Combining an x-ray free electron laser with a high-power laser driver enables the study of equations-of-state, high strain-rate deformation processes, structural phase transitions, and transformation pathways as a function of pressure to hundreds of GPa along different thermodynamic compression paths. Future high repetition-rate laser operation will enable data to be accumulated at >1 Hz, which poses a number of experimental challenges, including the need to rapidly replenish the target. Here, we present a combined shock compression and an x-ray diffraction study on epoxy (50% vol.)-crystalline grains (50% vol.) slurry targets, which can be fashioned into extruded ribbons for high repetition-rate operation. For shock-loaded NaCl-slurry samples, we observe pressure, density, and temperature states within the embedded NaCl grains consistent with observations from shock-compressed single-crystal NaCl.
The use of x-ray free electron laser (XFEL) sources, which deliver high-flux x-ray pulses (– photons at 6–25 keV over 50 fs) within a narrow photon-energy bandwidth (E/E ), has been transformative for the study of dynamic material properties and high energy density (HED) science.1,2 Combined with high-power laser drivers, this has allowed for measurements in single-shot dynamic compression experiments, which previously were possible only when performed under static compression and integrated in time, including complex crystallography,3–11 precise spectroscopy,12 and high-resolution imaging.13–15
Existing laser drivers at XFELs can shoot every 5 min.16 This implies a need for 100 targets per day, and target fabrication methods have been developed to meet target needs over a five day run. This large data collection capacity has revolutionized the way that high-quality dynamic experiments are done; instead of an experimental campaign spanning months or years at large laser facilities, XFEL HED science campaigns may collect sufficient data in a single day.
The commissioning of the DiPOLE laser at the High Energy Density instrument at the European XFEL (EuXFEL) (100 J in 15 ns, 10 Hz)17,18 will usher in a new era of experiments requiring the delivery of thousands of targets over a 15-min run. High repetition-rate experiments that combine rapidly adjustable laser pulse shaping with replenishable targets will allow for high-speed scanning of material properties over large regions of sample pressure–temperature space. These capabilities will also allow experimental data to be integrated over long periods of time (many thousands of shots), which will dramatically increase the signal-to-noise over standard single-shot experiments. This will be of particular importance to low signal phenomena, such as low-Z liquid diffraction, scattering off low-Z or low-symmetry materials, inelastic x-ray scattering from phonons,19,20 scattering from incommensurate guest structures,3 and potentially, localized electride quasi-atoms.21
There are three major challenges to overcome for high repetition-rate experiments: target construction and positioning, data collection and processing, and debris and heat load removal.22,23 To address the requirement for rapid target replenishment, it has been proposed to use simple tape targets mounted on a cassette and spooling at 3–5 cm/s22 (Fig. 1). This equates to 30–50 m of tape per 15-min run. However, the nature of this design requires initial target ductility and, therefore, precludes the study of a whole class of brittle ceramics materials. In addition, the production of extended ribbon targets will produce samples with a characteristic micro-structural texture and an x-ray texture pattern, which may be challenging for Rietveld refinement analysis and consequently for determination of phase fraction.5,24 We note, however, that for some reported x-ray diffraction studies, textured samples are desirable.25,26
Here, we describe the manufacturing and testing of epoxy-sample mixtures or slurry targets for use in high repetition-rate experiments on XFEL facilities. Slurry target designs can produce x-ray diffraction powder patterns for brittle materials and can be fashioned into extended ribbons for use in high repetition-rate cassette-spool target delivery systems (e.g., Fig. 1). A complete description of the sample preparation is given in the Appendix and is briefly described here. In our slurry targets, the material of interest is ground in a mortar and pestle, and the resultant powder is sieved through a mesh to ensure that individual grain sizes are less than 1 m. This powder is then thoroughly mixed with Stycast 1266 epoxy in a ratio to obtain a 50% volume packing and a random distribution of grains. Large area sheets of slurry material are then formed between polyimide and teflon layers at the uniform thickness needed for laser-shock experiments (30-m) by processing through rollers with precision separation.
A. Continuum studies of shock-compressed mixtures
There have been extensive studies spanning several decades aimed at determining the continuum response of mixtures27–37—and epoxy-sample slurry,31–37 in particular—under an applied shock, in terms of the aggregate stress–strain response,31–33,35–38 the influence of particulate size, packing, and distribution,33,36 direct imaging of particulate flow,32 and the partitioning of energy states within the constituent materials.30 A brief overview of these studies is presented here.
