Chromium (Cr) is one of the few transition metals whose body-centered cubic (bcc) structure remains stable over a wide pressure range, but its high-temperature stability and melting behavior at terapascal pressures are still elusive. Here, we use large-scale molecular dynamics simulations based on machine-learning interatomic potentials (MLIPs) to investigate the phase stability and melting of Cr at pressures up to 2 TPa. Gibbs free energies calculation and direct transformation simulations place the bcc-hcp boundary at 1393 GPa at 0 K and in the 1.4–2.0 TPa range at finite temperature. The melting temperature of Cr rises from 2135 K at ambient pressure to 12 925 ± 25 K at 2 TPa. Above ∼50 GPa and at temperatures approaching melting, bcc-Cr enters a dynamic regime in which atoms undergo collective jumps while the bcc lattice remains intact, which closely resembles the behaviors that have been reported for other bcc metals, such as Fe under Earth’s inner-core conditions and Ti near its ambient-pressure melting point. Finite-temperature phonon calculations reveal pronounced softening of the transverse acoustic branch along the Γ-N direction with increasing temperature, together with the defect-assisted fast diffusion along the 111 direction, provide the microscopic origin of the cooperative displacements. These results identify Cr as a useful high-pressure bcc system for examining the connection between anharmonic lattice dynamics, shear softening, and cooperative atomic transport under extreme compression.

First-principles calculations of solids close to mechanical instabilities, for example, in studies of martensitic transformations in shape-memory alloys, require careful convergence with respect to both supercell size and k-point sampling density. Naturally, any such simulation should employ well-converged parameters that allow one to capture the quantitatively correct energetics of the most important instability waves. We demonstrate that large supercells used in Ab Initio Molecular Dynamics (AIMD) with common but insufficient k-point sampling can also produce qualitatively incorrect predictions of mechanical stability. A simple but useful rule is suggested: the most important destabilizing wave is identified, the smallest preferably uniformly spaced supercell allowing for such a wave is taken, for which k-points are converged; then a general scaling relation for maintaining equivalent k-point density across different supercell sizes stating that the number of k-points should scale with the inverse cube root of the number of primitive cells in the supercell is used. We validate this approach considering high-temperature shape-memory alloy NbRu, in which accurate prediction of a mechanical instability is crucial for modeling the martensitic transition. Using the most important 〈110〉[11̄0] destabilizing wave in B2-structured NbRu we show that a typical in AIMD studies Γ-point sampling alone for a 128-atom or even a 432-atom supercell cannot correctly predict stability against the wave that drives the martensitic transition, whereas the parameters for convergence can be easily estimated, and the properly converged calculations exhibit the correct behavior. These findings have direct implications for computational materials design involving large-scale, time-conserving simulations, particularly for systems in which mechanical instabilities govern functional properties.

The phase stability, crystal structure, and melting of Nb have been examined under high pressure shock compression to 365 GPa using ultrafast in situ 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 Pnma 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.

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.

Shape-memory alloys exhibit the remarkable ability to recover from a deformed state through heating, strain, or a combination of both. Their industrial applications are expanding, with a growing demand for materials capable of operating at higher temperatures. The martensitic phase transition is well-established as the mechanism underlying high-temperature shape-memory (HTSM) behavior. In this work, we investigate the martensitic phase transition in a promising HTSM alloy, NbRu, using first-principles molecular dynamics. By accurately incorporating temperature effects, we reproduce the transition temperature and thermoelastic properties of NbRu, achieving good agreement with experimental observations. Furthermore, we uncover the significant impact of chemical disorder on the mechanical stability of NbRu, which can suppress the martensitic transition and compromise shape-memory functionality. Our findings suggest that such disorder effects could be a general feature of HTSM alloys when disorder is present near the martensitic transition temperature. We propose that this factor should be carefully considered in the design and discovery of new HTSM alloys.

Iron is a major component of the cores of the Earth and inhabited exoplanets. Its phase diagram at extreme pressures (P) and temperatures (T) is the subject of extensive debate. While recent experiments provide evidence for the stability of the body-centered cubic (bcc) phase, several theoretical studies point to the stability (even though marginal) of the hexagonal close-packed phase (hcp). None of those studies considered the itinerant magnetism of iron at extreme conditions. We compute the high-pressure phase diagram of Fe using density functional theory-based molecular dynamics (DFT MD) in which the paramagnetic nature of Fe is treated within the model of thermally induced longitudinal spin fluctuations (LSF). The LSF DFT MD with 16 valence electrons favors bcc phase stability. Two-phase large-scale simulations with quantum accurate machine learning potentials provide us with both melting and hcp-bcc phase boundaries. The computed phase diagram agrees with most of the experimental data and solves most of the numerous controversies. We conclude that the account for magnetism results in the new physics of iron under extreme conditions and brings the theory in agreement with experiment and seismic data. We expect that the approach we use can be applied to other metals where itinerant magnetism is important.

