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Insulator-metal transition in dense fluid deuterium

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Science  17 Aug 2018:
Vol. 361, Issue 6403, pp. 677-682
DOI: 10.1126/science.aat0970

Laser-shocking deuterium into metal

The conditions in which hydrogen disassociates and becomes an atomic metal occur in high-energy-density environments, such as the interiors of giant planets and nuclear explosions. Celliers et al. trained 168 lasers on deuterium samples at the National Ignition Facility to measure the pressure and temperature conditions of the hydrogen transition. Careful optical measurements led to the addition of four new points on the phase diagram, consistent with static estimates and theoretical calculations.

Science, this issue p. 677

Abstract

Dense fluid metallic hydrogen occupies the interiors of Jupiter, Saturn, and many extrasolar planets, where pressures reach millions of atmospheres. Planetary structure models must describe accurately the transition from the outer molecular envelopes to the interior metallic regions. We report optical measurements of dynamically compressed fluid deuterium to 600 gigapascals (GPa) that reveal an increasing refractive index, the onset of absorption of visible light near 150 GPa, and a transition to metal-like reflectivity (exceeding 30%) near 200 GPa, all at temperatures below 2000 kelvin. Our measurements and analysis address existing discrepancies between static and dynamic experiments for the insulator-metal transition in dense fluid hydrogen isotopes. They also provide new benchmarks for the theoretical calculations used to construct planetary models.

The transformation of hydrogen from a molecular insulator to an atomic metal at high densities has been a longstanding focus in physics and planetary science (1). The unique quantum metallic properties of the low-temperature solid (i.e., below 300 K) have drawn sustained interest (25), and characterizing the transformation in the hot, dense fluid is crucial for understanding the internal structure and dynamics of giant planets (6), including the origin of their large magnetic fields (7). Numerous studies of the insulator-metal (IM) transition in dense fluid hydrogen, beginning with theoretical work five decades ago, predicted a first-order transition in the fluid (810) with a critical point at very high temperatures (~13,000 to 15,000 K) and 60 to 90 GPa. However, the first experimental work on the IM transition in the fluid, carried out using dynamic compression techniques, provided evidence for a continuous transition with metallic states reached in the pressure range P = 50 to 140 GPa and temperatures T = 3000 to 8000 K (1113). More recent predictions (1417) placed the critical point at a much lower temperature (~2000 K). This motivated several experimental studies using static diamond anvil cell (DAC) techniques (1822) and dynamic compression (23) to probe the fluid properties below 2000 K and up to several hundred GPa.

Dynamic compression can explore a broad range of thermodynamic paths with time-varying manipulations of the applied pressure and controlled reverberation of pressure waves through the sample. This includes probing the dense fluid at temperatures below 2000 K, for example, with an initial jump in pressure delivered by a shock wave followed by shock reverberation or gradual ramp compression. The first demonstration of this strategy was carried out on deuterium with a magnetic compression technique at the Z facility (23). The results showed strong optical absorption beginning in the range 100 GPa < P < 130 GPa, followed by weak fluctuating reflectance in the range 130 GPa < P < 300 GPa, and culminated in abrupt jumps to high reflectance near 300 GPa. Knudson et al. (23) attributed the absorption to band gap closure and determined that the reflectance jumps were associated with the first-order IM transition. The reflectance jumps occurred at higher pressures upon compression than upon decompression, plausibly as a result of thermal conduction. Meanwhile, improvements in static compression methods have allowed the exploration of the behavior of the fluid over part of this pressure-temperature (P-T) range (up to 170 GPa and >1800 K) (1822, 2426). Changes in optical properties from 120 to 170 GPa depending on temperature were attributed to the IM transition (1820, 22), whereas other experiments suggest the persistence of a finite (~1 eV) band gap at similar conditions (21).

