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.

The complex coupling between charge carriers and phonons is responsible for diverse phenomena in condensed matter. We apply ultrafast electron diffuse scattering to unravel electron-phonon coupling phenomena in 1T-TiSe₂ in both momentum and time. We are able to distinguish effects due to the real part of the many-body bare electronic susceptibility, R[χ0(q)] , from those due to the electron-phonon coupling vertex, g_q, by following the response of semimetallic (normal-phase) 1T-TiSe₂ to the selective photo-doping of carriers into the electron pocket at the Fermi level. Quasi-impulsive and wave vector–specific renormalization of soft zone-boundary phonon frequencies (stiffening) is observed, followed by wave vector–independent electron-phonon equilibration. These results unravel the underlying mechanisms driving the phonon softening that is associated with the charge density wave transition at lower temperatures.

X-ray microdiffraction utilizing Fresnel zone plate focusing optics has been used to study microstructural properties of individual 90° ferroelectric domains in ${\mathrm{BaTiO}}_3$. Diffraction measurements at a microfocused spot resolution of $0.3\mu \mathrm{m}$ over domain widths of $\sim 10\mu \mathrm{m}$ unambiguously reveal features of lattice buckling, rotation, and strain near domain boundaries. Our results may be understood within the context of bound residual strain due to lattice mismatch and elastic interactions between neighboring domains.

Time-resolved multiterahertz (THz) spectroscopy is used to observe an ultrafast, nonthermal electronic phase change in SnSe driven by interband photoexcitation with 1.55 eV pump photons. The transient THz photoconductivity spectrum is found to be Lorentzian-like, indicating charge localization and phase segregation. The rise of photoconductivity is bimodal in nature, with both a fast and slow component due to excitation into multiple bands and subsequent intervalley scattering. The THz conductivity magnitude, dynamics, and spectra show a drastic change in character at a critical excitation fluence of approximately $6\mathrm{mJ}/{\mathrm{cm}}^2$ due to a photoinduced phase segregation and a macroscopic collapse of the band gap.

Beam splitters and delay lines are among the key building blocks of modern-day optical laser technology. Progress in x-ray free electron laser source development and applications over the past decade is calling for their counterpart operating at the Angstrom wavelength regime. Recent efforts in x-ray optics development demonstrate relatively stable delay lines that most often adopt the division-of-wavefront approach for the beam splitting and recombination. However, the two exit beams in such configurations struggle to achieve sufficient mutual coherence to enable applications such as interferometry, correlation spectroscopy, and nonlinear spectroscopy. We present an experimental realization of the generation of highly mutually coherent pulse pairs using an amplitude-split delay line design based on transmission grating beam splitters and channel-cut crystals. The performance of the prototype system was analyzed in the context of x-ray coherent scattering and correlation spectroscopy, where nearly identical high-contrast speckle patterns from both branches were observed. We show in addition the high level of dynamical stability during continuous delay scans, a capability essential for high sensitivity ultrafast measurements.

X-ray speckle visibility spectroscopy using X-ray free-electron lasers has long been proposed as a probe of fast dynamics in noncrystalline materials. In this paper, numerical modeling is presented to show how the data interpretation of visibility spectroscopy can be impacted by the nonidealities of real-life X-ray detectors. Using simulated detector data, this work provides a detailed analysis of the systematic errors of several contrast extraction algorithms in the context of low-count-rate X-ray speckle visibility spectroscopy and their origins are discussed. Here, it was found that the finite detector charge cloud and pixel size lead to an unavoidable `degeneracy' in photon position determination, and that the contrasts extracted using different algorithms can all be corrected by a simple linear model. The results suggest that experimental calibration of the correction coefficient at the count rate of interest is possible and essential. This allows computationally lightweight algorithms to be implemented for on-the-fly analysis.