The Hugoniot and chemistry of ablator plastic below 100 GPa

Transcription

1 The Hugoniot and chemistry of ablator plastic below 100 GPa M. C. Akin, D. E. Fratanduono, and R. Chau Lawrence Livermore National Laboratory, Livermore, CA (Dated: January 7, 2016) The equation of state (EOS) of glow discharge polymer (GDP) was measured to high precision using the two-stage light gas gun at Lawrence Livermore National Laboratory at pressures up to 70 GPa. Both absolute measurements and impedance matching techniques were used to determine the principal and secondary Hugoniots. GDP likely reacts at about 30 GPa, demonstrated by specific emission at 450 nm coupled with changes to the Hugoniot and reshock points. As a result of these reactions, the shock pressure in GDP evolves in time, leading to a possible decrease in pressure as compression increases, or negative compressibility, and causing complex pressure profiles within the plastic. Velocity wave profile variation was observed as a function of position on each shot, suggesting some internal variation of GDP may be present, which would be consistent with previous observations. The complex temporal and possibly structural evolution of GDP under shock compression suggests that calculations of compression and pressure based upon bulk or mean measurements may lead to artificially low pressures and high compressions. Evidence for this includes a large shift in calculating reshock pressures based on the reflected Hugoniot. These changes also suggest other degradation mechanisms for inertial confinement fusion (ICF) implosions. 6 I. INTRODUCTION The shock responses of plastics are increasingly important as plastics are used in a growing number of applications, including additively manufactured parts, material components, and laser ablators.[1] To understand these materials, shock physicists should consider the underlying polymer chemistry, which is a complex field unto itself. Due to this complexity, a practical approach is to consider the shock behavior of classes of plastics. A sample of seven relevant polymer Hugoniots[2] are shown in Figure 1. Most of the polymer Hugoniots overlap each other at small compressions but separate into two distinct classes as the compression increases. The first class including epoxy, polymethylmethacrylate (PMMA), polyethylene (PE), and high-density polyethylene (HDPE) have smooth Hugoniots in the region of interest. The second class, polyimide, polystyrene (PS), and polycarbonate, undergo a chemical-physical transition around GPa.[2, 3] This transition bears some resemblance to transitions seen among simple unsaturated hydrocarbons and related materials, e.g., benzene, graphite, fullerenes, and dienes.[3 5] Direct measurement of a specific plastic is required for high-precision studies because there exist enough variations in the plastics Hugoniots. This is the case with glow-discharge polymer (GDP) a man-made amorphous polymer of high strength, which has been characterized extensively elsewhere, [6 19] and is used heavily at the National Ignition Facility (NIF)[20 25] and on the akin1@llnl.gov LLNL-JRNL DRAFT. Lawrence Livermore National Laboratory is operated by Lawrence Livermore National Security, LLC, for the U.S. Department of Energy, National Nuclear Security Administration under Contract DE-AC52-07NA Pressure (GPa) FIG. 1: The calculated primary Hugoniot (black circles) and reshock points (grey circles) of GDP below 100 GPa, compared with representative plastics and previous data by Barrios et al. (red circles).[32] The dotted black lines connect each reshock point to its corresponding state on the primary Hugoniot. Alternate quartz standards (Hamel and Knudson/Desjarlais data[33, 35]) were used for impedance matching to show two alternate models; error bars have been left off of these points for greater clarity. Omega laser. [15, 23, 26 30] Little distinction between GDP and other plastics is shown in the extant literature [5, 31] with GDP often referred to as CH, the same term used for polystyrene. However, the stoichiometry of GDP is CH 1.36 O.0.08, intermediate to polystyrene ((CH) n ) and polyethylene ((CH 2 ) n ). To avoid confusion and to emphasize the specific nature of each material,

