Dynamic and transient processes in warm dense matter

In this paper, we discuss some of the key challenges in the study of time-dependent processes and non-equilibrium behaviour in warm dense matter. We outline some of the basic physics concepts that have underpinned the definition of warm dense matter as a subject area in its own right and then cover, in a selective, non-comprehensive manner, some of the current challenges, pointing along the way to topics covered by the papers presented in this volume. This article is part of the theme issue 'Dynamic and transient processes in warm dense matter'.

Crystal Structure and Melting of Fe Shock Compressed to 273 GPa: In Situ X-Ray Diffraction

Despite extensive shock wave and static compression experiments and corresponding theoretical work, consensus on the crystal structure and the melt boundary of Fe at Earth's core conditions is lacking. We present in situ x-ray diffraction measurements in laser-shock compressed Fe that establish the stability of the hexagonal-close-packed (hcp) structure along the Hugoniot through shock melting, which occurs between ∼242 to ∼247  GPa. Using previously reported hcp Fe Hugoniot temperatures, the melt temperature is estimated to be 5560(360) K at 242 GPa, consistent with several reported Fe melt curves. Extrapolation of this value suggests ∼6400  K melt temperature at Earth's inner core boundary pressure.

A New Reference for the Thermal Equation of State of Iron

The high-pressure, high-temperature behavior of iron was investigated to 140 GPa and 3500 K with in situ synchrotron X-ray diffraction. Iron samples were compressed in diamond-anvil cells and heated up with the double-sided laser-heating system installed at the high-pressure ID27 of the European Synchrotron Radiation Facility (ESRF). Three different structures, namely α-bcc, γ-fcc or ε-hcp Fe were identified as a function of pressure and temperature in the domain we explored. At pressures above 90 GPa, it is clearly shown that ε-iron is the single stable solid phase up to 160 GPa at high temperatures. The analysis of the P-V-T relationship allows us to propose a reliable experimental thermal equation of state (EoS) for iron. We also show that the addition of low pressure points to our EoS refinement yields more robust constrain on the determination of the reference volume V0 of the ε-hcp structure, which has important implications on the final parametrization of the equation of state. The extrapolation of the proposed EoS to core pressure conditions indicates that a pure iron core would have an excess of density of 3% compared to the PREM density profile.

Insight into structural stability and helium diffusion behavior of Fe-Cr alloys from first-principles

We have performed the first-principles method to study the structural stability and helium diffusion behavior of Fe–Cr alloys. The calculated bulk modulus of 284.935 GPa in the non-magnetic (NM) state is in good agreement with others. We have obtained solid evidence that the alloy structures meet the mechanical stability criteria and lattice dynamics conditions in the anti-ferromagnetism (AFM) and non-magnetic (NM) states. Compared with bulk γ-Fe, a slightly larger Young's modulus indicates that the doping of Cr helps to enhance the stiffness of the material and the ability to resist the reversible deformation of shear stress, but the ductility decreased slightly. Our results revealed that the addition of interstitial He atom promotes the expansion and deformation of the lattice, and further enlarges the cell volume. The presence of Cr in the alloy structures promotes the migration of a single helium atom between octahedral interstitials, and at the same time, inhibits the diffusion of helium atoms between tetrahedral interstitials to a large extent, which seem to be trapped in tetrahedral interstitials and cannot escape. The electronic properties show that the alloy materials exhibit obvious metallicity, and the doping of Cr generates an impurity state at lower energy, which is mainly formed by the s, p of Fe and s, p shell electrons of Cr. The charge density difference graphs corroborate that there is bonding interactions between Fe and Cr atoms. Bader charge analysis shows that a stronger polar covalent bond is formed between Fe and Cr in the non-magnetic (NM) state than in the anti-ferromagnetism (AFM) state. Our results provide useful information for understanding the initial growth of helium bubbles in experiments.

We have performed the first-principles method to study the structural stability and helium diffusion behavior of Fe–Cr alloys.

High-Pressure Induced Phase Transitions in High-Entropy Alloys: A Review

High-entropy alloys (HEAs) as a new class of alloy have been at the cutting edge of advanced metallic materials research in the last decade. With unique chemical and topological structures at the atomic level, HEAs own a combination of extraordinary properties and show potential in widespread applications. However, their phase stability/transition, which is of great scientific and technical importance for materials, has been mainly explored by varying temperature. Recently, pressure as another fundamental and powerful parameter has been introduced to the experimental study of HEAs. Many interesting reversible/irreversible phase transitions that were not expected or otherwise invisible before have been observed by applying high pressure. These recent findings bring new insight into the stability of HEAs, deepens our understanding of HEAs, and open up new avenues towards developing new HEAs. In this paper, we review recent results in various HEAs obtained using in situ static high-pressure synchrotron radiation x-ray techniques and provide some perspectives for future research.

