New frontiers in extreme conditions science at synchrotrons and free electron lasers

2.1.1. Static compression platforms

2.1.2. Shock dynamic compression

2.2.1. Static compression platforms

2.2.2. Shock dynamic compression

Planetary science is witnessing a revolution with the discovery of hundreds of extra-solar planets orbiting nearby stars [81]. Characterising such astrophysical objects requires the knowledge of physical properties of their main constituents at multi-Mbar pressures and few-eV temperatures (1 eV = 10 605 K). A first key requisite for this research is the establishment of phase diagrams in order to identify structural changes, phase transitions, metallization, and dissociation processes at planetary interior conditions. In the interior of celestial bodies, matter can be found in exotic states such as the warm dense matter (WDM) state, with densities of the same order of magnitude of a solid (between 0.01 and 100 g cm⁻³) and temperatures ranging from 0.1 eV to 100 eV, e.g. the temperature of stellar cores. Such dense plasmas are weakly ionized, strongly coupled and partially degenerate. This intriguing regime provides a tremendous challenge for theoretical models as conventional approximations that apply to condensed matter physics are not always valid for plasmas. WDM states are not only found in astrophysical objects or events, such as space impacts, but also in inertial confinement fusion and industrial applications such as laser machining. In this section we will discuss recent results and future opportunities for the investigations of matter at conditions relevant for planetary and energy science.

In the last decade, the coupling of dedicated laser heating systems [4, 58] to different synchrotron techniques such as XRD, XAS, SMS has allowed to determine melting curves of 3d metals like Fe, Co and Ni [3, 10, 72, 78, 154] and their alloys [9, 73, 89, 129] up to the Mbar range, and to measure the local structure of the compressed melts along their melting curve [89, 155]. These results find a direct application in geophysics and planetary science, where from the study of metallic melts physicochemical properties at extreme conditions, such as density, viscosity, electrical and thermal conductivity, it becomes possible to characterize the structure and geodynamic behavior of planetary bodies, among them the Earth. Here as a first example we focus on iron. The turbulent motions of the liquid Earth's our core, mainly constituted by FeNi alloys, in combination with the rotation of the Earth, generate the magnetic field that protect the surface from the incoming solar radiation, hence preserving a habitable planet. Being able to determine the melting temperature of iron at those pressures becomes of uttermost importance to improve our ability to understand and predict deep Earth's dynamics. After many years of controversies, i.e. [3, 11, 12, 54, 153], a final consensus on the melting temperature of iron at Earth's core pressures was reached and determined to be 4250(±250) K at the core mantle boundary, ca 136 GPa [78] (figure 3, left top panel). In these experiments Morard et al [78] coupled in situ LH-DAC to energy dispersive XAS at the Fe K-edge, taking full advantage of the large energy range simultaneously provided using XAS dispervise optics (polychromator), thus very fast acquisition (down to ms). Similar experiments were performed to investigate the local structure of Ni and Co melts at extreme pressures [155]. No phase transitions were detected in the melts, but a considerable shortening up to 8%–10% of the metal bonds distances was reported for Ni and Co at ca 100 and 80 GPa respectively. EXAFS data and related fittings are shown in figure 3 (left bottom panel).

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At the ESRF, iron has been investigated also up to the WDM regime, 500 GPa and 17 000 K, under dynamic solicitation by coupling a portable 35 J laser to time resolved XAS [130]. Single pulse (100 ps long) XAS data have been recorded showing modifications of the XANES and initial EXAFS shape that correspond to solid–solid bcc to hcp phase transition (black and purple lines in figure 3 (right panel), and solid–liquid (melting) transition (red and orange spectra). Interestingly, the persistence of EXAFS oscillation was observed at the most extreme conditions reached, indicating the existence of local ordering in the dense plasma. Moreover a close inspection at the edge region, not shown here, reveals a quite small redshift (0.5 eV) with respect to what predicted by QDM simulations at similar conditions, approximately 2 eV. In general, the K-edge shift indicates a modification of the electronic structure linked to a change in the relative energy difference between the 1s core level and the Fermi level, both affected by temperature and pressure. Such shift under very extreme conditions is not easily predicted by ab-initio theoretical models, mainly due to computational challenges to describe the core level variation, i.e. [154]. What is most notable in this proof of principle experiment is that the XAS data quality for spectra acquired during single bunch experiments is sufficiently good to allow standard EXAFS analysis in solid samples investigations and for a fine comparison to QMD simulations in the liquids.

