Measuring the melting curve of iron at super-Earth core conditions

Extended X-ray absorption fine structure of dynamically-compressed copper up to 1 terapascal

Large laser facilities have recently enabled material characterization at the pressures of Earth and Super-Earth cores. However, the temperature of the compressed materials has been largely unknown, or solely relied on models and simulations, due to lack of diagnostics under these challenging conditions. Here, we report on temperature, density, pressure, and local structure of copper determined from extended x-ray absorption fine structure and velocimetry up to 1 Terapascal. These results nearly double the highest pressure at which extended x-ray absorption fine structure has been reported in any material. In this work, the copper temperature is unexpectedly found to be much higher than predicted when adjacent to diamond layer(s), demonstrating the important influence of the sample environment on the thermal state of materials; this effect may introduce additional temperature uncertainties in some previous experiments using diamond and provides new guidance for future experimental design.

Collective motion in hcp-Fe at Earth's inner core conditions

Earth's inner core is predominantly composed of solid iron (Fe) and displays intriguing properties such as strong shear softening and an ultrahigh Poisson's ratio. Insofar, physical mechanisms to explain these features coherently remain highly debated. Here, we have studied longitudinal and shear wave velocities of hcp-Fe (hexagonal close-packed iron) at relevant pressure-temperature conditions of the inner core using in situ shock experiments and machine learning molecular dynamics (MLMD) simulations. Our results demonstrate that the shear wave velocity of hcp-Fe along the Hugoniot in the premelting condition, defined as T/Tm (Tm: melting temperature of iron) above 0.96, is significantly reduced by ~30%, while Poisson's ratio jumps to approximately 0.44. MLMD simulations at 230 to 330 GPa indicate that collective motion with fast diffusive atomic migration occurs in premelting hcp-Fe primarily along [100] or [010] crystallographic direction, contributing to its elastic softening and enhanced Poisson's ratio. Our study reveals that hcp-Fe atoms can diffusively migrate to neighboring positions, forming open-loop and close-loop clusters in the inner core conditions. Hcp-Fe with collective motion at the inner core conditions is thus not an ideal solid previously believed. The premelting hcp-Fe with collective motion behaves like an extremely soft solid with an ultralow shear modulus and an ultrahigh Poisson's ratio that are consistent with seismic observations of the region. Our findings indicate that premelting hcp-Fe with fast diffusive motion represents the underlying physical mechanism to help explain the unique seismic and geodynamic features of the inner core.

Double-Shock Compression Pathways from Diamond to BC8 Carbon

Carbon is one of the most important elements for both industrial applications and fundamental research, including life, physics, chemistry, materials, and even planetary science. Although theoretical predictions on the transition from diamond to the BC8 (Ia3[over ¯]) carbon were made more than thirty years ago, after tremendous experimental efforts, direct evidence for the existence of BC8 carbon is still lacking. In this study, a machine learning potential was developed for high-pressure carbon fitted from first-principles calculations, which exhibited great capabilities in modeling the melting and Hugoniot line. Using the molecular dynamics based on this machine learning potential, we designed a thermodynamic pathway that is achievable for the double shock compression experiment to obtain the elusive BC8 carbon. Diamond was compressed up to 584 GPa after the first shock at 20.5  km/s. Subsequently, in the second shock compression at 24.8 or 25.0  km/s, diamond was compressed to a supercooled liquid and then solidified to BC8 in around 1 ns. Furthermore, the critical nucleus size and nucleation rate of BC8 were calculated, which are crucial for nano-second x-ray diffraction measurements to observe BC8 carbon during shock compressions. The key to obtaining BC8 carbon lies in the formation of liquid at a sufficient supercooling. Our work provides a feasible pathway by which the long-sought BC8 phase of carbon can be reached in experiments.

Scaling Law for the Onset of Solidification at Extreme Undercooling

Quasi-isentropic compression enables one to study the solidification of metastable liquid states that are inaccessible through other experimental means. The onset of this nonequilibrium solidification is known to depend on the compression rate and material-specific factors, but this complex interdependence has not been well characterized. In this study, we use a combination of experiments, theory, and computational simulations to derive a general scaling law that quantifies this dependence. One of its applications is a novel means to elucidate melt temperatures at high pressures.

Toward better understanding of the high-pressure structural transformation in beryllium by the statistical moment method

Beryllium is a vital alkaline-earth metal for plasma physics, space science, and nuclear technology. Unfortunately, its accurate phase diagram is clouded by many controversial results, even though solid beryllium can only exist with hcp or bcc crystalline structures. Herein, we offer a simple quantum-statistical solution to the above problem. Our core idea is to develop the moment expansion technique to determine the Helmholtz free energy under extreme conditions. This strategy helps elucidate the underlying correlation among symmetric characteristics, vibrational excitations, and physical stabilities. In particular, our analyses reveal that the appearance of anharmonic effects forcefully straightens up the hcp-bcc boundary. This phenomenon explains why it has been difficult to detect bcc signatures via diamond-anvil-cell measurements. Besides, we modify the work-heat equivalence principle to quickly obtain the high-pressure melting profile from the room-temperature equation of state. The hcp-bcc-liquid triple point of beryllium is found at 165 GPa and 4559 K. Our theoretical findings agree excellently with cutting-edge ab initio simulations adopting the phonon quasiparticle method and the thermodynamic integration. Finally, we consider the principal Hugoniot curve and its secondary branches to explore the behaviors of beryllium under shock compression. Our predictions would be advantageous for designing inertial-confinement-fusion experiments.