For a random distribution of grains suspended within a cohesive epoxy matrix and subject to an applied instantaneous shock front, there are a number of physical processes that can modify the thermodynamic compression path.33 At low pressures, the “shock” rise time can be broadened by the viscoelastic response of the epoxy.34 If the shock front thickness is comparable to the grain size, the compression of the grain will be isentropic in nature.30 At increasing stress levels, however, the rise time of the shock wave decreases in a manner consistent with full-density metals,34,39 and the shock front thickness becomes small relative to the grain size. Here, as the shock enters an individual grain, there is an instantaneous state reached along the Hugoniot, which is dependent on the epoxy-sample impedance difference. This is followed by multiple inter- and intra-grain wave reverberations until a steady compression state is reached (Fig. 2). Experimentally, this has been observed in transmitted velocity profiles as a sharp rise (due to the shock), followed by a rounded push to a peak pressure state (due to reverberations), over a time period, which is dependent on the epoxy-sample impedance mismatch, the inter-grain compression-wave round trip time, and the granular packing fraction.32–34 Wave reverberations are accompanied by the relative motion of the sample grains and the epoxy matrix,32 where the shear strength of the components can affect the evolving grain distribution (average slurry density). For high packing fractions, inter-grain interactions may also need to be considered in a comprehensive model description of the states generated. At cessation of the applied shock, the resulting pressure release wave has been observed to be unexpectedly fast compared to the release wave velocity from full-density samples.34
While the timescale for epoxy-sample pressure equilibrium is relatively fast and can be constrained by transmitted wave profile measurements, the timescale for temperature equilibrium is longer and difficult to constrain. Indeed, partitioning of energy between the individual phases is not well understood.30 The temperature states reached (epoxy vs sample) are initially dependent on the individual equations-of-state (EOS) but at later times are also dependent on the thermal conductivities of the constituent materials (the heat flow between the sample and epoxy). In full-density samples, inertial confinement conditions and material strength may combine to increase sample temperature due to work heating.40 In slurry samples, lateral expansion of grains into the compressible epoxy is possible, which may reduce the levels of work heating. We note that diamond-slurry samples were recently used in x-ray diffraction experiments on the National Ignition Facility for laser ramp-compression to 2 TPa, with the goal at reducing sample temperatures at these extreme levels of compression.41
For many material-epoxy composites, the material states generated by an applied shock have been determined through shock-velocity ()—particle velocity () measurements,32,34,36 and models have been developed, which give good qualitative agreement to measured data.34–36,38 However, these data and models provide information only on the aggregate response. To qualify the use of slurry targets for future high repetition-rate XFEL target designs, it is important obtain an understanding on the compression state within the embedded granular material in terms of density () and temperature () as a function of pressure ().
Here, we describe combined laser-shock and x-ray diffraction (XRD) measurements on the matter in extreme conditions (MEC) endstation at the Stanford LCLS-XFEL, which provide a direct measure of granular density and crystal structure as a function of increasing shock pressure.4,5 The temperature in the sample is constrained by comparing crystal structure evolution as a function of sample density with recent similar data from full-density samples.42 Within the accuracy of our data, we find good agreement with the –– states generated within NaCl-slurry samples, with those from single-crystal NaCl  samples.
In these experiments, we combine laser-shock compression of an epoxy (50% vol.):NaCl (50% vol.) sample with in situ XRD to measure the crystal structure evolution as a function of compression (measured density).
