Anomalous sound propagation and slow kinetics in dynamically compressed amorphous carbon

We have performed molecular-dynamics simulations of dynamic compression waves propagating through amorphous carbon using the Tersoff potential and find that a variety of dynamic compression features appear for two different initial densities. These features include steady elastic shocks, steady chemically reactive shocks, unsteady elastic waves, and unsteady chemically reactive waves. We show how these features can be distinguished by analyzing time-dependent propagation speeds, time-dependent sound speeds, and comparison to multiscale shock technique (MSST) simulations. Understanding such features is a key challenge in quasi-isentropic experiments involving phase transformations. In addition to direct simulations of dynamic compression, we employ the MSST and find agreement with the direct method for this system for the shocks observed. We show how the MSST can be extended to include explicit material viscosity and demonstrate on an amorphous Lennard-Jones system.

Figure 1

(Color online) Amorphous Lennard-Jones shock wave profiles computed using the NEMD approach and the multiscale approach (this work) with and without extra (explicit) viscosity. Good agreement is achieved due to the Rayleigh constraint employed by MSST. Utilization of some explicit viscosity brings the multiscale simulations into better agreement with NEMD at short distances behind the shock front.

Figure 2

(Color online) Part of the simulation cell used for NEMD runs in dense a-carbon $\left(\rho =2.38\text{g}/{\text{cm}}^3\right)$. The cell has a square periodic cross section (parallel to xy plane) of dimensions $3.25\text{nm}\times 3.25\text{nm}$ and a length of $1.95\mu \text{m}$ ($z$ direction), with a total of $\sim 2.5\times {10}^6$. A slab of thickness 2 nm (atoms in yellow) at one end is defined as the piston, which is moved at a constant speed along the $z$ direction.

Figure 3

(Color online) Dynamic compression of dense a-carbon $\left(\rho =2.38\text{g}/{\text{cm}}^3\right)$. (a) MSST-computed final density as a function of shock velocity, indicating a sharp transition in the nature of shock propagation at a critical velocity of 14.5 km/s; NEMD-computed wave propagation for: (b) $v=14.8\text{km}/\text{s}$ $\left(v>v_{\text{critical}}\right)$ displaying a single sharp front, and (c) $v=11.6\text{km}/\text{s}$ (i.e., $v<v_{\text{critical}}$), showing a more complicated wave structure. In (b), the NEMD-computed shock front agrees well with the MSST-computed shock front (superimposed on the 50 ps front).

Figure 4

(Color online) Schematic illustrating how a region of negative curvature in a material isentrope can lead to a region of pressure inaccessible by a single shock. Possible single shocks are depicted by straight Rayleigh lines. The Rayleigh line that is tangent to the isentrope in the initial state defines the lowest possible pressure shock.

Figure 5

(Color online) Results on less-dense a-carbon $\left(\rho =2.23\text{g}/{\text{cm}}^3\right)$. (a) MSST-computed final density (after 500 ps simulation time) as a function of shock velocity. There is a sharp discontinuity in density at $v_{\text{critical}}\sim 12.5\text{km}/\text{s}$. (b) NEMD results for shock velocity of 13.4 km/s $\left(v>v_{\text{critical}}\right)$ showing a sharp front, in agreement with MSST front (orange) at this velocity. (c) and (d) NEMD-computed wave propagation for the case $v<v_{\text{critical}}$ displaying a slanted front and a pronounced foot, whose tip travels at speed $v_{\text{critical}}$. An orange MSST simulation starting at the end of the unsteady foot is shown in (c). The higher density portion of (c) propagates at a steady 9 km/s while the analogous portion in (d) is unsteady. See text for details.

Figure 6

(Color online) Instantaneous stress and stress after 20 ps in the direction of shock propagation $\left(P_{zz}\right)$ as a function of density $\left(\rho \right)$ for uniaxially strained: (a) dense a-carbon (starting $\rho =2.38\text{g}/{\text{cm}}^3$) showing chemical changes above $2.8\text{g}/{\text{cm}}^3$; and (b) less-dense a-carbon (starting $\rho =2.23\text{g}/{\text{cm}}^3$) showing chemical changes above $2.4\text{g}/{\text{cm}}^3$. These plots provide an approximate picture of the density regimes in which the dynamic compression waves are undergoing chemical changes.

Figure 7

(Color online) Longitudinal sound speed $\left(\sqrt{\frac{\partial P_{zz}}{\partial \rho }}\right)$ as a function of density $\rho$ for: (a) dense a-carbon (starting $\rho =2.38\text{g}/{\text{cm}}^3$); and (b) less-dense a-carbon (starting $\rho =2.23\text{g}/{\text{cm}}^3$). These curves exhibit anomalous behavior, decreasing with density over some regimes. This behavior leads to unsteady ramp waves when the material is dynamically compressed.