Shock compression experiments in the few hundred GPa (multi-Mbar) regime were performed on Lithium Deuteride single crystals. This study utilized the high velocity flyer plate capability of the Sandia Z Machine to perform impact experiments at flyer plate velocities in the range of 17–32 km/s. Measurements included pressure, density, and temperature between ∼190 and 570 GPa along the Principal Hugoniot—the locus of end states achievable through compression by large amplitude shock waves—as well as pressure and density of reshock states up to ∼920 GPa. The experimental measurements are compared with density functional theory calculations, tabular equation of state models, and legacy nuclear driven results that have been reanalyzed using modern equations of state for the shock wave standards used in the experiments.

Lithium hydride and lithium deuteride (LiH and LiD) represent the simplest alkali hydride and a prototypical ionic solid. As such it has been the focus of many studies, both experimental1–5 and theoretical.6–11 LiH is also one of the simplest compounds, making it a model system for studying mixture rules in the warm dense matter regime. Recent quantum molecular dynamics (QMD) and orbital-free molecular dynamics (OFMD) studies have evaluated the use of density and pressure mixing rules for obtaining equation of state (EOS), optical properties, such as frequency dependent absorption coefficients and Rosseland mean opacities, and dynamical properties, such as diffusion and viscosity, over a density and temperature range of 0.5–4 times ambient density and 0.5–6 eV, respectively.12,13

However, as illustrated in Fig. 1, a comparison of existing EOS models for 6LiD shows a significant discrepancy along the Principal Hugoniot—the locus of end states achievable through compression by large amplitude shock waves—in the several hundred GPa (several Mbar) range. In particular, the legacy EOS models at Lawrence Livermore National Labs (LLNL) and Los Alamos National Labs (LANL), X204014 and SESAME 7245 and 7247,15 respectively, as well as the more modern SESAME 7360 (Ref. 10) and 7363 (Ref. 16) recently developed at LANL, and recent ab-initio molecular dynamics (AIMD) calculations11 show significant differences even at a few Mbar. Several Mbar dynamic pressures in LiD are readily accessible by high-velocity, plate impact experiments at the Sandia Z Machine.17 Furthermore, the achievable precision and accuracy for Hugoniot measurements in this regime is sufficient to distinguish between the various EOS models.

FIG. 1.

LiD P-density compression Hugoniot with ρ0=0.8g/cm3. Models: red line, SESAME 7247;15 magenta line, SESAME 7245;15 dashed black line, SESAME 7360;10 solid black line, SESAME 7363;16 green line, X2040;14 and solid (dotted) gray line, all electron (one electron) AIMD.11Data: open circles, Marsh;1 open squares, Ragan.2,3

FIG. 1.

LiD P-density compression Hugoniot with ρ0=0.8g/cm3. Models: red line, SESAME 7247;15 magenta line, SESAME 7245;15 dashed black line, SESAME 7360;10 solid black line, SESAME 7363;16 green line, X2040;14 and solid (dotted) gray line, all electron (one electron) AIMD.11Data: open circles, Marsh;1 open squares, Ragan.2,3

Close modal

Here, we present the results of magnetically accelerated flyer plate experiments on single crystal LiD. These data in the range of 190–570 GPa along the Principal Hugoniot fill a sizable gap between lower pressure (P) gas gun experiments1 (P < 80 GPa) and higher P nuclear driven experiments2,3 (P1000 GPa). Temperature for some of these experiments was obtained through the use of radiometry. Furthermore, the present work obtained reshock data for LiD in the range of 730–920 GPa, providing additional constraints for LiD in the warm dense matter regime. Finally, we also present the result of new AIMD calculations of LiD and compare these calculations to the experimental data.

The experiments were complicated due to the fact that LiD readily reacts with moisture to form lithium hydroxide (LiOH). This necessitated encapsulation of the samples. We chose to use single crystal α-quartz as a material for encapsulation given that (i) α-quartz is transparent, allowing optical access to the LiD sample and (ii) recent Hugoniot18 and adiabatic release measurements in α-quartz19 have enabled the use of α-quartz as a high-precision standard for impedance matching measurements in the multi-Mbar regime. This use of α-quartz resulted in a negligible increase in uncertainty in the inferred shock response as compared to the precision achievable through direct impact experiments with aluminum flyer plates.

The experiments are discussed in Sections II and III, including characterization of the single crystal LiD samples and the experimental configuration. The results of the experiments are presented in Section IV, including the density, pressure, and temperature along the Hugoniot, as well as the density and pressure for reshock states. A reanalysis of legacy nuclear driven experiments is presented in Section V and discussed in the context of the present work. The results are summarized in Section VI.

The single crystal Lithium Deuteride (LiD) sample material was obtained from the Crystal Growth Lab at the University of Utah. The crystal was received in boule form and was cleaved within an argon atmosphere to nominally 4 mm in lateral dimensions and ∼0.5–0.8 mm in thickness prior to encapsulation within an aluminum and α-quartz sample holder. Shards from the cleaving process were used for further sample analysis described below.

Small LiD shards were ground within a ball mill to prepare a powdered sample. An x-ray diffraction (XRD) pattern was obtained from the powdered sample between 10° and 100° in two-theta, shown in Fig. 2. Diffraction lines were observed from both LiD and LiOH. The source of the LiOH diffraction lines was likely an opaque layer on the outside of the boule (which was present on some of the shards), presumably a hydroxide layer resulting from reaction of the LiD crystal with either moisture from air prior to the boule being placed in mineral oil for storage or from moisture within the mineral oil itself. Note that the presence of the hydroxide does not affect the lattice parameter measurement for the LiD crystal and is thus ignored. The measured lattice parameter was a=4.072±0.003 Å, resulting in a unit cell volume of 67.52±0.15Å3. Given that there are four LiD pairs per unit cell, the molar volume was determined to be 10.165±0.022cm3/mol. This allows the density of the sample to be determined given the isotopic fractions of Li6 to Li7 and H to D in the sample.

FIG. 2.