NaCl is an ionic solid of significant interest for high-pressure science, geoscience, and dynamic compression. It is widely used as a pressure standard and insulating material in diamond anvil cell experiments, and there has been much effort devoted to studying its strength,43–45 equation-of-state,46–50 and phase transitions.51–58 At room temperature, NaCl undergoes a transition from the B1 rocksalt structure (space group = Fmm) to the B2 cesium chloride structure (space group = Pmm) at about 25 GPa. The B1–B2 transition is of fundamental interest in Earth science as it is exhibited by oxides, such as CaO and MgO, at a much higher pressure.59,60 In NaCl, the B1–B2 transition has been extensively studied by static52–57 and dynamic techniques.51,58 Recent combined XRD-laser shock studies at MEC-LCLS on NaCl  single-crystal samples42 have observed transformation into the B2 phase at 28(2) GPa, B2-liquid coexistence between 54(4) and 66(6) GPa, with near full melt at 66(6) GPa. The states generated over nanosecond laser-compression timescales were found to be in agreement with measurements under static compression at approximately ten orders of magnitude lower compression rate, consistent with equilibrium conditions being achieved under laser-shock conditions.42
A. Experimental setup
The target assembly, as illustrated in Fig. 3(a), consists of a 50 m polyimide () ablator layer adhered directly onto a 30 m-thick NaCl-slurry target and, for some shots, a LiF window for velocimetry measurements [Fig. 3(b)]. A 0.1-m coating of Al was applied to the LiF to enhance target reflectivity.
The front surface of the polyimide was positioned within the focal plane of four laser beams, which delivered a combined energy of up to 80 J at 527-nm in a 15-ns flat-top pulse within a 300 m diameter focal spot. Laser energy absorbed by the polyimide ablator causes it to ablate and expand rapidly. The momentum transfer from this process causes a shock wave, with an initial 15-ns pulse duration, to propagate through the target assembly. The pressure in the sample and the temporal steadiness of the compression wave are controlled by varying the total laser power and laser pulse shaping, respectively.16 An example laser pulse shape is shown in Fig. 3(a). A line-imaging velocity interferometer (VISAR) was used to accurately determine the shock arrival time at the slurry free-surface or the slurry/LiF interface.62 In the experiments where a LiF window was used, the VISAR recorded the slurry/LiF particle velocity history (), which was used to constrain the sample pressure during the x-ray probe period.
The 50-fs output of the LCLS-XFEL at 14.5-keV was incident onto the target during shock transit within the slurry layer, at normal incidence, in a 50-m spot centered on the laser drive. The x-ray beam pointing and timing, relative to the laser-shock drive, is known to a few micrometers and <100 ps by measuring localized changes in VISAR reflectivity and fringe position due to the transient change in the refractive index of the LiF window caused by charge carrier generation by the x-ray pulse.42 X rays scattered from the compressed slurry sample were recorded in transmission geometry on several large area ePix detectors.61 The angular position of the detectors in 2– space was accurately determined by diffraction patterns from ambient pressure and standards, where 2 is the diffraction angle and is the azimuthal angle around the incident x-ray beam.7
Raw x-ray diffraction data obtained under shock compression, and projected into linear 2– angular space, are shown, for a subset of the ePix detectors, in Fig. 4(a). The location of diffraction peaks in 2 permits determination of atomic lattice d-spacing, through Bragg’s law, and the calculation of sample density. X rays are timed to probe the sample during shock transit within the NaCl-slurry layer, and therefore, the recorded diffraction pattern, which is volume-integrated, represents contributions from the shocked and unshocked regions of the slurry sample. Ahead of the shock front, diffraction from the uncompressed NaCl grains ()—embedded within the epoxy ()—produces a number of sharp ambient pressure peaks associated with the B1 structure [Fig. 4(a)]. The extent of intensity uniformity in is a function of the number of randomly orientated NaCl grains within the volume defined by the 50 m diameter x-ray beam and the thickness of the uncompressed slurry sample. Azimuthal intensity variations are due to a non-ideal distribution of grains within the x-ray probe volume. This has also been observed in our XRD measurements on shock-compressed - and -slurry samples (see Fig. S1 in the supplementary material). We note that although our samples were thoroughly mixed, we did not carry out a statistical analysis of the grain distribution. This can be improved for future experiments. A larger x-ray spot, with a more even grain distribution, and/or smaller grains, would produce more powder-like peaks. We also note that while the starting slurry thickness was 30-m, the region of uncompressed slurry contributing to the diffraction peaks is <15-m-thick. For future high repetition-rate operation where the XRD data are integrated over many shots to enhance signal-to-noise, this azimuthal intensity variation is expected to smooth out to produce a powder pattern suitable for Rietveld refinement analysis.5,24
Shown in Fig. 4(b) are a series of -averaged intensity profiles (over all ePix detectors) for different shots taken as a function of increasing laser energy (increasing shock pressure). The timing of the x-ray probe relative to the shock arrival at the slurry free-surface or the slurry/LiF interface ranged between and ns. This range results in shot-to-shot variations in the detected uncompressed slurry volume. At low levels of compression (), we observe broad peaks of the compressed B1 structure. We observe similar peak broadening in and slurry samples (Fig. S1 in the supplementary material). Peak broadening under shock compression is generally attributed to grain-size reduction due to plastic/brittle deformation.64,65 An additional contributor to peak broadening is the distribution of pressure states within the sample (see Fig. 5). At higher compression (shot no. r265, ), we observe diffraction peaks consistent with a mixed B1+B2 phase assemblage.
