## 3 Results
The atomic system then still remains cold, as the 100 fs timescale is too short for advancing a significant energy exchange between the hot electronic system and the lattice. Let us recall that the electron-lattice thermalization typically occurs on a picosecond timescale [18]. A lattice temperature below the melting point clearly indicates that the structural transition observed at the 100% of the nominal pump fluence is predominantly nonthermal. Figure 2 shows the calculated atomic structure in a Si crystal at 500 fs after the maximum of the pump pulse. As expected, at the highest absorbed dose (corresponding to 100% of the nominal fluence), there is a lattice disorder present in the system. This indicates that silicon amorphization due to nonthermal melting significantly progressed in this time. For the medium dose, only some local atomic disorder can be observed, i.e., the thermal structural transition is still ongoing there. In the case of the lowest dose (10% of the nominal fluence), which lies below any structural damage threshold, the crystal atomic order is fully preserved. Figure 2: Calculated single-shot snapshots of atomic arrangements in silicon crystal at 500 fs after its irradiation with an X-ray pulse of 5.95 keV photon energy, duration of 25 fs FWHM, at the average absorbed doses in the material of **(a)** 2.70 eV/atom, **(b)** 1.35 eV/atom, and **(c)** 0.27 eV/atom. These correspond to 100%, 50%, and 10% of the nominal peak fluence, respectively. A comparison of the model predictions with the Si(333) Bragg reflection recorded in the experiment by [PERSON] et al. is shown in Figure 3. First, let us emphasize here that the temporal characteristics of the signal decay strongly depend on the radiation dose absorbed in the crystal. If (as a study case) we used a spatially uniform pump pulse of the 100% nominal fluence, the predicted decrease of the probe signal would start already at \(\sim\)50 fs after the maximum of the pump pulse and complete at \(\sim\)500 fs, dropping finally below the value of \(\sim\)0.1 of the initial signal. Such a rapid signal decay is completely inconsistent with the experimental data. In contrast, for the lowest fluence value (10%), the signal oscillates; however, its average value remains unchanged at all times. We attribute these oscillations to the displacive excitation of coherent phonons [44]. In the case of ultrafast intense X-ray irradiation such coherent phonon modes can be observed in the excited materials. For the respective theoretical explanation, see, e.g., [45]. Due to the non-uniform irradiation of the crystal by the pump pulse in experiment, a proper volume integration of the scattering amplitude over the probed crystal region is necessary in order to compare the experimental data with theoretical results. In what follows, we will only consider the volume averaging in the plane lateral to the X-ray beam (see the 'Materials and Methods' section for detailed justification). We performed volume integration for the theoretically predicted signal, and compared the result to the experimental data from Figure 3 in [12]. These predictions were obtained, using the code XSINC [29] developed to coherently calculate a scattered X-ray signal from samples exhibiting non-uniform dynamics of atoms (see the 'Materials and Methods' section for more details). Here, it was applied to the snapshots of sample arrangement obtained with the code XTANT. For the current calculations, we used atomic scattering factors for neutral Si atoms, as the average ionization degree per Si atom for all fluences considered was low, reaching maximally 0.56 per atom at the 100% nominal fluence. This ionization degree led to the decrease of the scattering factor by only 4% for the momentum transfer, \(q=0\). The theoretical and experimental results were in good agreement, except for the data point at \(150\pm 40\) fs, which our volume-integrated predictions did not reproduce. However, after completing our calculations, we became aware of the recently published Erratum [12].