## 2 Materials and Methods
### Description of the Experimental Data, Including Beam Characteristics  
Below, we recall the details of the experiment presented in [12]. During this measurement, single silicon crystals cut out in the silicon wafer [35], were irradiated with 5.95 keV X-ray photons. Pulse duration was 25 fs FWHM. The pulse was split into a pump and a probe beam, arriving with various delays. The delay between the pump and the probe was in the range between 100 and 400 fs. According to the authors of [12], the focusedhard X-ray beam yielded an average absorbed dose of \(\sim\)4 eV/atom (with a peak dose up to 9 eV/atom) on the material surface. For the purpose of the actual model calculations, we re-estimated the dose value: (i) approximating the spatial pulse profile as a 2D Gaussian function in the plane perpendicular to the propagation direction of X rays, (ii) assuming a Gaussian temporal pulse profile, and (iii) using the information on the fraction of the pump pulse energy absorbed within an elliptical limiting contour from the wave front propagation simulations presented in [12] (Figure 2 in [12]). The simulations were shown to agree well with the independent beam imprint analysis performed in [12]. Vertical projection of the pulse profile in the simulated intensity plot indicated its non-Gaussian shape. As our modeling tool can currently use only a 2D Gaussian pulse profile for the volume integration of the scattering amplitude (see section below), we recalculated the dose, approximating the spatial pulse profile as a 2D Gaussian function. From the information in Figure 2 of [12] on the fraction of the pump pulse energy absorbed within an elliptical limiting contour (65%) and the limiting dose at the contour (1.5 eV/atom), we estimated the parameters of the 2D Gaussian pulse corresponding to this energy deposition. For that 2D Gaussian pulse, the estimated peak dose on the surface was 4.28 eV/atom. Note the difference with the peak dose of 9 eV/atom dose for the initial non-Gaussian pulse in [12]. The recalculation of the surface dose into the average absorbed dose, i.e., the absorbed dose within the material layer down to the photon penetration depth (see e.g., [34]) yielded a peak dose of 2.70 eV/atom within the layer. We used this dose as the maximal dose for the simulations in the paper. It is comparable with the doses considered in our previous studies on X-ray-induced structural transitions in Si [36]. Below, we list for clarity all the assumptions applied in our simulations for the beam characteristics and give their justification. These approximations are frequently applied in the interpretation of X-ray pump-X-ray probe experimental results with XFELs (see, e.g., [37; 38; 39]). 1. _The \"average\" 2D Gaussian spatial profile was used._ As the signal was integrated over different X-ray shots, obtained with pulses of differing spatial characteristics, the \"average\" 2D Gaussian spatial profile used for our calculations was a reliable approximation. 2. _Gaussian temporal pulse profile was used._ The pump-probe experiment was performed at X-ray fluences still within a linear absorption regime (i.e., with the X-ray photoabsorption rate only linearly dependent on the pulse intensity). Therefore, the specific spiky time characteristics of the pulse intensity in each shot did not play much role for the sample evolution (and sample imaging). The respective check was performed in [32]. The final experimental signal did not originate from a single shot but was integrated over signals resulting from many different FEL shots. This justifies the usage of a Gaussian temporal pulse as the \"average\" case. 3.