Dynamic fracture of tantalum under extreme tensile stress

The understanding of fracture phenomena of a material at extremely high strain rates is a key issue for a wide variety of scientific research ranging from applied science and technological developments to fundamental science such as laser-matter interaction and geology. Despite its interest, its study relies on a fine multiscale description, in between the atomic scale and macroscopic processes, so far only achievable by large-scale atomic simulations. Direct ultrafast real-time monitoring of dynamic fracture (spallation) at the atomic lattice scale with picosecond time resolution was beyond the reach of experimental techniques. We show that the coupling between a high-power optical laser pump pulse and a femtosecond x-ray probe pulse generated by an x-ray free electron laser allows detection of the lattice dynamics in a tantalum foil at an ultrahigh strain rate of [Formula: see text] ~2 × 10⁸ to 3.5 × 10⁸ s^-1. A maximal density drop of 8 to 10%, associated with the onset of spallation at a spall strength of ~17 GPa, was directly measured using x-ray diffraction. The experimental results of density evolution agree well with large-scale atomistic simulations of shock wave propagation and fracture of the sample. Our experimental technique opens a new pathway to the investigation of ultrahigh strain-rate phenomena in materials at the atomic scale, including high-speed crack dynamics and stress-induced solid-solid phase transitions.

Planetary science. Shock compression of stishovite and melting of silica at planetary interior conditions

Deep inside planets, extreme density, pressure, and temperature strongly modify the properties of the constituent materials. In particular, how much heat solids can sustain before melting under pressure is key to determining a planet's internal structure and evolution. We report laser-driven shock experiments on fused silica, α-quartz, and stishovite yielding equation-of-state and electronic conductivity data at unprecedented conditions and showing that the melting temperature of SiO2 rises to 8300 K at a pressure of 500 gigapascals, comparable to the core-mantle boundary conditions for a 5-Earth mass super-Earth. We show that mantle silicates and core metal have comparable melting temperatures above 500 to 700 gigapascals, which could favor long-lived magma oceans for large terrestrial planets with implications for planetary magnetic-field generation in silicate magma layers deep inside such planets.

Importance of correlation effects in hcp iron revealed by a pressure-induced electronic topological transition

We discover that hcp phases of Fe and Fe(0.9)Ni(0.1) undergo an electronic topological transition at pressures of about 40 GPa. This topological change of the Fermi surface manifests itself through anomalous behavior of the Debye sound velocity, c/a lattice parameter ratio, and Mössbauer center shift observed in our experiments. First-principles simulations within the dynamic mean field approach demonstrate that the transition is induced by many-electron effects. It is absent in one-electron calculations and represents a clear signature of correlation effects in hcp Fe.

Pure iron compressed and heated to extreme conditions

The results of a first-principles study supported by the temperature-quenched laser-heated diamond anvil-cell experiments on the high-pressure high-temperature structural behavior of pure iron are reported. We show that in contrast to the widely accepted picture, the face-centered cubic (fcc) phase becomes as stable as the hexagonal-close-packed (hcp) phase at pressures around 300-360 GPa and temperatures around 5000-6000 K. Our temperature-quenched experiments indicate that the fcc phase of iron can exist in the pressure-temperature region above 160 GPa and 3700 K, respectively. This, in particular, means that the actual structure of the Earth's core may be a complex phase with a large number of stacking faults.

Body-Centered Cubic Iron-Nickel Alloy in Earth's Core

Cosmochemical, geochemical, and geophysical studies provide evidence that Earth's core contains iron with substantial (5 to 15%) amounts of nickel. The iron-nickel alloy Fe(0.9)Ni(0.1) has been studied in situ by means of angle-dispersive x-ray diffraction in internally heated diamond anvil cells (DACs), and its resistance has been measured as a function of pressure and temperature. At pressures above 225 gigapascals and temperatures over 3400 kelvin, Fe(0.9)Ni(0.1) adopts a body-centered cubic structure. Our experimental and theoretical results not only support the interpretation of shockwave data on pure iron as showing a solid-solid phase transition above about 200 gigapascals, but also suggest that iron alloys with geochemically reasonable compositions (that is, with substantial nickel, sulfur, or silicon content) adopt the bcc structure in Earth's inner core.