Using laser-induced dynamic compression to address planetary interiors remains a challenge, because planetary core conditions are typically colder than the typical thermodynamical states achievable by single laser pulse generated dynamic compression, i.e. Hugoniot states. Laser ramp-compression [100] overcomes this problem by shocking multiple times the sample with increasing shock intensities thus limiting the heat flow, and achieving a quasi-isentropic temperature path [33]. Scientists at LCLS used a two stage ramp-compression coupled to XRD to probe the dissociation of hydrogen from carbon (diamond) at 150 GPa and 5000 K in shocked polystyrene (C₈H₈), simulating conditions of the interior of Neptune and Uranus [62]. However, a disadvantage of this technique are the potential shock wave instabilities caused by large-amplitude pressure waves, and the required laser energy, which for a multistage ramp-compression to several Mbar is too high for the lasers presently installed at large x-ray facilities. An alternative technique is the combination of a laser shock with a sample that is pre-compressed in a DAC. The higher density of the pre-compressed sample with respect to ambient conditions, allows probing material properties at colder states with respect to Hugoniot ones. So far, this technique has been demonstrated only at large laser facilities [15, 16, 34, 75, 76] using moderate pre-compression pressures (within 5 GPa). The initial onset pressure of the pre-compressed sample is extremely important not only as it determines the achievable final pressure and compression path, but also because within the same chemical composition, pressure induced phase transitions can influence the subsequent compression-density curve upon shock. The development of this setup is at present carried out at EuXFEL, and will be available in the next few years for the user community.

Metallization and spin transitions are among the most common pressure-induced electronic transitions being investigated at x-ray facilities. Metallization occurs when the material develops a solid lattice of ions under compression, while the electrons of the interacting atoms delocalize: instead of orbiting their respective metal atom, electrons move freely throughout the lattice between the atomic nuclei. The most famous example is hydrogen metallization, which is driving the research efforts of an entire community since decades, as outlined in reference [47] and references therein reported. In the years after its first prediction in 1935 by Wigner and Huntingon [140], metallic hydrogen was attributed very fascinating properties such as room temperature superconductivity [5] and superfluidity [6]. Its discovery was described by the Noble Price winner Ginzburg as one of the most important and interesting questions in physics and astrophysics of the century [43], mainly because hydrogen is the most abundant element in the Universe and the main component in production of clean energy via fusion reactions. Recently this year, Loubeyre et al [74] reported synchrotron infrared absorption measurements demonstrating that the amount of infrared light going through a hydrogen sample at 425 GPa is reduced by a factor of around 10⁻² compared to lower pressure, suggesting a first order phase transition to metal hydrogen near 425 GPa. Further studies will have to reproduce similar results to finally reach the consensus from the community, but there seems to be a general convergence of results that points to pressures above 400 GPa for metallization to happen i.e. [30, 35, 156]. Hydrogen is only the simplest and lightest element to metallize, but any system, molecular or atomic, exhibits the same behavior at sufficiently high pressures. For example, at ambient temperature the metallization of xenon was determined at 130 GPa [27], while the metallization of krypton is only predicted to occur beyond 400 GPa [111]. Helium, the second most abundant element in the Universe, is predicted to metallize only at P > 10 TPa [146] or 13 g cm⁻³ at 0 K, but band gap closure might occur at lower densities, ∼1.9 g cm⁻³, provided the effect of high temperatures (>60 000 K)f is taken into account [16]. The latter results were obtained by optical measurements of reflectivity and temperature by shock-compressed high density (pre-compressed) He in DAC. Clearly, the biggest challenge in the detection of these transitions is to overcome the limits imposed by the experimental setups and diagnostic techniques, thus the development of large scale facilities that provide state-of-the-art experimental and x-ray methods to probe these phenomena at extreme conditions becomes essential.

