Liquid Structure of Tantalum under Internal Negative Pressure

In situ femtosecond x-ray diffraction measurements and ab initio molecular dynamics simulations were performed to study the liquid structure of tantalum shock released from several hundred gigapascals (GPa) on the nanosecond timescale. The results show that the internal negative pressure applied to the liquid tantalum reached $-5.6(0.8)\mathrm{GPa}$, suggesting the existence of a liquid-gas mixing state due to cavitation. This is the first direct evidence to prove the classical nucleation theory which predicts that liquids with high surface tension can support GPa regime tensile stress.

Figure 1

Experimental configuration and data. Two different types of probes: XFEL and VISAR were used to record XRD pattern and shock breakout timing, respectively [24].

Figure 2

(a) X-ray diffraction profiles of the shock-compressed Ta with various pressures up to 222 (7) GPa. The peak positions of diffraction from unshocked Ta are indicated by gray lines. The peaks corresponding to the compressed bcc (110) and (211) planes are highlighted by blue arrows for the 222 (7) GPa data. The pressure uncertainty for solid data is estimated from the broadness (FWHM) of the XRD peaks. (b) Recorded XRD image of Ta shock compressed to 222 (7) GPa. Dotted curves and lines indicate constant scattering angle ($2\theta$) and azimuth angle ($\phi$), respectively. (c) Diffractions patterns of liquid Ta at shock released states with different residual temperatures. Black inverted triangles denote peaks of back-transformed bcc phase with a density of $15.5(0.2)\mathrm{g}/{\mathrm{cm}}^3$. (d) Recorded XRD image of Ta at shock released state of $-4.9(0.8)\mathrm{GPa}$ and 4100 (1100) K. Uncompressed peaks are from Ta at outside of the drive laser focal spot. The signal intensities are lower at higher azimuthal angles, as the absorption of diffracted x rays by the Ta sample itself becomes more significant at higher azimuthal angles.

Figure 3

(a) Structure factors of Ta at the shock-released states. The shown profiles of $Q<1.72$ were extrapolated from those of $Q\geqq 1.72$. (b) Corresponding pair distribution functions of Ta. The experimental results (black solid profiles) are compared with the AIMD simulation results (blue dotted profiles).

Figure 4

(a) Density as a function of the temperature at the released state. The uncertainty of the density is estimated based on the uncertainties of the $r$-min cutoff value and the differences in the densities obtained for each iteration process. The gray line indicates the melting temperature of Ta at 0 GPa (3270 K) and the green solid line shows the density-temperature relationship measured at 0 GPa [42]. (b) Pressures at the released states determined by AIMD simulations using the measured density and temperature as initial simulation parameters. The shown error bars on the pressure are estimated from the fluctuation of the AIMD simulations [24] and the uncertainties on the initial calculation parameters (temperature and density) are not considered. The blue solid curve shows the temperature dependence of the cavitation pressure $P_C$ ($T$) predicted by the classical nucleation theory. The red dashed curve and red open diamond are the cavitation pressures calculated using MD simulations by Hahn et al. [44] and the cavitation pressure of Ta estimated from the experimental results of Ashitkov et al. [47], respectively. At pressures lower than $P_C$ ($T$), liquid Ta is likely to form small-vapor-filled cavities. (c) Coordination number at different residual temperatures.