Single-pulse (100 ps) extended x-ray absorption fine structure capability at the Dynamic Compression Sector

Planar shock wave compression—generated via rapid deposition of energy on a planar surface by methods such as plate impact loading or ablation from a high-energy laser—results in near discontinuous changes in stress and density and can bring materials to extreme pressure–temperature conditions on nanosecond timescales.^1,2 As such, shock wave compression has been used to examine materials under extreme conditions such as iron at earth core pressures³ and phase transformations in carbon at terapascal pressures.⁴ By measuring both shock wave velocity and particle velocity behind the shock wave, stress, density, and internal energy can be calculated using the Rankine–Hugoniot jump conditions,^1,2,4 which provides valuable equation of state information. However, such continuum measurements lack detailed atomic level information. Using brilliant x rays from modern light sources, in situ x-ray diffraction measurements can now directly investigate shock-induced solid–solid phase transformations,^5,6 defects,^7,8 and melting⁹ on nanosecond timescales.

X-ray absorption fine structure spectroscopy (XAFS) is another x-ray diagnostic that can be useful for examining atomic level information in shocked solids.^10–18 It is a powerful experimental tool to determine the local atomic structure for selected atomic species.^19–22 It can probe a variety of systems including liquids, crystalline and non-crystalline solids, and disordered materials. Thus, XAFS is complementary to the standard x-ray diffraction (XRD) technique, which probes long range atomic order in crystalline materials. XAFS is based on the x-ray photoelectric effect, where a photo-electron is ejected from a core atomic orbital after the absorption of an incident x-ray photon by an atom. The photo-electron wave scatters from the atoms surrounding the absorbing atom, creating interferences between the scattered and outgoing parts of the photo-electron wavefunction, resulting in an energy-dependent XAFS spectrum.^21,22 This spectrum consists of two regions—x-ray absorption near edge spectroscopy (XANES) within ∼30 eV of the absorption edge and extended x-ray absorption fine structure spectroscopy (EXAFS) from ∼30 eV above the edge to 100s of eV above the edge. XANES generally requires high energy resolution to resolve the detailed structure around the absorption edge and provides information on the oxidation state and local coordination chemistry. EXAFS refers to the oscillatory component of the absorption spectrum well above the absorption edge, and a large energy bandwidth above the edge is generally needed to get accurate structural and thermal information. The periods of the EXAFS modulations provide information on atomic distances and coordination numbers, while the decay of the modulation is dependent on the Debye–Waller factors, from which the material temperature can be determined.^19–22 

Over the last decade, developments have been made in measuring in situ EXAFS under dynamic compression at the Omega Laser (University of Rochester)^10–17 using a laser driven spherical implosion x-ray source.²³ The x rays transmitted through the target are energy-dispersed by a multi-angle flat crystal spectrometer.¹⁵ Based on the same principle, an EXAFS capability is also being developed at the National Ignition Facility (NIF).^24,25 Single shot EXAFS measurements under dynamic compression have been reported in a series of materials for energies below 8 keV, including V (K-edge 4.96 keV),^10,11,14 Ti (K-edge 5.46 keV),^10,11 and Fe (K-edge 7.11 keV).^12,13,15,16 However, extending to higher energies has been a challenge due to the loss of x-ray flux by a factor of ∼8 to 10 between 6.5 keV and 10 keV^17,25 for laser driven implosion x-ray sources.

An alternate approach to the studies above is to have a real time EXAFS capability under dynamic compression using a synchrotron source. A synchrotron x-ray source can typically provide greater spectral resolution, more energy tunability, and better pulse-to-pulse reproducibility than the laser-based x-ray sources. Recently, EXAFS measurements under ambient and laser shock conditions have been performed at beamline ID24²⁶ of the European Synchrotron Radiation Facility (ESRF) using a 35 J laser.^27,28 In this case, a divergent x-ray beam is focused and energy-dispersed by a bent crystal monochromator. The x-ray focal spot is at the target, and the transmitted x rays diverge onto a position sensitive detector. The bent crystal monochromator provides high resolution (ΔE/E ∼ 10⁻⁴), necessary for probing the XANES region,^26–28 but provides limited energy bandwidth for EXAFS measurements^27,28 (for example, ∼300 eV bandwidth near the Fe K-edge energy²⁸).

In this paper, we present a newly developed single synchrotron x-ray pulse (∼100 ps) EXAFS capability at the Dynamic Compression Sector (DCS) located at the Advanced Photon Source (APS). This EXAFS capability is developed as a diagnostic to examine dynamically compressed materials using the DCS 100 J laser as the driver.²⁹ To date, the laser drive capabilities at the DCS have focused on single shock compression, and as such, the temperature is governed by the material Hugoniot. The laser was designed to also achieve ramp compression (5 ns–10 ns rise times), resulting in lower temperatures, and these experiments will be undertaken in the future.