For –, only compressed B2 is observed. While not shown in Fig. 4, we note that at late times and along a pressure release path from an initially compressed state within the B2 phase, we observe the reverse B2B1 transition.
For –, a mixed B2+liquid assemblage is observed. Increased compression over this density range results in a diminished intensity of the B2 peaks and an increased broad background intensity from liquid diffraction. This is consistent with the expected phase evolution as the Hugoniot crosses the melt line.42,66
A. Pressure determination
Constraints of sample pressure in laser-shock experiments typically rely on measurements of the sample/LiF interface velocity and standard impedance-matching techniques. This approach requires a knowledge of the – Hugoniot relations for both the sample and the LIF window. While there have been extensive experimental and theoretical studies aimed at determining the continuum response of epoxy-sample mixtures under an applied shock load,32,34–36,38 the determined Hugoniots represent the average bulk response and, therefore, do not give direct information on local granular density states. However, due to multiple wave reverberations in the slurry sample (Fig. 2), sample-epoxy pressure equilibrium is expected to be rapidly obtained, and impedance matching can then be used to constrain the sample pressure.
A review of different theoretical models for determining the composite Hugoniot response for mixtures is given in Ref. 35. The models all assume that the internal energy and density of the mixture are related to the weighted sum of the individual component properties. Here, we consider the simplest of those models—which assumes that the mixture is under pressure equilibrium and that the material velocity of the mixture can be determined by averaging the material velocities on the individual component Hugoniots according to a velocity based mixture rule.35 Applying this approach to the epoxy (50% vol.):NaCl (50% vol.) slurry used in our experiments, the mixture velocity is obtained for a given pressure from the following relation:
where and are the particle velocities for the NaCl and epoxy components, respectively, at a given pressure on their respective individual Hugoniots. represents the mass fraction of individual components. For the epoxy (50% vol.):NaCl (50% vol.) slurry, . This expression is shown to give a good representation of slurry target Hugoniot relations in many composite materials (see Fig. S2 in the supplementary material and Ref. 35).
In Fig. 5, the – curves for LiF, NaCl, and epoxy are shown along with the calculated composite response of the NaCl-slurry based on Eq. (1). Using the measured slurry-LiF particle velocity [e.g., Fig. 3(b) and inset to Fig. 5] and standard impedance matching, the pressure in the NaCl grains may be determined.
In Fig. 6, previously reported pressure–density Hugoniot values for single-crystal NaCl (open squares, colored open circles) are plotted alongside values obtained from the current NaCl-slurry study (colored filled circles). For the majority of the NaCl-slurry shots, no LiF window was used, and therefore, pressure determination based on impedance matching (as in Fig. 5) was not possible. For these shots, the measured density values were fixed to the pressures determined from the full-density NaCl Hugoniot measurements.58 For two slurry shots, LiF windows were used, and the pressure was determined though impedance matching [white crossed symbols in Fig. 6(a)]. These pressure–density points are in good agreement with previous XRD measurements on single-crystal NaCl samples.42
We note that in the model depicted in Fig. 2, the final steady-state crystalline-sample density—along the combined shock + reverberation path—is expected to be higher than the Hugoniot at an equivalent pressure. However, within the accuracy of our measurements, this effect is not apparent.
