# From Femtoseconds to Hours--Measuring Dynamics over 18 Orders of Magnitude with Coherent X-rays
## 4 Studies
### Towards Microsecond Real-Time XPCS at Storage-Ring Sources
#### 4.1.1 Dynamical Heterogeneities via Two-Times Correlations  
One of the main directions of XPCS research in recent years focussed on the measurement of dynamical heterogeneities. As introduced above, the use of higher-order correlation functions reveals non-equilibrium processes by accessing the age-dependence of the relaxation time in real-time experiments. Dynamical heterogeneities are particularly present in gels [47; 104; 105], elastomers [106], in glasses and close to the glass transition [29; 107; 108; 109; 110], as well as reported recently during liquid-liquid separations in dense protein dispersions [39]. Here, we want to highlight few recent examples. In an combined XPCS-XRD experiment, [PERSON] et al. studied the transition from high-density amorphous ice (HDA) to low-density amorphous ice (LDA) in the SAXS regime [29]. At temperature around 89 K, the dynamics are dominated by viscoelastic relaxation and stress release of the metastable HDA. Upon heating, a second relaxation process appeared above 110 K that further speeded up at higher temperatures. This is accompanied by an abrupt decay of \(\chi\) indicating a transition from heterogeneous to more homogeneous dynamics. These observations let to the conclusion that the HDA-LDA transition is actually taking place via high- and low-density liquid forms of water named HDL and LDL, i.e., a HDA-HDL-LDL-LDA transition was observed. This study provided one of the first experimental evidence for the existence of two forms of liquid water, that has been strengthened in subsequent FEL studies on water [111; 112; 113]. Recently, two-time correlations have been used in in-operando studies. [PERSON] et al. investigated the dynamics of nanoparticles in epoxy resin during 3D printing in real-time [114]. By mapping the sample both spatially and temporally its dynamics and morphology was found to reach a quasi-equilibrium state during the first few seconds after deposition and were characterized by slow aging similar to colloidal clay suspensions. The dynamics are anisotropic during the recovery process of the printed material, indicating structural alignment on the nanoscale induced by the extrusion and deposition. The dynamics associated with the curing of an industrial epoxy adhesive at different temperatures was investigated by [PERSON] et al. [115]. Tracer particles have been used to perform the XPCS experiment in SAXS geometry. Approaching the curing temperature, the dynamics speed up and slow down rapidly once this temperature is reached. Both in operando XPCS studies provided new information on industrial products which may help to improve the design of future generations of tailor-made products. A particular application of two-time correlations is the stress-relaxation in amorphous matter. Such spontaneous events are hardly visible in ensemble-averaged experimental quantities, but can be tracked by higher-order correlations. Therefore, we discuss four recent examples on interfaces, colloidal glasses and gels. [PERSON] et al. probed the stress-relaxation of a monolayer of nanoparticles on the water surface [116]. The particles formed island that have been laterally compressed. After the compression had been stopped the dynamics showed aging, i.e., continuously slowed down with different characteristics depending on the stressed state, including sudden rearrangements visible as \"pinch-points\" in the two-time correlation matrix. At the same time, the average structure was unchanged. In general, the extraction of a two-time correlation function relies on sufficient statistical accuracy. Therefore, 2D detectors are essential, because the correlation function is averaged over many 1000 pixels forming an iso-q ring. Recently, thanks to the increased detector performance and coherent flux, direction-dependent structural heterogeneities could be accessed for different samples, calculated from fractions of pixels. [PERSON] et al. studied the aging of a colloidal gel after quenching it close to and below the gelation point [105].