Effect of shear strain on the α-ε phase transition of iron: a new approach in the rotational diamond anvil cell

The effect of shear strain on the iron α-ε phase transformation has been studied using a rotational diamond anvil cell (RDAC). The initial transition is observed to take place at the reduced pressure of 10.8 GPa under pressure and shear operation. Complete phase transformation was observed at 15.4 GPa. The rotation of an anvil causes limited pressure elevation and makes the pressure distribution symmetric in the sample chamber before the phase transition. However, it causes a significant pressure increase at the centre of the sample and brings about a large pressure gradient during the phase transformation. The resistance to the phase interface motion is enhanced due to strain hardening during the pressure and shear operations on iron and this further increases the transition pressure. The work of macroscopic shear stress and the work of the pressure and shear stress at the defect tips account for the pressure reduction of the iron phase transition.

High-Pressure Microscopy

When bombarded with electrons, carbon nanotubes shrink, creating high internal pressures. The effect on molecules within the tubes can be studied at atomic resolution.

Generation of a double shock driven by laser

The feasibility and reliability of a multiple laser shock generation to study the equation of state surface off the principal Hugoniot curve and to approach an isentropic compression has been demonstrated. The technique is based on the use of a double laser pulse. A strong shock was generated in iron targets precompressed by a first weak shock. The effect of precompression was studied. The experiment was performed at the Laboratoire pour l'Utilisation des Lasers Intenses laboratory.

Melting of iron at the physical conditions of the Earth's core

Seismological data can yield physical properties of the Earth's core, such as its size and seismic anisotropy. A well-constrained iron phase diagram, however, is essential to determine the temperatures at core boundaries and the crystal structure of the solid inner core. To date, the iron phase diagram at high pressure has been investigated experimentally through both laser-heated diamond-anvil cell and shock-compression techniques, as well as through theoretical calculations. Despite these contributions, a consensus on the melt line or the high-pressure, high-temperature phase of iron is lacking. Here we report new and re-analysed sound velocity measurements of shock-compressed iron at Earth-core conditions. We show that melting starts at 225 +/- 3 GPa (5,100 +/- 500 K) and is complete at 260 +/- 3 GPa (6,100 +/- 500 K), both on the Hugoniot curve-the locus of shock-compressed states. This new melting pressure is lower than previously reported, and we find no evidence for a previously reported solid-solid phase transition on the Hugoniot curve near 200 GPa (ref. 16).

Stability of the body-centred-cubic phase of iron in the Earth's inner core

Iron is thought to be the main constituent of the Earth's core, and considerable efforts have therefore been made to understand its properties at high pressure and temperature. While these efforts have expanded our knowledge of the iron phase diagram, there remain some significant inconsistencies, the most notable being the difference between the 'low' and 'high' melting curves. Here we report the results of molecular dynamics simulations of iron based on embedded atom models fitted to the results of two implementations of density functional theory. We tested two model approximations and found that both point to the stability of the body-centred-cubic (b.c.c.) iron phase at high temperature and pressure. Our calculated melting curve is in agreement with the 'high' melting curve, but our calculated phase boundary between the hexagonal close packed (h.c.p.) and b.c.c. iron phases is in good agreement with the 'low' melting curve. We suggest that the h.c.p.-b.c.c. transition was previously misinterpreted as a melting transition, similar to the case of xenon, and that the b.c.c. phase of iron is the stable phase in the Earth's inner core.

Texturing of the Earth's inner core by Maxwell stresses

Elastic anisotropy in the Earth's inner core has been attributed to a preferred lattice orientation, which may be acquired during solidification of the inner core or developed subsequent to solidification as a result of plastic deformation. But solidification texturing alone cannot explain the observed depth dependence of anisotropy, and previous suggestions for possible deformation processes have all relied on radial flow, which is inhibited by thermal and chemical stratification. Here we investigate the development of anisotropy as the inner core deforms plastically under the influence of electromagnetic (Maxwell) shear stresses. We estimate the flow caused by a representative magnetic field using polycrystal plasticity simulations for epsilon-iron, where the imposed deformation is accommodated by basal and prismatic slip. We find that individual grains in an initially random polycrystal become preferentially oriented with their c axes parallel to the equatorial plane. This pattern is accentuated if deformation is accompanied by recrystallization. Using the single-crystal elastic properties of epsilon-iron at core pressure and temperature, we average over the simulated orientation distribution to obtain a pattern of elastic anisotropy which is similar to that observed seismologically.