B. Temperature determination
While we do not get any direct temperature measurement from our data, we can compare with previous data on NaCl single crystals42 to constrain the temperature evolution of the NaCl-slurry grains as a function of pressure. Figure 6(b) shows the – diagram for NaCl with stability regions for B1, B2, and liquid, as defined by static compression data (gray circles52,53,55,56). Also plotted is the model Hugoniot and estimated shock temperatures from a recent shock compression study from single-crystal NaCl samples (colored open circles42). Here, temperatures were estimated using a multi-phase EOS model for NaCl. Along the Hugoniot NaCl transforms from B1B2 at K and melt initiates at K. The consistency of phase evolution with compression between the NaCl-slurry data and NaCl single-crystal data [Fig. 6(a)] indicates a comparable thermodynamic compression path.
We note that the physical model depicted in Fig. 2 implies that the NaCl grains would experience an initial shock followed by ramp-compression to a peak pressure state. To model this behavior, we plot in Fig. 6(b) shock + ramp-compression paths, calculated for different initial shock levels, from the EOS model reported in Ref. 42 (blue dashed curves). Here, an isentrope originating from the initial Hugoniot state is used to approximate the ramp-compression path. As the estimated high-T isentropes do not intersect the NaCl melt line, we conclude that the small grains in the NaCl-slurry, which exhibit partial melting above 50-GPa, experience compressive states consistent with the full-density Hugoniot. We considered the possibility that additional heating from the surrounding epoxy might increase the NaCl temperature; however, given the expected higher temperature within the NaCl grains (see Fig. S3 in the supplementary material), this is deemed unlikely. The extent to which late time inter-grain reverberations play a role in the – path of slurry samples is likely dependent on the sample-epoxy impedance mismatch and the size of the grains.
C. Prospects for the future use of slurry targets at XFELs
One current limitation on the widespread use of slurry targets in laser-driven XFEL experiments is the lack of an extensive database describing the thermodynamic compression path followed by the granular component for different applied loads (e.g., shock, ramp, shock+ramp). The use of in situ x-ray diffraction techniques, as described here, allows for a direct measurement of slurry density during nano-second laser compression. To constrain pressure using standard impedance-matching techniques, this slurry study and others35 have shown that a simple mixing model describes the sample P– path under an applied shock. However, most of these cases have been with low mechanical impedance samples. Future studies will need to determine the accuracy of the mixing model in Eq. (1), or other models,35 for different slurry types: variations in sample grain size, sample volume percentage, sample-epoxy impedance differences, and multi-component systems. The flexibility of the slurry design opens up the possibility that, in a multi-component system, one of the scattering components could serve as a pressure standard. Future work is needed to develop these capabilities.
In addition, further work is needed to more accurately determine the sample temperature for a given applied time-dependent pressure load/slurry design. These issues are not unique to slurry targets, however, as standard laser-compression XFEL experiments on full-density materials rely on previously determined Hugoniot data to constrain sample pressure and EOS models to infer temperature. We note that techniques are currently being developed to directly measure temperature under laser-shock compression, e.g., EXAFS,71,72 Debye–Waller analysis of XRD data,73,74 and inelastic x-ray scattering from phonons.19,20
We have demonstrated the ability to produce powder diffraction patterns from crystalline brittle materials by suspending the sample within a ductile epoxy matrix. This opens up the possibility to study brittle samples in high repetition-rate laser operation on XFEL facilities using a cassette design as illustrated in Fig. 1. In addition, the use of slurry targets permits the study of analogs to real-world samples that are porous and multi-component in nature.
High repetition-rate diffraction from slurry samples would produce high-quality powder diffraction, which lends itself to Rietveld refinement analysis from which phase fraction information can be extracted.5 Our diffraction data on shock-compressed epoxy (50% vol.):NaCl (50% vol.) slurry is consistent with the NaCl grains being compressed close to the full-density Hugoniot. We observe phase evolution from B1, B2, and liquid with increasing pressure. Future work is needed to accurately determine the thermodynamic compression path for different composite mixtures.
See the supplementary material for additional XRD data on alumina () and enstatite () (Fig. S1). Hugoniot data for , , and slurry samples are shown in Fig. S2. Pressure, density and temperature along the full density NaCl and epoxy Hugoniots are shown in Fig. S3.