Using a flat plate of highly oriented pyrolytic graphite (HOPG) as the spectrometer element in combination with a high quantum efficiency detector (>90%), we have been able to obtain EXAFS spectra with a good signal-to-noise ratio (SNR) ∼10³, an x-ray flux on the sample ∼10⁶ photons/eV per x-ray pulse (∼100 ps), a resolution of ∼10 eV at 10 keV (ΔE/E ∼ 0.1%), an energy bandwidth of over 500 eV for the Ge K-edge, and a good pulse to pulse reproducibility (<2.0% SD) of our single pulse EXAFS measurements. Here, we also report, for the first time, EXAFS measurements under dynamic compression above 8 keV at 11.1036 keV (Ge K-edge³⁰). Using our system, we have also obtained single pulse ambient EXAFS spectra for other materials with absorption edges ranging from ∼9 keV to 13 keV. Our setup, however, does not have the resolution for XANES, which requires a resolution of ∼1 eV (ΔE/E ∼ 10⁻⁴).

In Sec. II, we describe our new approach for single shot EXAFS measurements using a low divergence broadband x-ray source and a flat HOPG mosaic crystal as a spectrometer. We demonstrate the spectrometer efficiency and the corresponding energy resolution and bandwidths, with Ge as a primary example. In Sec. III, we first show ambient EXAFS spectra for Cu (K-edge 8.98 keV)³⁰ and Au (L3-edge 11.92 keV)³⁰ and compare them to the reference data obtained from the APS XAFS library.³¹ Next, we present our EXAFS results on ambient and shock compressed Ge samples, along with a fit of a simulated EXAFS spectrum for the ambient Ge. The excellent match between the measured and simulated ambient Ge EXAFS spectra, as well as the comparison of ambient and reference spectra for Cu and Au, demonstrates the quantitative capability of our EXAFS technique. Concluding remarks are given in Sec. IV.

Figure 1 shows the configuration for single pulse EXAFS measurements in the C-station (laser-shock station) of the DCS. As shown in Fig. 1(a), a combination of two rotating choppers [High Heat Load (HHL) chopper and J$ü$lich chopper] and a millisecond x-ray shutter (ms-shutter) are used to isolate a single x-ray pulse (∼100 ps duration) incident on the laser shock target chamber.²⁹ A single x-ray pulse can be isolated in either the APS 24-bunch mode operation, which has periodic x-ray pulses every 153.4 ns, or in the APS hybrid mode operation, which has a single x-ray pulse separated in time from other x-ray pulses by 1.59 µs. Single pulse EXAFS measurements have been obtained at the DCS using the configuration described in this section using both APS operating modes. However, the hybrid mode is preferable because the x-ray flux from the hybrid singlet is approximately four times larger than that of a single pulse in the 24-bunch mode, resulting in a better SNR. Selected parameters for the APS operating modes are provided in Table I.

The chopped x-ray pulse passes through a target located at the laser target chamber center (TCC) and is then incident on a flat plate of highly oriented-pyrolytic-graphite (HOPG) located downstream of the target chamber [see Fig. 1(b)]. HOPG has the graphite c-axis nominally normal to the plate face with a full-width-at-half-maximum (FWHM) mosaic spread of the order of one degree, with the actual mosaic spread value depending on the HOPG grade. The HOPG acts as an efficient energy dispersive spectrometer with diffraction of incident x rays from the (002) graphite plane.^32,33

As shown in Fig. 2, the HOPG is oriented to have the diffraction vector nominally in the y–z plane. A pair of horizontal and vertical x-ray slits centered on the incident x-ray beam were placed just upstream of the HOPG in order to have a well defined spectrometer element. The x rays diffracted from the HOPG have an angle–energy correlation described by Bragg’s law,³⁴ 

In Eq. (1), λ is the x-ray wavelength related to x-ray energy E via E = hc/λ, where h is Planck’s constant and c is the speed of light, d₍₀₀₂₎ is the d-spacing for the (002) planes of graphite, and θ is the Bragg angle.

The energy dispersed x rays pass through a helium filled tube (∼2.5 m in length, with 50 μm thick Kapton windows on both ends) to limit x-ray scattering and absorption (only ∼1% scattering loss at 11 keV). The x rays are then detected using a Rayonix SX165 x-ray area detector. The detector has 2048 × 2048 pixels with 79 μm pixel size. The x-ray detector vertical plane (x–z) is located at a distance R_d (∼2.5 m) along the incident x-ray beam direction from the intersection of the x-ray beam and the HOPG. Figure 2 shows a typical single pulse spectrum on the Rayonix detector without a target. X-ray energy is related to height z above the direct x-ray beam in the detector plane,

