In situ x-ray diffraction measurements of the $c/a$ ratio in the high-pressure $\epsilon$ phase of shock-compressed polycrystalline iron

The structure of laser-shock-compressed polycrystalline iron was probed using in situ x-ray diffraction over a pressure range spanning the $\alpha$-$\epsilon$ phase transition. Measurements were also made of the $c/a$ ratio in the $\epsilon$ phase, which, in contrast with previous in situ x-ray diffraction experiments performed on single crystals and large-scale molecular dynamics (MD) simulations are close to those found in high-pressure diamond anvil cell experiments. This is consistent with the observation that significant plastic flow occurs within the nanosecond time scale of the experiment. Furthermore, within the sensitivity of the measurement technique, the fcc phase that had been predicted by MD simulations was not observed.

Figure 1

Schematic of the experimental setup. The sample is oriented such that the plane normal makes an angle $i={45}^{°}$ to the axis of the cylinder and incoming x rays. The drive laser beam is defocused to give a drive spot 2 mm in diameter. The deflection angle $2\theta$ is measured with respect to the axis of the CPPC.

Figure 2

(a) An example of raw data for a foil shock compressed to 15 GPa (as determined by VISAR) showing diffraction from both hcp and bcc structures. (b) Integrated line outs with the background subtracted for pressures of 0, 10, and 15 GPa. The relevant peaks used in the structural determination are labeled; the feature marked A is diffracted from the collimating tube.

Figure 3

(a), (b) A plot of lattice compression as a function of angle for (112) bcc at 15 GPa on two different shots, showing behavior consistent with low levels of strength. (c) A plot of hcp $(10\overline{1}1)$ showing a limiting strength of 10 GPa, although a best fit to close to zero strength.

Figure 4

A $P-V$ plot of the iron-shock Hugoniot. Pressure is interpreted from free-surface velocity measurements made by VISAR, and volume is measured using x-ray diffraction. The bcc structure is marked with squares where the hollow ones denote diffraction when only the bcc phase was observed, while the hcp is marked with circles, and the gas-gun Hugoniot is plotted as a solid line. In the transition region, the plot shows (13–30 GPa) where both bcc and hcp phases are observed in the diffraction at densities that do not lie on the Hugoniot.

Figure 5

Free-surface velocity measurements from experiment with diffraction shown in Fig. 2.

Figure 6

A time versus pressure plot of the Swegle-Grady relation for iron, the transition time scale from Ref. 25, and the rise time of the free-surface velocity for the laser experiments where the hollow circles denote points where no hcp was observed in the diffraction.