Simultaneous 8.2 keV phase-contrast imaging and 24.6 keV X-ray diffraction from shock-compressed matter at the LCLS

In this work, we demonstrate simultaneous phase-contrast imaging (PCI) and X-ray diffraction from shock compressed matter at the Matter in Extreme Conditions endstation, at the Linac Coherent Light Source (LCLS). We utilize the chromaticity from compound refractive X-ray lenses to focus the 24.6 keV 3rd order undulator harmonic of the LCLS to a spot size of 5 μm on target to perform X-ray diffraction. Simultaneous PCI from the 8.2 keV fundamental X-ray beam is used to visualize and measure the transient properties of the shock wave over a 500 μm field of view. Furthermore, we demonstrate the ability to extend the reciprocal space measurements by 5 A−1, relative to the fundamental X-ray energy, by utilizing X-ray diffraction from the 3rd harmonic of the LCLS.

In this work, we demonstrate simultaneous phase-contrast imaging (PCI) and X-ray diffraction from shock compressed matter at the Matter in Extreme Conditions endstation, at the Linac Coherent Light Source (LCLS). We utilize the chromaticity from compound refractive X-ray lenses to focus the 24.6 keV 3rd order undulator harmonic of the LCLS to a spot size of 5 lm on target to perform X-ray diffraction. Simultaneous PCI from the 8.2 keV fundamental X-ray beam is used to visualize and measure the transient properties of the shock wave over a 500 lm field of view. Furthermore, we demonstrate the ability to extend the reciprocal space measurements by 5 Å À1 , relative to the fundamental X-ray energy, by utilizing X-ray diffraction from the 3rd harmonic of the LCLS. Knowledge of the behavior of matter at extreme pressures and temperatures is necessary for understanding materials at the core of giant planets, in impact events, and in nuclear fusion processes. [1][2][3] One avenue to create such matter is through laser-driven shock compression, whereby Mbar pressures and eV temperatures may be generated over nanosecond timescales. The $100 fs hard X-ray pulses produced by the Linac Coherent Light Source (LCLS), are essential for investigating the structure and behavior of matter at extreme conditions. In such dynamic compression experiments, in-situ X-ray diffraction has been proven to be a key diagnostic, and numerous studies to date have combined this technique with high power nanosecond laser drivers at the Matter in Extreme Conditions (MEC) endstation at the LCLS. 1,2,[4][5][6][7][8][9][10][11] In many shock wave experiments, the material conditions inferred are diagnosed using optical velocimetry (VISAR), 12 an interferometric technique whereby the velocity of a reflecting rear surface is measured as a shock wave exits it. However, this technique does not provide direct structural information, and provides limited insight into how the complex waves behave inside the sample.
Hard X-ray free-electron lasers, like the LCLS, provide an avenue to image shock waves inside optically opaque samples. Schropp et al., have demonstrated the ability to measure the properties of a shock wave as it progresses through a sample using a phase-contrast imaging (PCI) technique. 13 Since shock waves typically travel through samples at speeds of a few lm/ ns, the 100 fs duration of the X-ray pulses available at the LCLS allows one to take a snapshot of the shock wave as it traverses the sample. However, in such a configuration the large illumination spot necessary for imaging will diffract from several hundred microns of the sample, scattering from both the static uncompressed sample and the high-pressure, high-temperature states generated by the shock wave, within a typically far smaller optical focal spot. Therefore, it becomes increasingly difficult to discern the nature of the high pressure phase as diffraction patterns can be dominated by scattering from the uncompressed sample. Furthermore, as one is illuminating the entire shock wave, it is challenging to resolve the onset of phase transitions.
In this letter, we present simultaneous phase-contrast imaging of a shock wave propagating through opticallyopaque laser shock-compressed germanium (Ge), combined with X-ray diffraction from a specific region of the sample. Ge was chosen as the crystal of study as it exhibits a complex multi-wave response following dynamic loading, which would display clear signatures in both imaging and diffraction. [14][15][16] We achieve the simultaneous imaging and diffraction by using the fundamental X-ray beam at 8.2 keV to perform the imaging, and the 24.6 keV X-rays in the 3rd harmonic of the LCLS to perform X-ray diffraction measurements. We take advantage of the wavelength dependence of the X-ray focusing optics to create a micron sized X-ray spot with the 24.6 keV X-rays, which is centered on the large illuminating field of the fundamental X-rays at 8.2 keV. This is an important demonstration of using high X-ray energy to probe dense, high-Z matter.