The IM transition is the subject of a number of continuing theoretical studies (1417, 2729) that consistently predict a discontinuous transition below a critical point near ~2000 K, but over a broad range of pressures. Density functional theory (DFT)–based calculations show a spread in the transition pressure spanning 150 GPa, arising from the sensitivity of the boundary to the choice of exchange-correlation functional used and whether zero-point energy is accounted for (1, 16). Quantum Monte Carlo (QMC) calculations should provide improved bounds on the transition pressures (16, 17), although they disagree with a recent benchmarking experiment (30). Transition pressures for hydrogen and deuterium are expected to be different because of isotope effects, but with a small relative magnitude. The transition in deuterium from QMC simulations is 30 GPa higher than in hydrogen at 600 K, decreasing to 10 GPa higher at 1200 K (16). Despite experimental support for a first-order IM transition (19, 20, 22, 23), the critical point has not been experimentally identified. Furthermore, the broad discrepancies in the measured transition pressure (20, 22, 23) and character (2023) have made resolving the differences between the theoretical models challenging.

We completed a series of five dynamic compression experiments at the National Ignition Facility (NIF) to probe the IM transition up to 600 GPa at temperatures ranging from 900 K to 1600 K. The experiments were carried out using 168 laser beams to deliver up to 300 kJ of ultraviolet light that drove a near-isentropic reverberation compression of a cryogenic liquid deuterium sample. We adjusted the time dependence of the laser delivery (pulse shape) to control the compression sequence imposed on the sample as a function of time. Line-imaging Doppler velocimetry recorded both the compression history and the evolution of the optical properties of the D2 sample during the nanosecond compression process, using a probe laser operating at 660 nm.

In our experimental setup, the fluid deuterium sample is sandwiched between a copper piston and a LiF window and is viewed through the window by the diagnostic (Fig. 1). The upper half of the view shows signal from the light reflected at the D2-LiF interface where a 100-nm-thick aluminum film was deposited (position >0 μm in top panels of Fig. 1, B and C). The lower half shows the signal from light reflected initially at the piston surface (double-passed through the transparent sample layer). Because the two reflecting interfaces move differently, the two halves of the field of view display different apparent velocities (different fringe phases) until the time when the light intensity on the sample side reaches a minimum. At later times, the apparent velocity on the sample side matches that of the Al-LiF interface (common fringe phase), indicating that the optical reflection has shifted from the piston surface to the D2-LiF interface.

Fig. 1 Schematic of target and experiment together with raw data.

(A) A planar sample layer of liquid deuterium, 31 μm thick, contained between a 70-μm-thick copper piston and a 500-μm-thick LiF window, is mounted onto the side of a hohlraum (brown in bottom sketch), driven with the NIF laser (blue arrows), and diagnosed with a line-imaging Doppler velocity interferometer (sensor positioned on right). (B) Example data record from experiment N150914-2. Fringe amplitude encodes reflectivity and fringe phase is proportional to the Doppler shift of the reflected light (piston and window interface velocities); the frame below shows apparent velocity signals extracted from the fringe phase and corresponding simulated velocities. At times 30 < t < 31 ns, simulations (black dashed curve) with the extrapolated Dewaele et al. (36) refractive index fit do not match the observations and require a corrected index (green dashed curve) to match observations; additional frames below show pressure, temperature, and density at a point in the center of the sample estimated from simulations matched to the velocity data based on three different EOS models for deuterium. (C) Details of the information presented in (B) with magnified time axis. Vertical gray lines denote the transition from partially transparent to opaque; vertical magenta lines indicate the time when the reflectivity at the D/LiF interface exceeds 30%. The normalized reflectance shows independent measurements from the two detectors.

The copper piston (lower half) started moving near t = 10 ns when an initial weak shock was transmitted into the sample layer. We controlled the first shock strength for each experiment in order to follow different isentropic compression paths. The first shock strengths varied from 1.8 GPa to 3.4 GPa (table S1). After the first shock crossed the sample layer, it reverberated against the LiF window (upper half, 16 ns) and continued to reverberate between the piston and the window while the sample layer was compressed. After several reverberations, both the piston and window interface approached a common apparent velocity by 27 ns. At this point, the sample was compressed to conditions estimated to be near density ρ ≈ 0.8 g/cm3, P ≈ 20 to 30 GPa, and T ≈ 600 to 900 K and was observed to be fully transparent. A second pressure wave arrived at the sample layer at 30 ns and initiated a second set of reverberations, further pressurizing the sample to nearly 600 GPa in four experiments and to 215 GPa in one experiment. The duration of this second set of reverberations was shorter than the first, accomplishing much of the pressure increase in less than 3 ns. The transition from optically transparent to strongly reflecting occurred during the second set of reverberations and is attributed to the IM transition in deuterium.

