Patrick G. Heighway

The phase stability, crystal structure, and melting of Nb have been examined under high pressure shock compression to 365 GPa using ultrafast x-ray diffraction measurements on two x-ray free electron laser facilities. On compression, Nb remains stable in the bcc phase up to 220 GPa, with coexistence of bcc-Nb and liquid from 249 to 298 GPa, and complete melting at 301 GPa, with melt identified by diffuse liquid diffraction. Melting initiates at higher pressure than expected based on theoretical predictions, and the data consistently excludes the presence of other suggested phases of Nb at these pressures, including and hcp, thereby resolving the long-standing structural discrepancy. Singh-type strength analysis provides experimental evidence for a change in sign of the elastic anisotropy parameter at 121 GPa, consistent with the previously reported heat-induced hardening to heat-induced softening transition in Nb.

We present calculations of the millielectronvolt-scale x-ray scattering spectra of multilayered dynamic-compression targets comprising an unstructured ablator layer and a crystalline, textured sample layer. Our model builds on the classic formulation of x-ray thermal diffuse scattering by Warren [Acta Crystallogr. 6, 803 (1953)] and includes both elastic and first-order (single-phonon) inelastic scattering contributions to the dynamic structure factor S(q, ω). We focus on the umklapp scattering regime (i.e., at momentum transfers outside the first Brillouin zone) where the ablator scattering that threatens to overwhelm the inelastic scattering from the crystalline layer of interest is suppressed. We show that, despite the considerably more complex structure of the inelastic scattering spectra in this intermediate-q regime, it is still possible to reliably deduce the temperature of the crystal using Dornheim’s Laplace-transform–based formalism [Dornheim et al., Phys. Plasmas 30, 042707 (2023)], regardless of the details of the sample’s texture.

We present a model of x-ray thermal diffuse scattering (TDS) from a cubic polycrystal with an arbitrary crystallographic texture, based on the classic approach of Warren [B. E. Warren, Acta Crystallogr. 6, 803 (1953)]. We compare the predictions of our model with femtosecond x-ray diffraction patterns gathered from ambient and dynamically compressed rolled copper foils obtained at the High Energy Density instrument of the European X-Ray Free-Electron Laser facility and find that the texture-aware TDS model yields more accurate results than does the conventional powder model owed to Warren. Nevertheless, we further show: with sufficient angular detector coverage, the TDS signal is largely unchanged by sample orientation and in all cases strongly resembles the signal from a perfectly random powder; shot-to-shot fluctuations in the TDS signal resulting from grain-sampling statistics are at the percent level, in stark contrast to the fluctuations in the Bragg-peak intensities (which are over an order of magnitude greater); and TDS is largely unchanged even following texture evolution caused by compression-induced plastic deformation. We conclude that TDS is robust against texture variation, making it a flexible temperature diagnostic applicable just as well to off-the-shelf commercial foils as to ideal powders.

We present a model of x-ray thermal diffuse scattering (TDS) from a cubic polycrystal with an arbitrary crystallographic texture, based on the classic approach of Warren. We compare the predictions of our model with femtosecond x-ray diffraction patterns obtained from ambient and dynamically compressed rolled copper foils obtained at the High Energy Density (HED) instrument of the European X-Ray Free-Electron Laser (EuXFEL), and find that the texture-aware TDS model yields more accurate results than does the conventional powder model owed to Warren. Nevertheless, we further show that: with sufficient angular detector coverage, the TDS signal is largely unchanged by sample orientation and in all cases strongly resembles the signal from a perfectly random powder; shot-to-shot fluctuations in the TDS signal resulting from grain-sampling statistics are at the percent level, in stark contrast to the fluctuations in the Bragg-peak intensities (which are over an order of magnitude greater); and TDS is largely unchanged even following texture evolution caused by compression-induced plastic deformation. We conclude that TDS is robust against texture variation, making it a flexible temperature diagnostic applicable just as well to off-the-shelf commercial foils as to ideal powders.