2 we will avoid this terminology, using GDP, PS, and PE instead. Barrios et al. [32] measured the Hugoniot of GDP at pressures P > 100 GPa. Their laser-based impedance matching technique relied upon a reflective shock in quartz and GDP and thus precluded the collection of Hugoniot data at P <100 GPa. These data are sensitive to the choice of quartz standard chosen, with current models favoring the Knudson standard.[33] A change in the quartz standard can significantly shift Barrios s measured Hugoniot of GDP, as shown in Figure 1. As a result, predictive models of NIF shots relying upon the Hugoniot as measured by Barrios and extrapolated to pressures less than 100 GPa perform inadequately, requiring factors of 2-5 to be applied to, e.g., capsule surface roughness, to match the data[23, 24]. Substitution of other plastics Hugoniots, such as PS or PE, does not explain the behavior of GDP or improve the extrapolations.[32, 34] Direct measurement of the Hugoniot and reshock points in this region are important because many plastics and hydrocarbons, including PS (the standard substitute for GDP [32, 35]) undergo pressure-induced chemical reactions in the GPa region that lead to volume collapses, changes in sound speed, changes in compressibility, and variation in reshock properties. It is well established that hydrocarbons and carbohydrates under similar conditions have shown the formation of C-rich particles and other products such as H 2, CO 2, or H 2 O[36 42] which in a plastic ablator could lead to undesired local variation in density capable of potentially roughening the shock front. These changes directly impact the compression path and efficiency of the ablator/target in inertial confinement fusion (ICF) implosions. For example, one of NIF s shock patterns requires an initial compression to GPa, which propagates from the outer surface of the spherical GDP target toward the center, which is filled with deuterium-tritium (DT) fuel.[43, 44] When this first shock interacts with the DT, the GDP releases to GPa before dropping further. The GDP nearest the DT fuel remains in this shock-released state for at least 4 ns, until the second shock arrives. Any reaction faster than this time may be a matter of concern, especially if it produces high-density nano diamonds, graphenes, or mixed phases such as melt. In addition to seeding spatial irregularities and fuel instabilities, such reactions generate a new distinct material, which would require an adjusted Hugoniot for proper convergence. To provide insight into the observed performance of GDP, we report measurements of the principal Hugoniot at < 100 GPa and the associated reshock points using a two-stage light gas gun. The Hugoniot measurements were supplemented by a simultaneous pyrometry/emission measurement when possible in the hope of gaining either chemical or thermal information. We found that the chemistry of GDP plays a crucial role in this range, where it alters the GDP structure and result ing reshock Hugoniot. We find that the GDP Hugoniot at low pressure is softer than most other plastics, but above 30 GPa, is intermediate, indicating a phase change. Extrapolation of our data agrees best with the original Barrios data, [32] not with the modified Knudsonstandardized data[35] currently in use. However, extrapolation from the high pressure phase is based on only two points. II. METHODS A. Sample Preparation GDP samples were purpose-grown as a single batch by General Atomics of San Diego, CA for this experiment. Prior to being shot, the samples were characterized for density (ρ), overall flatness, local flatness, surface structure/machining damage, porosity, response to vacuum, pressure dependence of refractive index (used for photon Doppler velocimetry, or PDV, correction factors), composition, chemical bonding, mass gain during handling, and chemical changes during handling. The provided GDP samples were found to be similar to those used in NIF capsules, though significantly rougher due to machining of the disk, and of slightly higher mean density. While characterizing the GDP samples, we observed unusual variations in the behavior of the GDP. The details of the variations uncovered during sample characterization such as the effect of low-grade vacuum exposure and work damage caused by machining are described in detail in a related technical report [45]. For the purposes of this study and the Hugoniot calculations, we found that changes to the density have the greatest impact on the results. Mass changes in bulk GDP prior to shooting were about 3%; infrared spectra indicate that most of this additional mass is from oxygen uptake. Likely sources of such oxygen are atmospheric water and oxygen. Scanning electron microscopy (SEM) images indicate extreme work damage to the machined surface [45], which shows porelike structures 1-3 µm in diameter. In comparison, the as-grown side is very smooth. Based on the SEM images, it appears as though small regions of higher strength were torn out of a weaker matrix by the machining. Some work-melting is also present. The distribution of oxygen within the GDP could not be measured with our techniques, but given the extreme roughness of the machined surface, we entertained the possibility that a density gradient was created in the GDP prior to the experiment. However, the specifications for density gradation in as-grown GDP are less than 1%; General Atomics regularly grows GDP with specific changes in density for NIF that meets this specification. Gases comparable to O 2, such as N 2, readily diffuse through GDP.[14, 16] Therefore we assume in our analysis that the observed density increase is homogeneous throughout the sample when calculating compres-

