Shock waves in polycrystalline iron: Plasticity and phase transitions

At a pressure of around 13 GPa iron undergoes a structural phase transition from the bcc to the hexagonal close-packed phase. Atomistic simulations have provided important insights into this transition. However, while experiments in polycrystals show clear evidence that the $\alpha$-$\epsilon$ transition is preceded by plasticity, simulations up to now could not detect any plastic activity occurring before the phase change. Here we study shock waves in polycrystalline Fe using an interatomic potential which incorporates the $\alpha$-$\epsilon$ transition faithfully. Our simulations show that the phase transformation is preceded by dislocation generation at grain boundaries, giving a three-wave profile. The $\alpha$-$\epsilon$ transformation pressure is much higher than the equilibrium transformation pressure but decreases slightly with increasing loading ramp time (decreasing strain rate). The transformed phase is mostly composed of hcp grains with large defect density. Simulated x-ray diffraction displays clear evidence for this hcp phase, with powder-diffraction-type patterns as they would be seen using current experimental setups.

Figure 1

Spatial profiles of the (a) atom velocity in $z$ direction, $v_z$, the (b) pressure component parallel to the shock wave propagation, $p_{zz}$, the (c) shear stress, and the (d) fraction of non-bcc material. The so-called knees in the profiles are marked by a dot; see text. The simulation is performed for the Ackland potential [15] and a loading rise time of 15 ps.

Figure 2

Snapshots of a region of the sample extending between 250 and 350 nm from the position where the shock wave starts, before launch of the shock wave (top), and 60 ps after start of the shock wave (bottom) for the Ackland potential. Light gray: bcc; gray: hcp; black: fcc; white: other (defects, grain boundaries, etc.). Identified via adaptive CNA analysis.

Figure 3

Cross-sectional view of the sample at 70 ps using the Ackland potential and the DXA tool. A slice at a depth of 381.5 nm with a thickness of 1.5 nm is shown. Only shown are atoms which belong to either GBs or dislocations or that are in otherwise strongly perturbed environment. Color code indicates depth of atoms (blue [dark gray], front; red [gray], behind). Shock wave started from behind. Note a grain containing several straight screw dislocations which have already crossed that grain. Visualization has been prepared using Ovito [31].

Figure 4

Simulated powder diffraction patterns at 70 ps. (a) Line profiles from elastically compressed (depth 400–410 nm, dotted blue [gray]) and phase changed (depth 220–230 nm, solid black) sections of the sample. The center profile (dashed red [gray]) shows the simulated diffraction profile from only those atoms in the shocked region identified as hcp by CAT. Also shown are indexing for hcp fit to the powder pattern (solid downward-facing triangles), commensurate fcc (hollow downward-facing triangles), and bcc (solid upward-facing triangles). In addition, ray tracings are displayed, simulating the diffraction patterns in an experimental geometry for (b) unshocked and (c) phase-changed sections of the sample. The diffraction pattern is simulated for a $50\times 50$ mm film, placed 30 mm in transmission, using an incoming x-ray of energy 8.05 keV (Cu $K_{\alpha }$), perpendicular to the film.