## 2 Materials and Methods  
### Simulations of X-ray-Irradiated Solid Materials with XTANT Code  
In order to understand the dynamics of ultrafast melting in detail, we performed respective theoretical simulations, using the irradiation parameters from the above-mentioned pump-probe study [12]. For these simulations, we applied our hybrid code XTANT (X-ray-induced Thermal And Nonthermal Transitions) [18; 19; 20; 30]. The code consists of a few modules dedicated to simulate various processes induced by incoming X-ray FEL radiation:  
1. The core of the model is the transferable tight binding (TB) Hamiltonian, which treats the electronic band structure and atomic potential energy surface. The latter evolvesin time, depending on the positions of atoms in the simulation box. Periodic boundary conditions are applied. Tight-binding parametrization from [31] is used here. 2. Atomic positions are propagated in time, using a classical molecular dynamics (MD) scheme. It solves Newton equations for nuclei with the potential energy surface evaluated from the TB module. 3. Electron occupation numbers on the transient energy levels are assumed to follow the Fermi-Dirac distribution with a transient temperature and chemical potential evolving in time. The electron temperature changes due to the interaction of band electrons with X-rays and high-energy electrons or due to their nonadiabatic interaction with nuclei (through electron-ion scattering [19]). 4. The non-equilibrium part of the electron distribution at high energies and Auger decays of core holes are treated with a classical event-by-event Monte Carlo (MC) simulation. This stochastically models the X-ray-induced photoelectron emission from the K-shell or from the valence band, the Auger decays, and the scattering of high-energy electrons. 5. Electron-ion energy exchange is calculated with a nonadiabatic approach [19], in which matrix elements are calculated as an overlap of TB wave-functions plugged into the Boltzmann collision integral. This energy is transferred to atoms by respective velocity scaling at each MD step. This combined approach allows the treatment of predominant processes within an X-ray FEL-irradiated sample, including the non-equilibrium evolution stage, thermal and nonthermal processes, and phase transitions [32]. In particular, all X-ray-induced processes that excite electrons are taken into account in the model. However, they have different probabilities. For example, in case of hard X-ray-irradiation of Si, the electron excitation from a core level (with the resulting Auger decay) is the most probable one. Please also note that the X-ray-induced electronic excitation ends within \(\sim\)ten femtoseconds after the X-ray pulse is over. After this time, only collisional processes and electron-lattice energy exchange contribute to the evolution of electronic distribution. Ballistic electrons are considered in our model as high energy electrons. In the bulk material, which we simulate here, they propagate within the restriction of periodic boundaries. We checked that the corresponding electron range was below 250 nm (according to our dedicated simulation tool XCascade3D [33]), i.e., much smaller than the laser spot size. Since the actual absorbed energy distribution is typically even narrower than the electron range [34], the fast electron escape should not influence the spatial distribution of the absorbed dose. XTANT simulates the dynamics using periodic boundary conditions. Our final simulations were preceded by careful convergence studies in respect to the supercell size. They showed that, for this type of simulation (performed within the bulk material under the pulse conditions corresponding to the current experiment), the calculations with a 216-atom-large supercell provided a sufficient accuracy for the results. Therefore, for the current simulations, a supercell containing 216 atoms was used.