Experiments were conducted at the MEC endstation 17 at the LCLS using the PCI instrument. 18 Single crystal samples of Ge, with 50 lm polyimide ablators, were shock compressed via irradiation with the nanosecond pulsed Nd:glass laser system. A schematic of the setup used may be seen in Fig. 1. The laser light was frequency-doubled to 527 nm, and a 50 ns temporally square pulse was combined with phase plate optics to produce a 250 lm spot on the ablator surface. 19 This setup provided laser intensities in the range 6.1 Â 10 11 W/cm 2 -1.4 Â 10 12 W/cm 2 on target. In this work, a transverse geometry was employed, where the X-ray probe beam was incident perpendicular to the shock propagation direction. The X-ray pulse length, generated by selfamplified spontaneous emission (SASE) from the LCLS, was approximately 80 fs, and the jitter between the optical drive laser and the X-ray beam was 610 ps. 17 The target configuration may be seen in Fig. 1. Discs of single crystal Ge, oriented in the [110] direction (Semiconductor Wafer, Inc.), were polished to a thickness of 100 lm, and diced to dimensions of 100 lm (X-ray direction) Â 100 lm (shock direction) Â 2 mm. Bonded to the drive surface (the surface upon which the shock laser was incident), was 50 lm of polyimide, with a 100 nm flash coating of aluminum to prevent the penetration of drive light at early time, and hence prevent tamped ablation. The targets were 100 lm in the X-ray direction and the polyimide ablator was 300 lm wide, extended to shield the laser light from hitting the side of the target.
VISAR measurements were recorded on every shot to determine the wave profile as a function of laser intensity. Furthermore, this diagnostic allowed the sample pressure to be inferred using the Rankine-Hugoniot relations. Figure 2 shows a 1D velocity-time trace of a typical shock wave in Ge. In this work, t ¼ 0 ns is defined as when the rising edge of the laser drive pulse is incident on the ablator surface. We observe, consistent with previous studies, a strong elastic response, beginning at 27 ns, reaching a peak velocity of $0.5 km/s, corresponding to a Hugoniot Elastic Limit (HEL) of 5 GPa. [14][15][16] Following the strong elastic wave, a second wave emerges, and the material is compressed up to a peakpressure state of 12 GPa.
A stack of beryllium compound refractive lenses (Be CRLs) 20 were used, consisting of 57 individual bi-concave lenses, each with a radius of curvature of 50 lm and a geometric aperture of 300 lm. The chromaticity of the optics allows one to focus higher energy 24.6 keV (3rd harmonic beam) photons directly on target, while simultaneously imaging the sample via magnified PCI by focussing the lower energy 8.2 keV (fundamental beam) photons further upstream, as depicted in Fig. 1.
We used the fundamental undulator harmonic at 8.2 keV for PCI, at which the Be CRL has a numerical aperture (NA) of 0.93 Â 10 À3 and a focal length of f 1 ¼ 98 mm. Diffraction data were collected with the 3rd undulator harmonic at 24.6 keV. Here, the Be CRL has an NA of 0.17 Â 10 À3 and a focal length of f 3 ¼ 791 mm. The position of the 3rd harmonic focal plane was determined by moving a copper grid (1000 mesh, Gilder Grids) along the optical axis, through the focal plane in 10 mm steps, performing a linear regression on the field of view. To tailor the beamsize on target for X-ray diffraction measurements with the 3rd harmonic to approximately 5 lm in diameter the sample was moved downstream from the focal plane by z D ¼ 20.5 mm. The distance from the fundamental focal plane to the target is geometrically fixed both the beamline and CRL stack transmission, the X-ray intensity for a single pulse on target was determined to be $6.7 Â 10 9 W/cm 2 at 8.2 keV and $1.7 Â 10 1 W/cm 2 at 24.6 keV. The PCI detector was placed at a distance z d ¼ 4800 mm downstream of the 3rd harmonic focal plane (cf. Fig. 1) resulting in a magnification of M ¼ (z s þ z d )/z s ¼ 7.7. For imaging we used a high-resolution YAG:Ce scintillator based X-ray camera with an effective pixel size of 2.25 lm. In the given geometry this leads to an effective pixel size of 292 nm in the phase-contrast images. The YAG:Ce scintillator had a thickness of 50 lm and absorbs 80% of the fundamental, and 33% of the 3rd harmonic. In order to pinpoint the position of the 3rd harmonic in the field of view of the magnified image from the fundamental, we filtered the fundamental by Si attenuators, effectively only imaging the 3rd harmonic.
