## 3 Data Analysis  
The following strategy was implemented for the data analysis. First, for the patterns with sufficiently high intensity (more than 5000 counts per single diffraction pattern) of the XFEL pulse,  
Figure 4: Single-shot diffraction patterns (in logarithmic scale) from colloidal crystals made from **(a)** PS; **(b)** PS covered with Al layer, and **(c)** silica samples measured at LCLS. Squares indicate Bragg peaks considered in the further analysis. Figure 3: The infrared (IR) laser energy calibration curve. The maximum of the IR laser energy used in the experiments for three samples is marked with arrows. For the PS colloidal crystal covered with Al layer, the maximum IR laser energy was 326 \(\upmu\)J, and for the pure PS and silica samples, 691 \(\upmu\)J.  
we selected Bragg peaks located far away from the detector gaps (see Figure 4). Patterns with a lower signal were not treated. Using this procedure, typically three to four Bragg peaks were selected for the analysis (see Figure 4). Next, the Bragg peak positions were extracted using the center of mass of their intensity distributions as well as the relative distances between the opposite Bragg peaks. The change of the relative positions of the Bragg peaks as a function of the time delay allowed us to probe the lattice dynamics along specific crystal directions. The following parameters as a function of time delay were analyzed in order to reveal the dynamics of the colloidal crystals, induced by the IR laser: Bragg peak position \(q(\tau)\), as well as FWHMs in the radial \(w_{q}(\tau)\) and azimuthal \(w_{\phi}(\tau)\) directions in reciprocal space. The temporal variation of the momentum transfer vector \(q(\tau)\) is related to the dynamics in the inter-particle spacing, while \(w_{q}(\tau)\) corresponds to the dynamics of the average particle size, and \(w_{\phi}(\tau)\) defines angular misorientation of coherent scattering domains [26]. Due to the nature of the SASE process, each XFEL pulse has a unique fine spatial structure that was mapped by the intensity distribution at each Bragg position. A multi-spiked structure of the Bragg peaks varying from pulse to pulse was observed in our experiment (see Figure 5). From these diffraction patterns spatial and temporal coherence properties of hard XFEL could be determined by spatial correlation analysis [27]. Due to the different shape of each FEL pulse (see Figure 5), it was not possible to perform deconvolution of each scattered pulse shape. For the same reason (non-Gaussian structure of Bragg peaks) fitting of the peaks with the two-dimensional Gaussian function was not reliable (see Figure 6a). In order to improve Bragg peak characterization, projections of their intensities on azimuthal and radial directions were performed. These data were fitted with the one-dimensional Gaussian function (see Figure 6b), and peak broadening in the radial (\(w_{q}\)) and azimuthal (\(w_{\phi}\)) directions was determined. Figure 5: Four single-shot diffraction patterns measured at the same Bragg peak position. The spike-shaped peaks demonstrate an influence of the individual structure of each XFEL pulse on the Bragg peak. Figure 6: (**a**) The cross-section of a two-dimensional Bragg peak along azimuthal direction and (**b**) the projection of the same Bragg peak on the same direction. It is seen that the cross-section dataset (**a**) deviates from the Gaussian fit (red line), whereas the projection points are fitted with the Gaussian function with higher accuracy.