At DCS, x rays are generated from one of the two undulators—U27 or U17 with periods of 2.7 cm or 1.72 cm, respectively. Figure 3 compares the tuning curves for each of the undulators, showing the coverage of the energy range. The on-axis brilliance was calculated using the XOP software package³⁵ with parameters for U27 (period length: 2.7 cm and number of periods: 88) and U17 (period length: 1.72 cm and number of periods: 137) and with an APS beam current of 100 mA and 7 GeV energy. The x rays from the first harmonic of the U27 undulator are used for the EXAFS measurements giving a peak energy range of 7.2 keV–16.8 keV. However, the intensity falls off drastically above 15 keV. On the lower energy side, below 8 keV, there is an additional issue of higher harmonic contamination, as discussed later. Figure 4 shows the calculated number of x-ray photons/eV emitted from a U27 undulator with the first harmonic peaked at ∼11.5 keV (using XOP³⁵). This energy spectrum is used for Ge K-edge (11.1036 keV)³⁰ EXAFS measurements. The bandwidth of the U27 undulator output is 560 eV FWHM and 1380 eV wide at 10% maximum, wide enough for EXAFS measurements. Figure 5 shows how the FWHM of the U27 first harmonic varies as a function of energy. Tapering the undulator gap can give a broader incident x-ray spectrum if desired, but at the expense of the decreased x-ray flux at a given energy.

The x-ray beam sizes and divergences are different in the horizontal and vertical directions and are defined by the front-end beam apertures [white-beam slits, 1.2 mm (V) × 1.5 mm (H)] and several x-ray focusing mirrors. The details of the x-ray beamline and the relative distances between the x-ray focusing components are shown in Fig. 1(a). The beam is focused on the sample at the target chamber with a beam spot size of ∼30 μm (V) × ∼50 μm (H). The vertical focus is achieved by a single vertical focusing Kirkpatrick–Baez (KB) mirror in the A-station (A-VFM) with a pitch of 2.1 mrad. The horizontal focus is achieved by a combination of two horizontal focusing KB mirrors: one in the A-station (A-HFM) with a pitch of 2.1 mrad and the other in the C-station (C-HFM) with a pitch range of 2.1 mrad–2.7 mrad. The beam spot size at the HOPG spectrometer is ∼40 μm (V) × ∼250 μm (H). The EXAFS configuration shown in Figs. 1 and 2 is well matched to the DCS x-ray source and optics, which provide a low vertical divergence x-ray beam (∼13 μrad FWHM) and a small vertical beam size (tens of micrometers tall) near the sample and HOPG.

In addition to focusing the x-ray beam, the KB mirrors also act as low pass filters, removing unwanted higher order harmonics from the x-ray beam incident on the sample. Removing higher harmonics from the incident x-ray beam is important because the second and third order harmonics will be diffracted from (004) and (006) graphite planes at the same scattering angle as the first harmonic from (002) graphite planes. The Si stripe on the KB mirrors is used for these EXAFS measurements since it has the proper cutoff energy at a given pitch. The two A-station mirrors (A-HFM and A-VFM) with Si stripes at 2.1 mrad pitches have a low-pass cutoff energy of ∼15.1 keV and the C-station mirror (C-HFM) with the Si stripe at 2.4 mrad pitch has a cutoff energy of ∼13.2 keV. Figure 4 shows that the KB mirrors effectively filter out the higher harmonics when the undulator gap is set to examine the Ge K-edge. However, for energies below 8 keV, the contribution from the second harmonic will gradually become more significant as energy decreases. With a maximum possible C-HFM pitch of 2.7 mrad, the second harmonic peak intensity is ∼0.5% of that of the first harmonic at 7.9 keV, which increases to ∼1.3% at 7.2 keV.

HOPG with different degrees of mosaic spread are commercially available. For example, SPI Supplies offers grades 1, 2, and 3 HOPG with mosaic spreads of 0.4° ± 0.1°, 0.8° ± 0.2°, and 3.5° ± 1.5°, respectively. We can calculate the energy FWHM for each grade from Bragg’s law using dE = (E/tan θ)dθ, where dθ is the mosaic spread and θ is the Bragg angle for the graphite (002) reflection at energy E. Figure 5 shows the FWHM energy ranges that are diffracted from the various grades of HOPG as a function of center energy. It also shows the FWHM of the flux spectrum from the first harmonic of undulator U27. The U27 parameters were 2.7 cm period length, number of periods, N = 88, and calculations were performed using the standard APS simulation code TCAP with a ring current of 100 mA and 7 GeV energy. The FWHM of the flux spectrum from the U27 first harmonic is bracketed by the FWHMs diffracted by SPI grades 1 and 2 HOPG, making either grade a candidate for the spectrometer element. The SPI grade 2 HOPG was chosen as the spectrometer element because the U27 undulator flux spectrum has a large tail on the low energy side (see Fig. 4), and to capture the entire U27 undulator first harmonic with a reasonable reflectivity (>10%) requires a larger FWHM for the x rays diffracted from the HOPG than the U27 undulator first harmonic FWHM.

