Examining the high-pressure response and shock melting in cerium using optical pyrometry

The ability to measure temperature in shock wave experiments has been a long-standing scientific challenge complicated by the short timescales involved ($<1$ microsecond) and the presence of nonthermal or external light sources that pollute measured radiances using optical pyrometry methods. In the current work, we present the first experimental data on cerium metal designed to measure the temperature on-Hugoniot from the low-pressure $\alpha$ phase well into the high-pressure liquid phase. Radiance data obtained in this work were used to determine the Hugoniot curves for solid ($\alpha$-Ce) and liquid cerium by measuring the longitudinal stress and temperature simultaneously in the shocked state. These data were used to estimate the temperature for incipient shock melting and complete melting, and to further constrain a multiphase equation of state developed to describe the dynamic response of cerium at high pressures.

Figure 1

Schematic of the phase diagram for Ce. The Hugoniot (blue line) and the melt boundary (solid black curve) obtained from a published EOS [43]. Blue-filled circles represent DAC data for the melt boundary [24, 25]. Dashed black lines represent two of the reported boundaries for the $\alpha \text{−}\epsilon$ region of the phase diagram. The solid red line indicates the Hugoniot developed in this work based on measurements of temperature and stress.

Figure 2

Schematic of the experimental configuration for temperature measurements on shocked cerium. The target and projectile configuration consisted of a foam-backed impactor, cerium sample, and LiF window. The dual PDV-radiance probe is indicated along with a close-up that illustrates the optical fiber packing pattern. The pyrometer configuration shows that light collected from the Ce-LiF interface is coupled to the five-channel pyrometer. The system collimates broadband optical and near-infrared signal light out of the input fiber through a lens element (L) and passes the beam through a series of increasing-wavelength dichroic beam splitters (D). The spectrally selected beams, further filtered through an optical bandpass filter (B) centered around each given wavelength, are focused onto the detector photosensitive areas by further lensing.

Figure 3

Schematic showing the shock wave configuration. A shock wave is shown propagating toward the Ce-LiF interface, and then reflecting from the interface with two scenarios possible. For low impact velocities where the longitudinal stress is less than 13 GPa, the impedance of $\alpha$-Ce is less than LiF resulting in a reflected shock wave to a higher stress state (red-dashed lines). For impact stresses greater than 13 GPa, the shock impedance of cerium exceeds that of LiF resulting in a release wave to a lower stress state (black lines). The red arrow indicates the radiance and PDV measurement monitoring the Ce-LiF interface.

Figure 4

Wave profile data for six experiments (black curves) along with calculated profiles (red curves) obtained using a one-dimensional hydrocode that used appropriate material models for the impactor and target materials. Note that differences in the release wave profile were observed because the model neglects strength effects and a nominal value of 1.5 was used for Gruneisen $\mathrm{\Gamma }$.

Figure 5

Radiance data for five wavelengths plotted versus time for shot 2S-598. The particle velocity obtained from the PDV is plotted on the same time axis for comparison (scaled by $30\times$ arbitrarily). The data clearly show a significant increase in light at shock arrival up to a near steady state; it begins to decrease rapidly with the arrival of the release wave which takes the cerium to lower stress and temperature states.

Figure 6

Top: Average shocked temperature (blue curve) for Ce shot 2S-598 along with bounding temperatures. PDV data are plotted for comparison (arbitrarily scaled by $2\times$). Note the slight increase in temperature near $t=23.3\mu \mathrm{s}$ which corresponds to a slight jump in particle velocity or stress caused by shock reverberation in the cerium sample. Bottom: Calculated temperatures from radiance data shown in Fig. 5. Average temperatures obtained from each channel are shown (red curves) along with all upper temperature bounds (black curves) and lower temperature bounds (blue curves). The shaded regions represent two estimates of the measurement uncertainty.

Figure 7

Plot of temperature (K) vs longitudinal stress (GPa) for $\alpha$-Ce ($P_x<10$ GPa). A linear fit to the data results in the equation $T\left(P_x\right)=76.18P_x+273.2$. The green-filled data point represents an outlier that was not used in the fit. The incipient melt transition temperature was taken as the value that corresponded to the temperature at the incipient melt stress determined from previous sound speed measurements [29] (white-filled circle). Also shown is the temperature that corresponds to intersection of the measured Hugoniot with a published melt boundary (blue-filled circle) [25]. The solid-blue curve represents the solid Hugoniot obtained using the published multiphase EOS [43]. The red-shaded region indicates the estimated uncertainty in the fitted Hugoniot curve.

Figure 8

Plot of temperature (K) vs longitudinal stress (GPa) for liquid Ce ($P_x>10$ GPa). A linear fit to the data results in the equation $T\left(P_x\right)=79.91P_x+202.57$ K (red dashed line). The solid black curve represents the melt boundary obtained using the published multiphase EOS [43]. The modified Hugoniot curve [44] obtained from the multiphase EOS (blue curve) constrained using the $T,P$ data from this work is shown along with the previous Hugniot (blue-dashed line) constrained by earlier work [43]. The red-shaded region indicates the estimated uncertainty in the fitted Hugoniot curve.