Probing the Solid Phase of Noble Metal Copper at Terapascal Conditions

Ramp compression along a low-temperature adiabat offers a unique avenue to explore the physical properties of materials at the highest densities of their solid form, a region inaccessible by single shock compression. Using the National Ignition Facility and OMEGA laser facilities, copper samples were ramp compressed to peak pressures of 2.30 TPa and densities of nearly $30\mathrm{g}/\mathrm{cc}$, providing fundamental information regarding the compressibility and phase of copper at pressures more than 5 times greater than previously explored. Through x-ray diffraction measurements, we find that the ambient face-centered-cubic structure is preserved up to 1.15 TPa. The ramp compression equation-of-state measurements shows that there are no discontinuities in sound velocities up to 2.30 TPa, suggesting this phase is likely stable up to the peak pressures measured, as predicted by first-principal calculations. The high precision of these quasiabsolute measurements enables us to provide essential benchmarks for advanced computational studies on the behavior of dense monoatomic materials under extreme conditions that constitute a stringent test for solid-state quantum theory. We find that both density-functional theory and the stabilized jellium model, which assumes that the ionic structure can be replaced by an ionic charge distribution by constant positive-charge background, reproduces our data well. Further, our data could serve to establish new international secondary scales of pressure in the terapascal range that is becoming experimentally accessible with advanced static and dynamic compression techniques.

Figure 1

The measured free-surface velocity as a function of time $u_{\mathrm{fs}}(t)$ determined from VISAR [8]. The extracted $u_{\mathrm{fs}}(t)$ profiles are shown for Cu thicknesses of 91.44 (black), 101.43 (blue), 111.43 (green), and $121.43\mu \mathrm{m}$ (red). Arrows on individual step profiles indicate the arrival of a reverberation wave, which results in a secondary acceleration and analysis termination. (Inset) The target design is shown. A multistepped copper physics package is mounted on the equator of $11\times 6\text{−}\mathrm{mm}$ hohlraum.

Figure 2

(a) Lagrangian sound velocity $C_L$ versus particle velocity $u_p$ was calculated from $u_{\mathrm{fs}}$ versus sample thickness data (Fig. 1). Six experiments, each with two independent velocity measurements, yielded $C_L(u_p)$ data and their averages (bold blue curve) are shown. (b) Experimentally determined pressure-density data along an isentrope to 2.30 TPa are shown as the bold blue curve with dashed blue lines representing $1\text{−}\sigma$ bounding uncertainties. We also show a previous low-pressure measurement of Cu isentrope (red dashed line) [5], a range of calculated cold curves [13, 14, 15, 16, 17, 18, 19, 20, 21], and extrapolations from low-pressure 300-K static compression data (white circles) [22]. Our x-ray diffraction points along a ramp-compressed path are shown as light blue symbols. (Inset) We illustrate the percent correction applied to reduce the measured stress-density response to a hydrostatic pressure-density isentrope.

Figure 3

(a) The target design on the OMEGA laser experiment to measure the crystal structure of Cu to 1200 GPa. [25, 26] (b) 1D-VISAR image and extracted diamond free-surface velocity profile which is used to determine sample pressure.(c) X-ray diffraction image for Cu at 1165 GPa projected into $2\theta \text{−}\varphi$ angular space, where $\theta$ is the scattering angle and $\varphi$ is the azimuthal angle around the incident x-ray direction. The red vertical dotted lines show positions of ambient pressure Pt x-ray diffraction peaks used for diffraction angle calibration. The blue arrow indicates the position of the Cu (111) and Cu (200) fcc peaks.

Figure 4

The $d$ spacing of our experimentally determine diffraction peaks (red points) and low-pressure DAC measurements (white circles and squares) are shown. These data are compared with the fcc, hcp, 9R and bcc phases, the 4 most energy favorable structures predicted from ab initio LDA calculations [17, 20]. Our measurements agree with only the fcc phase which DFT predicts to be the most energy favorable energy to 10 TPa.