Theoretical x-ray reflectivities were calculated for HOPG as a function of thickness d_HOPG and mosaic spread using XOP software.³⁵ The calculations were done for graphite (002) reflection with the energy centered at 11.3 keV. Figures 6(a)–6(c) show the calculated HOPG reflectivities for the three HOPG grades at several HOPG thicknesses as a function of energy over an energy range suitable for Ge K-edge EXAFS measurements. Figure 6(d) shows the peak reflectivity as a function of HOPG thickness for the three different grades. The HOPG plate/x-ray beam angle in the y–z plane was chosen such that the (002) graphite planes, without misorientation, diffract 11.3 keV x rays. The SPI grade 2 HOPG provides a good combination between the high peak reflectivity and a fairly flat reflectivity curve (less than a factor of 2 variation in reflectivity over 1000 eV). Although the thicker HOPG has a higher overall reflectivity, as discussed next, energy resolution becomes poorer as the HOPG thickness increases. Therefore, an HOPG thickness of 100 μm was chosen as a compromise between reflectivity and energy resolution considerations. The corresponding average calculated HOPG reflectivity between 10.8 keV and 11.8 keV is 17.3%.

The actual reflectivity of a ∼100 μm thick SPI grade 2 HOPG was measured for x-ray spectra peaked near 12 keV and near 13 keV. A diode was first used to record a signal proportional to the flux of the direct x-ray beam at the location of the HOPG spectrometer. The same diode was then moved to record a signal proportional to the x-ray flux diffracted by the HOPG. The x-ray beam/HOPG angle was scanned to find the angle at which the reflectivity was maximized, resulting in ∼17% peak reflectivity for x rays near 12 keV and ∼16% peak reflectivity for x rays near 13 keV. The HOPG reflectivity calculations using XOP software³⁵ along with these measurements demonstrate that the HOPG acts as an efficient spectrometer suitable for the x-ray flux in single event experiments.

Energy resolution in EXAFS measurements is an important consideration as poor resolution will wash out sharp absorption features. Several parameters affect the achievable energy resolution.^32,33,36,37 These include the thickness of the HOPG, d_HOPG, the vertical size of the x-ray beam h at the HOPG, the vertical divergence δθ_v of the x-ray beam incident on the HOPG, the detector point spread function (DPSF), and the intrinsic diffraction broadening of the HOPG. The intrinsic diffraction broadening is due to a combination of the finite size of graphite crystallites along the c-axis in the HOPG (size broadening³⁴) and the c-axis d-spacing distribution δd₍₀₀₂₎ in the graphite (strain broadening^32,36). The effects of finite d_HOPG, h, and DPSF on the energy resolution are mitigated by increasing the HOPG to the detector plane distance R_d, but the DCS C-station configuration limits R_d to a maximum value of ∼2.5 m.

Before presenting measurements for the energy resolution of the EXAFS system, we estimate the energy resolution due to several parameters, presently ignoring any component of the HOPG c-axis misorientation transverse to the nominal diffraction plane; later, we comment on the effects of transverse misorientation on the energy resolution. The effective energy broadening δE₁ for purely monochromatic incident x rays due to finite d_HOPG and h can be calculated ignoring x-ray extinction in the HOPG,

In Eq. (3), w_d = [h + 2d_HOPG cos θ]/cos(2θ) is the height of the detected signal on the detector plane for monochromatic x rays solely due to d_HOPG and h. The energy spreads δE₂ solely due to the vertical divergence δθ_v of the x-ray beam incident on the HOPG, δE₃ solely due to DPSF, δE₄ solely due to crystallite size L_c of the HOPG grains along the c-axis,³⁴ and δE₅ solely due to c-axis lattice spacing distributions are given by Eqs. (4)–(7), respectively,

The actual energy resolution was measured as a function of energy using the Si(111) double crystal monochromator in the DCS A-station to produce an x-ray beam of bandwidth ∼1 eV incident on the HOPG spectrometer. The x rays dispersed by the HOPG were detected by a Rayonix SX165 x-ray area detector. The measured spectra were fitted to a pseudo-Voigt function to extract the FWHM. For these measurements, R_d = 1860 mm, d_HOPG = 100 μm, h ≈ 34 μm, the detector point spread function is ∼150 μm, and θ_v is ∼13 μrad. Figure 7(a) shows the FWHM of the measured energy spectra diffracted from the HOPG as a function of energy. The blue dashed line shows the energy resolution calculated by adding in quadrature to the various sources described above, other than intrinsic broadening of the HOPG (δE₄ and δE₅). The calculations also include the Darwin width of the Si(111) double crystal monochromator.³⁸ The energy resolution due to the Darwin width varies linearly with energy (from ∼0.9 eV at 7 keV to ∼1.8 eV at 14 keV). The large difference between the calculated and measured energy resolutions indicates that intrinsic broadening from the HOPG crystal contributes substantially to the overall energy resolution. Using reasonable values of L_c = 3 μm and δd₍₀₀₂₎ = 0.0025 Å to calculate the total energy resolution results in a good match between the calculated (red solid line in Fig. 7) and the measured energy resolutions, although independently determining precise values for L_c and δd₍₀₀₂₎ from the (002) graphite peak diffraction is not possible. In any case, the measured energy resolution is a better indicator of the actual energy resolution than the calculated energy resolution. Near the Ge K-edge at 11.1 keV, the energy resolution is ∼12 eV. Figure 7(b) shows the same data and calculations as in Fig. 7(a), except that E/ΔE is plotted rather than ΔE. The measured values of E/ΔE range from ∼800 to 1000, similar to the other reported E/ΔE values when the (002) graphite planes of HOPG are used to energy disperse x rays.^32,36 As we will show later, this resolution is good enough for EXAFS measurements, but not sufficient to resolve the fine structures near the edge in the XANES region.