Electronic transitions have been predicted and observed in many systems at sufficiently high pressures, e.g. [31]. In particular, pressure induced spin transitions in 3d metal compounds are among the most commonly studied because of the ability of 3d metals to exists in multiple valence states, thus forming an incredible number of compounds with different electronic configurations. In a field-free transition-metal ion, the d-electrons are fully degenerate (i.e. the energy of the five d-orbitals is identical). When the ion is placed in a negative electric field, for instance an octahedral field as could be experienced by Fe²⁺ surrounded by six oxygen anions, the degeneracy of the d-levels is destroyed and the orbitals group into two sets of unequal energy, two higher energies e_g and three lower energies t_2g orbitals [48]. These are related to the different spatial configurations of the d-orbitals in relation to the octahedral field [42]. This electronic configuration is known as high-spin (HS) state. If the splitting of the levels becomes sufficiently large at high pressures due to the shortening of the bond lengths, the electrons may obtain a sufficient energy from the coupling to overcome the repulsion barrier and may pair, where all 3d electrons are in the lower energy t_2g orbitals. This electronic configuration is known as low-spin (LS) state. Pressure-induced spin transitions have been extensively investigated at synchrotrons for Fe-bearing materials of geological relevance [69]. The pairing of Fe 3d electrons causes the collapse of the unit cell, which shrinks, but generally does not lead to a structural phase transition. Low-spin structures have higher densities, affecting properties such as the heat transport and chemical partitioning but also the speed and direction of propagation of seismic waves through the Earth. Spin crossover is also of interest in nanotechnology, where Fe-containing nanomaterials showed potential applications in sensing, actuating, and information processing devices [87]. Studies of spin transitions at synchrotrons have been performed using a wide variety of techniques, from XRD [66, 70, 122] to XAS [17, 59, 118], SMS [18, 64, 87, 122], XES [80, 114] and XRS [137, 138], providing information on the effects of this process at the structural, electronic and nuclear levels. In a recent combined effort between HED scientists and external collaborators (figure 4, caption), a spin transition in FeCO₃ was detected at the HED instrument using a combination of XRD and XES techniques, in vacuum at 13 keV photon energy. The setup was installed in IC1 and used a single Si (531) cylindrically bent von Hamos crystal coupled to an ePIX100 detector to measure the Kβ emission line with 0.4 eV spectral resolution. Jungfrau and ePIX100 detectors were placed downstream of the sample to collect simultaneously the XRD signal (figure 4). This experiment benchmarks the possibility to study materials at P above 50 GPa in DACs at XFELs, simultaneously acquiring XES and XRD data, also in combination with high temperatures (>2000 K) generated via x-ray heating (section 3.3.1). In the future, four cylindrically bent Si (531) von Hamos crystals will be available, significantly increasing the detection efficiency and reducing the acquisition times for XES spectra, thus opening up new capabilities for the study of electronic transitions in liquids at high pressures.

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3.3.1. Ultrafast x-ray heating at XFELs

The ultrashort, intense and fully tunable x-ray pulses of an XFEL can excite the electronic system of matter to extreme states. Typical conditions at EuXFEL, i.e. photons of energy 6–10 keV, ∼2 mJ pulse energy delivered in ∼25 fs lead to intensities of the order of 2 × 10¹⁷ W cm⁻² when focused to a 5 μm FWHM area. These focused x-ray pulses excite solid-density matter volumetrically, as nonlinear effects are negligible and the photo absorption follows the Lambert–Beer law. However, saturation effects can occur at high intensities [91, 107], which make the energy deposition along the beam more homogeneous. The x-ray pulses excite bound electrons at timescales shorter than a phonon vibrational period, and predominantly couple to certain atomic orbitals when the photon energy is close to atomic resonances or absorption edges [124, 134, 145]. This can be used to excite buried layers or dopants, and higher-Z materials in low-Z containments such as DACs, to electron temperatures exceeding several 100 eV. It is, however, also a potential disturbance to a measurement when intense x-ray are required, e.g. for 'photon hungry' IXS studies, as the intense x-rays excite the electrons and subsequently the ions. In some cases, heating of the sample, or damage and even destruction of the DAC, are undesired side effects.

In a metallic solid, photo-electrons equilibrate with the remaining electronic subsystem into a temperature-like distribution within a few 100 femtoseconds [84]. As the excitation happens faster than any hydrodynamic motion, the ionic lattice at the time of excitation is still cold and the density is constant. Consequently, energy transfer from electrons to ions, which typically occur on picosecond time scales, can only be studied with ultrashort XFEL sources [150].

Another unique possibility at EuXFEL is x-ray excitation of a sample with a MHz burst of subsequent x-ray pulses. Free standing or contained samples (e.g., in DAC) can be sequentially and volumetrically heated and studied with x-ray and optical techniques at the same time. While the minimum delay between two pulses is limited to 222 ns, in the future the HED instrument will also provide x-ray pump–x-ray probe capabilities with delays down to the fs scale, using either a split-and-delay line [79] or a two-pulse mode of the EuXFEL itself.

The x-ray heating of samples in DACs is an interesting alternative to laser heating methods usually adopted to achieve high temperatures at high pressures. The rapid irradiation by the intense hard x-ray pulses generates heating that on the longer timescales (ns, μs) can be considered to be in equilibrium (in terms of electrons and ions temperature). DAC experiments at HED can take advantage of this to reach high temperature states simply by irradiating samples with high repetition x-ray pulses. The volumetric absorption of the x-rays generates much more uniform heating along the x-ray propagation direction as compared to e.g. infrared laser heating. The cooling rates in a typical DAC configuration were calculated to be of the order of few microseconds [85], giving the possibility to simultaneously create and study high temperature states by subsequent x-ray pulses at 2.2 or even 4.5 MHz. Figure 5 illustrates the simulated temperature evolution of a DAC sample subjected to low (0.45 MHz) and high (4.5 MHz) x-ray repetition rates. At x-ray pulse spacing longer than 2 μs (0.45 MHz), the temperature of the sample drops to almost the initial value before the arrival of the next pulse (figure 5, left). At higher repetition rates, however, the pulse train increases the sample temperature in a step-wise manner with the peak temperatures eventually reaching a saturation value after about 10 pulses (figure 5, right). The temperature plateau is given by a balance between the cooling rates and the heat added by the x-ray pulses [85].

