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.