3 To detectors To radiometer Al baseplate PDV LiF window GDP flyer FIG. 2: Conceptual diagram of the target as viewed from the side (not to scale). The Al impactor arrives from the right, impacting on the 32 mm diameter Al baseplate. PDV probes (dark gray) and visible fibers (rainbow) collect light through 5 mm thick LiF windows. This allows direct measurement of the Al baseplate and GDP surface motion, through PDV, and GDP emission through the visible fibers. sion on the Hugoniot, and that no significant internal density gradient occurs prior to the shot. B. Target Design Unlike previous laser based experiments, we used a two-stage light gas gun for these measurements as it provides flat supported shocks with minimal uncertainty, and has sufficient experimental lifetimes to observe chemistry in the plastic. The experiment and target design is based on a variation on the standard top hat design used previously in precision equation of state (EOS) experiments on gas guns.[48, 49] Adjustments were made for the thickness h of the GDP samples, which were 92 µm instead of the typical 1-5 mm used in previous experiments. A schematic of the experiments is shown in Figure 2. To simplify the analysis, we used Al impactors in all of the experiments so that the impactor and baseplate were impedance matched. To avoid the use of glue, the GDP was held in the center of the Al baseplate and compressed by a LiF window under an o-ring. For some targets, the GDP was coated with Ag to provide a reflective layer. The as-grown side of the sample, which is much smoother than the machined side, was oriented toward the Al baseplate. This was done both to eliminate possible variations in shock structure due to mechanicallyinduced pores, and to orient the Ag coating, if present, toward the PDV probe. The gas gun launches an Al impactor at a target. The target comprises a 32 mm diameter diamond turned Al 1100 baseplate with total thickness variation <2 µm, a 5.75 mm diameter GDP sample, and LiF windows Upon impact, a shock is launched, which travels through the baseplate, GDP, and LiF. PDV measures the breakout times and particle velocities at the Al/LiF, Al/GDP, and the GDP/LiF interfaces, which are used to find the transit time and shock velocity in the GDP.[49] Because the sample is backed by a higher impedance LiF window, when the shock arrives at the GDP/LiF interface a reshock state in the GDP occurs. This state is found by impedance matching to the LiF window using U p as measured by velocimetry. Due to the small size of the sample, custom built PDV probes were made by National Securities Technologies using a pre-existing probe design for gas gun experiments and used on the GDP samples. These probes incorporate seven radiometry fibers with the central six PDV fibers and a focal lens, which enabled us to obtain visible emission data of the GDP during these shots. The location of each beam spot and its shape were measured at the baseplate/gdp or baseplate/lif surface using an Ophir/Spiricon Scor-20 or Gras-20 camera with a Mitutoyo focusing lens, enabling mapping at the ± 1 µm level. The radiometry fibers were fed to a six-channel pyrometer using 923 model photomultiplier tubes (PMTs) on Tektronix 684 oscilloscopes. Color filters were used for the radiometer to chop the signal into 80nm wide bands spaced roughly 50 nm apart. Neutral density filters were applied only to the red channels as the Ag coating and an anti-reflection lens coating (to enhance PDV) provided sufficient filtering. The anti-reflective coating filtered nearly all green light, so signals from the 500 and 550 nm pyrometry channels are not shown. Six additional LiF windows were placed in a ring around the central window to measure the Al baseplate motion (See Figure 2). C. Determination of transit times, shock velocities, and particle velocities The shock velocity U s in GDP was determined by measuring transit time through the sample using two methods. The transparency of the GDP allowed, in some cases, for us to observe the shock breakout at the Al/GDP interface and the shock breakout at the GDP/LiF interface on a single PDV channel by looking at the changes in particle velocity (U p ), mean power, and peak-to-peak amplitude. In these cases, the uncertainty in transit time is less than 100 ps for a single channel. U s was then calculated by dividing the measured GDP sample thickness by measured shock transit time. When this was not possible, tilt and transit times were determined by mapping shock breakout times t Al at the Al baseplate and the GDP surface. An initial least squares fit to a plane, t Al = ax + by + d, is chosen using three of the available baseplate (x, y, t) points. This planar fit is then refined to a J 0 Bessel function with radius of mm on the baseplate. Transit time is calculated by fitting the GDP breakout times to the 3