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First DAC experiments at HED in IC1 and IC2 confirmed the predictions about the effect of the pulse trains on heating as a function of the XFEL repetition rate. X-ray diffraction experiments show no thermal shift of peaks due to lattice expansion at 0.45 MHz repetition rates. At 2.2 MHz pulse repetition, however, shifts in all sample diffraction lines towards lower diffraction angles are observed corresponding to the elevated sample temperature (at the moment of the incident x-ray pulse). Additional time-resolved diagnostics is available to measure thermal emission from the heated sample to constrain the temperature evolution during the xfel pulse train. An optical streaked pyrometry system detects the emitted light in the visible spectral range with nanosecond time-resolution. A typical time window used is 5 μs during which thermal response from 10 xfel pulses at 2.2 MHz can be detected (figure 6). At each point of time (in the vertical axis) the spectrum can be fitted to Planck's law to derive the temperature evolution during the pulse train. Additionally to the x-ray heating, the experimental setup features a nanosecond IR pulsed laser for sample heating. Figure 6 demonstrates an example of an experiment where a 300 ns IR pulse arrives ahead of the 10 pulse xfel train. Thermal signal integrated on the time axis shows large thermal response from the laser pulse due to predominantly surface heating and laser spot size being larger than that of the x-ray. After dissipation of the laser pulse energy (cooling time > 1 μs), heating by subsequent x-ray pulses are visible in the step-wise increase of the thermal emission signal. Temperature determination from the time-resolved spectral intensity distribution will be discussed in more detail elsewhere.

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3.3.2. Inelastic x-ray scattering and the dielectric function

Matter at extreme conditions may be partially ionized, or exhibit metallic properties. The properties of this subsystem of free and quasi-free electrons define key thermodynamic properties [67], optical properties (refractive index, dielectric function) [22, 123], and transport properties (electrical and thermal conductivity) [142].

Several models exist for the response of the materials electronic subsystem to an external electromagnetic field, the dielectric function, for example the Drude model. Other concepts use the Bohm–Gross approach and yield a semi-classical approximate solution in random phase approximation which does not include collisions [13]. Refinements include quantum mechanical effects [142], electron–ion collisions [128], electron–electron correlations, and quantum degeneracy [40]. The importance of these effects for different areas in the phase diagram of matter at extremes has to be validated by experimental data. Here, a powerful connection exists to inelastic x-ray scattering [44], since the structure factor of the electrons is related to the imaginary part of the inverse dielectric function for collective, longitudinal electron waves, the plasmons.

In order to scatter photons from plasmon waves rather than from individually moving electrons, the scattering lengths needs to exceed the electronic screening length [44]. At the densities of relevance here, this requires photon energies of order 5–10 keV at scattering angles of 5–45°. In this context, an advantage of XFELs with respect to synchrotrons is the higher beam intensity at lower photon energy. This enables to work at lower x-ray energies (down to 5 keV) and larger scattering angles (up to 45 deg), overcoming background scattering and k-vector blurring [147].

The frequency of the longitudinal electron wave (the plasmon resonance), is related to the free electron density. In shock-compressed matter up to a few Mbar, the internal energy gain is typically not sufficient to further pressure-ionize matter. Therefore, the free-electron density n_e has a fixed ratio to the atomic density n, and the measurement of the plasmon resonance is a measurement of the density.

Typical values of plasma frequencies of metals at ambient conditions are ∼10–20 eV. In order to resolve the plasmon resonance position to determine the density, an energy resolution better than 10 eV at 5–10 keV is required. At XFELs, this is achieved with hard x-ray self-seeding [2] or monochromators (i.e. Si(111)) which both yield and energy bandwidth ΔE < 1 eV. Note that at XFELs, spectrometers are used to analyze the full IXS spectrum of each exposure in dispersive mode [38, 103, 148], rather than scanning the incident photon energy and having a fixed-energy analyzer, as commonly done in static synchrotron measurements.

In a photon scattering experiment, a redistribution of scattered photons is observed from the elastic peak to inelastic lines due to (de-)excitation of a plasmon. At local thermal equilibrium, the amplitude ratio of these peaks is related to the electron temperature by a Boltzmann factor, the detailed balance relation [44]. This relation provides a model-independent temperature measurement. However, a significant amplitude of the up-shifted plasmon requires electron temperatures of the order of the plasmon shift, which limits this method to high temperatures >10 eV [67].