X-ray diffraction data from a powdered LiD sample between 10° and 100° in two-theta. Diffraction lines from both crystalline LiD (green lines) and LiOH (blue lines) are observed. The measured LiD lattice parameter was a=4.072±0.003Å, resulting in a unit cell volume of 67.52±0.15Å3.

FIG. 2.

X-ray diffraction data from a powdered LiD sample between 10° and 100° in two-theta. Diffraction lines from both crystalline LiD (green lines) and LiOH (blue lines) are observed. The measured LiD lattice parameter was a=4.072±0.003Å, resulting in a unit cell volume of 67.52±0.15Å3.

Close modal

Small LiD shards were dissolved and used as the sample for inductively coupled plasma mass spectroscopy (ICP-MS) measurements to determine the isotopic concentration of Li in the actual sample material. The results of the measurement indicated a Li6 composition of between 2.2% and 2.4% and a Li7 composition of between 97.6% and 97.8%. This is outside of the natural abundance ratio for Li, which has Li6 and Li7 compositions of 7.59 ± 0.04% and 92.41 ± 0.04%, respectively.20 These results suggest that the sample material for this study is somewhat Li7 rich but not pure Li7.

It was not possible to determine the isotopic ratio of hydrogen to deuterium through ICP-MS. However, the lattice parameter measurement strongly suggests that the sample material for this study was highly deuterium enriched. Fig. 3 shows the measured lattice parameters for LiH6,nLiH,LiH7,6LiD,nLiD, and LiD7, as a function of the molar mass21 (Lin refers to an isotopic ratio consistent with the natural abundance referred to above). Also shown in Fig. 3 is the measured lattice parameter and the molar mass one would infer for a pure D concentration (black diamond). Given the significantly larger lattice parameter for pure H concentration (black squares) versus the pure D concentration (gray squares), clearly the measured lattice parameter for this sample is consistent with the D isotope. Given the measured Li isotopic concentration, assumed pure D concentration, and the measured molar volume of the crystal sample, one can determine the density of the sample fairly precisely. The density was determined to be 0.886 ± 0.002 g/cm3, an uncertainty of roughly 0.22%.

FIG. 3.

Measured lattice parameters21 as a function of molar mass for LiH6,nLiH, and LiH7 (black squares), and LiD6, LiDn, and LiD7 (gray squares). The measured lattice parameter for the material used in this study was a=4.072±0.003 Å (black diamond), which is consistent with LiD7 and not consistent with LiH7.

FIG. 3.

Measured lattice parameters21 as a function of molar mass for LiH6,nLiH, and LiH7 (black squares), and LiD6, LiDn, and LiD7 (gray squares). The measured lattice parameter for the material used in this study was a=4.072±0.003 Å (black diamond), which is consistent with LiD7 and not consistent with LiH7.

Close modal

The refractive index is important for proper interpretation of the shock velocity in the LiD sample obtained from velocimetry measurements (Section III). Given the fact that LiD readily reacts with moisture and must be handled within an inert environment, an accurate measurement of the refractive index of this particular sample material was not possible. It was determined that the most accurate reported value for the refractive index in the literature was from Ref. 22. That study reported measurement of the refractive index at wavelengths of 435.8, 546.1, and 589.2 nm. Interpolation of these measurements to the wavelength used in this study (532 nm) results in an inferred refractive index of n=2.007±0.005. This is the value used in the analysis described in Section III. We note that the uncertainty in refractive index translates into an uncertainty in shock velocity (see Section III), and consequently uncertainties in ρ and P. A 1% uncertainty in refractive index would result in 1%, ∼2%, and ∼1% uncertainties in shock velocity, ρ, and P, respectively.

A series of planar, plate-impact, shock-wave experiments were performed at the Sandia Z machine,17 a pulsed power accelerator capable of generating ∼20 MA currents and ∼10 MG magnetic fields in a short circuit load. The load, which is nominally 4–5 cm in each dimension, is designed to compress the cathode and explode the anode outward as a flyer-plate,23,24 producing impact velocities in excess of 30 km/s.

Two different load geometries were used in this study. The first, referred to as a coaxial load, has anode plates completely surrounding a central rectangular cathode stalk.23 Two of these anode plates are designed to be aluminum flyer-plates with initial dimensions of approximately 40 mm in height, 20 mm in width, and 1 mm in thickness. The anode box is intentionally aligned asymmetric about the cathode stalk, with feed gaps of 1 and 1.4 mm on the two flyer-plate sides. This asymmetry allows for different magnetic pressures in the two gaps, resulting in two different peak flyer-plate velocities for each firing of the Z machine, thereby increasing data return.

The second load geometry, referred to as a stripline load, has a single anode plate opposite a similar cathode plate, with a single feed gap.24 In this case, both the anode and cathode are flyer-plates with initial dimensions of approximately 36 mm in height, 10 mm in width, and 1 mm in thickness. The benefit of this design is that a significantly larger current density is achieved with respect to the coaxial load, thereby enabling higher flyer-plate velocities to be achieved. However, in this case both flyer-plates reach essentially the same impact velocity and thus only a single Hugoniot point is obtained for each firing of the Z machine.

Upon discharge of the stored energy within the Marx capacitor banks, a shaped current pulse of ∼300 ns duration and ∼20 MA in magnitude is directed through the experimental load. The large current induces a large magnetic field and the resulting J × B force propels the flyer-plates outward. With proper load design and temporal shaping of the current pulse, accelerations of a few tens of giga-g are produced that drive the solid aluminum panels across a 3–5 mm vacuum gap, ultimately reaching impact velocities of 17–32 km/s depending upon the load geometry and the peak charge voltage of the accelerator. More details regarding the flyer-plate launch and the state of the flyer-plates at impact can be found in Refs. 23 and 24.

