William J. Evans

Experiments accessing extreme conditions at x-ray free electron lasers (XFELs) involve rapidly evolving conditions of temperature. Here, we report time-resolved, direct measurements of temperature using spectral streaked optical pyrometry of x-ray and optical laser-heated states at the High Energy Density instrument of the European XFEL. This collection of typical experiments, coupled with numerical models, outlines the reliability, precision, and meaning of time dependent temperature measurements using optical emission at XFEL sources. Dynamic temperatures above 1500 K are measured continuously from spectrally- and temporally-resolved thermal emission at 450–850 nm, with time resolution down to 10–100 ns for 1–200 μs streak camera windows, using single shot and integrated modes. Targets include zero-pressure foils free-standing in air and in vacuo, and high-pressure samples compressed in diamond anvil cell multi-layer targets. Radiation sources used are 20-fs hard x-ray laser pulses at 17.8 keV, in single pulses or 2.26 MHz pulse trains of up to 30 pulses, and 250-ns infrared laser single pulses. A range of further possibilities for optical measurements of visible light in x-ray laser experiments using streak optical spectroscopy are also explored, including for the study of x-ray induced optical fluorescence, which often appears as background in thermal radiation measurements. We establish several scenarios where combined emissions from multiple sources are observed and discuss their interpretation. Challenges posed by using x-ray lasers as non-invasive probes of the sample state are addressed.

High-pressure and high-temperature experiments using a resistively heated diamond anvil cell have the advantage of heating samples homogeneously with precise temperature control. Here, we present the design and performance of a graphite resistive heated diamond anvil cell (GRHDAC) setup for powder and single-crystal x-ray diffraction experiments developed at the Extreme Conditions Beamline (P02.2) at PETRA III, Hamburg, Germany. In the GRHDAC, temperatures up to 2000 K can be generated at high pressures by placing it in a water-cooled vacuum chamber. Temperature estimates from thermocouple measurements are within +/−35 K at the sample position up to 800 K and within +90 K between 800 and 1400 K when using a standard seat combination of cBN and WC. Isothermal compression at high temperatures can be achieved by employing a remote membrane control system. The advantage of the GRHDAC is demonstrated through the study of geophysical processes in the Earth’s crust and upper mantle region.

The ability to visualize a sample undergoing a pressure-induced phase transition allows for the determination of kinetic parameters, such as the nucleation and growth rates of the high-pressure phase. For samples that are opaque to visible light (such as metallic systems), it is necessary to rely on x-ray imaging methods for sample visualization. Here, we present an experimental platform developed at beamline P02.2 at the PETRA III synchrotron radiation source, which is capable of performing simultaneous x-ray imaging and diffraction of samples that are dynamically compressed in piezo-driven diamond anvil cells. This setup utilizes a partially coherent monochromatic x-ray beam to perform lensless phase contrast imaging, which can be carried out using either a parallel- or focused-beam configuration. The capabilities of this platform are illustrated by experiments on dynamically compressed Ga and Ar. Melting and solidification were identified based on the observation of solid/liquid phase boundaries in the x-ray images and corresponding changes in the x-ray diffraction patterns collected during the transition, with significant edge enhancement observed in the x-ray images collected using the focused-beam. These results highlight the suitability of this technique for a variety of purposes, including melt curve determination.

Fast compression experiments performed using dynamic diamond anvil cells (dDACs) employing piezoactuators offer the opportunity to study compression-rate dependent phenomena. In this paper, we describe an experimental setup which allows us to perform time-resolved x-ray diffraction during the fast compression of materials using improved dDACs. The combination of the high flux available using a 25.6 keV x-ray beam focused with a linear array of compound refractive lenses and the two fast GaAs LAMBDA detectors available at the Extreme Conditions Beamline (P02.2) at PETRA III enables the collection of x-ray diffraction patterns at an effective repetition rate of up to 4 kHz. Compression rates of up to 160 TPa/s have been achieved during the compression of gold in a 2.5 ms fast compression using improved dDAC configurations with more powerful piezoactuators. The application of this setup to low-Z compounds at lower compression rates is described, and the high temporal resolution of the setup is demonstrated. The possibility of applying finely tuned pressure profiles opens opportunities for future research, such as using oscillations of the piezoactuator to mimic propagation of seismic waves in the Earth.