A first density measurement of shock-compressed matter at an XFEL has been successfully demonstrated in 2015 [39]. In semiconductors and half-metals, the detailed relation of the plasmon shift (at a fixed scattering angle) to compression can reveal influences of band gap closure [151]. If, on the other hand, the plasmon resonance is measured at different scattering angles for a fixed compression condition, the plasmon dispersion is determined. Its shape, in particular at larger momentum transfer exceeding the Fermi wavevector, allows to distinguish the influence of collisional processes and local field corrections at high pressures [104].

In addition to the plasmon shift and amplitude ratio, also its detailed shape can be measured, i.e. the intensity of the inelastically scattered light as a function of energy loss ℏω. This spectrum is in essence the structure factor of the free electrons S_ee which related to the imaginary part of the inverse dielectric function ɛ

$$\begin{equation}{S}_{\text{ee}}\left(\hslash \omega ,k\right)=\frac{{\varepsilon }_{0}\hslash {k}^{2}}{\pi {e}^{2}{n}_{\mathrm{e}}}\frac{\mathrm{I}\mathrm{m}\enspace {\varepsilon }^{-1}\left(k,\hslash \omega \right)}{1-{\mathrm{exp}}^{\frac{-\hslash \omega }{{k}_{\mathrm{B}}{T}_{\mathrm{e}}}}}\end{equation} \tag{ 1 }$$

where $k=\vert \overrightarrow {k}\vert$ is the wavenumber, ɛ₀ is the electrical susceptibility, ℏ the reduced Planck constant, e the electrons charge, n_e the electron density, k_B Boltzmann's constant, and T_e the electron temperature.

If the measured spectrum extends over a sufficiently large spectral range, the Kramers–Kronig relation can be used to retrieve also the real part of the inverse dielectric function. An example of this approach is shown in figure 7. Here, intense focused 8 keV XFEL pulses from LCLS heat and scatter simultaneously from a thin Al foil. The right panel shows the derived dielectric function for aluminum at extreme conditions. Details of this experiment can be found in reference [123].

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IXS measurements can be extended from the free electrons to loosely bound electrons when measuring at higher momentum transfer, where the recoil energy during the scattering is sufficient to ionize bound electrons. Depending on the scattering angle, energy losses of up to several 100 eV allow to measure the position and shape of, e.g., the L-edges in Mg, Al, Si or the K-edge of C.

Finally, it is also possible to perform bound–bound scattering from the electrons that are bound to the atoms. Direct ion temperature measurements via detailed balance using collective scattering from acoustic waves requiring meV spectral resolution have been demonstrated at the LCLS and EuXFEL [25, 82].

Measurements of the detailed shape of the IXS signals have to date only been performed at XFELs with statically or x-ray heated samples, since this photon-hungry technique requires 10² − 10³ individual exposures in order to achieve a sufficient signal-to-noise ratio [123]. At EuXFEL, using the DiPOLE laser with up to 10 Hz repetition rate, shock-compression experiments using high-quality IXS will become possible for the first time [149].

At static high pressure conditions, IXS measurements are also routinely performed at synchrotron sources [51, 125]. The small incident x-ray bandwidths and the possibility of using efficient non-dispersive Rowland-circle spectrometers allows precise mapping of the dynamic structure factor S(q, ω), which is directly proportional to the imaginary part of the inverse dielectric function. Plasmon line shapes and dispersions are measured to high precision [71]. An exciting emergent IXS technique, x-ray Raman scattering (XRS) spectroscopy, studies electronic absorption edges of low-Z element containing samples under extreme conditions [116, 117, 121]. At low momentum transfers, S(q, ω) can be shown to be directly proportional to soft x-ray absorption spectra [88]. Much progress has been made in order to expand the reachable pressure range and high-energy-resolution spectra of Si L_2,3-edge and O K-edge of glassy SiO₂ have been recently measured at pressures exceeding 1 Mbar [96].

Physical and chemical phenomena induced by the application of high pressure and temperature can occur in a range of different time scales (figure 8). Capturing their nature, progress and underlying mechanisms requires therefore adapted acquisitions speeds but also the option to study them in static and dynamic regimes. As can be seen in figure 8 and table A.1 there is a large complementarity of accessible time-scales at synchrotrons and XFELs. The example of the melting curve of MgSiO₃ (figure 8, bottom) clearly shows the advantages and disadvantages to study static and dynamic processes. Static studies allow for a fine P/T stepping of experimental conditions to determine the melting line at s to ms time scales [152]. Gas-gun experiments, in turn, 'open the door' to fast processes, i.e. happening at ms–μs intervals and at P/T conditions comparable (or slightly higher) to the static regime, thus permitting to probe e.g. the crystallization process of MgSiO₃-bridgmanite (Pv) (figure 8). Laser-shock dynamic compression reveals instead transient states observable on ns time scales and, depending on the characteristics of the laser and experimental setup, might also be capable to extend the accessible P/T experimental conditions. For instance, in the specific case of MgSiO₃-bridgmanite, the dynamic compression experimental curve shows a 'cold' compression path that allowed to probe transitory states before crystallization of Ppv (post-perovskite).