Single crystal LiD samples were cleaved from a boule obtained from the Crystal Growth Lab at the University of Utah. Nominal sample sizes were ∼4 mm in lateral dimensions and ∼0.5–0.8 mm in thickness. Given that LiD readily reacts with moisture to form LiOH, the samples were encapsulated within aluminum and α-quartz target holders. The holders, the particular details of which evolved over the experimental series, were essentially aluminum sleeves with single crystal α-quartz windows as end caps. Nominal thicknesses of the front and rear α-quartz windows were ∼0.3 and ∼1.5 mm, respectively. The cleaving and encapsulation were performed within an argon glove box to protect the sample integrity. The target holders were then mounted into a panel back at a prescribed flight distance between 3 and 5 mm, depending upon the desired peak impact velocity.

The flyer plates, α-quartz windows, and LiD samples were diagnosed using a velocity interferometer (VISAR, Velocity Interferometer System for Any Reflector25). Since the LiD sample is transparent in the visible spectrum, the 532 nm laser light could pass through the target holder and reflect off the flyer plate surface. This allowed an in-line measurement of the flyer velocity from initial motion to impact. Upon impact a several hundred GPa shock was sent through the α-quartz and LiD sample. This shock was of sufficient magnitude that the resulting plasma became a weak metal, providing significant reflectivity in the visible range. This allowed for direct measurement of the shock velocity of both the α-quartz and LiD with the VISAR diagnostic. Ambiguity in the fringe shift was mitigated through the use of three different VISAR sensitivities or velocity per fringe (vpf) settings.

A correction to the sensitivity of the VISAR diagnostic is necessary to obtain the correct shock velocity in both the α-quartz and LiD sample. This is due to the fact that as the shock transits through the initially transparent material, the thickness of the un-shocked material through which the laser passes decreases with time, introducing a further Doppler shift in addition to the Doppler shift produced by the moving shock front. It can be shown that for this case the measured apparent velocity, va, must be reduced by a factor equal to the refractive index, n, of the un-shocked material; v=va/n. The refractive index values used in this study for α-quartz and LiD were 1.547 and 2.007, respectively.22,26 Representative velocity profiles are shown in Fig. 4.

FIG. 4.

Representative experimental data: black line, measured velocity profile from VISAR; dark gray line, hydrodynamic simulation with no gaps between the LiD and quartz; and light gray line, hydrodynamic simulation with 10 μm gaps between the LiD and quartz.

FIG. 4.

Representative experimental data: black line, measured velocity profile from VISAR; dark gray line, hydrodynamic simulation with no gaps between the LiD and quartz; and light gray line, hydrodynamic simulation with 10 μm gaps between the LiD and quartz.

Close modal

Note that in the example shown in Fig. 4 the shock velocity in the LiD sample has an initial ramp before saturating at a value of ∼27.5 km/s. This was the result of a small gap between the front α-quartz window and the LiD sample. Because the LiD readily reacts with moisture the α-quartz/LiD/α-quartz sample stack was not glued together with epoxy (the typical procedure for these types of experiments). As a result, evidence of small gaps at the front and/or rear interface was observed for most experiments. To determine the effect of these gaps on the analysis of the experiments, several one-dimensional simulations of the experiments were performed using the radiation magneto-hydrodynamic (MHD) code ALEGRA.27 Typical simulations were pure hydrodynamic simulations started at the moment of impact with a flyer plate initialized with the density, temperature, and velocity profile obtained from a one-dimensional MHD optimization of the flyer plate launch, similar to that described in Ref. 28. The aluminum flyer plate, the front and rear α-quartz windows, and the LiD sample were discretized to 0.5 μm cell sizes and modeled using SESAME equations of state (EOS) 3700,29 q7360,30 and 7363,16 respectively. Note that an isotopically scaled version of SESAME 7363 was used for LiDn.

As can be seen in Fig. 4, the simulations capture qualitatively the behavior observed in the experiment. In particular, the simulated shock velocity in the LiD sample for a simulation that included a 10 μm gap between the front α-quartz window and the LiD sample (light gray line) exhibits a similar ramp in velocity prior to saturation, the result of plasma blow off from the shocked α-quartz front window reverberating between the α-quartz window and the LiD sample. Comparing this simulation with a second simulation that did not include a gap between the front α-quartz window and the LiD sample (dark gray line) suggests that the saturated velocity is a reasonable estimate of the expected shock velocity immediately upon the shock entering the sample.

These small gaps introduced additional complications with the experiment. In particular, the gaps resulted in significant interface reflections, which were especially severe in the first experiment. Given the large refractive index of LiD (n = 2.007), dielectric coatings were put on the α-quartz windows to minimize reflections assuming that the α-quartz would be directly in contact with the LiD sample. However, with a gap present there are then two interfaces, each with two surfaces of n = 2 against n = 1 (α-quartz/gap and gap/LiD), resulting in a total reflection of ∼45% (each surface has a reflection of ∼11.1%; see Fig. 8). In an attempt to mitigate these reflections, the subsequent target holders were designed such that a mineral oil based index fluid (n = 1.7) could be placed between the α-quartz and LiD sample. This configuration still resulted in reverberation (although the reverberations were mitigated given the relative impedance of the oil to the LiD); however, the overall reflections at the interfaces were reduced to a few percent.

Emission from the shocked α-quartz windows and LiD sample was collected in an optical fiber and delivered to a streaked visible spectroscopy (SVS) diagnostic which consisted of a spectrometer coupled to a streak camera to provide spectrally and temporally resolved data. A typical SVS image is shown in Fig. 5. In this image time is running down and wavelength increases to the right. The first bright horizontal band (around 19–20 mm in the time direction) is emission from the shocked front α-quartz window. The lighter band (between 20 and 22 mm) is emission from the shocked LiD sample. The next brighter band (between 22 and 26.5 mm) is emission from the shocked rear α-quartz window. The bright vertical band (near 19 mm in the wavelength direction) corresponds to the 532 nm VISAR laser. The other vertical bands correspond to wavelength (457.9, 543.5, and 632.8 nm) and time (20 ns impulse comb) fiducials. The analysis of these data to infer temperature of the shocked LiD sample will be described in Section IV B.

FIG. 5.

Representative SVS data showing spectrally and temporally resolved emission; time increases down and wavelength increases to the right.