The thermodynamic path of the sample was inferred from hydrodynamic simulations constrained by the measured interface velocities (31), similar to previous work (23). Different equation of state (EOS) models for deuterium (3234) resulted in calculated pressures that are nearly the same to within 1% independent of the EOS model. We estimate that the pressure along the compression path is accurate to ±3 GPa (measurement error of the velocities), enabling determination of the metallization pressure to <3% accuracy (after accounting for measurement error in the reflectance). The EOS models compare well with recent benchmarking experiments (13, 30, 35). However, none of the current EOS models represent the IM transition as a first-order phase transition (i.e., with a density jump and latent heat), and the range of temperature predictions among EOS models is large, leading to uncertainties of as much as ±260 K near the IM transition. Density differs by less than ±6% among the models.

Several optical signatures are associated with the transition from transparent to reflecting (Fig. 2). While the sample layer remained partially transparent, we determined the absorption coefficient up to a magnitude of about 1 μm−1 (Fig. 2B), when the optical depth of the sample layer exceeded ~2 and the layer became opaque. When the sample was opaque, light continued to be returned from the target because of the reflection from the D2-LiF interface, with reflectance near 10%. While the sample was still partially transparent, we observed changes in the real part of the index of refraction that are consistent with band gap closure. We extracted the real part of the index of refraction (Fig. 2C) by fitting to the apparent velocity of the piston (observed through the deuterium sample) self-consistently with our hydrodynamic simulation (31) (Fig. 1). The real part of the index agrees closely with that of insulating hydrogen at lower pressure (36) but deviates from the low-pressure linear density dependence as the band gap decreases.

Fig. 2 Optical signatures of the insulator-metal transition.

Curves in all frames are matched for the five experiments following isentropes that correspond to the colored P-T bands in Fig. 3. (A) Reflectivity at the D2-LiF interface as a function of pressure, after the D2 layer becomes opaque. Inset: Raw data from experiment N171105-3, showing a sharp reflectivity jump just before t = 32 ns. (B) Absorption coefficient; legend indicates experiment number and T along isentrope near P = 200 GPa. Colors and line types apply to all panels. (C) Index of refraction from simulations matched to the observed Doppler shifts and, for comparison, extrapolation of the Dewaele et al. (36) refractive index fit to higher density (solid gray curve). (D) For P < 150 GPa, optical (AC) conductivity as extracted by combining the data in (B) and (C) (symbols with colors matched to curves) and corresponding Lorentz model fits (curves); for P > 150 GPa, the DC conductivity inferred from the reflectivity data in (A) and the Smith-Drude model with τ = 0.075 fs (31). Error bars in (A) to (C) represent SD of multiple measurements collected in a set of velocity bins and mapped to the pressure scale.

The gap energy, which we estimated from the refractive index (31), approaches ~2 eV when the sample layer becomes opaque, consistent with the probe photon energy of 1.9 eV. Extrapolation (linear in density) suggests that for the fluid deuterium states achieved in our study, the band gap closes in the range 200 GPa < P < 250 GPa (31) depending on the experiment (fig. S22B). The ~10% reflectance we observed when the sample becomes opaque (Fig. 2A) is consistent with the expected reflectivity of the pressurized interface between materials of different indices of refraction, nD2 ≈ 2.8 and nLiF ≈ 1.5, and represents a minimum reflectivity of insulating deuterium in this experiment. Further pressurization reveals a rapid increase in reflectivity at the D2-LiF interface eventually reaching a saturation level near 55%. Reflectivity of ~30% at the D2-LiF interface corresponds to the minimum metallic electrical conductivity σDC ≈ 2000 S/cm (11, 37); values exceeding this indicate metallic behavior (31). From this measurement, we inferred that the IM transition occurs in the pressure range between approximately 150 GPa and 250 GPa. Although we did not observe a discontinuous change in reflectivity through this range for three of our experiments, finite temporal resolution in the measurements may have obscured a sharp transition; one experiment (Fig. 2A, magenta dashed curves and inset) recorded at higher time resolution revealed a sharp reflectivity increase. In all cases, the reflectivity increase steepened noticeably near 200 GPa. Of the four experiments that reached 600 GPa peak pressure, we recorded some of the reflectivity data during pressure relaxation; unlike prior experiments (23), there is no evidence for different reflectivity signals during increasing (dP/dt > 0) and decreasing (dP/dt < 0) pressurization.

