Ion-Beam Nanopatterning

Investigating the relationship between structure and dynamical processes is a central goal in condensed matter physics. Perhaps the most noted relationship between the two is the phenomenon of de Gennes narrowing, in which relaxation times in liquids are proportional to the scattering structure factor. Here, a similar relationship is discovered during the self-organized ion-beam nanopatterning of silicon using coherent x-ray scattering. However, in contrast to the exponential relaxation of fluctuations in classic de Gennes narrowing, the dynamic surface exhibits a wide range of behaviors as a function of the length scale, with a compressed exponential relaxation at lengths corresponding to the dominant structural motif-self-organized nanoscale ripples. These behaviors are reproduced in simulations of a nonlinear model describing the surface evolution. We suggest that the compressed exponential behavior observed here is due to the morphological persistence of the self-organized surface ripple patterns which form and evolve during ion-beam nanopatterning.

Aging in the Long-Range Ising Model

The current understanding of aging phenomena is mainly confined to the study of systems with short-ranged interactions. Little is known about the aging of long-ranged systems. Here, the aging in the phase-ordering kinetics of the two-dimensional Ising model with power-law long-range interactions is studied via Monte Carlo simulations. The dynamical scaling of the two-time spin-spin autocorrelator is well described by simple aging for all interaction ranges studied. The autocorrelation exponents are consistent with λ=1.25 in the effectively short-range regime, while for stronger long-range interactions the data are consistent with λ=d/2=1. For very long-ranged interactions, strong finite-size effects are observed. We discuss whether such finite-size effects could be misinterpreted phenomenologically as subaging.

Universal dynamics of coarsening during polymer-polymer thin-film spinodal dewetting kinetics

The dewetting dynamics of a supported bilayer polymer thin film on a solid substrate is investigated using grazing incidence x-ray photon correlation spectroscopy. We find that the top layer dewets via the spinodal mechanism. The kinetics of the dewetting is studied by monitoring the time evolution of the surface diffuse x-ray scattering intensity. We study the time evolution of fluctuations about the average surface structure by measuring the two-time x-ray intensity fluctuation correlation functions. Using these two-time correlation functions we quantify the crossover from early-time diffusive dynamics to hydrodynamics. The early diffusive regime satisfies dynamic universality. The two-time correlation functions also quantify the onset of hydrodynamic effects. The hydrodynamic regime is observed during the spinodal dewetting process as these interactions are not screened.

On the use of two-time correlation functions for X-ray photon correlation spectroscopy data analysis

Multi-time correlation functions are especially well suited to study non-equilibrium processes. In particular, two-time correlation functions are widely used in X-ray photon correlation experiments on systems out of equilibrium. One-time correlations are often extracted from two-time correlation functions at different sample ages. However, this way of analysing two-time correlation functions is not unique. Here, two methods to analyse two-time correlation functions are scrutinized, and three illustrative examples are used to discuss the implications for the evaluation of the correlation times and functional shape of the correlations.

Differential optical spectropolarimetric imaging system assisted by liquid crystal devices for skin imaging

Skin cancer diagnosis depends not only on histopathological examination but also on visual inspection before and after the excision of suspected lesion. Neoplasm is accompanied with changes in birefringence of collagen, pleomorphicity, and hyperchromatic state of epithelial nuclei. These phenomena can be measured by spectral and polarization changes of light backscattered by the examined tissue. A new differential spectropolarimetric system is proposed using liquid crystal devices, one as a tunable filter and the other as a polarization rotator, both operating at wide spectral ranges from the visible to the near-infrared. Since collagen's fibrils texture orientation depends on its location in the skin and since it is not well organized, our system scans the bipolarization states by continuously rotating the linearly polarized light incident on a skin lesion, and collecting differential contrasts between sequenced images when simultaneously averaging the statistical readout of a video camera. This noninvasive method emphasizes areas on skin where the neoplasm, or tumor, minimizes the statistical polarization change of the scattered light from the lesion. The module can be considered as an assistant tool for epiluminescence microscopy. Images of skin tumors were captured in vivo before the patients having their surgery and compared to histopathological results.

Phase retrieval from speckle patterns of ordering systems

The time dependence of the Fourier transform phase of coherently scattered radiation from a system undergoing ordering is studied. Specifically, we derive a simple model that takes into account the known scaling laws for ordering dynamics to predict the statistical behavior of the Fourier transform phase. We consider a two-dimensional system of domains undergoing ordering for both the nonconserved and conserved order-parameter cases (models A and B, respectively). Predictions from our model are compared with numerical experiments, where a time-dependant Ginzburg-Landau equation is integrated to compute the dynamics of the real-space system; then a simple numerical (discrete) Fourier transform is applied to compute the Fourier phase as well as the amplitude (directly related to scattering intensity). An average phase-decorrelation time (the average time it takes for the phase to change by a specific amount) is obtained using both our theoretical model and the numerical results. This quantity is then used to implement a phase-retrieval strategy that consists of measuring scattering intensities of the same nonequilibrium system at different times and then applying an iterative phase-retrieval algorithm (like Fienup's hybrid input-output) recursively with improved initial estimates for faster convergence and higher convergence rates.

Diffraction with a coherent X-ray beam: dynamics and imaging

Methods for carrying out coherent X-ray scattering experiments are reviewed. The brilliance of the available synchrotron sources, the characteristics of the existing optics, the various ways of obtaining a beam of controlled coherence properties and the detectors used are summarized. Applications in the study of the dynamics of speckle patterns are described. In the case of soft condensed matter, the movement of inclusions like fillers in polymers or colloidal particles can be observed and these can reflect polymer or liquid-crystal fluctuations. In hard condensed-matter problems, like phase transitions, charge-density waves or phasons in quasicrystals, the study of speckle fluctuations provides new time-resolved methods. In the domain of lensless imaging, the coherent beam gives the modulus of the sample Fourier transform. If oversampling conditions are fulfilled, the phase can be obtained and the image in the direct space can be reconstructed. The forthcoming improvements of all these techniques are discussed.

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.

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.