Beer’s law²¹ describes the transmission of x rays through the sample as

In Eq. (8), I₀(E) is the x-ray flux incident on the sample, I_trans(E) is the x-ray flux transmitted through the sample, μ(E) is the energy-dependent absorption coefficient, and t is the effective sample thickness (thickness of the sample material along the x-ray beam path).

The two-dimensional image shown in Fig. 2, obtained without a sample in the x-ray beam, is integrated horizontally (along $x^$⁠) to obtain the monitor spectrum I_monitor(E),

In Eq. (9), I_source(E) is the spectral flux from the undulator source modified by the mirror reflectivities and any absorption along the beamline (air gaps and Kapton windows), excluding sample absorption. R_HOPG(E) is the energy dependent reflectivity of the HOPG via diffraction from (002) graphite planes. S_Det(E) is the energy dependent quantum efficiency of the Rayonix detector. Figure 8 shows a typical single pulse monitor spectrum I_monitor(E) with a configuration setup to examine Ge K-edge EXAFS. The width and shape of the monitor spectrum are largely due to the undulator source spectrum.

The two-dimensional x-ray image recorded with a sample in the x-ray beam path is also integrated horizontally to obtain I(E),

The horizontal pixel range used in the integration is the same as used to determine I_monitor(E). A representative single pulse spectrum I(E) for a Ge sample is shown in Fig. 8. In Eq. (10), T_sample(E) is the transmission of x rays through the sample as a function of energy. All factors common to Eqs. (9) and (10) are nominally identical during the measurements of I_monitor(E) and I(E), and the product of the absorption coefficient times the effective sample thickness is given by

The effective sample thickness t = d_sample/sin ϕ is known from the metrology of the actual sample thickness d_sample and the x-ray beam/sample angle ϕ. Thus, with the x-ray absorption spectroscopy configuration used at the DCS, an absolute measure of μ(E) can be directly determined from the measurements of I_monitor(E) and I(E), provided the product of I_source(E), R_HOPG(E), and S_Det(E) does not change between single x-ray pulse measurements. The stability of this product or I_monitor(E) is demonstrated in Sec. III. The product μ(E)t vs energy calculated from the single pulse monitor and sample spectra (see Fig. 8) is shown in Fig. 9(a).

To determine the pixel range over which the horizontal integration is performed when calculating I_monitor(E) and I(E), the image is first integrated vertically (along $z^$ in Fig. 2) and the horizontal pixel indices at the peak value and at the two half peak values are determined. The horizontal integration range extends three times from the difference between the peak-value pixel index and the half-peak-value pixel indices. A background is also subtracted from I_monitor(E) and I(E) to account for the small offset in counts in each pixel.

The reason that the recorded x-ray signal is broad in the $x^$ direction is due to the HOPG c-axis mosaic spread. The HOPG mosaic spread component in the y–z plane provides the energy dispersion vertically on the detector, and the transverse mosaic spread component causes the broadening in the $x^$ direction. Because the diffracted x rays at a fixed energy form a diffraction cone, integrating horizontally along a row of pixels on the detector introduces an additional contribution, reducing energy resolution. For a typical configuration, this additional broadening in a single row of pixels is less than 1 eV and is a small fraction of the overall energy resolution.

Due to the high single pulse x-ray flux (∼4 × 10⁹ x rays per pulse), high HOPG integrated reflectivity (∼15%), and high detector quantum efficiency (>90% over the 9 keV–13 keV range for the 80 μm thick phosphor used in the Rayonix SX165 detector), a high signal to noise ratio (SNR) can be achieved in EXAFS measurements at the DCS. As an example, we consider the Ge K-edge EXAFS measurement shown in Fig. 9(a). To obtain the incident number of photons/eV on the detector, the red dashed curve in Fig. 4 is multiplied by (1) the transmission through windows and air gaps (calculated to be 0.5), (2) transmission through the Ge sample given by the measured ratio of I(E)/I_monitor(E), where the two spectra are shown in Fig. 8, (3) the HOPG reflectivity [blue curve in Fig. 6(b)], and (4) the detector quantum efficiency. The calculated SNR for μ(E)t was based on a Poisson distribution for the number of x-ray photons reaching the detector per row of pixels. Readout noise in each pixel (9e⁻) was also included in the SNR calculation and corresponds to approximately one x-ray photon/pixel. The noise is dominated by the photon statistics. The calculated SNR and the estimated SNR based on the measurements are shown in Fig. 9(b). To estimate the SNR for the measurement, a smoothing function was generated from the data, which was then used as a baseline to calculate the average variance within an energy window. The measured SNR is ∼1000, while the calculated SNR for μ(E)t is ∼500 for each row of pixels (∼1 eV energy range/pixel) over the energy range used for Ge EXAFS measurements. The calculation seems to underestimate the actual SNR by a factor of 2. Because the energy resolution solely due to the height of a single pixel (∼1 eV resolution) is significantly smaller than the total energy resolution (∼12 eV), it is possible to average the signal over several rows of pixels to improve the calculated SNR without significant additional broadening of the absorption spectra. For example, averaging over seven rows of pixels increases the calculated SNR to over 1000.