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Another important aspect is the effect of strain rate (or compression rate) on high-pressure phase transformation mechanisms and kinetics, in particular when kinetics is diffusion-limited. A famous example is given by the case of water. The response of H₂O to dynamic processes, such as meteorite or asteroid impacts, is critical to model and predict the state and structure of high pressure ices in planetary bodies in and outside of our Solar System. When large thermodynamic driving forces are applied, local instabilities may lead to different and unforeseen outcomes, such as crystal growth at the crystal-liquid interfaces [61]. Specifically, under dynamic loading, an over-pressure is likely to be applied causing morphological transitions and anomalously fast crystal growth as a function of compression rate. The high strain rate affects not only such macroscopic phenomena but will evidently have an impact on crystalline structure formation as well. Recent laser-driven shock dynamic compression experiments on Si [83] and Bi [46, 95] show discrepancies in the phase transition pressures derived from the static DAC and dynamic shock experiments, thus suggesting that the different strain rates achieved in the two experimental methods play an important role on the structural stability of the materials under investigation. In order to apply the results obtained from dynamic shock experiments to the hydrostatic, low strain rates conditions of planetary interiors, it becomes essential to investigate the effects of high strain rates and shock induced shear on phase transitions [83]. Not only the kinetic properties of the material may shift the P/T boundaries of the stable crystallographic phases but may as well yield new metastable phases. In ice, for instance, a metastable high density amorphous phase forms from ice VI only under rapid compression [20]. Direct probes of the materials' structure during rapid compression are however scarce and so far limited to optical Raman spectroscopy and microphotography techniques.

The difference between the strain rates achieved in static DAC and dynamic compression experiments can be more than 15 orders of magnitude (i.e., from 10⁻⁵ s⁻¹ to 10¹¹ s⁻¹). The systematic study of matter under intermediate strain rates (between these two extremes) was not possible until the recent development of the piezo-electric-actuator driven DAC (dynamic DAC, dDAC) technique [37, 55], which enables very precise control of the pressure variation. The dDAC has been shown to achieve compression rates >100 TPa s⁻¹ in Au, i.e. a strain rate of 10² s⁻¹. At 3rd generation synchrotron sources, x-ray flux is the major limitation to deliver quality diffraction information on such short times scales. Results from first experiments on high-Z materials such as Bi (Husband et al, submitted) provide promising insights into kinetic properties at moderate strain rates.

EuXFEL offers an ideal x-ray probe for dDAC applications, by exploiting the pulse structure to follow rapid compression ramps, with a sampling rate of up to 4.5 MHz (a diffraction pattern every 222 ns). The high repetition rate of EuXFEL x-ray pulses is matched to the frame rate of the AGIPD detector [1], capable of collecting diffraction pattern snapshots along the compression ramp over several 100 microseconds. The experimental platform at the HED's IC2 has been designed specifically to enable these moderate strain rate experiments using dDAC technologies and generate high quality diffraction data even from low-Z materials.

The response of natural and man-made materials to shock and compression is of crucial importance to understand phenomena such as earthquakes (i.e. fracture of rocks) or failure of engineering devices (i.e. crack propagation in silicon wafers). The combination of polychromatic synchrotron radiation with ultra-high speed image acquisition schemes allows to study such highly aperiodic processes in a single-shot manner: x-ray movies, i.e. series of radiographies acquired continuously at MHz rates that allow to visualize compression waves in granular media and foams or the propagation of cracks in solid media. The use of synchrotron radiation not only gives access to fast acquisition rates: thanks to large source-experiment distance, the (partial) spatial coherent illumination substantially increases sensitivity by means of propagation-based x-ray phase contrast (XPCI). The use of hard x-rays at a long beamline such as ID19 of ESRF gives access to studying macroscopic structures, i.e. with a field-of-view of commonly up to 10 mm × 10 mm. Damage or shock is frequently induced by means of gas guns, shock lasers or explosion [92]. This section illustrates these advantages through selected examples of applications at beamline ID19 of ESRF: cavity collapse induced by impact and shock waves in water induced by wire explosion. Other examples include compression waves in foams as well as crack propagation in a single crystal [93, 105].