4 4 TABLE I: Initial thicknesses h and densities ρ 0 of GDP samples, including standard deviation of measurements (σ h ), which is used as an estimator of flatness and cupping. h indicates total uncertainty, which includes total instrument uncertainty of 0.4 µm, with 0.04 µm repeatability. These measurements reflect the effects of aging and water uptake pear to affect the correction factor, a determination of the U p in shocked GDP through PDV measurement was difficult for each shot. We found the Hugoniot calculated from U s to be more robust. D. Calculation of reshock points shot h σ h h ρ 0 ρ 0 U flyer P Al tilt µm µm µm g/cm 3 g/cm 3 km/s GPa deg baseplate function plus a fixed time t. Directly fitting the Bessel function to the observed data while skipping the planar fit was found to result in poorly constrained functions, and so was avoided. This method was compared to the more traditional tilt measurement method of Mitchell and Nellis[48] and found to closely agree. Tilt was found to be approximately 1 degree on all shots, with the exception of the slowest shot, where it was 5 degrees (see Table I). The tilt was corrected for in U s and U p ; in the case of the slowest shot, which had the greatest correction, the correction is approximately 0.4%. This fitting method provided improved means to measure transit times. Uncertainties in observed times are 200 ps or less for a single channel in these cases. Uncertainties in transit times calculated through the fitting method are estimated by: 1) testing all three-point combinations chosen for the initial planar fit, 2) fitting the Bessel function to each of these combinations while excluding a single baseplate (x, y, t) point, and 3) fitting the GDP breakout times to each of these Bessel functions while excluding a single GDP (x, y, t) point. The standard deviation of the resulting times and shock speeds is used as the uncertainty estimator. Impedance matching to the measured U s and impactor velocity through the Rankine-Hugoniot equations was used to calculate U p. To do so, we used LiF Hugoniot of Trunin[47] the Al Hugoniot of Mitchell and Nellis[48, 50, 51], and the Al release of SESAME 3720[52]. The Rankine-Hugoniot equations were also used to determine pressure, energy, and density (compression) as usual. Alternatively, the Hugoniot can be extracted from the U p measured from the PDV velocity profiles at the Al/GDP interface. This requires knowing the PDV correction factor for GDP. We determined the PDV correction factor for GDP to be 1.02 ±0.01 at 1550 nm based on measurements made at the lowest pressure. As we discuss in detail in Section IV, we observed significant variation and acceleration in the U p of shocked GDP. Combined with chemical changes in the GDP that ap Upon reshock into the LiF window the measurement position changed, and the PDV correction factor for GDP was no longer relevant. Thus reshock pressures were determined using PDV measurements at the GDP/LiF interface. The measured U p was impedance matched to the LiF Hugoniot and the calculated shock states for GDP. We used a correction factor of for the LiF, based on measurements made in this study, and comparable to the factor determined by Jensen et al.[46] III. RESULTS A. The Principal Hugoniot Because U p was observed to vary with time in our experiments, the GDP data presented here were determined using the U s calculated from the transit time measurements. Results for the Hugoniot and reshock are given in Table II. Pressure P and compression η of the shocked and reshocked states are shown in Figure 1. Due to the differences in initial density ρ 0 and to mass changes caused by oxygen uptake, the Hugoniot of GDP is shown in P-η space rather than P-ρ space. Figure 3 shows the U s -U p relationship, with U p determined through impedance matching. Least-squares fitting was used to determine the Hugoniot relations for single phase and two-phase models for GDP below 100 GPa. The single phase model uses a unique U s -U p relationship that spans the measured date, while the two-phase model uses two U s -U p relationships due to phase changes along the Hugoniot. The resulting U s -U p coefficients for each of these models are given in the first section of Table III. There appears to be a discontinuity in the U s -U p relation near U s = 6 km/s, indicating the existence of a phase boundary or chemical reaction at 20 GPa similar to that seen in PS. A twophase model incorporating this break extrapolates well to the high-pressure data. Extrapolation of the single phase model to high pressures significantly overestimates the shock speed compared to Barrios et al. s measurements. These gas gun data were combined with existing data from Barrios et al.,[32] Knudson and Desjarlais,[33] and Hamel et al.,[35] to calculate the Hugoniot assuming a transition at 20 GPa. These models are shown in the final section of Table III. Insufficient data exist to create a Hugoniot relation between 2.5 < U p < 3.6 km/s.