FIG. 5.

Representative SVS data showing spectrally and temporally resolved emission; time increases down and wavelength increases to the right.

Close modal

The shocked state of the LiD was determined using the impedance matching method and the Rankine-Hugoniot (RH) jump relations.31 The jump relations, derived by considering conservation of mass, momentum, and energy across a steady propagating shock wave, are a set of equations that relate the initial energy, E, volume, V, and pressure, P, with steady-state, post-shock values

(E1E0)=(P1+P0)(V0V1)/2,
(1)
(P1P0)=ρ0Us(up1up0),
(2)
ρ1=ρ0[Us/(Us(up1up0))],
(3)

where ρ, Us, and up denote the density, shock velocity, and particle velocity, respectively, and the subscripts 0 and 1 denote initial and final values, respectively.

The shocked state of the α-quartz drive plate was determined by the known α-quartz Hugoniot18 and the measured α-quartz shock velocity, UsQ. This defines a point (PQ,upQ) from which the release adiabat emanates. A recently developed α-quartz release model19 was used to calculate this release path. Given Eq. (2), the shocked state of the LiD is constrained to lie on the Rayleigh line, given by slope ρ0UsLiD. The intersection of the release path and the Rayleigh line provides (P1,up1); the remaining kinematic variables are determined through Eqs. (2) and (3). Using a Monte Carlo technique,32 the one-sigma uncertainties in up1, P1, and ρ1 were found to be ∼0.5%, ∼0.5%, and ∼1%, respectively.

A total of four plate impact experiments, one coaxial and three stripline, were performed on single crystal LiD. The pertinent parameters for these experiments are listed in Table I. UsQ and UsLiD denote the measured shock velocities in the front α-quartz window and the LiD sample, respectively. up1 denotes the inferred particle velocity in the LiD, and P1 and ρ1 denote the inferred pressure and density of the LiD in the shocked state, respectively. The Hugoniot data for LiD are shown in both Usup and Pρ in Figs. 6 and 7.

TABLE I.

LiD Hugoniot data. UsQ and UsLiD are the measured shock velocities in the front α-quartz window and LiD sample, respectively. up1, P1, and ρ1 are the inferred particle velocity, pressure, and density in the Hugoniot state, respectively.

ExptUsQ (km/s)UsLiD (km/s)up1 (km/s)P1 (GPa)ρ1 (g/cm3)
Z2586 15.77±0.03 18.92±0.06 11.18±0.07 187.5±1.2 2.167±0.023 
Z2497N 23.21±0.03 27.63±0.06 18.62±0.08 455.7±2.1 2.716±0.029 
Z2497S 24.75±0.03 29.55±0.06 20.21±0.09 529.1±2.5 2.804±0.031 
Z2577 25.21±0.03 30.29±0.06 20.66±0.09 554.6±2.6 2.787±0.030 
Z2692 25.46±0.03 30.54±0.06 20.93±0.09 566.5±2.7 2.816±0.031 
ExptUsQ (km/s)UsLiD (km/s)up1 (km/s)P1 (GPa)ρ1 (g/cm3)
Z2586 15.77±0.03 18.92±0.06 11.18±0.07 187.5±1.2 2.167±0.023 
Z2497N 23.21±0.03 27.63±0.06 18.62±0.08 455.7±2.1 2.716±0.029 
Z2497S 24.75±0.03 29.55±0.06 20.21±0.09 529.1±2.5 2.804±0.031 
Z2577 25.21±0.03 30.29±0.06 20.66±0.09 554.6±2.6 2.787±0.030 
Z2692 25.46±0.03 30.54±0.06 20.93±0.09 566.5±2.7 2.816±0.031 
FIG. 6.

LiD Usup Hugoniot. Blue (cyan) line, AIMD LiDn (6LiD), this work. All other lines and symbols as in Fig. 1 for LiDn and 7LiD.

FIG. 6.

LiD Usup Hugoniot. Blue (cyan) line, AIMD LiDn (6LiD), this work. All other lines and symbols as in Fig. 1 for LiDn and 7LiD.

Close modal
FIG. 7.

LiD Pρ Hugoniot. Lines and symbols as in Fig. 6.

FIG. 7.

LiD Pρ Hugoniot. Lines and symbols as in Fig. 6.

Close modal

In addition to the experimental study, we also performed ab-initio molecular dynamics (AIMD) calculations of the LiD Hugoniot for both 6LiD and LiDn. The calculations employed the Vienna ab-initio simulation package (VASP33) with the electronic wave functions described by a plane-wave basis set with the Perdew-Burke-Ernzerhof34 (PBE) exchange and correlation functional. The deuterium potential is a hard core projector-augmented wave (PAW) potential of the recent “GW” class within the VASP library.35 The lithium PAW potential is a hard-core, all-electron potential built with particular care in capturing accurate higher energy scattering properties.36 Zero point energy corrections were included in the 300 K reference state for the AIMD Hugoniot calculations. Energy cutoffs for the plane waves and augmentation charges were set to 1800 eV and 3600 eV, respectively, providing excellent convergence of the energy and stress. The standard MD simulation employed the Baldereschi mean-value point with 32 6Li or Lin and 32 D atoms. The time steps were 0.2 fs, with trajectory lengths of several thousand time steps. Kubo-Greenwood calculations of the optical properties were performed on ten well separated snapshots selected from the MD time histories in order to determine the emissivities of the LiD in the shocked states.

The results from the AIMD calculations are shown along with the Hugoniot data in Figs. 6 and 7. Also shown are the predicted response from X2040 and SESAME 7247, 7360, and 7363 along with recent AIMD calculations from Minakov and Levashov11 using both all electron and a single valence electron. Note that we only had access to the 6LiD EOS models for both SESAME 7247 and X2040. To account for the higher molar mass of our samples, which are very close to LiDn, we performed a simple shift in the Usup response from these models downward by 0.37 km/s in Us for a given up. This shift was determined by comparison of AIMD calculations for LiD6 and LiDn, as well as comparing isotopically scaled versions of the SESAME 7360 (Ref. 10) and 7363 (Ref. 16) EOS models for LiD6 and LiDn. The experimental data suggest that the X2040 EOS is systematically too compressible and the SESAME 7247 EOS is significantly too stiff. In contrast, the data are in quite good agreement with our AIMD calculations and the all electron AIMD calculations of Minakov and Levashov, as well as the more modern SESAME 7360 (Ref. 10) and 7363 (Ref. 16) EOS models.