We present an equation of state for the solid and liquid phases of lithium fluoride that covers a wide range of conditions from ambient pressure and temperature to the high pressures and temperatures exhibited in shock- and ramp-compression studies. The particular solid phase we have focused on in this work is the B1 phase. We have followed an approach where the pressure and heat-capacity functions of both phases are fit to experimental data and our own quantum molecular dynamics simulations and are then integrated in a thermodynamically consistent way to obtain the corresponding free-energy functions. This approach yields a two-phase equation of state that provides better overall agreement with experimental data than other equations of state for lithium fluoride, such as SESAME 7271v3, LEOS 2240, and the model presented by Smirnov. The last of these is a three-phase equation of state that predicts a B1–B2 transition along the shock Hugoniot at a pressure of about 140 GPa. This solid–solid transition has been a topic of speculation and debate in the literature for over 50 years, culminating in the work of Smirnov, who has developed the only potentially viable equation of state that allows for this transition. We explain why the proposed B1–B2 transition at 140 GPa is not consistent with recent velocimetry data.

The measurement of transient temperatures less than 1000 K for samples in laser-heated diamond anvil cells remains a challenge. Here we present the design and performance characteristics of a multi-channel pyrometer that works in the near-infrared from 1200 to 2000 nm. It has a relatively small footprint, is portable, requires only low voltage power supplies, and can report temperatures down to 800 K on the millisecond scale or faster. A single data point without averaging can be acquired in 14 µs (sampling rate of 7 kilosamples per second). In conjunction with a diamond anvil cell, the system delivers accurate and rapid measurements down to ∼830 K. The pyrometer has been successfully interfaced several times with the combined x-ray diffraction and laser heating system at the High Pressure Collaborative Access Team at the Advanced Photon Source at Argonne National Laboratories.

Static compression experiments over 4 Mbar are rare, yet critical for developing accurate fundamental physics and chemistry models, relevant to a range of topics including modeling planetary interiors. Here we show that focused ion beam crafted toroidal single-crystal diamond anvils with ~9.0 μm culets are capable of producing pressures over 5 Mbar. The toroidal surface prevents gasket outflow and provides a means to stabilize the central culet. We have reached a maximum pressure of ~6.15 Mbar using Re as in situ pressure marker, a pressure regime typically accessed only by double-stage diamond anvils and dynamic compression platforms. Optimizing single-crystal diamond anvil design is key for extending the pressure range over which studies can be performed in the diamond anvil cell.

Using combined experimental and computational approaches, we show that at 43 GPa and 1300 K gallium phosphide adopts the super-Cmcm structure, here indicated with its Pearson notation oS24. First-principles enthalpy calculations demonstrate that this structure is more thermodynamically stable above ∼20 GPa than previously proposed polymorphs. In contrast to other polymorphs, the oS24 phase shows a strong bonding differentiation and distorted fivefold coordination geometries of both P atoms. The shortest bond of the phase is a single covalent P–P bond measuring 2.171(11) Å at synthesis pressure. Phosphorus dimerization in GaP sheds light on the nature of the super-Cmcm phase and provides critical new insights into the high-pressure polymorphism of octet semiconductors. Bond directionality and anisotropy explain the relatively low symmetry of this high-pressure phase.

Optically detected magnetic resonance of nitrogen vacancy centers in diamond offers a route to both DC and AC magnetometry in diamond anvil cells under high pressures (>3 GPa). However, a serious challenge to realizing experiments has been the insertion of microwave radiation into the sample space without screening by the gasket material. We utilize designer anvils with lithographically deposited metallic microchannels on the diamond culet as a microwave antenna. We detected the spin resonance of an ensemble of microdiamonds under pressure and measured the pressure dependence of the zero field splitting parameters. These experiments enable the possibility for all-optical magnetic resonance experiments on nanoliter sample volumes at high pressures.

The behavior of the f-electrons in the lanthanides and actinides governs important macroscopic properties but their pressure and temperature dependence is not fully explored. Cerium with nominally just one 4f electron offers a case study with its iso-structural volume collapse from the γ-phase to the α-phase ending in a critical point (p_C, V_C, T_C), unique among the elements, whose mechanism remains controversial. Here, we present longitudinal (c_L) and transverse sound speeds (c_T) versus pressure from higher than room temperature to T_C for the first time. While c_L experiences a non-linear dip at the volume collapse, c_T shows a step-like change. This produces very peculiar macroscopic properties: the minimum in the bulk modulus becomes more pronounced, the step-like increase of the shear modulus diminishes and the Poisson’s ratio becomes negative—meaning that cerium becomes auxetic. At the critical point itself cerium lacks any compressive strength but offers resistance to shear.