As mentioned in Sec. II, the stability of I_monitor(E) [see Eq. (9)] is important for the accuracy and reproducibility of the extracted EXAFS oscillations. Assuming that the quantum efficiency of the Rayonix detector S_Det(E) is constant, the stability of I_monitor(E) depends on the HOPG reflectivity R_HOPG(E) and the source spectrum I_source(E). While I_source(E) should not change, except for the minor variation in the flux, R_HOPG(E) can vary depending on the mosaic distribution of the HOPG crystal, which can vary spatially in the HOPG. Therefore, in order to maintain a defined spectrometer element on the HOPG, two important steps were taken. First, a back-end x-ray camera was placed downstream of the HOPG to establish the half-cut and the zero angle (i.e., 2θ = 0° in Fig. 2) of the HOPG spectrometer. Using this as a fiducial, we can then adjust for any vertical drift in the x-ray beam during the experiment. Second, a pair of horizontal and vertical x-ray slits centered on the incident x-ray beam were placed just upstream of the HOPG to define the size of the x-ray beam incident on the HOPG. If we did not establish a stringent horizontal window of the x-ray beam, we found distinct changes in the monitor x-ray spectrum that drifted in time. Therefore, the horizontal x-ray slit had an opening width ∼100 μm narrower than the horizontal width of the incident x-ray beam on the HOPG. The final width of the horizontal x-ray slit was ∼170 μm. The vertical x-ray slit was kept relaxed. The vertical position was monitored with the back-end camera and adjusted as needed by changing the A-station vertical mirror pitch. These steps established a well defined stable region of the HOPG, acting as the spectrometer element.

Figure 10(a) shows a series of five monitor spectra from five single x-ray pulses, showing a minor pulse-to-pulse variation in maximum intensity. When normalized to the maximum intensity, all the scans fall almost on the same curve, as shown in Fig. 10(b). The percentage differences of the individual scans from their mean curve are within ±2% [Fig. 10(c)], and the standard deviation is ∼1.0% to 2.0% over the scan range [Fig. 10(d)], confirming the stability and reproducibility of the monitor spectra.

Figure 11 shows the normalized absorption spectra for Cu (K-edge 8.98 keV)³⁰ and Au (L3-edge 11.92 keV).³⁰ The single pulse x-ray measurements were performed on 5 μm thick Cu and Au foils under ambient conditions. Our data are compared with the reference data available from the APS XAFS spectra library.³¹ As pointed out previously, our measurements do not have high enough resolution to resolve the fine structures associated with XANES (the region about 10 eV below the absorption edge and ∼20 eV above the edge). Instead, our system has been designed and optimized for the EXAFS region. For both Cu and Au, clear EXAFS features can be observed up to ∼400 eV above the absorption edge, which are in good agreement with the reference spectra. The EXAFS signal χ(k) can be calculated by

where k is the wave number of the photo-electron given by $k=2mℏ2(E−E0)$⁠, m is the electron mass, ℏ is the reduced Planck’s constant, μ(k) is the measured absorption coefficient, μ₀(k) is the background absorption coefficient ignoring photoelectron scattering from neighboring atoms, and Δμ₀(k) is the jump in the absorption coefficient at the threshold energy E₀. Figure 12 shows the k² weighted χ(k) for Cu and Au, calculated using the ATHENA software package.³⁹ The results are compared to the k²χ(k) obtained for the reference data. The usable χ(k) is in the range k = 3 Å⁻¹–10 Å⁻¹ above which it becomes increasingly noisy. Over this range, the main oscillations and their amplitudes are in good agreement with the reference data for both Cu and Au. However, as expected from a single x-ray pulse measurement, our data are slightly noisier than the reference data. Below ∼3 Å⁻¹ our observed EXAFS oscillation amplitudes, particularly for Au, are also significantly smaller than the reference data likely due to the lower spectral resolution in our single pulse configuration.⁴⁰ 

