Direct Observations of a Dynamically Driven Phase Transition with in situ X-Ray Diffraction in a Simple Ionic Crystal

We report real-time observations of a phase transition in the ionic solid ${\mathrm{CaF}}_2$, a model $A{B}_2$ structure in high-pressure physics. Synchrotron x-ray diffraction coupled with dynamic loading to 27.7 GPa, and separately with static compression, follows, in situ, the fluorite to cotunnite structural phase transition, both on nanosecond and on minute time scales. Using Rietveld refinement techniques, we examine the kinetics and hysteresis of the transition. Our results give insight into the kinetic time scale of the fluorite-cotunnite phase transition under shock compression, which is relevant to a number of isomorphic compounds.

Figure 1

Experimental Hugoniot data in the shock velocity ($U_S$) versus particle velocity ($U_P$) plane, for five shots (two data points are overlapped). Five solid red stars (two are overlapped) represent ${\mathrm{CaF}}_2$ at $75\%\pm 1\%$ TMD investigated in this work. Open symbols refer to literature data for ${\mathrm{CaF}}_2$ at various initial densities [17, 32, 33].

Figure 2

Example of the temporal connection between XRD images acquired and the evolution of the shock event as measured by PDV (circles). Dashed lines show times when Debye-Scherrer rings were recorded (corresponding diffraction shown in Fig. 3). Simulated $U_P$ traces (solid lines, using the Hugoniot data of Ref. [33]) illustrate the shock state of the sample at three locations.

Figure 3

In situ XRD patterns under shock compression measured as a function of time, showing (a) a shot to 7.8 GPa, below the phase transition conditions, (b) a shot to 22.6 GPa, with a phase transition, and (c) in situ XRD patterns under static compression in a diamond anvil cell (DAC) as a function of pressure and temperature. Times are relative to impact ($t=0$). Inset in (a) shows a zoom of the [111] diffraction line, where shock compression and release are seen in the evolution of line position. In (b) arrows indicate new lines of the cotunnite phase; stars indicate the reappearing fluorite phase upon shock release. Fractions refer to intensity scaling done for display purposes. In (c) “Au” marks diffraction lines of the gold pressure calibrant and “RT” stands for room temperature.

Figure 4

The evolution of the ${\mathrm{CaF}}_2$ unit cell volume versus stress/pressure obtained from dynamic (shock) and from static compression (DAC). Solid triangles and stars represent the fluorite and cotunnite unit cell volume, respectively, under shock compression. Open squares and inverted triangles refer to static compression at 298 K to 36 GPa in nonhydrostatic conditions. Solid red circles represent compression at 500 K. Open pentagons are from Ref. [10]. The inset on the right shows a Rietveld structural refinement at 370 ns, of the shock-driven phase transition from fluorite to cotunnite.

Figure 5

Phase percentage versus time. The phase transition lags behind the shock front, marked with a grey line. The colored lines are various fits to the data using the KJMA formalism of Eq. (1).