Enhanced densification under shock compression in porous silicon

Under shock compression, most porous materials exhibit lower densities for a given pressure than that of a full-dense sample of the same material. However, some porous materials exhibit an anomalous, or enhanced, densification under shock compression. We demonstrate a molecular mechanism that drives this behavior. We also present evidence from atomistic simulation that silicon belongs to this anomalous class of materials. Atomistic simulations indicate that local shear strain in the neighborhood of collapsing pores nucleates a local solid-solid phase transformation even when bulk pressures are below the thermodynamic phase transformation pressure. This metastable, local, and partial, solid-solid phase transformation, which accounts for the enhanced densification in silicon, is driven by the local stress state near the void, not equilibrium thermodynamics. This mechanism may also explain the phenomenon in other covalently bonded materials.

Figure 1

Low porosity silicon Hugoniot curves for 1% (blue circles) and 5% (green circles) shocked along the $\langle 100\rangle$ orientation from molecular dynamics simulation. The principal Hugoniot curves for defect-free single-crystal silicon shocked along $\langle 100\rangle$ (black squares) and $\langle 111\rangle$ (red squares), as well as defective crystal with 1% vacancy (pink triangles) are shown for comparison.

Figure 2

Sample geometries for silicon with 50% porosity. (Left) Cut spherical voids from a single crystal; (right) assembly of polycrystal from randomly oriented spherical grains.

Figure 3

Slices showing atoms near collapsing voids in 1% void silicon after a 20 GPa shock passes, moving along $\langle 100\rangle$ (left to right in each image). On the left, atoms are colored for coordination number, indicating diamond (gray) and high-density phase (red). On the right, atoms are colored for shear stress, $\tau =P_{zz}-(P_{xx}+P_{yy})/2$, with blue for low $\tau$ and red for high. Times are approx. $-6$, 2, 4, 8, and 44 ps (top to bottom) relative to shock overtake.

Figure 4

One-dimensional spatial profiles of the propagating shock, with piston velocity of 1.2 km/s, in 5% porous silicon after 20 ps (black) and 32 ps (red).

Figure 5

An atomistic snapshot of the partial phase transition in silicon. The image shows the higher-density crystal phase between two diamond phases. This snapshot is from a simulation at 1.4 km/s in near perfect crystal.

Figure 6

High porosity silicon Hugoniot curves for 25% (brown) and 50% (purple) shocked along the $\langle 100\rangle$ orientation. Two Hugoniot curves are shown for each porosity representing the cut void (circles) and aggregated polycrystal (diamonds) construction methods. The principal Hugoniot curve for defect-free $\langle 100\rangle$ single-crystal silicon (black squares) and 5% low porosity (green circles) are shown for comparison.

Figure 7

Temperature versus density for silicon with various degrees of initial porosity. Symbols are the same as in Figs. 1 and 4.