Cooperative diffusion in body-centered cubic iron in Earth and super-Earths' inner core conditions

The physical chemistry of iron at the inner-core conditions is key to understanding the evolution and habitability of Earth and super-Earth planets. Based on full first-principles simulations, we report cooperative diffusion along the longitudinally fast⟨111⟩directions of body-centered cubic (bcc) iron in temperature ranges of up to 2000-4000 K below melting and pressures of ∼300-4000 GPa. The diffusion is due to the low energy barrier in the corresponding direction and is accompanied by mechanical and dynamical stability, as well as strong elastic anisotropy of bcc iron. These findings provide a possible explanation for seismological signatures of the Earth's inner core, particularly the positive correlation between P wave velocity and attenuation. The diffusion can also change the detailed mechanism of core convection by increasing the diffusivity and electrical conductivity and lowering the viscosity. The results need to be considered in future geophysical and planetary models and should motivate future studies of materials under extreme conditions.

Imaging velocity interferometer system for any reflector (VISAR) diagnostics for high energy density sciences

Two variants of optical imaging velocimetry, specifically the one-dimensional streaked line-imaging and the two-dimensional time-resolved area-imaging versions of the Velocity Interferometer System for Any Reflector (VISAR), have become important diagnostics in high energy density sciences, including inertial confinement fusion and dynamic compression of condensed matter. Here, we give a brief review of the historical development of these techniques, then describe the current implementations at major high energy density (HED) facilities worldwide, including the OMEGA Laser Facility and the National Ignition Facility. We illustrate the versatility and power of these techniques by reviewing diverse applications of imaging VISARs for gas-gun and laser-driven dynamic compression experiments for materials science, shock physics, condensed matter physics, chemical physics, plasma physics, planetary science and astronomy, as well as a broad range of HED experiments and laser-driven inertial confinement fusion research.

Accurate temperature diagnostics for matter under extreme conditions

The experimental investigation of matter under extreme densities and temperatures, as in astrophysical objects and nuclear fusion applications, constitutes one of the most active frontiers at the interface of material science, plasma physics, and engineering. The central obstacle is given by the rigorous interpretation of the experimental results, as even the diagnosis of basic parameters like the temperature T is rendered difficult at these extreme conditions. Here, we present a simple, approximation-free method to extract the temperature of arbitrarily complex materials in thermal equilibrium from X-ray Thomson scattering experiments, without the need for any simulations or an explicit deconvolution. Our paradigm can be readily implemented at modern facilities and corresponding experiments will have a profound impact on our understanding of warm dense matter and beyond, and open up a variety of appealing possibilities in the context of thermonuclear fusion, laboratory astrophysics, and related disciplines.

Optimized x-ray emission from 10 ns long germanium x-ray sources at the National Ignition Facility

This study investigates methods to optimize quasi-monochromatic, ∼10 ns long x-ray sources (XRS) for time-resolved x-ray diffraction measurements of phase transitions during dynamic laser compression measurements at the National Ignition Facility (NIF). To support this, we produce continuous and pulsed XRS by irradiating a Ge foil with NIF lasers to achieve an intensity of 2 × 10¹⁵ W/cm², optimizing the laser-to-x-ray conversion efficiency. Our x-ray source is dominated by Ge He-α line emission. We discuss methods to optimize the source to maintain a uniform XRS for ∼10 ns, mitigating cold plasma and higher energy x-ray emission lines.

Model for the Solid-Liquid Interfacial Free Energy at High Pressures

The free energy involved in the formation of an interface between two phases (e.g., a solid-liquid interface) is referred to as the interfacial free energy. For the case of solidification, the interfacial free energy dictates the height of the energy barrier required to nucleate stable clusters of the newly forming solid phase and is essential for producing an accurate solidification kinetics model using classical nucleation theory (CNT)-based methods. While various methods have been proposed for modeling the interfacial free energy for solid-liquid interfaces in prior literature, many of these formulations involve making restrictive assumptions or approximations, such as the system being at or near equilibrium (i.e., the system temperature is approximately equal to the melt temperature) or that the system is at pressures close to atmospheric. However, these approximations and assumptions may break down in highly non-equilibrium situations, such as in dynamic-compression experiments where metastable liquids that are undercooled by hundreds of kelvin or overpressurized by several gigapascals or more are formed before eventually solidifying. We derive a solid-liquid interfacial free-energy model for such high-pressure conditions by considering the enthalpies of interactions between pairs of atoms or molecules. We also consider the contribution of interface roughness (disordering) by incorporating a multilayer interface model known as the Temkin n-layer model. Our formulation is applicable to a diverse variety of materials, and we demonstrate it by developing models specifically for two different materials: water and gallium. We apply our interfacial free-energy formulation to CNT-based kinetics simulations of several suites of dynamic-compression experiments that cause liquid water to solidify to the high-pressure solid polymorph ice VII and have found good agreement to the observed kinetics with only minor empirical fitting.