5 TABLE II: Calculated shock and reshock pressures and compression in GDP. P 1 and η 1 are the pressure and compression of the first shock, respectively. P 2 and η 2 are the reshock values. Reshock pressures and associated compressions were determined through impedance matching mean U p values to the LiF Hugoniot.[47] Standard deviations resulting from data are shown in parentheses. Note: η 2,tot = ρ 2 /ρ 0. PDV measurements show initial U p of 3.54 km/s. PDV measurements indicate a velocity of 4.56 km/s. 5 Shot U s,1 U p,1 P 1 η 1 U p,2 U s,2 P 2 η 2,tot η 2 km/s km/s GPa km/s km/s GPa (.03) (.003) 6.53 (.05) (.007) (.017) 10.25(.14) (.03) (.003) (.05) 1.882(.008) 9.53(.16) 1.652(.014).930 (.015) 9.99 (.3) 16.3(.3) (.005) (.22) 2.47(.02) 14.0 (.5) 1.86 (.08) (0.004) 9.6 (.5) 27.66(.09) (.011) (.034) (.009) (.25) 1.911(.012) 2.63(.02) 11.06(.11) 59.9(.6) (.007) (.26) 5.11 (.05) 54.1 (1.5) 2.15 (.10) 3.76(.08) 11.2(.8) (3.0) (.06) TABLE III: U s -U p relationships for GDP. Coefficients for the equation U s = a + bu p are given in the table below. The Hugioniot relation was calculated as a single phase and a two-phase model for these data. Extrapolation of the single phase model significantly overestimates the high-pressure data from Barrios et al.[32]; weighting the fit by uncertainty of the point worsened this effect. Recalculating the Barrios data using different quartz standards as in Hamel et al.[35] and Knudson and Desjarlais[33] does not significantly improve the fit. Separating the data from this study into two phases above and below 30 GPa leads to a much better U s -U p that extrapolates well to the Barrios data, regardless of impedance standard. Fits given below are unweighted, with one exception: the best fit is to the original data from Barrios et al., for which we include a fit weighted by the uncertainty of each point. model a b comments single phase, this study 1.96± ±0.08 U p <5.2 two phase, this study >30 GPa 2.97± ±0.18 U p >3.6 <30 GPa 2.70± ±0.06 U p <2.5 Barrios data, combined with this data for U p > 3 Original 2.96± ±0.007 unweighted Original 2.90± ±0.003 weighted Hamel et al. 3.53± ±0.016 unweighted Knudson and Desjarlais 3.30± ±0.011 unweighted B. Spectral emission upon compression We gathered visible pyrometry data simultaneously with the PDV transit time measurements. Although the original intention was to obtain temperature (T) data for a complete equation of state, this was only possible on one shot. Instead, we obtained pyrometric data (Figure 4) that suggest the observed transition may be chemical in nature. For shot 4090, temperature was estimated by color fitting to be 1750K. Temperature estimates were not available for other shots due either to poor quality of data (e.g., the lowest pressure shot was too cold to emit at a detectable level) or because emission signals were too complicated. Of the remaining pyrometry signals, the most valuable is the emission signal from shot 4093, shown in Figure 4, which was shocked to 30 GPa. Initially this signal shows a rapid increase in emission across all wavelengths, peaking after 3-4 ns. Following this peak, the 450 nm channel peaks again, to a value more intense than the original thermal signal. This bright blue emission is clearly non-thermal, with a different temporal signature, and is consistent with chemical emission processes seen in plastics at comparable pressures and temperatures[53]. The onset begins well before the shock has transited the plastic, and peaks within 10 ns. Shock transit time was 12 ns. Because pyrometry and velocimetry systems were not cross-timed, it is unclear if the timings are a coincidence. These emission data, combined with the break in the Hugoniot and changes in the reshock properties, all indicate that a phase transition occurs at this pressure, similar to that observed in PS, PE, and polyimide[3] and calculated for PS[5]. It is also consistent with the predicted fragmentation onset in PE at densities of g/cm 3. [54] C. Reshock Reshock points are shown in Fig. 1 as a grey circle. Each is connected by a dotted line to a black dot,

6 6-0.7 transition region single phase model 2 phase model, low 2 phase model, high photosignal (mv) nm nm 700 nm 400 nm 10 time (ns) offscale FIG. 4: The self emission of GDP at 30 GPa (shot 4093), corrected for filtering. Following an initial emission upon shock, a second, brighter emission is seen in the 450 nm band. Note that the photomultipliers (PMT) and PDV system do not have synchronized time FIG. 3: The single phase (brown) and two-phase (green, blue) U s -U p models of GDP. The single-phase model extrapolates poorly to existing data above 100 GPa, regardless of the quartz standard used. The upper phase model, even though it is defined by only two data points, agrees well with data above 100 GPa. Inset: Extrapolation of the Barrios data[32] to low pressures (red curve) slightly underestimates observed shock pressure (black points; black dashed curve shown to guide the eye). Reflection of the single-phase (brown) and two-phase (green, blue) models to predict reshock (blue) significantly underestimates pressure above 30 GPa. transformed velocity (km/s) Shock breakout at Al/GDP Breakout at GDP/ Vacuum interface Tail of release fan, Al/GDP interface Spall signature Front of release fan, Al/GDP interface time (ns) which indicates the corresponding P η state of the first shock. These reshock compressions are significantly different from estimates of reshock that rely upon