Temperature (T) of the shocked LiD sample was determined by using the emission from the α-quartz front and rear windows as a T standard. Previous shock wave experiments on α-quartz in the multi-Mbar regime have determined the T and reflectivity of α-quartz as a function of shock speed,37 enabling α-quartz to be used as a standard for inferring T. Emission from the rear α-quartz window was used as a calibration for the SVS image. Given the shock velocity in the rear α-quartz window, and the T and reflectivity of α-quartz at that shock speed, a calibration factor was determined for each SVS image. Furthermore, given the shock velocity in the front α-quartz window, and the T and reflectivity of α-quartz at that shock speed, the emission one would expect to observe from the front α-quartz window was also determined. Typically, the expected emission from the front α-quartz window was greater than what is actually observed; the difference being attributed to reflection loses at the two α-quartz/LiD interfaces (see discussion in Section III). Under the assumption that these two interfaces contribute equally to the reflection losses, the observed LiD emission was corrected accordingly. Finally, given the emissivity of LiD in the multi-Mbar regime, determined through AIMD calculations, the T of the shocked LiD was determined.

This procedure, which is illustrated for a lineout at ∼480 nm in Fig. 8, was followed at each wavelength across the recorded SVS spectrum. A relatively flat inferred T was obtained across the 450–650 nm spectrum, lending confidence in the method used to infer the T of the shocked LiD. The inferred temperature was then averaged across the 450–650 nm spectrum to obtain the LiD T in the shocked state. The inferred T from four of the experiments is shown in Fig. 9. Also shown in Fig. 9 are three AIMD calculations (black circles) and the predictions from SESAME 7360 (Ref. 10) and 7363 (Ref. 16) (dashed and solid black lines, respectively).

FIG. 8.

Relative temperature analysis procedure. The measured UsQ and emission in the rear quartz window was used to determine a calibration factor for the SVS image at each wavelength. The measured UsQ in the front window was used to determine the expected emission; the difference between the expected and observed emission provided a measure of reflection loses at each LiD/quartz interface. This was in turn used to adjust the observed emission in the LiD.

FIG. 8.

Relative temperature analysis procedure. The measured UsQ and emission in the rear quartz window was used to determine a calibration factor for the SVS image at each wavelength. The measured UsQ in the front window was used to determine the expected emission; the difference between the expected and observed emission provided a measure of reflection loses at each LiD/quartz interface. This was in turn used to adjust the observed emission in the LiD.

Close modal
FIG. 9.

LiD temperature along the Hugoniot. Solid (dashed) black line, SESAME 7363 (Ref. 16) (7360 (Ref. 10)); black circles, AIMD, this work. Gray diamonds, experiment, this work.

FIG. 9.

LiD temperature along the Hugoniot. Solid (dashed) black line, SESAME 7363 (Ref. 16) (7360 (Ref. 10)); black circles, AIMD, this work. Gray diamonds, experiment, this work.

Close modal

The compressibility of LiD was further explored by performing reshock experiments. In four of the Hugoniot experiments described above, the reflected shock from the rear α-quartz window drove the LiD from a Hugoniot state to a reshocked state at higher P and ρ. P1, ρ1, and up1 were determined from the measured shock velocity in the LiD immediately prior to reflection from the rear α-quartz window, along with a fit to the Usup Principal Hugoniot data (listed in Table I). The measured shock velocity in the rear α-quartz window and the known Hugoniot of α-quartz provided the double-shocked P2 and up2 for LiD. The velocity of the second shock in the LiD, Us2LiD, was then determined by evaluating Eq. (2) using the change in pressure and particle velocity, (P2P1) and (up2up1). Given Us2LiD, ρ1, and (up2up1), the reshock density, ρ2, was determined from Eq. (3). Using the Monte Carlo technique, the one-sigma uncertainties in P2 and ρ2 for the reshock states were found to be ∼0.5%–1% and ∼1%–2%, respectively. Although the uncertainty for the reshock data is larger than that for the principal Hugoniot data (entirely due to the larger uncertainty in the initial state), the precision of the present data provides a stringent constraint of the reshock response of LiD in the multi-Mbar regime.

The pertinent parameters for these reshock experiments are listed in Table II. Us1LiD and Us2Q denote the measured shock velocities in the LiD sample and the rear α-quartz window, respectively. P1 and ρ1 denote the density and pressure of the LiD in the Hugoniot state immediately prior to the shock reflecting from the rear α-quartz window, respectively, and P2 and ρ2 denote the inferred P and ρ of the LiD in the reshocked state, respectively.

TABLE II.

LiD reshock data. Us1LiD (Us2Q) is the measured shock velocity in the LiD sample (rear α-quartz window) immediately prior to (after) shock reflection from the rear α-quartz window. P1 and ρ1 are the inferred pressure and density in the shocked LiD sample, as determined from Us1LiD and a fit to the Hugoniot data in Table I. P2 and ρ2 are the inferred pressure and density in the reshocked state, respectively.

