Ultrafast Dynamic Compression Technique to Study the Kinetics of Phase Transformations in Bismuth

Preheated Bi (296–532 K) was ramp compressed with 15–35 ns rise times to a peak stress of $\sim 11\mathrm{GPa}$ to explore structural phase-transformation kinetics under dynamic loading conditions. At high strain rates, $\dot{\mathit{\epsilon }}>5\times {10}^6{\mathrm{s}}^{-1}$, deviation from equilibrium phase boundaries suggests that compression time scales are comparable to the new phase incubation period. The dependence of $\Delta P/kT$ on $\dot{\mathit{\epsilon }}$ is consistent with a thermally activated transformation.

Figure 1

Target design for laser-driven ramp compression of a Bi foil.

Figure 2

The time histories for the (a) $\mathrm{Bi}/\mathrm{LiF}$ interface velocity with $T_i$ ($A$–$F$) of 296, 349, 443, 467, 493, and 495 K, respectively, and (b) the $\mathrm{Bi}/\mathrm{\text{sapphire}}$ interface velocity with initial $T_i$ ($a$–$f$) of 296, 343, 393, 443, 463, and 476 K, respectively. The 463 K (e) profile was extracted from the VISAR data shown in Fig. 1. Trace $b$ was a $50\mu \mathrm{m}$ thick sample as opposed to the standard $20\mu \mathrm{m}$ thick samples. Also shown are velocity profiles calculated from the nonequilibrium model described by Kane et al. [22] using the input pressure profile from Fig. 1.

Figure 3

A characteristics view of wave propagation through a $\mathrm{Bi}/\mathrm{LiF}$ sample. Upon entering the mixed phase region there is a drop in the material sound speed, which causes a separation of the characteristics, and produces a shoulder point followed by a plateau on the measured $\mathrm{Bi}/\mathrm{LiF}$ interface velocity.

Figure 4

$P\mathrm{\text{−}}T$ plot of Bi shown with I, II, and liquid equilibrium phase boundaries. Points from a series of preheated Bi samples are shown for the two different window materials used (LiF, sapphire) along with the points taken by Bastea [7] and Asay [8].

Figure 5

$\Delta P/kT$ as a function of strain rate across equilibrium Bi I-II equilibrium phase boundary.