Chemical interaction of Fe and Al(2)O3 as a source of heterogeneity at the Earth's core-mantle boundary

Seismological studies have revealed that a complex texture or heterogeneity exists in the Earth's inner core and at the boundary between core and mantle. These studies highlight the importance of understanding the properties of iron when modelling the composition and dynamics of the core and the interaction of the core with the lowermost mantle. One of the main problems in inferring the composition of the lowermost mantle is our lack of knowledge of the high-pressure and high-temperature chemical reactions that occur between iron and the complex Mg-Fe-Si-Al-oxides which are thought to form the bulk of the Earth's lower mantle. A number of studies have demonstrated that iron can react with MgSiO3-perovskite at high pressures and high temperatures, and it was proposed that the chemical nature of this process involves the reduction of silicon by the more electropositive iron. Here we present a study of the interaction between iron and corundum (Al(2)O3) in electrically- and laser-heated diamond anvil cells at 2,000-2,200 K and pressures up to 70 GPa, simulating conditions in the Earth's deep interior. We found that at pressures above 60 GPa and temperatures of 2,200 K, iron and corundum react to form iron oxide and an iron-aluminium alloy. Our results demonstrate that iron is able to reduce aluminium out of oxides at core-mantle boundary conditions, which could provide an additional source of light elements in the Earth's core and produce significant heterogeneity at the core-mantle boundary.

The plastic deformation of iron at pressures of the Earth's inner core

Soon after the discovery of seismic anisotropy in the Earth's inner core, it was suggested that crystal alignment attained during deformation might be responsible. Since then, several other mechanisms have been proposed to account for the observed anisotropy, but the lack of deformation experiments performed at the extreme pressure conditions corresponding to the solid inner core has limited our ability to determine which deformation mechanism applies to this region of the Earth. Here we determine directly the elastic and plastic deformation mechanism of iron at pressures of the Earth's core, from synchrotron X-ray diffraction measurements of iron, under imposed axial stress, in diamond-anvil cells. The epsilon-iron (hexagonally close packed) crystals display strong preferred orientation, with c-axes parallel to the axis of the diamond-anvil cell. Polycrystal plasticity theory predicts an alignment of c-axes parallel to the compression direction as a result of basal slip, if basal slip is either the primary or a secondary slip system. The experiments provide direct observations of deformation mechanisms that occur in the Earth's inner core, and introduce a method for investigating, within the laboratory, the rheology of materials at extreme pressures.

New beta(fcc)-cobalt to 210 GPa

We report a new phase transition in cobalt from the magnetic varepsilon(hcp) to a beta(fcc) phase, likely nonmagnetic, at 105 GPa. It occurs martensitically in an extended pressure region between 105 and 150 GPa without any apparent volume change. The fcc phase of Co is in systematic accordance with the 4d and 5d counterparts. The pressure-volume isotherm of beta-Co resembles those of alpha(fcc)-Ni and varepsilon(hcp)-Fe within 1%. The phase diagram of cobalt suggests that the fcc stability increases with increasing occupancy of d-band electrons from Fe to Co to Ni.

In situ X-Ray study of thermal expansion and phase transition of iron at multimegabar pressure

The density of varepsilon-iron has been calculated at pressures and temperatures up to 300 GPa and 1300 K, respectively. We observe varepsilon to beta phase transition at pressures between 135 and 300 GPa and temperature above 1350 K; the pattern can be interpreted in terms of double hexagonal close-packed structure. The density calculated at high pressure and temperature (330-360 GPa and 5000-7000 K) closely matches with preliminary reference Earth model density, thereby imposing constraint on the composition of the Earth's inner core.

Density of phonon states in iron at high pressure

The lattice dynamics of the hexagonal close-packed (hcp) phase of iron was studied with nuclear inelastic absorption of synchrotron radiation at pressures from 20 to 42 gigapascals. A variety of thermodynamic parameters were derived from the measured density of phonon states for hcp iron, such as Debye temperatures, Gruneisen parameter, mean sound velocities, and the lattice contribution to entropy and specific heat. The results are of geophysical interest, because hcp iron is considered to be a major component of Earth's inner core.

Magnetic properties of hexagonal closed-packed iron deduced from direct observations in a diamond anvil cell

The attraction of hexagonal closed packed (hcp) iron to a magnet at 16.9 gigapascals and 261 degrees centigrade suggests that hcp iron is either paramagnetic or ferromagnetic with susceptibilities from 0. 15 to 0.001 and magnetizations from 1800 to 15 amperes per meter. If dominant in Earth's inner core, paramagnetic hcp iron could stabilize the geodynamo.

Synchrotron X-Ray Study of Iron at High Pressure and Temperature

X-ray synchrotron experiments with in situ laser heating of iron in a diamond-anvil cell show that the high-pressure epsilon phase, a hexagonal close-packed (hcp) structure, transforms to another phase (possibly a polytype double-layer hcp) at a pressure of about 38 gigapascals and at temperatures between 1200 and 1500 kelvin. This information has implications for the phase relations of iron in Earth's core.