Cavity collapse is a phenomenon of high interest as it can generate strongly localised increases in pressure and temperature. Single-stage and two-stage gas guns can be used to generate impulsively-driven cavity collapse in combination with MHz radioscopy using hard synchrotron radiation. Besides understanding the fundamental processes, cavity collapse studies can also be applied to other fields, such as cleaning of surfaces, shock lithotripsy as well as targeted drug delivery, all of which utilise the localising effects of cavity collapse. Ignition is another important field of application: different mechanisms associated with the collapse of a cavity can substantially lower the ignition threshold. Cavity collapse is currently widely accessible by simulations only, the latter frequently lacking experimental data for verification. The example discussed here provides insight into the collapse process in a solid by impacting cavities in a polymethyl methacrylate medium. Ultra-high speed radioscopy with MHz acquisition rates is used to study cavities impacted to a range of dynamic stress states. Here, single-stage and two-stage gas guns were used, to reach shock pressures ranging from ∼0.5 to 16.6 GPa. The ESRF operated in 16-bunch mode (174 ns bunch separation time). The gas gun is aligned perpendicular to the x-ray beam. The indirect detector deployed consists of two high-speed cameras lens-coupled to the same single-crystal scintillator effectively acquiring images continuously at 3.79 MHz repetition rate (more details on the experimental setup including a sketch are given in the reference) [36]. A selection of acquired images capturing cavity collapse are shown in figure 9 (top), where fluid-dominated dynamics of cavity collapse are probed in the time series of radiographies: the impact is on the left side of the picture, outside of the field of view. The first picture is taken already after the impact, i.e. where part of the cavity is already inverted (left side). In these frames the formation of a jet is also visible, which is an expected phenomenon for strong shock-cavity interactions in a fluid.

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Shock waves in fluids (water) can also be studied by means of propagation-based phase contrast radioscopy. Wire explosion experiments (such as single wire, two wire or x-pinch) conducted by pulsed power combined with synchrotron-based single-bunch imaging allows for example to image shock propagation in water. For the images shown in figure 9 (bottom) a pulser containing four 50 kV Maxwell pulse capacitors (each capacitance of 220 nF), charged to 32 kV (total stored energy of approximately 450 J) immediately before the experiment, was used to explode a 200 μm copper wire (the pulser had a rise time of approximately 1000 ns). In frame 2 the beginning of the expansion of the wire can be seen. A cylindrical shock wave is launched into the water. The density gradient across the shock front is visible thanks to propagation-based phase contrast. Shock fronts remain visible (partially) in frames 3 and 4, traveling at approximately 2 km s⁻¹. The final frame shows vertical fractures across the image related to cracks appearing in the acrylic sample chamber as a result of the shock. When using a cylindrical arrangement the shock waves generated by electrical explosion can be used to study the merger of shock waves. This can reveal a cylindrical and highly symmetrical shock wave converging on the axis: it is expected to produce a high density, strongly coupled plasma which is ideally suited for WDM research. Images like this provide a direct and quantitative measurement on the formation of the convergent shock wave. Phenomena such as the increased density of water on the axis caused by its arrival as well as its 'bounce' after arrival on the axis can be studied as well. The obtained radiographs can be compared with hydrodynamic simulations, e.g. to reproduce the observed dynamics and to cross-check the agreement with density values [144].

Dynamic compression experiments using gas guns or other means of shock loading such as laser-induced shock, energetic materials, wire explosion or split-Hopkinson pressure bars bridge the time scales between static pressure on one side and XFELs experiments with higher spatio-temporal resolution on the other side. Static experiments under high pressure combined with microtomography include for example research on rock fracture in order to understand the origins of earthquakes [109]. Other examples are static microtomography studies that allow determining density changes across fine P/T intervals to constrain liquid–liquid transitions [49], or studies on the elasticity and viscosity of silicate melts which are key parameters to understand melt migration and volcanic eruptions but which cannot be extracted from dynamic studies [56, 57, 108]. Compared to XFEL-based experiments, high-energy storage rings such as the ESRF give access to higher photon energies as well as larger field of views, for instance frequently required to study sample volumes and materials relevant for engineering applications [132].

Future perspectives for imaging at extreme conditions will be the development of volumetric (3D) MHz tomography at XFELs (see outlook) and the installation of high-flux EBS-beamlines, like the foreseen HPLF-II at ESRF, which will pave the way towards single-bunch imaging outside the classic 16 and 4-bunch timing modes, i.e. GHz image acquisition rates [136]. This will rely on the parallel development of comparably fast diagnostics.