In dynamic-compression experiments, the line-imaging Velocity Interferometer System for Any Reflector (VISAR) is a well-established diagnostic used to probe the velocity history, including wave profiles derived from dynamically compressed interfaces and wavefronts, depending on material optical properties. Knowledge of the velocity history allows for the determination of the pressure achieved during compression. Such a VISAR analysis is often based on Fourier transform techniques and assumes that the recorded interferograms are free from image distortions. In this paper, we describe the VISAR diagnostic installed at the HED-HIBEF instrument located at the European XFEL along with its calibration and characterization. It comprises a two-color (532, 1064 nm), three-arm (with three velocity sensitivities) line imaging system. We provide a procedure to correct VISAR images for geometric distortions and evaluate the performance of the system using Fourier analysis. We finally discuss the spatial and temporal calibrations of the diagnostic. As an example, we compare the pressure extracted from the VISAR analysis of shock-compressed polyimide and silicon.

Carbon has a central role in biology and organic chemistry, and its solid allotropes provide the basis of much of our modern technology¹. However, the liquid form of carbon remains nearly uncharted², and the structure of liquid carbon and most of its physical properties are essentially unknown³. But liquid carbon is relevant for modelling planetary interiors^4,5 and the atmospheres of white dwarfs⁶, as an intermediate state for the synthesis of advanced carbon materials^7,8, inertial confinement fusion implosions⁹, hypervelocity impact events on carbon materials¹⁰ and our general understanding of structured fluids at extreme conditions¹¹. Here we present a precise structure measurement of liquid carbon at pressures of around 1 million atmospheres obtained by in situ X-ray diffraction at an X-ray free-electron laser. Our results show a complex fluid with transient bonding and approximately four nearest neighbours on average, in agreement with quantum molecular dynamics simulations. The obtained data substantiate the understanding of the liquid state of one of the most abundant elements in the universe and can test models of the melting line. The demonstrated experimental abilities open the path to performing similar studies of the structure of liquids composed of light elements at extreme conditions.

We present in situ x-ray diffraction and velocity measurements of Fe_{2}O_{3} under laser shock compression at pressures between 38-122 GPa. None of the high-pressure phases reported by static compression studies were observed. Instead, we observed an isostructural phase transition from α-Fe_{2}O_{3} to a new α^{'}-Fe_{2}O_{3} phase at a pressure of 50-62 GPa. The α^{'}-Fe_{2}O_{3} phase differs from α-Fe_{2}O_{3} by an 11% volume drop and a different unit cell compressibility. We further observed a two-wave structure in the velocity profile, which can be related to an intermediate regime where both α and α^{'} phases coexist. Density functional theory calculations with a Hubbard parameter indicate that the observed unit cell volume drop can be associated with a spin transition following a magnetic collapse.

We present 50-fs, single-shot measurements of the x-ray thermal diffuse scattering (TDS) from copper foils that have been shocked via nanosecond laser ablation up to pressures above ∼135 GPa. We hence deduce the x-ray Debye–Waller factor, providing a temperature measurement. The targets were laser-shocked with the DiPOLE 100-X laser at the High Energy Density endstation of the European X-ray Free-Electron Laser. Single x-ray pulses, with a photon energy of 18 keV, were scattered from the samples and recorded on Varex detectors. Despite the targets being highly textured (as evinced by large variations in the elastic scattering) and with such texture changing upon compression, the absolute intensity of the azimuthally averaged inelastic TDS between the Bragg peaks is largely insensitive to these changes, and allowing for both Compton scattering and the low-level scattering from a sacrificial ablator layer provides a reliable measurement of T/ΘD2, where ΘD is the Debye temperature. We compare our results with the predictions of the SESAME 3336 and LEOS 290 equations of state for copper and find good agreement within experimental errors. We, thus, demonstrate that single-shot temperature measurements of dynamically compressed materials can be made via thermal diffuse scattering of XFEL radiation.

We present measurements on Fe 2 O 3 amorphization and melt under laser-driven shock compression up to 209(10) GPa via time-resolved x-ray diffraction. At 122(3) GPa, a diffuse signal is observed indicating the presence of a noncrystalline phase. Structure factors have been extracted up to 182(6) GPa showing the presence of two well-defined peaks. A rapid change in the intensity ratio of the two peaks is identified between 145(12) and 151(12) GPa, indicative of a phase change. The noncrystalline diffuse scattering is consistent with shock amorphization of Fe 2 O 3 between 122(3) and 145(12) GPa, followed by an amorphous-to-liquid transition above 151(12) GPa. Upon release, a noncrystalline phase is observed alongside crystalline α − Fe 2 O 3 . The extracted structure factor and pair distribution function of this release phase resemble those reported for Fe 2 O 3 melt at ambient pressure.