ExptUs1LiD (km/s)Us2Q (km/s)P1 (GPa)Ρ1 (g/cm3)P2 (GPa)ρ2 (g/cm3)
Z2497N 26.94±0.06 21.33±0.03 430.1±2.6 2.679±0.023 727.0±3.9 3.530±0.056 
Z2497S 28.60±0.06 22.66±0.03 491.3±2.8 2.751±0.024 835.6±4.3 3.615±0.057 
Z2577 29.65±0.06 23.43±0.03 531.7±3.0 2.794±0.025 902.4±4.5 3.701±0.060 
Z2692 29.85±0.06 23.56±0.03 539.6±3.0 2.801±0.025 914.0±4.6 3.727±0.061 
ExptUs1LiD (km/s)Us2Q (km/s)P1 (GPa)Ρ1 (g/cm3)P2 (GPa)ρ2 (g/cm3)
Z2497N 26.94±0.06 21.33±0.03 430.1±2.6 2.679±0.023 727.0±3.9 3.530±0.056 
Z2497S 28.60±0.06 22.66±0.03 491.3±2.8 2.751±0.024 835.6±4.3 3.615±0.057 
Z2577 29.65±0.06 23.43±0.03 531.7±3.0 2.794±0.025 902.4±4.5 3.701±0.060 
Z2692 29.85±0.06 23.56±0.03 539.6±3.0 2.801±0.025 914.0±4.6 3.727±0.061 

The reshock data for LiD are shown in Fig. 10, where first shock states are shown as diamonds; the light gray points correspond to the principal Hugoniot measurements listed in Table I, and plotted in Fig. 7, while the dark gray points correspond to the state immediately prior to reshock, as determined by Us1LiD immediately prior to reshock and a fit to the Hugoniot data in Table I. The reshock states are shown as dark gray triangles. Also shown are the Principal and reshock Hugoniots from SESAME 7360 (dashed black line) and 7363 (solid black line), along with individually calculated AIMD Hugoniot and reshock states (black circles). The white (gray) squares are the reshock states obtained from impedance matching calculations with α-quartz as the rear window using SESAME 7360 (7363). Note that the experimental reshock data appear to be systematically softer than the AIMD and EOS model predictions, similar to the trend observed for the Principal Hugoniot. Since we did not have access to a LiDn version of either SESAME 7247 or X2040, we were unable to make reshock comparisons with these models.

FIG. 10.

LiD reshock data. Dashed (solid) black line, Principal and reshock Hugoniots for SESAME 7360 (Ref. 10) (7363 (Ref. 16)); dot-dashed black line, Principal Hugoniot for AIMD, this work. Light gray diamonds, Principal Hugoniot from IM measurements; Dark gray diamonds (triangles), inferred P and ρ immediately prior to (after) reshock; P1 and ρ1 were determined by Us1LiD and a fit to the Hugoniot data in Table I. White (gray) squares, reshock states from α-quartz rear window for SESAME 7360 (7363); black circles, Hugoniot and reshock states for AIMD.

FIG. 10.

LiD reshock data. Dashed (solid) black line, Principal and reshock Hugoniots for SESAME 7360 (Ref. 10) (7363 (Ref. 16)); dot-dashed black line, Principal Hugoniot for AIMD, this work. Light gray diamonds, Principal Hugoniot from IM measurements; Dark gray diamonds (triangles), inferred P and ρ immediately prior to (after) reshock; P1 and ρ1 were determined by Us1LiD and a fit to the Hugoniot data in Table I. White (gray) squares, reshock states from α-quartz rear window for SESAME 7360 (7363); black circles, Hugoniot and reshock states for AIMD.

Close modal

Ragan2,3 published results of nuclear driven experiments on both 6LiD and 6LiH. Both of these publications suggest a somewhat more compressible response than all of the models considered here, including X2040 (see Fig. 1). However, two aspects of the experiments and analysis bring into question the reported results; (i) the treatment of the shock standards upon release and (ii) the steadiness of the shock and how that was accounted for in the analysis. Both these aspects of the experimental analysis tend to result in a softer response. Thus, reanalysis tends to result in a stiffer response, bringing the inferred results into better agreement with the recent calculations and experiments.

Both molybdenum and beryllium were used as standards for the 6LiD experiments reported in Ref. 2. According to Ref. 2, SESAME tables 2980 (Refs. 15 and 38), 2981 (Refs. 15 and 38), and 2020 (Refs. 15 and 38) were used for molybdenum and beryllium, respectively. Table 2981 is a new table developed by Kerley specifically for the analysis of this particular nuclear-driven experiment. Comparing the Hugoniot response of 2981 and the older 2980 to experimental data for molybdenum in the several TPa range from Ragan,39 Al'tshuler et al.,40 Trunin et al.,41 and Mitchell et al.42 (the Mitchell et al. results were reanalyzed with a more reasonable aluminum Hugoniot,43 resulting in slightly higher inferred P and ρ) shows that 2981 is significantly stiffer than 2980 and is in better agreement with available data.

However, as Ragan points out, the release isentropes for 2981 and 2980 from the inferred shocked states of the molybdenum base plate (which differ in particle velocity by 3% for the two tables) are nearly identical in the vicinity of the 6LiD Hugoniot. This is rather surprising. One would expect the release from these pressures and temperatures (5 TPa and 15 eV) to be adequately described by a Mie-Gruneisen (MG) model with Gamma (Γ) of ∼2/3.19,43 Comparing release isentropes from 2981 and 2980 with such a model suggests that 2981 is the outlier, inferring a release path that exhibits too high a particle velocity for a given pressure. To perform the reanalysis of this datum, the 2981 Hugoniot was used as a reference for a MG model with Γ of 2/3.

For the beryllium standard experiment, Ragan used SESAME table 2020. Several different beryllium EOS tables were evaluated with respect to Hugoniot data in the few TPa range from Ragan2 and Nellis et al.44 (the Nellis et al. data were reanalyzed with a more reasonable aluminum Hugoniot,43 resulting in slightly higher inferred P and ρ). The most reasonable agreement with these data was found for table 2010,45 which is a table developed by Kerley circa 2002. To perform a reanalysis of this datum, the SESAME 2010 Hugoniot was used as a reference for a MG model with Γ of 2/3.

The 6LiH experiment,3 used carbon as the standard. Unfortunately, there are no Hugoniot data in the TPa range for comparison, and so SESAME table 7831 (Refs. 15 and 38) was used, the same table used by Ragan in his analysis. However, again the SESAME 7831 Hugoniot was used as the reference for a MG model with Γ of 2/3.