This work was performed under the auspices of the U.S. Department of Energy by the Lawrence Livermore National Laboratory under Contract No. DE-AC52-07NA27344. This work was supported through the Laboratory Directed Research and Development Program at LLNL (Project Nos. 17-ERD-014 and 21-ERD-032). C.A.B. would like to acknowledge support from Science Campaign 2 at Los Alamos National Laboratory, which is operated for the National Nuclear Security Administration of the U.S. Department of Energy under Contract No. DE-AC52-06NA25396. Use of the Linac Coherent Light Source (LCLS), SLAC National Accelerator Laboratory was supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under Contract No. DE-AC02-76SF00515. The MEC instrument is supported by the U.S. Department of Energy, Office of Science, Office of Fusion Energy Sciences, under Contract No. SF00515.
Conflict of Interest
The authors have no conflicts to disclose.
Raymond F. Smith: Conceptualization (equal); Formal analysis (equal); Writing – original draft (equal); Writing – review & editing (equal). Vinay Rastogi: Formal analysis (equal). Amy E. Lazicki: Conceptualization (equal). Martin G. Gorman: Formal analysis (equal). Richard Briggs: Formal analysis (equal). Amy L. Coleman: Formal analysis (equal). Carol Davis: Data curation (equal). Saransh Singh: Formal analysis (equal). David McGonegle: Formal analysis (equal). Samantha M. Clarke: Formal analysis (equal). Travis Volz: Formal analysis (equal). Trevor Hutchinson: Formal analysis (equal). Christopher McGuire: Formal analysis (equal). Dayne E. Fratanduono: Formal analysis (equal). Damian C. Swift: Formal analysis (equal). Eric Folsom: Data curation (equal). Cynthia A. Bolme: Formal analysis (equal). Arianna E. Gleason: Funding acquisition (equal). Federica Coppari: Formal analysis (equal). Hae Ja Lee: Data curation (equal). Bob Nagler: Data curation (equal). Eric Cunningham: Data curation (equal). Philip Heimann: Data curation (equal). Richard G. Kraus: Formal analysis (equal). Robert E. Rudd: Formal analysis (equal). Thomas S. Duffy: Formal analysis (equal). Jon H. Eggert: Formal analysis (equal). June K. Wicks: Formal analysis (equal).
The data that support the findings of this study are available from the corresponding author upon reasonable request. The code used for the XRD analysis is openly available in GitHub at https://github.com/HEXRD.
APPENDIX: PROCEDURE FOR MAKING SLURRY SAMPLES
For hard spheres, there is a maximally random jammed (MRJ) packing fraction of about 0.64.75 For slurry samples with this packing fraction, the remaining 0.36 of the volume would be filled by epoxy. However, we find that for granular volumes 50%, viscosity increases strongly, which makes it difficult to mix. A 50% epoxy: 50 sample volume ratio is ideal for maximizing the packing fraction while keeping the viscosity low enough for thorough mixing. The procedure we employed to produce the slurry samples used in this study is described below.
Crystalline samples are ground to a fine powder, with a mortar and pestle, and sieved through a mesh to ensure individual grains <1 m.
The powder is then fully baked in a vacuum oven to remove all moisture (otherwise, in the case of diamond powder,41 the final mixture is visibly heterogeneous).
Stycast 1266 was chosen for the epoxy () due to its transparency, low viscosity, working time, and shelf life (clear, 650 cP, 30 min, days in a freezer).76 The viscosity can be further lowered by increasing the temperature, but that shortens the working time.
The epoxy must be vacuum de-aired to ensure a void-free embedment, as is necessary for this application. This is achieved by placing the epoxy in a bell jar while applying a vacuum. Initially, the glue will foam up as the air bubbles escape. After a period of time, visual inspection will confirm that the epoxy is bubble free.
The desired amount of epoxy is placed onto a small tray using a syringe. With a 0.01-mg accuracy scale, the mass is then recorded and the epoxy volume is calculated.
The commensurate mass of the powdered sample—to achieve the desired epoxy-sample volume ratio—is then added to the epoxy. The epoxy+sample components are then thoroughly mixed to ensure a random distribution of grains.
The epoxy mixture may then be fashioned into a planar film as illustrated in Fig. 7. Here, the slurry is placed between a polyimide layer and a teflon layer and passed through rollers with a separation to produce the target thicknesses described in Fig. 3(a). From the resultant sheet of polyimide + slurry, targets for laser-shock experiments may be punched out (2-mm diameters). Following this approach, large areas of slurry samples may be produced as is needed for future high repetition-rate target designs (Fig. 1).