Structural inhomogeneities in glasses via cavitation

Using large-scale molecular-dynamics simulations for a system of ${10}^6$ particles, the response of a dense amorphous solid to the continuous expansion of its volume is investigated. We find that the spatially uniform glassy state becomes unstable via the formation of cavities, which eventually leads to failure. By scanning through a wide range of densities and temperatures, we determine the state points at which the instability occurs and thereby provide estimates of the coexistence density of the resultant glass phase. Evidence for long-lived, inhomogeneous configurations with a negative pressure is found, where the frozen-in glass structure contains spherical cavities or a network of void space. Furthermore, we demonstrate the occurrence of hysteretic effects when the cavitated solid is compressed to regain the dense glassy state. As a result, a new glass state is obtained, the pressure of which is different from the initial one due to small density inhomogeneities that are generated by the dilation-compression cycle.

Figure 1

Schematic diagram indicating the various paths traversed across the $T\text{−}\rho$ phase diagram in our numerical experiments. (1) quench from supercooled liquid; (2) expansion of amorphous solid until cavitation is observed; (3) expansion of cavitated solid to explore low-density states; (4) compression of the cavitated solid back to initial high density.

Figure 2

(a) Evolution of pressure $\left(P\right)$ with decreasing density $\rho$ for the different temperatures $T=0.01$, 0.1, 0.2, 0.3, 0.4, and 0.5, with expansions starting from ${\rho }_0=1.3$. The inset shows the rapid increase in pressure when cavitation occurs inside the material; data are shown for $T=0.01$. (b) For each temperature $T$, the density at which cavitation occurs for $\delta t={10}^3$ is marked, by filled blue squares, on the phase diagram of the binary LJ mixture (the data are obtained from Ref. [23]). We also mark, using empty blue squares, the density of the amorphous solid $\left({\rho }_{\mathrm{g}}\right)$, which is in coexistence with the gas phase. (c) For different temperatures, the partial structure factor $S_{\mathrm{AA}}\left(q\right)$ after cavitation is displayed. (d) $P$ vs $\rho$ at $T=0.2$ for states having initial densities ${\rho }_0=1.2$, 1.3, and 1.4.

Figure 3

(Top) (a) At $T=0.01$ (in black), the evolution of pressure with time, after cavitation, if the expansion is stopped (i.e., global density remains fixed). Also shown are the corresponding data for $T=0.66$ (in blue). In the inset, the density of the amorphous solid coexisting with the low-density phase inside the cavity is shown for $T=0.01$. (b) Evolution of the structure factor: $S_{\mathrm{AA}}\left(q\right)$ measured at different times as marked in the main panel of (a) for $T=0.01$. The inset shows that there is a shift in the location of the first sharp diffraction peak of $S_{\mathrm{AA}}\left(q\right)$ between $t=450$ and $110000$, indicating a densification. (Bottom) Growth of the cavity as a function of time: density plot showing the evolution of the gas-solid interface at the above marked times.

Figure 4

Potential energy maps, after cavitation, across the $xy$ plane, for a slice of thickness $\mathrm{\Delta }z=4\sigma$ at $T=0.01$ (top) and 0.50 (bottom).

Figure 5

Continuing expansion. (Top) $T=0.2$: (Left) evolution of pressure for different $\delta t={10}^4$ (blue), ${10}^3$ (black), ${10}^2$ (red), and 25 (green). (Right) $S_{\mathrm{AA}}\left(q\right)$ for $\rho =1.3$, 1.076, 0.963, 0.713, and 0.469, corresponding to $\delta t=25$. The inset shows the $P$ vs $\rho$ data for the corresponding path across the phase diagram. (Bottom) Evolution of the density field for $\delta t=25$, with green and yellow representing, respectively, the solid and gas sides of the interfaces.

Figure 6

$T=0.2$: Evolution of the density field for $\delta t={10}^3$, with green and yellow representing, respectively, the solid and gas sides of the interfaces.

Figure 7

Sequence of snapshots during volume expansion at $T=0.2$, using $\delta t=25$. From left: $\rho =0.963$, 0.714, 0.529, 0.392, 0.113, and 0.057.

Figure 8

(Top) (a) For $T=0.2$ and $\delta t=25$, the evolution of the pressure with density (filled symbols) during compression, starting from different low densities (different colors). The corresponding $P\text{−}\rho$ data for the expansion path are shown as empty symbols. (b) $S_{\mathrm{AA}}\left(q\right)$ at $\rho =1.30$ for the quenched amorphous state (in green) and the solid formed via compression starting from $\rho =0.856$ (in red) and $\rho =1.069$ (in purple). (Bottom) Density plots demonstrating how void spaces decrease in size as the material is compressed.