Fig. 1. (a) Setup of the NEMD simulations, where a shock wave propagates along the z axis. The red dashed lines indicate the positions of the shock front at 0.2 ps and 0.4 ps. The shock front emerges from the initial free surface (z = 400 Å) at about 0.6 ps. The three-dimensional structure of the medium at 0.8 ps is illustrated in the inset, where the red particles represent those containing higher kinetic energy E_k and the blue particles those with lower E_k. (b) Distributions of density and velocity for ⁴X atoms along the z axis at t = 0.6 ps. The corresponding piston speed is v_p = 50 km/s.

Fig. 2. Effects of atomic mass m_X and piston speed v_p on the velocity of the reflecting surface, v_f. The reflecting surface is near n_c = 2.348 × 10²¹ cm⁻³, and the piston speed is (a) v_p = 75.0 km/s, (b) v_p = 50.0 km/s, or (c) v_p = 25.0 km/s.

Fig. 3. Effect of critical number density n_c on v_f. Two isotopes of X, namely, ⁴X and ⁸X, are taken as examples.

Fig. 4. Distributions of thermal and virial pressures at (a) t = 0.6 ps and (b) t = 2.0 ps. The areas between the black vertical dashed lines and between the orange vertical dashed lines represent the ranges of the reflecting surfaces of the ⁴X and ⁸X media, respectively. The critical number density determining the reflecting surface is n_c = 2.348 × 10²¹ cm⁻³ for both media.

Fig. 5. Comparison of the distributions of number density and velocity. (a) and (b) show the number density and velocity, respectively, in the z direction at t = 0.8 ps, while (c) and (d) show those at t = 2.0 ps. The areas between the black vertical dashed lines and between the orange vertical dashed lines represent the ranges of the reflecting surfaces of the ⁴X and ⁸X media, respectively. The critical number density determining the reflecting surface is n_c = 2.348 × 10²¹ cm⁻³ for both media.

Fig. 6. Scaling law of v_f. The blue dashed line represents the best-fitting curve, and the scattered dots are the simulation results for various piston speeds and atomic masses, as shown in the key.

Table 1. Best fitting parameters for the scaling law of v_f.