From Femtoseconds to Hours—Measuring Dynamics over 18 Orders of Magnitude with Coherent X-rays

Abstract

X-ray photon correlation spectroscopy (XPCS) enables the study of sample dynamics between micrometer and atomic length scales. As a coherent scattering technique, it benefits from the increased brilliance of the next-generation synchrotron radiation and Free-Electron Laser (FEL) sources. In this article, we will introduce the XPCS concepts and review the latest developments of XPCS with special attention on the extension of accessible time scales to sub-μs and the application of XPCS at FELs. Furthermore, we will discuss future opportunities of XPCS and the related technique X-ray speckle visibility spectroscopy (XSVS) at new X-ray sources. Due to its particular signal-to-noise ratio, the time scales accessible by XPCS scale with the square of the coherent flux, allowing to dramatically extend its applications. This will soon enable studies over more than 18 orders of magnitude in time by XPCS and XSVS.

Analysis Strategies for MHz XPCS at the European XFEL

“…Strictly speaking, Equation (1) only holds for stationary dynamics, i.e., when the dynamics only depend on the delay time but not on the absolute time during the measurement. To measure time-dependent sample dynamics and catch time dependent detector artifacts, we will calculate two-time correlation functions (TTCs) [5,[27][28][29][30]:…”

“…These techniques have been developed at synchrotron radiation sources since the 1990s [1][2][3][4]. Applications cover a broad range of materials and scientific questions, such as diffusion dynamics in soft matter, glass transition, and gelation, as well as domain-wall dynamics; see [5] for a recent overview.…”

“…with the speckle contrast β that is determined by the coherence properties of the beamline [5]. While XPCS at storage-ring sources typically covers dynamics in the range between hours down to (sub-)millisecond time scales, its main application at XFEL facilities are fast time scales in the femto-to nanosecond domain [6][7][8], using either double-pulse approaches via split-and-delay devices or modification of the X-ray pulse length between a few to about 100 fs.…”

“…The apparent gap of time scales between nano-and milliseconds originates from the limitations of the time resolution of two-dimensional detectors. Modern photon-counting detectors used for XPCS at storage-ring facilities reach kHz repetition rates [5] and thus define the experimental limit. Recently, this limit has been reduced to microsecond dynamics using new detector generations [9,10].…”

Demonstration of 3D photon correlation spectroscopy in the hard X-ray regime

“…Investigations of the structural and dynamic properties of a sample system based on speckle correlation techniques have played a key role in understanding various complex systems in condensed matter physics, such as colloids [1][2][3][4], polymers [5,6], capillary waves [7], metallic glasses [8,9], molecular glasses [10], and water [11][12][13]. The main assumption in the speckle analysis is that photons interact within the sample weakly, i.e., the single scattering approximation is valid [14].…”