translating or reflecting the principal Hugoniot, shown in the inset of Fig. 3. At pressures over 30 GPa, reflections of the Hugoniot in P U p space, a common technique to estimate reshock pressures, underestimate the pressure for a given U p by up to 25% (Figure 3, inset). This is the same pressure at which band-specific emission was observed (Figure 4). These data suggest that this observed change in reshock compression may be indicative of the phase and chemical transitions occurring in GDP. D. Spall A second GDP sample was used on shot 4099, without a LiF window to tamp it. Spall was observed from the free surface of this GDP sample, shown in Figure FIG. 5: The transformed PDV signal from shot 4099 used to determine the window correction factor (1.02). Measurement at the Al/GDP interface (blue) was used to estimate sound speed and spall strength. Following breakout, the free surface velocity (black) appears, including a distinct spall signal. The tensile strength can be calculated using the classical approximation [55] σ R = 0.5ρ 0 c 0 u (1) where c 0 is the sound speed at ambient conditions and u is the change in particle speed. Unfortunately the sound speed of GDP at ambient pressure is unknown. We estimate it here by assuming that it will be similar to the sound speed of GDP shocked and released to zero pressure. In other words, it will be equal to the sound speed of the tail of the release fan, when the full thick-

7 ness of the GDP sample has unloaded to zero pressure. The arrival of the release tail at the Al/GDP interface at 73ns is distinct, with the released Al U p equal to the impact velocity (1.8 km/s). Since the release starts when breakout from GDP into vacuum occurs ( 28ns), the transit time of the release tail can be calculated. In this case it is equivalent to a local sound speed of 1.55 km/s, which is comparable to sound speeds of other plastics.[56] We estimate the spall strength to be 0.45 GPa through these means. We also calculate the sound velocity of compressed GDP, c, based on the transit time of the head of the release wave (observed at 45 ns) to the Al interface. Under weak (1.5 fold) compression, it is 3.4 km/s. This estimate of the ambient sound speed also allows us to estimate the bulk modulus, K, of GDP. Using K = c 2 ρ, (2) we estimate the bulk modulus at ambient conditions to be 2.54 GPa. This value is comparable to or slightly less than other plastics: PS is typically 4 GPa, teflon (PTFE) 2.8 GPa, and polypropylene 4.3 GPa.[56] Under the same weak compression (η=1.5, P = 6.5 GPa), the bulk modulus increased to 16.3 GPa. IV. DISCUSSION A. Hugoniot Results Below 20 GPa, GDP is more compressible than other plastics by a significant margin. As discussed, GDP undergoes some transition or reaction by 30 GPa; this is consistent with the transitions seen at 20 GPa in polycarbonate, polyimide, and PS. Following this transition, GDP s Hugoniot falls between those of the two groups of plastics, though it is more consistent with the softer group than with the stiffer group. Previous equation of state models have started with PS as a starting point;[32, 35] these data suggest that where data are unavailable, a mean plastic Hugoniot should be used above 20 GPa instead transformed velocity (km/s) Al 2 U p 0 Al impedance matched to GDP Shock enters LiF; U p, corrected =2.61 km/s 10 time (ns) Ring up in LiF to final U p FIG. 6: A transformed PDV signal from shot This figure illustrates the changes in apparent U p associated with the shock wave crossing an interface. Accelerating U p is observed beginning at 0 ns. Additional changes in reflectivity and amplitude are apparent in the unprocessed PDV trace. Prior to 0 ns, the observed U p is that of the Al baseplate crossing a gap before it impacts the GDP. in U p [t]. The consistent value for U p indicates that a single U s for each sample is a reasonable assumption. These changes are monotonic in all cases, rather than a large random noise signal. Similar changes, though of smaller magnitude, were seen at other interfaces on other shots. This acceleration in U p suggests that processes other than simple compression occur within GDP. At least four phenomena could generate the observed acceleration of U p shown in Figure 6: 1. density gradients or ramp waves in the GDP; B. Accelerating particle velocities The acceleration in U p (Figure 6) presents difficulties in the analysis. The Rankine-Hugoniot equations use a single value of U p in the analysis under the assumption of an initially steady shock. This assumption is valid, as shown by the data from the Al/LiF interfaces: PDV signals from the Al interface are constant to within 1.5% over long time periods (100 ns). In contrast, PDV signals from Al/GDP and GDP/vacuum interfaces were observed to change by as much as 8% over a 10 ns period, as shown for a single channel in Figure 6 between 0 and 10 ns. Other channels from this shot were within 1% of the velocities shown, which is the measurement uncertainty of our PDV system, and also showed acceleration changes in the refractive index at 1550 nm. 3. a reflecting secondary (reaction) front behind the shock front in GDP; and 4. volumetric compaction in GDP, which may occur with a transparent reaction front; We were able to either eliminate (density gradients), or do not have enough data to analyze (secondary front, changes in refractive index) the first three cases, and will discuss them briefly before expanding upon the case of volumetric compaction.