Figure 13(a) shows the experimental configuration for laser shock compression of a Ge(100) sample. The target consisted of a 50 μm thick aluminized Kapton ablator epoxy bonded to a ∼15 μm thick Ge(100) single crystal, which was mounted on an aluminum bar, as shown in Fig. 13(b). The Al bar had a countersunk through-hole located beneath the Ge/Kapton allowing the laser drive and x rays to directly reach the Kapton/Ge without reflection or absorption from the Al bar. The aluminum bar was attached to a rotating sample holder wheel, which itself was attached to a kinematic stage.²⁹ Velocity interferometry measurements were performed using a central VISAR (Velocity Interferometer System for Any Reflector)⁴¹ probe with ∼600 ps time resolution and four Photon Doppler Velocimetry (PDV) probes.⁴² One PDV probe was reflecting from the center of the sample (overlapping with VISAR), and three PDV probes were reflecting from a circle around it on a 125 μm radius at 120° spacing around the circle. The VISAR spot size was 90 μm FWHM, and the PDV spot sizes were 20 μm. The PDV data were analyzed using a Fast Fourier Transform (FFT) window-size of 1.28 ns and a Hamming window-function of 0.67 ns FWHM. The x-ray monitor signal was measured with a calibration target consisting of 50 μm aluminized Kapton while the ambient Ge measurements were performed just before the sample was shocked. For shock compression, the aluminized side of the Kapton was ablated using a 10 ns duration laser pulse with ∼16 J of energy. The laser pulse is incident at 7° from the sample-normal in order to minimize the laser reflection from the ablator front surface back to the upstream optics and laser system. The temporal profile of the 10 ns duration laser pulse with 500 μm Distributed Phase Plate (DPP) is shown in the inset of Fig. 13(c). Laser ablation of the Kapton results in the formation of a 500 μm diameter plane shock wave in the Kapton, which then propagates into the Ge sample.

The free surface velocity histories of the Ge(100) sample recorded using the VISAR⁴¹ and the four PDV probes⁴² are shown in Fig. 13(c). They show an elastic wave followed by a slower phase transformation wave. All four of the measured shock breakouts using the PDV probes were within 100 ps. This is close to the 40 ps/point PDV digitization rate and also close to the ±40 ps relative timing accuracy between PDV probes. We cannot resolve any spatial variations in shock breakout timing due to the possible target thickness variations over the 250 μm PDV probe diameter. However, we note that the spatial shock stress variations are expected to be less than 1% over the 250 μm PDV probe diameter since the average peak state free surface velocities from each PDV probe agree within ±1%. The peak state free surface velocities and phase change shock arrival times are also consistent between all four PDV probes and the VISAR probe. By comparing the free surface velocity after the phase transformation wave arrival with the previous results from Gust and Royce,⁴³ the peak state stress is determined to be 29(2) GPa. For this peak stress, continuum results suggest transformation to a high-pressure structure,⁴³ which was recently identified as the β-Sn structure using in situ XRD measurements in Ge(100) subjected to plate impact loading.⁴⁴ 

Figure 14 shows the single pulse x-ray absorption spectra from a Ge(100) single crystal prior to shock compression and during laser shock-compression, plotted as a function of photon energy transfer, E − E_k, where E is the incident energy and E_k = 11.1036 keV is the Ge K-edge. The ambient spectrum shows distinct EXAFS features up to 500 eV above the K-edge. The small peak around ∼570 eV energy transfer is due to extinction via Laue diffraction from the single crystal Ge. The laser shocked Ge spectrum at 29(2) GPa shows EXAFS features that are distinctly different from the ambient data. The absorption spectrum from the shocked Ge was obtained shortly before the phase transformation shock wave reached the rear surface of the Ge sample, so the majority of the Ge is expected to be in the β-Sn structure⁴⁴ during the EXAFS measurement. Detailed analysis and fits to the EXAFS data on laser shocked Ge will be presented elsewhere. Here, we present our analysis of the ambient Ge spectrum.

Quantitative analysis of the ambient Ge absorption spectrum is performed using the ATHENA and ARTEMIS software packages.³⁹ The EXAFS signal χ(k) was obtained after removing the background and normalizing the data with the edge-step using ATHENA. The k-weighted EXAFS signal χ(k) is shown in Fig. 15(a), while the modulus of the Fourier transform of χ(k) is shown in Fig. 15(b). The simulated EXAFS signal was then fitted to the data using ARTEMIS. Ge is in the cubic diamond phase under ambient conditions.⁴⁵ Back-scattering amplitudes and phases were thus calculated using the cubic diamond structural model, and the first three neighboring shell Ge–Ge paths were considered for the modeling. Assuming only volumetric lattice expansion, only one parameter is needed for varying the Ge–Ge distances during the fit. Additionally, the amplitude reduction factor $S02$⁠, energy shift E₀, and the Debye–Waller factors for the three paths $σi2$ (i = 1, 2, 3) were also allowed to vary. The coordination number, N, for each scattering path was fixed during the fitting. The Fourier transform from χ(k) to χ(R) was performed within a Hanning window of k-range 3.0 Å⁻¹–11.5 Å⁻¹. The fit to the model was performed in χ(R) space within a R-range of 1.25 Å–4.7 Å, as shown in Fig. 15(b). From the fit, $S02$ was found to be 0.93 ± 0.07, while E₀ was 3.0 ± 0.8 eV. The fitted values of bond lengths (R_fit) and σ² values are shown in Table II. The Debye–Waller factors, $σi2$⁠, correspond to the mean-square relative displacement along the different bond directions, and the fitted values are within the reported range.^46–48 The fitted bond lengths (R_fit) are in agreement with the known structural parameters (R_eff) and published results.^45,46 This is also represented in Fig. 15(b), where the three distinct measured peaks are contributions from the first three neighboring shell Ge–Ge paths; the simulated peaks provide an excellent match to the measured peaks.

