Dynamic compression of copper to over 450 GPa: A high-pressure standard

An absolute stress-density path for shocklessly compressed copper is obtained to over 450 GPa. A magnetic pressure drive is temporally tailored to generate shockless compression waves through over 2.5-mm-thick copper samples. The free-surface velocity data is analyzed for Lagrangian sound velocity using the iterative Lagrangian analysis (ILA) technique, which relies upon the method of characteristics. We correct for the effects of strength and plastic work heating to determine an isentropic compression path. By assuming a Debye model for the heat capacity, we can further correct the isentrope to an isotherm. Our determination of the isentrope and isotherm of copper represents a highly accurate pressure standard for copper to over 450 GPa.

Figure 1

Schematic stripline geometry used for the shockless compression experiment on copper. The current density (J) flows on the inner surface of the anode to the cathode, creating a magnetic field vector (B), which interacts with the current density and accelerates the anode and cathode away from each other. VISAR probes measure the free surface velocity of the copper anode and cathode and are shown in green.

Figure 2

Average free-surface velocity profiles for each of the four pairs of samples on shot Z2689. Shown within each subplot are the thickness measurements for both of the samples.

Figure 3

Average free-surface velocity profiles for each of the four pairs of samples on shot Z2791. Shown within each subplot are the thickness measurements for both of the samples.

Figure 4

Measured Lagrangian sound velocity as a function of the free-surface velocity for two pairs on shot Z2791 (solid lines) and 4 pairs on shot Z2689 (dashed lines). Below are plotted the residuals for each of the sound velocity measurements relative to the weighted average sound velocity of all the traces.

Figure 5

Grüneisen parameter determined from comparison of principal and porous Hugoniot data with measured isentrope. Also included is our best fit.

Figure 6

High-pressure yield strength data determined along the principal Hugoniot. Also presented is a scaled fit to the Steinberg-Guinan strength model along the Hugoniot (red) and isentrope (blue), where the strength along the Hugoniot drops to zero at 224 GPa due to shock melting.

Figure 7

Required corrections and associated uncertainties for reducing shockless compression data to the 298 K isotherm of copper. Plotted are the corrections for the deviatoric stress (black), thermal pressure due to plastic work heating (red), and thermal pressure correction from the principal isentrope to the 298 K isotherm (blue solid line).

Figure 8

Equation of state data for copper on the principal Hugoniot and the 298 K isotherm. Shown are Hugoniot data from Mitchell and Nellis [34], Altshuler et al. [33], and Nellis et al. [35]; and isotherms from Dewaele et al. [9], Holzapfel [45], and this paper.

Figure 9

Equation of state data for copper up to 120 GPa. Shown are Hugoniot data from Mitchell and Nellis [34], and isotherms from Dewaele et al. [9], Chijioke et al. [4], Holzapfel [45], and this paper.

Figure 10

Comparison of fits to the pressure dependence of the ruby R1 line by Mao et al. [46], Aleksandrov et al. [49], Dewaele et al. [9], Holzapfel [51], Chijioke et al. [48], Dewaele et al. [52], Holzapfel [45], and this paper. Also shown as black dashed lines are the 1-$\sigma$ uncertainty bounds on the ruby R1 line calibration of this work. Above 150 GPa, these fits are no longer constrained by data and are presented as extrapolations for comparison purposes.

Figure 11

Sum total of the required corrections and associated uncertainties for reducing shock compression data (red) and shockless compression data (blue) to the 298 K isotherm of copper.