8 Density gradients or ramp waves as a cause of accelerating U p Density gradients along the compression axis could potentially be created during the deposition process, and would help explain the observed 3% variations in bulk density that we measured.[45] However, hydrodynamic simulations show that such a gradient needs to be approximately 20%, ranging from 0.95 to 1.15 g/cm 3 across the 92 µm thickness of the sample, to match the data. Such a steep gradient is implausible; measurements on NIF capsules have detected density differences of 3%, and have not detected any density gradient comparable to 20%.[11, 57] Our simulations show that a ramp wave due to releases in the Al baseplate also would not lead to these velocity signals. 2. Dynamic changes to refractive index as a cause of accelerating U p Changes in the refractive index at 1550 nm would affect the apparent U p if they affected the PDV correction factor. We observed that the correction factor appears to be pressure dependent. However, these changes are a likely result if a chemical process is occurring in GDP. Therefore, little can be done to determine whether this process is a cause or a symptom of the observed acceleration with available data assumed to release from its initial pressure. The U p is matched to the Al release path to calculate P at the Al/GDP interface. These particle velocities, measured on different channels, are within 1% of each other, consistent with variation in the PDV diagnostic. On a release curve, acceleration in U p corresponds to a drop in pressure. Over the course of the shock transit, pressure at the Al/GDP interface drops 10%. Correspondingly, we can use the calculated U s and U p to determine the bulk compression of the shocked sample with time, assuming a single U s of km/s. [58] The shocked GDP compresses with time, starting with an initial compression of 1.91, listed in Table II, and increasing to [59] By pairing these values, we find that the pressure drops in the shocked GDP as it compresses (Fig. 7). Therefore, assuming constant diameter, this is a case of observed negative compressibility (and imaginary sound speed). Thermodynamically, a negative compressibility is forbidden, and is indicative of an unstable state such as would occur during a phase transition or chemical reaction.[60, 61] time Ch. 1 Ch. 2 Ch Reflecting secondary or reactive front There are two possible locations to measure the U p of GDP on the data presented in this study: at the Al/GDP interface, and at an internal reflecting front in the GDP located behind the shock front. The former corresponds to volumetric compaction of GDP; the latter to an opaque secondary front, such as a reaction front, in GDP. Opacity increases with the reaction coordinate in hydrocarbons such as benzene and cyclohexane,[63, 64] and so it would be unsurprising if such were the case in GDP. Since the putative reactive front s position is unknown, further analysis is not possible with these data, and future work would require dedicated studies. 4. Volumetric compaction as a cause of accelerating U p To analyze the case of volumetric compaction, with measurement occurring at the Al/GDP interface, we assume that the correction factor for GDP does not change. For shot 4093, we used the value determined by the ratio of the mean initial observed U p, 3.54, compared to the calculated U p, 3.669, leading to a correction factor of We note that this is rather different from that measured at lower pressure, 1.02, which is consistent with the idea that the GDP is undergoing a transition. Al is FIG. 7: The calculated η[t] and pressure at the Al/GDP interface, determined by impedance matching to U p as measured on three channels from shot Error bands are not shown for clarity, and time dependence is given to guide the eye. In all cases, the trend remains: as compression increases in GDP, the pressure decreases. This result indicates that GDP is undergoing a phase or chemical transition. The observed blue luminescence suggests that a chemical reaction is responsible. To better gain an understanding of the possible processes involved, and to identify potential reaction time scales, we modeled the ongoing compression of the GDP as a series of small shocks. In this model, the compressive or reactive front is located between the Al/GDP interface and the large initial shock traversing the sample. The initial state of the evolving GDP is that state found immediately after the shock transit (t=0), equivalent to the Hugoniot state of the material. GDP is assumed to have a uniform U s and ρ 0 in this analysis. The final state at each time step is that of the material which has had the longest time to react, located at the Al/GDP interface. Conservation of energy and work determine the