We can fit our results to simple models of the evolution of the optical properties through the transparent, optically absorbing, and optically reflecting regimes. The absorption has a steep pressure dependence and increases with temperature (Fig. 2B), most likely as a result of disorder in the material. In the partially transparent regime, we extracted the optical conductivity (Fig. 2D, symbols) directly from our data, using the expression σ(ω) = nαc (Gaussian units) combining n (Fig. 2C) and the absorption coefficient α (Fig. 2B); here, c is the speed of light. A Lorentz optical model incorporating a density-dependent oscillator frequency matches these data (Fig. 2D, curves below 150 GPa). We estimated the DC conductivity above the transition (Fig. 2D, P > 150 GPa) with the Smith-Drude model (21, 38) evaluated with a fixed relaxation time τ = 0.075 fs and variable backscatter parameter matched to the optical reflectivity (Fig. 2A and fig. S25). The conductivities determined here exhibit trends similar to those calculated theoretically (14).

We plotted the optical absorption and reflectivity signatures along the calculated temperature versus pressure (T-P) paths extracted from the simulation models (Fig. 3), referred to by their T near 200 GPa (table S1). Our observations of the onset of optical absorption (Fig. 3, open circles) are in good agreement with the results of McWilliams et al. (21) and Knudson et al. (23) (Fig. 3, black dashed line). These observations, along with the extrapolated band gap energy as a function of P (fig. S22B), imply that the band gap remains finite leading up to the IM transition. These conclusions differ from those of several DAC measurements performed at similar conditions (1820, 22). The DAC measurements using laser heating produced plateaus in temperature with increasing laser power that were interpreted as a signature of the metallization transition (1820, 22). However, the heating plateaus in the static experiments are better correlated with the onset of absorption in our experiment rather than metallization, consistent with alternative interpretations of those data (21, 23, 39). The observation of absorption well below the point of band gap closure is also found in the solid at lower temperatures (40, 41).

Fig. 3 Phase diagram of H2/D2 at high P-T conditions.

Present results: Threshold where optical absorption coefficient exceeds ~1 μm−1 at 660 nm and the band gap is ~2 eV (black open circles connected by thick dashed line); points where the D/LiF interface reflectivity exceeds R = 30% (black solid circles), corresponding to the minimum metallic conductivity σ Embedded Image2 × 103 S/cm; vertical error bars are systematic (see below); horizontal error bars are estimated from a systematic component (~1% of P) and random uncertainties in the velocity, reflectivity, and absorption data (~6 GPa). The thick black curve connects these points to the metallization transition, σ Embedded Image2 × 103 S/cm, identified by Weir et al. (solid black triangle, error bar estimated from systematic and random uncertainties) (11). The colored solid curves and associated bands show the compression paths of the present experiments; shading indicates estimated systematic uncertainty used to estimate the error bars in T. Previous experimental results on H2: Ohta et al. (×) (19) and Dzyabura et al. (+) (18), both from heating curve analyses of laser-heated DACs; Zaghoo et al. (open pentagons) (20) from absorption and reflectance in laser-heated DAC; McWilliams et al. (open triangles) (21) determination of the onset of absorption from transient DAC optical transmission measurements; Zaghoo and Silvera (solid pentagons) (22) reflectance saturation data; melting measurements of Zha et al. (dotted red curve) (24). Previous results on D2: Knudson et al. (open squares) (23) absorption onset for 532-nm wavelength; Knudson et al. (inverted gray triangles) (23) reported IM transition and revised with our interpretation (inverted black-edged triangles); vertical error bar estimates are explained in (31). Selected theoretical curves reported by Pierleoni et al. (16) and Knudson et al. (23) are shown, including the CEIMC calculation for deuterium (dashed green curve) and DFT calculations with quantum corrections for the ions [vdW-DF1 for deuterium (dot-dashed blue curve), vdW-DF2 for deuterium (dark blue curve), and PBE for hydrogen (dashed orange curve)].