X-ray diffraction patterns were collected in transmission through the sample in a Debye-Scherrer geometry on Cornell Stanford Pixellated Area Detectors (CSPADs) at a sampledetector distance of 300 mm. Three CSPADs were used to cover a 2h range of between 4.5 to 26.5 , 4.5 to 23.1 , and 27.0 to 37.4 , corresponding to a Q-range of between 1 Å À1 and 8 Å À1 . The equivalent Q-range that would be probed by the 8.2 keV X-rays on the same detectors would be 0.33 Å À1 -2.67 Å À1 . To ensure that the X-ray diffraction patterns measured were due to scattering from the 3rd harmonic at 24.6 keV, and not due to scattering from the fundamental 8.2 keV beam, 500 lm of aluminum foil was used on the detector active area as a filter. The transmission of 8.2 keV X-rays through 500 lm of Al is 0.25%, whereas for 24.6 keV the transmission is 79.1%. Figure 3 shows an example of PCI data. Figure 3(a) shows a reference measurement taken from an uncompressed sample. PCI of shock-compressed Ge is shown in Figs. 3(b)  and 3(c), where the X-rays probed at 30 ns and 40 ns, respectively. The break out time of the elastic wave, t ¼ 27 ns, is determined from the velocimetry data in Fig. 2. In Fig. 3(b), the shock wave has traversed the sample. Although the Xrays were timed at 30 ns, 3 ns after the breakout time as determined by the VISAR there is no evidence of spall in the imaging data. In Fig. 3(c), the X-rays probed at 40 ns. The elastic shock wave break out at the Ge/vacuum interface on the right of Fig. 3(c), and was followed by the 2nd wave. These waves were then reflected back into the Ge sample, interacting with the shock wave, creating an off-Hugoniot state. It is worth noting the ns-drive laser (t ¼ 50 ns) is still driving a forward-moving shock into the sample while the X-rays probe the sample. Therefore, PCI can be used to observe such complex wave interactions that result from these reflecting waves within the target.
The 5 lm spot size of the 24.6 keV 3rd harmonic is centered on the spot illuminated by the fundamental beam, thereby allowing accurate spatial probing of the material conditions relative to the position of the shock wave that is simultaneously imaged with PCI. The position and size of the 24.6 keV X-ray beam used for diffraction is shown by the small yellow spot, concentric to the green circle in Fig. 3. Figure 4 shows 1D integrated X-ray diffraction patterns using the 24.6 keV X-rays. The Ge is initially a single crystal, the Bragg condition is not satisfied on the limited h-/ space covered by the CSPAD, resulting in an integrated 1D pattern with no measurable X-ray signal (black line) Fig. 4(a).
X-ray diffraction patterns corresponding to the PCI data in Figs. 3(b) and 3(c) are shown in Figs. 4(c) and 4(d), respectively. As a consequence of the shock wave, the single crystal breaks up into small nanometer-scale grains, resulting in powder-like rings on the CSPAD detector. The evidence of a high pressure solid structure may be seen by the appearance of sharp peaks at 2.7 Å À1 and 3.8 Å À1 . The peak in Fig.  4(c) at 3.4 Å À1 is due to scattering from the compressed ambient pressure phase which has been rotated into the Xray beam due to the shock wave.
Although we have focussed on demonstrating simultaneous PCI and X-ray diffraction, and have shown how useful this technique can be when investigating shock-compressed materials, in particular those which exhibit complex multiwave features, or targets undergoing release, there are other advantages to using the much higher X-ray energies available in the 3rd harmonic. Figures 4(b) and 4(e) show additional examples of the X-ray diffraction possible at 24.6 keV. A distinct advantage of using such a high X-ray energy is that for the same 2h range, one may access a significantly larger Q range. Here, we can measure an X-ray signal to a Q of 8 Å À1 for a scattering angle of 47 . Using the highest stable energy of the fundamental beam-of about 11 keV-one may only reach a Q of 3.6 Å À1 over this same angular range. Taking advantage of a higher X-ray energy allows for direct X-ray probing of atomic scale structures over a larger range of reciprocal space. Such information may be necessary when investigating the nature of phase transitions under dynamic processes. Figure 4(b) shows diffraction from a compressed single crystal of the cubic diamond phase of Ge, which has been rotated into the X-ray beam, satisfying the Bragg condition. One may see the (111) reflection at 2.00 Å À1 , corresponding to a lattice parameter of the cubic diamond structure of a ¼ 5.44 Å , and a V/V 0 of 0.89. The peak at 7.06 Å À1 corresponds to the (531) reflection of the uncompressed cubic diamond structure.
At the highest laser intensities and hence highest pressures reached, the sample was observed to melt completely, as shown by the disappearance of Bragg scattering and appearance of the broad diffuse feature at 2.7 Å À1 [ Fig.  4(e)], and the possibility of a weaker diffuse feature at 5 Å À1 indicating the second coordination shell (subject to further analysis). This is consistent with previous high pressure Xray diffraction studies of liquid Ge. 21 In conclusion, we have implemented an experimental platform to perform simultaneous phase-contrast imaging with microfocussed X-ray diffraction using both the fundamental and 3rd harmonic of the LCLS. We have directly observed complex wave interactions within the sample that arise during both shock and release, and have isolated such structures in the same shot with a microfocussed 24.6 keV beam for X-ray diffraction. Furthermore, we have demonstrated proof-of-principle diffraction patterns, including liquid scattering, using the 3rd harmonic of the LCLS, allowing one to access a significantly higher Q range. Such structural information is vital for understanding the properties of matter at extreme pressures and temperatures.