9 Rankine formulation of the total change in energy of this volume collapse: E[t] E[0] = 1 ( 1 2 (P [t] + P [0]) ρ 0 η[0] 1 ) (3) ρ 0 η[t] Ch. 1 Ch. 2 Ch where t = 0 is defined as shock breakout into the GDP, t is each time step following breakout, and ρ 0 is the ambient density of GDP. In this model, we have used P as determined by the Al release and the bulk compression. It would be preferable to use η at the Al/GDP interface, but doing so requires additional assumptions about local densities in the shocked sample. The calculated change in energy at t 12ns is about 0.3 kj/g. For comparison, the energy of the first shock is 6.7 kj/g, and the energy of reshock is 5.2 kj/g. Total kinetic energy change per GDP unit mass can be determined through the measured U p of the Al/GDP interface, U p [t] 2 2 U p[0] 2, (4) 2 where t = 0 is the initial breakout time. The two energy values should be equal, except for a difference of a combined heating/reactive term, which we now calculate Q[t] = m(u p[t] 2 U p [0] 2 ) (P [t] + P 0)(V 0 V [t]) 2 2 (5) The difference between the kinetic energy and the compression energy, Q[t], is shown in Figure 8. Q[t] increases for 4ns, reaching a steady level of 0.3 kj/g (1 kcal/mol), and remaining nearly constant for the remainder of the transit time. This suggests that this unstable process, whether a reaction or a phase transition, has gone to a steady state after 4 ns. We note that the channel-to-channel differences observed in U p and compression are much reduced, indicating that changes in heating are more uniform than compression. For such a volumetric collapse to be spontaneous, the Gibbs free energy must be negative. Typical heats of polymerization are kcal/mol, and the latent heat of the order-disorder transition in C 60 is about 1.7 kcal/mol.[19, 62]. In comparison, the observed change is small, and could be readily accomplished through fractional changes in the existing polymerization of GDP. V. CONCLUSIONS AND FUTURE WORK This study measured the Hugoniot and reshock points of GDP below 100 GPa. The best fit to the data indicates the presence of a phase transition at 30 GPa, consistent with observed spectral data. No major differences were observed between the principal Hugoniot extrapolated from Barrios s data[32] and the limited number of points measured in this study. Extrapolation from this work agrees best with the initial results of FIG. 8: The reaction energy of a unit mass located at the Al/GDP interface as calculated from Equation 5. Each curve represents a data channel. Error bands represent a 1% uncertainty in U p from the PDV. The energy released steadily increases for 4 ns, after which it is nearly constant, suggesting a steady state may be reached. Barrios[32] and not with results based on more recent quartz standards[33, 35]. However, this extrapolation is based on only two points. Accelerations in U p were consistently observed. These variations complicate analysis and are indicative of multiple processes, e.g., chemistry, occurring on the first shock. Possible negative compressibility is explained as evidence of a chemical phase transition, with a steady state reached after 4ns. We note that this time scale is relevant to capsule studies at NIF. Translation, extrapolation, and reflection of the Barrios Hugoniot are inadequate for calculating reshock points, and suggests an area for future work to improve capsule performance. Considering the relatively low pressures spanned in this study, C-rich graphitic particles[42, 65] may be a possible product of the chemistry observed which may create time-dependent spatial density variations within the GDP. These effects would be compounded by any pre-existing variation in initial local density. Examples include crystallites in a matrix, possibly indicated by variation in U p, and variations in bulk density, observed in this work. However, dedicated studies are required to confirm the presence of such particles. These are possible new sources of performance degradation, which should be considered with other sources such as surface roughness or drive inefficiency. Events (including chemistry) occurring upon the first shock and release, below plasma formation conditions, set the path through P T space and create the spatial structure of subsequent shock fronts. Three obvious consequences of such events can be treated in existing models: 1) changes in compressibility of GDP on the second shock; 2) the creation of density gradients in the GDP, as an increased fraction of C would be incorporated into C-rich regions and separated from H; and 3) the creation or worsening of spatial density variation that amplifies and seeds

10 instabilities in the shock front. VI. ACKNOWLEDGEMENTS We thank our operators and support staff, without whom this research would not be possible: Bob Nafzinger for target fabrication and metrology; Paul Benevento for projectile fabrication; Sam Weaver, Cory McLean, Steve Caldwell, and Jim van Lewen for firing and maintaining the light gas gun and its associated electrical sys tems; Doug Hahn, Gerard Jacobson, Pat Ambrose, and Phil Watts, for diagnostics operation/support and crosstiming on PDV. We also thank Bob Tipton, Peter Celliers, Jesse Pino, Omar Hurricane, Tom Dittrich, Larry Fried, Reed Patterson, Rip Collins, Jeff Nguyen, Neil Holmes, and Steve Haan for their useful discussions, insight into implosions and ablator performance on NIF, and ideas, and thank Sebastien Hamel and Ting Ting Qi for modeling GDP and its reactions on the Hugoniot. 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