We found saturation of the reflectivity above ~280 GPa in the four experiments carried out to the highest pressures. In these datasets, the transition temperature exhibited a clear trend decreasing with pressure by ~20 K/GPa. The lowest observation at T ~ 1100 K showed the transition occurring at 221 GPa. One experiment at even lower T ~ 940 K did not reveal reflectivity greater than 10% to the maximum P ~ 215 GPa, but does not rule out the possibility of a transition at higher P. Pulsed-heating DAC experiments on H2 (20, 22) found reflectivity saturation at temperatures similar to our experiments and at pressures that were lower by ~20 GPa, which may be consistent with the expected isotope effect.

The steep increase in reflectivity with pressure that we observe near 200 GPa contrasts with the interpretation of the ramp compression experiment on deuterium carried out at the Z facility (23). Although the onset of optical absorption is consistent with our work, the subsequent weak reflectivity followed by jumps near 300 GPa (attributed to the IM transition) occurred at higher pressure than observed here and in other later studies (20, 22), whereas the low (<2%) reflectivity of the D2-LiF interface recorded at intermediate conditions is not consistent with either insulating or semiconducting deuterium and LiF under pressure (31, 36, 42, 43). Our data indicate onset of the IM transition at P ~ 200 GPa; the optical reflectivity saturates to a constant value of ~55% near 280 GPa and remains stable over hundreds of GPa, similar to the pressures where high reflectivity is displayed in the Z experiments. This shows that both experiments are probing similar states at onset and completion of the IM transition, but not at intermediate conditions.

We propose that the different results are related to the time scale of the Z experiments being two orders of magnitude longer, allowing turbulent lateral flows within the sample layer to be established during the observations. These effects lead to a different interpretation of the reflectivity jumps observed in the Z data, correlating these with completion rather than onset of the IM transformation (31). This requires a correction of the inferred transition temperatures from the Z-machine to lower values (table S3), owing to the latent heat of the IM transition. Although there are uncertainties in the temperature estimates in both experiments, we expect that those uncertainties are accentuated by the longer time scales, which give rise to multiple mechanisms of heat transport in the Z experiments. The much shorter time scales in our experiments preclude these from occurring, so that the temperature estimates for our experiments depend primarily on the EOS models in the molecular fluid phase.

We interpreted the onset of reflectivity above 10% as the beginning of pressure-induced molecular dissociation associated with the IM transition. The extent and P-T range of the IM transition are in approximate agreement with the DFT-based molecular dynamics calculations using the van der Waals (vdW-DF1) exchange-correlation functional (44) reported in Knudson et al. (23). Our observations and analyses are also consistent with the coupled electron-ion Monte Carlo method (CEIMC) calculations of Pierleoni et al. (16) and with the quantum Monte Carlo calculations of Mazzola et al. (17). They are about 100 GPa higher than DFT calculations based on the Perdew-Burke-Ernzerhof (45) (PBE) exchange-correlation functional (15, 29) and about 50 GPa lower than DFT calculations based on the van der Waals vdW-DF2 functional (23, 46). In the saturation regime, the estimated σDC ≈ 104 S/cm is in good agreement with the recent estimates from lower-pressure experiments (22) and with calculations (14).