Ragan noted that there was evidence of attenuation of the shock waves as they traversed the various layers (Mo/LiD/Be and Mo/Be/LiD for the 6LiD experiments3). To account for this, it appears that Ragan assumed a 1% attenuation in shock velocity across the various samples. He then used the appropriate upshifted or downshifted velocity as the shock velocity at the front or rear of the material when performing the impedance match calculation. This correction results in a less compressible response than one would get if the average shock velocities obtained directly from the transit time measurements were used, ignoring the effects of attenuation. Furthermore, if one were to assume a larger attenuation (i.e., a larger percentage drop in shock velocity across the sample), the corrected result would be even less compressible.

It is interesting that the assumed attenuation for the 6LiH experiment, 3%, is significantly larger than that assumed for the 6LiD experiments, particularly given that the experimental configuration for the EOS package was nearly identical to that used in the 6LiD study. Indeed, the thicknesses of lead, molybdenum, and various samples were essentially the same for the two studies. The only difference being that the shocked state in the molybdenum was higher (∼6 TPa) for the 6LiH experiment than it was (∼5 TPa) for the 6LiD experiments. It is not clear why the attenuation was assumed to be larger, but it does question the magnitude of the attenuation used to correct the 6LiD data. If one were to assume that the magnitude of the attenuation was underestimated in the 6LiD experiments, the correction for attenuation would be larger and would bring the inferred results closer in line with the recent AIMD calculations for 6LiD, as shown in Fig. 11. This figure shows the reanalyzed results along with the AIMD Hugoniots for 6LiH, 6LiD, and LiDn. Given this exercise, it can be concluded that the results from the nuclear driven experiments are consistent with the recent theoretical and experimental studies of LiD.

FIG. 11.

Reanalysis of Ragan2,3 results compared to AIMD Hugoniots. White (light gray) symbols, as published (reanalyzed) results. Dark gray symbols are reanalyzed results for 6LiD assuming a 2% attenuation of the shock (as opposed to 1%).

FIG. 11.

Reanalysis of Ragan2,3 results compared to AIMD Hugoniots. White (light gray) symbols, as published (reanalyzed) results. Dark gray symbols are reanalyzed results for 6LiD assuming a 2% attenuation of the shock (as opposed to 1%).

Close modal

A series of shock compression experiments were performed on LiD single crystals using the high velocity flyer plate capability of the Sandia Z Machine. Pressure, density, and temperature were inferred along the Principal Hugoniot between ∼190 and 570 GPa. Pressure and density of reshock states were also inferred up to ∼920 GPa. These data were found to be in disagreement with the legacy equation of state (EOS) models at LLNL and LANL, X2040 and SESAME 7245 and 7247, respectively. In contrast, the results were found to be in reasonably good agreement with ab-initio molecular dynamics calculations performed in this study and recent all electron calculations performed by Minakov and Levashov,11 as well as two new EOS models, SESAME 7360 and 7363, developed at LANL.10,16 Finally, legacy nuclear driven experiments2,3 on 6LiD and 6LiH were reanalyzed, using modern EOS tables and better release models. The reanalyzed data were found to be consistent with the recent theoretical and experimental work on LiD.

We would like to thank Dan Dolan for locating the single crystal LiD boule. Michael Siegal is thanked for providing access to the argon glove box used in target preparation. Mark Rodriguez and Jeff Reich are thanked for performing x-ray diffraction and inductively coupled plasma mass spectrometry measurements, respectively, to characterize the sample material used in these experiments. We also thank the large team at Sandia that contributed to the design and fabrication of the flyer plate loads and the fielding of the shock diagnostics. Sandia National Laboratories is a multi-mission laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under Contract No. DE-AC04-94AL85000.