Diamond possesses exceptional physical properties due to its remarkably strong carbon-carbon bonding, leading to significant resilience to structural transformations at very high pressures and temperatures. Despite several experimental attempts, synthesis and recovery of the theoretically predicted post-diamond BC8 phase remains elusive. Through quantum-accurate multimillion atom molecular dynamics (MD) simulations, we have uncovered the extreme metastability of diamond at very high pressures, significantly exceeding its range of thermodynamic stability. We predict the post-diamond BC8 phase to be experimentally accessible only within a narrow high pressure-temperature region of the carbon phase diagram. The diamond to BC8 transformation proceeds through premelting followed by BC8 nucleation and growth in the metastable carbon liquid. We propose a double-shock compression pathway for BC8 synthesis, which is currently being explored in experiments at the National Ignition Facility.

Iron is the major element of the Earth's core and the cores of Earth-like exoplanets. The crystal structure of iron, the major component of the Earth's solid inner core (IC), is unknown under the high pressures (P) (3.3-3.6 Mbar) and temperatures (T) (5000-7000 K) and conditions of the IC and exoplanetary cores. Experimental and theoretical data on the phase diagram of iron at these extreme PT conditions are contradictory. Though some of the large-scale ab initio molecular dynamics (AIMD) simulations point to the stability of the body-centered cubic (bcc) phase, the latest experimental data are often interpreted as evidence for the stability of the hexagonal close-packed (hcp) phase. Applying large-scale AIMD, we computed the properties of iron phases at the experimental pressures and temperatures reported in the experimental papers. The use of large-scale AIMD is critical since the use of small bcc computational cells (less than approximately 1000 atoms) leads to the collapse of the bcc structure. Large-scale AIMD allowed us to compare the measured and computed coordination numbers as well as the measured and computed structural factors. This comparison, in turn, allowed us to suggest that the computed density, coordination number, and structural factors of the bcc phase are in agreement with those observed in experiments, which were previously assigned either to the liquid or hcp phase.

Knowledge of high-pressure melting curves of silicate minerals is critical for modeling the thermal-chemical evolution of rocky planets. However, the melting temperature of davemaoite, the third most abundant mineral in Earth's lower mantle, is still controversial. Here, we investigate the melting curves of two minerals, MgSiO3 bridgmanite and CaSiO3 davemaoite, under their stability field in the mantle by performing first-principles molecular dynamics simulations based on the density functional theory. The melting curve of bridgmanite is in excellent agreement with previous studies, confirming a general consensus on its melting temperature. However, we predict a much higher melting curve of davemaoite than almost all previous estimates. Melting temperature of davemaoite at the pressure of core-mantle boundary (similar to 136 gigapascals) is about 7700(150) K, which is approximately 2000 K higher than that of bridgmanite. The ultrarefractory nature of davemaoite is critical to reconsider many models in the deep planetary interior, for instance, solidification of early magma ocean and geodynamical behavior of mantle rocks.

The solid Earth's inner core (IC) is a sphere with a radius of about 1300 km in the center of the Earth. The information about the IC comes mainly from seismic studies. The composition of the IC is obtained by matching the seismic data and properties of candidate phases subjected to high pressure (P) and temperature (T). The close match between the density of the IC and iron suggests that the main constituent of the IC is iron. However, the stable phase of iron is still a subject of debate. One such iron phase, the body-centered cubic phase (bcc), is dynamically unstable at pressures of the IC (330-364 GPa) and low T but gets stabilized at high T characteristic of the IC (5000-7000 K). So far, ab initio molecular dynamics (AIMD) studies attempted to compute the bcc elastic properties for a small (order of 102) number of atoms. The mechanism of the bcc stabilization cannot be enabled in such cells and that has led to erroneous results. Here we apply AIMD to compute elastic moduli and sound velocities of the Fe bcc phase for a 2000 Fe atom computational cell, which is a cell of unprecedented size for ab initio calculations of iron. Unlike in previous ab initio calculations, both the longitudinal and the shear sound velocities of the Fe bcc phase closely match the properties of the IC material at P = 360 GPa and T = 6600 K, likely the PT conditions in the IC. The calculated density of the bcc iron at these PT conditions is just 3% higher than the density of the IC material according to the Preliminary Earth Model. This suggests that the widely assumed amount of light elements in the IC may need a reconsideration. The anisotropy of the bcc phase is an exact match to the most recent seismic studies.