Our interpretation of the Z experiments does not alter the conclusion that the abrupt reflectivity jumps observed in those experiments are evidence of a first-order IM transition. The revised T ≈ 700 K is well below the predicted critical-point temperature TCP, whereas one of our experiments provides evidence for first-order behavior up to 1100 K. The extrapolated band gap energies (linear in density; fig. S22B) reach closure at higher P than the corresponding observed transition P, indicating that the gap closes nonlinearly and could indicate first-order behavior at temperatures as high as 1640 K. Therefore, although TCP is not yet precisely identified, it is bounded in the range 3000 K > TCP > 1100 K, as indicated by our data and by continuous transformations observed in prior experiments to higher temperature (11).

Our revision of the IM transition data from the Z experiments produces points that lie close to and even below previous melting-line studies on hydrogen (24, 26). A straight line connecting our data to the revised Z data has a slope of –5 K/GPa. This invites speculation as to whether a thermodynamic triple point with coexisting crystalline solid, insulating fluid, and liquid metal phases is located near 600 K and 300 GPa. If so, at higher pressures the insulating crystalline solid would transform directly to the liquid metal. Because the melting line of deuterium has not been determined and because quantum effects are important, the existence and location of such a triple point remains an open question.

Demixing in dense H-He fluid mixtures, an important process expected to occur inside giant planets (47, 48), is closely connected with the IM transition (49). Recent state-of-the-art calculations of H-He demixing are all based on ab initio calculations with increasing levels of sophistication (4955). The two most recent calculations of H and He EOS for planetary models are based on DFT molecular dynamics (56, 57) with the PBE exchange-correlation functional, and until this year, ab initio–based demixing studies (53, 54) were also based on PBE. The emerging theoretical (16, 17) and experimental (23) evidence that PBE underestimates the IM transition pressure motivated Schöttler and Redmer (55) to examine H-He demixing with the vdW-DF1 functional. They showed a clear shift of the demixing boundary to higher pressure and lower temperature relative to PBE-based calculations. Thus, although the first-order IM transition occurs at much lower temperature than the Jupiter and Saturn isentropes, it plays an important role as a benchmarking feature to validate the functional on which the H-He demixing calculations are based. Our data suggest that the vdW-DF1 functional is the current best choice.

Supplementary Materials

www.sciencemag.org/content/361/6403/677/suppl/DC1

Materials and Methods

Supplementary Text

Figs. S1 to S34

Tables S1 to S3

References (58108)

References and Notes

  1. See supplementary materials.
Acknowledgments: We thank J. Kroll, the target fabrication team at LLNL, and the NIF operations crew for experimental support. We thank the anonymous referees for extensive and detailed comments and questions that resulted in an improved manuscript. Funding: This work was performed under the auspices of the U.S. Department of Energy by LLNL under contract DE-AC52-07NA27344, Lawrence Livermore National Security, LLC. This material is based on work supported by the Department of Energy National Nuclear Security Administration (DOE/NNSA) under grant DE-NA0001944, the University of Rochester, and the New York State Energy Research and Development Authority. Also supported by EPSRC under grant Ep/P024513/1 (R.S.M.); the Army Research Office (56122-CH-H), the National Natural Science Foundation of China (21473211), and the Chinese Academy of Science (YZ201524) (A.F.G.); DOE/NNSA (including DE-NA0003607) and the University of California (R.J.); and DOE/NNSA (DE-NA0002006, CDAC) (R.J.H.). Author contributions: R.S.M., R.J., R.J.H., G.W.C., P.M.C., M.M., S.B., P.L., J.R.R., A.F.G., and J.H.E. conceived the experiments; J.L.P., N.B.M., P.M.C., M.M., D.E.F., and S.B. designed the experiments; P.M.C., M.M., S.L.P., S.B., D.E.F., and A.F.G. executed the experiments; P.M.C., S.B., M.M., and R.S.M. analyzed the data and performed post-shot simulations; P.M.C., R.J.H., R.S.M., M.M., and R.J. wrote the manuscript; and all authors reviewed and discussed the manuscript during preparation. Competing interests: All authors declare no competing interests. Data and materials availability: All data are available in the manuscript or the supplementary materials.
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