The laser system consists of two main sub-systems: a front-end amplifier based on an INTREPID amplifier made in continuum (San Jose, USA) and a P-100 amplifier made by Amplitude Technologies (Lisses, FR). The INTREPID delivers up to 15 J at 1053 nm, and will have pulse shaping capabilities from 4 ns to 15 ns and will include the SSD technology (smoothing by spectral dispersion) to control the transverse beam profile at the ESRF target zone. The P-100 amplifier wille get the energy at 1053 nm to the 100 J level using a Nd:glass disk for the amplifying heads. The laser-x-rays delay can be adjusted with 0.25 ns step. Phase plates of different sizes (100, 250 or 500 μm diameter) are foreseen to obtain flat-top focal spot profiles. The laser has a repetition rate up to 1 full-energy shot every 4 min.

A list and description of the beamlines compatible for dynamic compression experiments at ESRF is given below.

ID24-ED provides x-rays in the energy range between 5–28 keV. The beam size at the sample position is ∼2–3 microns at low energies (<10 keV) and up to several tens of microns at high energies. The time resolution is given by the x-ray pulse length, i.e. 100 ps at the ESRF. This is well adapted to laser-shock induced dynamic compression, as the life-time of shocked states lies in the nanosecond range.

Beamline ID09 [143] is optimized for time resolved diffraction and historically dedicated to structural biology. However in recent years dynamic compression experiments have been developed using a 350 mJ laser interfaced to the beamline [14, 95]. While these first studies were limited to moderate pressures of 8–15 GPa, they clearly pointed out the feasibility and potential of coupling laser shock compression to XRD, leading eventually to the HPLF-II proposal.

Beamline ID19 is dedicated to full-field hard x-ray imaging with a strong focus on the use of x-ray phase contrast in combination with microtomography taking advantage of polychromatic photon energy configurations (up to white beam). ID19 is excellently suited to perform ultra-high speed radioscopy up to single-bunch imaging [106]. In special timing modes, defined by the electrons filling pattern in the storage ring, continuous acquisition of images at rates of 1.4 MHz (4-bunch) or 5.6 MHz (16-bunch) allows for recording movies of transient processes propagating up to the speed of sound. With a field of view of up to 10 mm × 10 mm at MHz-acquisition rates, dynamic events can be studied within macroscopic objects. Shock compression can also be routinely coupled to XRI: available installations in the frame of the user program are a single-stage gas gun as well as a split-Hopkinson pressure bar [21, 115]. Laser-shock experiments have been performed with equipment supplied by external groups [93].

IC1 is rectangular and about (2.3 × 1.4 × 1 m³) in size.

A von Hamos spectrometer for emission spectroscopy (XES) experiments in DAC can be installed inside IC1 and consists of 4 Si(531) crystals with 250 mm radius with 0.3–0.4 eV resolution. The spectrometer is coupled to single-photon counting ePIX [8] and Jungfrau [90] detectors for simultaneous detection of emission lines and diffraction patterns. Possibly in the future, other spectroscopy techniques such as XAS and IXS will be available.

IC2 is round and about 1.4 m in diameter. In IC2, depending on the adopted configuration and the position of the sample stack, the minimum sample detector distance that can be achieved with a 1-megapixel AGIPD detector (frame rate up to 4.5 MHz) [1] will be 150 mm, which results in a coverage up to Q = 9 Å in the vertical at 25 keV photon energy.

The optical system in IC2 for time-resolved temperature measurements consists of a ns laser (SPI lasers, 100 W) operating in pulsed (10–500 ns) and also CW mode, and is employed for double-sided DAC heating in on-axis geometry (co-linear with the x-ray beam). A special feature of this system is an HAMAMATSU streak camera with an S-20 photocathode that guarantees fast acquisitions (ns) of thermal emission spectra from the DAC used for temperature determination via SOP [41].

Both IC1 and IC2 are equipped with high-precision motor stages that allow fine sample alignment with a spatial resolution down to 100 nm.

The DIPOLE 100-X laser installed at HED instrument can work at 10 Hz and provides pulse shaping capabilities with a resolution of 125 ps to deliver arbitrary temporal pulse shaping between 2 and 15 ns. The laser will be frequency-doubled to 515 nm with expected energies of 70 J at 10 ns pulse length. The laser focal spot at full energy can be as small as 2–3 times the diffraction limit, but for shock generation flat-top focal spot profiles will be obtained through the use of adapted phase plates. The standard configurations provided by the facility are focal spot diameters of 100, 250 or 500 μm diameter.

In IC2, both the DIPOLE and VISAR beam paths can be rotated around the interaction point (sample position) in specific angular positions, allowing different angles between shock propagation and x-ray beam direction. Particularly, a configuration with x-rays and shock propagation nearly co-linear or perpendicular is possible. Inside IC2, in a vacuum compatible air pocket, a VAREX flat panel x-ray detector can be also rotated around the sample position to adapt the angular coverage in diffraction experiments.