We have demonstrated that high quality real-time single x-ray pulse EXAFS measurements on dynamically compressed materials can be performed at the DCS for materials with absorption edges ranging from ∼9 keV to 13 keV. Using a flat plate of HOPG as the spectrometer element to energy disperse x rays, in combination with a high quantum efficiency detector (>90%), we have obtained good SNRs (∼10³), an energy resolution of ∼10 eV at 10 keV, and pulse to pulse reproducibility (<2.0% SD) of our single pulse EXAFS measurements. This can be confirmed from the comparison of ambient and reference spectra of Cu and Au. The energy resolution of ∼10 eV is good enough for the EXAFS experiment, but not sufficient for XANES. The lower spectral resolution also results in the reduced amplitude of EXAFS oscillations in the low-k region as observed in the Au spectrum, where the amplitude of k²χ(k) agrees poorly in the low-k region but matches well in the high-k region.⁴⁰ This will not affect the evaluation of the atomic bond distances but may affect the coordination numbers and Debye–Waller factors extracted from the fitting process.⁴⁰ However, we note that for the ambient Ge EXAFS data presented here, the Debye–Waller factors obtained from fitting are within the ranges of the previously published values.^46–48 

Based on our EXAFS measurements using the new DCS system on a variety of elements with absorption edges between 9 keV and 13 keV, clear single pulse EXAFS oscillations were observed up to ∼350 eV to 550 eV beyond the absorption edge, depending on the material. For example, for Cu, Ge, and Au, clear EXAFS oscillations were observed up to 400 eV, 550 eV, and 350 eV beyond the edge, respectively. The useable ranges of EXAFS oscillations were all smaller than expected based on the FWHM of the HOPG reflectivity (red curve in Fig. 5). This is, in part, because the FWHM of the undulator flux spectrum is narrower than the HOPG reflectivity FWHM. In addition, we had less than optimal matching between undulator energies and HOPG spectrometer angles for some of our measurements (for example, Au). For the Ge measurements, the useable EXAFS energy range was ∼400 eV smaller than expected based on the FWHM of the HOPG reflectivity curve at 11.5 keV. A potential option for expanding the useable EXAFS energy range is to taper the U27 undulator gap. This will increase the bandwidth of incident x rays to better match the width of the HOPG reflectivity, provided the HOPG center angle (energy) and the undulator energies are well matched. However, tapering the undulator will reduce the number of incident x rays/eV and will lower the SNR. Because tapering the undulator to extend the useable EXAFS range has not yet been explored experimentally at the DCS, future DCS users can safely expect ∼350 eV to 550 eV of useable EXAFS oscillations for absorption edges between 9 keV and 13 keV.

We have performed EXAFS measurements on a shock-compressed material for energies above 8 keV for the first time at the Ge K-edge of 11.1036 keV. Fitting a simulated ambient Ge EXAFS spectrum to the ambient Ge data gives an excellent match using the known structural parameters. The EXAFS spectrum obtained for the shock compressed Ge exhibits substantial changes from the ambient Ge spectra, indicating significant changes in the local structure of the shock compressed Ge.

For reference, the DCS 100 J laser can currently provide peak stresses between ∼30 GPa and 400 GPa, depending on the sample material, through single shock loading. As demonstrated in the present work for Ge, at the lower end of the accessible stress range for shocked Ge, the increased temperature due to shock compression does not diminish the EXAFS oscillation amplitudes significantly. The EXAFS Debye–Waller factor decreases with compression and increases with temperature, and for a single material phase, EXAFS oscillation amplitudes will increase up to a certain shock stress, followed by a rapid reduction with shock stress when the material becomes stiffer and temperature increases rapidly with shock stress. For high enough shock stress, the material will melt, resulting in even weaker EXAFS oscillations. The 100 J laser was also designed for ramp compression, which results in lower temperature for a given peak stress. Future laser compression experiments with the new EXAFS capability at the DCS will elucidate the degree of thermal disorder that can be quantitatively examined with the current system. Finally, the EXAFS capability presented here—combined with the DCS laser shock capability—is ready for user experiments.

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Dr. J. Hawreliak and Dr. S. Sharma are thanked for useful discussions regarding this work. This publication is based on the work performed at the Dynamic Compression Sector, which is operated by Washington State University under the U.S. Department of Energy (DOE), National Nuclear Security Administration (NNSA) Award No. DE-NA0002442. This research used resources of the Advanced Photon Source, a DOE Office of Science User Facility operated for the DOE Office of Science by Argonne National Laboratory under Contract No. DE-AC02-06CH11357. This publication is also based on work supported by the DOE NNSA under Award No. DE-NA0002007.