1.
LASL Shock Hugoniot Data
, edited by
S. P.
Marsh
(
University of California Press
,
Berkeley, CA
,
1980
).
2.
C. E.
Ragan
 III
,
Phys. Rev. A
25
,
3360
(
1982
).
3.
C. E.
Ragan
 III
,
Phys. Rev. A
29
,
1391
(
1984
).
4.
P.
Loubeyre
,
R. L.
Toullec
,
M.
Hanfland
,
L.
Ulivi
,
F.
Datchi
, and
D.
Hausermann
,
Phys. Rev. B
57
,
10403
(
1998
).
5.
A. L.
Kritcher
,
P.
Neumayer
,
C. R. D.
Brown
,
P.
Davis
,
T.
Döppner
,
R. W.
Falcone
,
D. O.
Gericke
,
G.
Gregori
,
B.
Holst
,
O. L.
Landen
,
H. J.
Lee
,
E. C.
Morse
,
A.
Pelka
,
R.
Redmer
,
M.
Roth
,
J.
Vorberger
,
K.
Wünsch
, and
S. H.
Glenzer
,
Phys. Rev. Lett.
103
,
245004
(
2009
).
6.
J.
Hama
,
K.
Suito
, and
N.
Kawakami
,
Phys. Rev. B
39
,
3351
(
1989
).
7.
R.
Ahuja
,
O.
Eriksson
, and
B.
Johanssen
,
Phys. B: Condens. Matter
265
,
87
(
1999
).
8.
T.
Ogitsu
,
E.
Schwegler
,
F.
Gygi
, and
G.
Galli
,
Phys. Rev. Lett.
91
,
175502
(
2003
).
9.
S.
Lebègue
,
M.
Alouani
,
B.
Arnaud
, and
W. E.
Pickett
,
Europhys. Lett.
63
,
562
(
2003
).
10.
D.
Sheppard
,
J. D.
Kress
,
S.
Crockett
,
L. A.
Collins
, and
M. P.
Desjarlais
,
Phys. Rev. E
90
,
063314
(
2014
).
11.
D. V.
Minakov
and
P. R.
Levashov
,
Comput. Mater. Sci.
114
,
128
(
2016
).
12.
D. A.
Horner
,
J. D.
Kress
, and
L. A.
Collins
,
Phys. Rev. B
77
,
064102
(
2008
).
13.
D. A.
Horner
,
F.
Lambert
,
J. D.
Kress
, and
L. A.
Collins
,
Phys. Rev. B
80
,
024305
(
2009
).
14.
P.
Stern
, personal communication (
2014
).
15.
S. P.
Lyon
and
J. D.
Johnson
, “
SESAME: The Los Alamos National Laboratory Equation of State Database
,”
Technical Report No. LA-UR-92-3407
(Los Alamos National Laboratory,
1992
).
16.
D. G.
Sheppard
,
J. D.
Kress
,
S.
Crockett
,
L. A.
Collins
, and
C. W.
Greeff
, SESAME 7363: A New Li(6)D Equation of State,
Technical Report No. LA-UR-15-27354
(Los Alamos National Laboratory,
2015
).
17.
M. K.
Matzen
 et al,
Phys. Plasmas
12
,
055503
(
2005
).
18.
M. D.
Knudson
and
M. P.
Desjarlais
,
Phys. Rev. Lett.
103
,
225501
(
2009
).
19.
M. D.
Knudson
and
M. P.
Desjarlais
,
Phys. Rev. B
88
,
184107
(
2013
).
20.
K. J. R.
Rossman
and
P. D. P.
Taylor
,
Pure Appl. Chem.
70
,
217
(
1998
).
21.
J. L.
Anderson
,
J.
Nasise
,
K.
Philipson
, and
F. E.
Pretzel
,
J. Phys. Chem. Solids
31
,
613
(
1970
).
22.
E.
Staritzky
and
D. I.
Walker
,
Anal. Chem.
28
,
1055
(
1956
).
23.
R.
Lemke
,
M. D.
Knudson
,
A.
Robinson
,
T.
Haill
,
K.
Struve
,
J.
Asay
, and
T.
Mehlhorn
,
Phys. Plasmas
10
,
1867
(
2003
).
24.
R.
Lemke
,
M. D.
Knudson
, and
J.-P.
Davis
,
Int. J. Impact Eng.
38
,
480
(
2011
).
25.
L. M.
Barker
and
R. E.
Hollenbach
,
J. Appl. Phys.
43
,
4669
(
1972
).
27.
R. M.
Summers
,
J. S.
Perry
,
M. W.
Wong
,
E. S.
Hertel
, Jr.
,
T. G.
Trucano
, and
L. C.
Chhabildas
,
Int. J. Impact Eng.
20
,
779
(
1997
).
28.
R.
Lemke
,
M. D.
Knudson
,
D. E.
Bliss
,
K.
Cochrane
,
J.-P.
Davis
,
A. A.
Giunta
,
H. C.
Harjes
, and
S. A.
Slutz
,
J. Appl. Phys.
98
,
073530
(
2005
).
29.
G. I.
Kerley
,
Int. J. Impact Eng.
5
,
441
(
1987
).
30.
G.
Kerley
, “
Equations of state for composite materials
,”
Kerley Publishing Services Report No. KPS99-4
(Kerley Publishing Services,
1999
).
31.
G. E.
Duvall
and
R. A.
Graham
,
Rev. Mod. Phys.
49
,
523
(
1977
).
32.
M. D.
Knudson
,
M. P.
Desjarlais
,
R. W.
Lemke
,
T. R.
Mattsson
,
M.
French
,
N.
Nettelmann
, and
R.
Redmer
,
Phys. Rev. Lett.
108
,
091102
(
2012
).
33.
G.
Kresse
and
J.
Furthmüller
,
Phys. Rev. B
54
,
11169
(
1996
).
34.
J. P.
Perdew
,
K.
Burke
, and
M.
Ernzerhof
,
Phys. Rev. Lett.
77
,
3865
(
1996
).
35.
G.
Kresse
and
D.
Joubert
,
Phys. Rev. B
59
,
1758
(
1999
).
36.
A. E.
Mattsson
, “
A lithium projector augmented wave potential suitable for use in VASP at high compression and temperature
,”
Technical Report No. SAND2012-7389
(Sandia National Laboratories,
2012
).
37.
P. M.
Celliers
,
P.
Loubeyre
,
J. H.
Eggert
,
S.
Brygoo
,
R. S.
McWilliams
,
D. G.
Hicks
,
T. R.
Boehly
,
R.
Jeanloz
, and
G. W.
Collins
,
Phys. Rev. Lett.
104
,
184503
(
2010
).
38.
SESAME83: Report on the Los Alamos Equation of State Library
,”
Technical Report No. LALP-83-4
(Los Alamos National Laboratory,
1983
).
39.
C. E.
Ragan
 III
,
M. G.
Silbert
, and
B. C.
Diven
,
J. Appl. Phys.
48
,
2860
(
1977
).
40.
L. V.
Al'tshuler
,
A. A.
Bakanova
,
I. P.
Dudoladov
,
E. A.
Dynin
,
R. F.
Trunin
, and
B. S.
Chekin
,
J. Appl. Mech. Tech. Phys.
22
,
145
(
1981
).
41.
R. F.
Trunin
,
G. V.
Simakov
,
Y. N.
Sutulov
,
A. B.
Medvedev
,
B. D.
Rogozkin
, and
Y. E.
Fedorov
,
Sov. Phys. - JETP
69
,
580
(
1989
).
42.
A. C.
Mitchell
,
W. J.
Nellis
,
J. A.
Moriarty
,
R. A.
Heinle
,
N. C.
Holmes
,
R. E.
Tipton
, and
G. W.
Repp
,
J. Appl. Phys.
69
,
2981
(
1991
).
43.
M. D.
Knudson
,
M. P.
Desjarlais
, and
A.
Pribram-Jones
,
Phys. Rev. B
91
,
224105
(
2015
).
44.
W. J.
Nellis
,
J. A.
Moriarty
,
A. C.
Mitchell
, and
N. C.
Holmes
,
J. Appl. Phys.
82
,
2225
(
1997
).
45.
G.
Kerley
, “
Equations of state for Be, Ni, W, and Au
,”
Technical Report No. SAND2003-3784
(Sandia National Laboratories,
2003
).