Dynamic x-ray diffraction and nanosecond quantification of kinetics of formation of $\beta$-zirconium under shock compression

We report the atomic- and nanosecond-scale quantification of kinetics of a shock-driven phase transition in Zr metal. We uniquely make use of a multiple shock-and-release loading pathway to shock Zr into the $\beta$ phase and to create a quasisteady pressure and temperature state shortly after. Coupling shock loading with in situ time-resolved synchrotron x-ray diffraction, we probe the structural transformation of Zr in the steady state. Our results provide a quantified expression of kinetics of formation of $\beta$-Zr phase under shock loading: transition incubation time, completion time, and crystallization rate.

Figure 1

The phase diagram of Zr, the Hugoniot [27], and the three stages of our dynamic mSR experiments: shock compression (#1—hollow stars), the release (#2—long arrow), and the steady $P$ and $T$ state, where we probe the kinetics of formation of $\beta$-Zr (#3—solid stars). A line of arrows marks the path of static compression and heating in DAC, culminating in the same $P\text{−}T$ region as the mSR experiments.

Figure 2

Our multiple shock-and-release (mSR) experiment: (a) the measured PDV, modelled PDV, and modelled $P$ and $T$ state (see Supplemental Material [33]) and (b) geometry of time-resolved synchrotron DXRD. The PDV signals illustrate the stages of our experiment: the dynamic loading (dark blue, ∼10 ns) and the quasisteady $P\text{−}T$ state (light blue, ∼250 ns). Black dots mark time stamps of DXRD patterns. Insets show example DXRD images of Debye rings.

Figure 3

Selected in situ time-resolved DXRD patterns of (a)–(c) mSR dynamic compression with the pre-shot at $t=0$ and quasisteady state at $t=15$ ns and $t=168$ ns after impact, and (d)–(f) XRD of static compression in DAC. Overlapped are the measured and modeled patterns, the background and Miller indices for each phase. DXRD phase fraction errors are in Fig. 4. The path of static compression and heating in DAC (d)–(f) culminates in the $P\text{−}T$ region where diffraction of the mSR experiments is measured (b),(c). We use the Zr structures extracted from XRD DAC data as starting points in the Rietveld analysis of DXRD. Re and Au are reflections from the gasket and the pressure standard, respectively.

Figure 4

Kinetics of formation of $\beta$-Zr over ∼250 ns. (a) Quantitative analysis of the evolution of $\beta$-Zr phase fraction from our analysis of time-resolved DXRD. Error bars are two standard deviations. The fit of KJMA kinetics model is shown in orange. The short incubation time and the long time needed to complete the transition show that atomic displacement during the transition requires tens of ns to complete. (b) Modeled time evolution of $P$ and $T$ in Zr, along the path of the x-ray beam, illustrating the two stages of our mSR experiment: dynamic loading (dark-blue window, ∼10 ns) and the steady $P\text{−}T$ state (light-blue window, ∼250 ns).