Abstract Solid iron-silicon alloys play an important role in planetary cores, especially for planets that formed under reducing conditions, such as Mercury. The CsCl (B2) structure occupies a considerable portion of the Fe-Si binary phase diagram at pressure and temperature conditions relevant for the core of Mercury, yet its thermodynamic and thermoelastic properties are poorly known. Here, we report in situ X-ray difraction measurements on iron-silicon alloys with 7–30 wt% Si performed in laser-heated diamond-anvil cells up to ~120 GPa and ~3000 K. Unit-cell volumes of the B2 phase at high pressures and high temperatures have been used to obtain a composition-dependent thermal equation of state of this phase. In turn, the thermal equation of state is exploited to determine the composition of the B2 phase in hcp+B2 mixtures at 30–100 GPa and to place constraints on the hcp+B2/B2 phase boundary, determined to vary between ~13–18 wt% Si in the considered pressure and temperature range. The hcp+B2/B2 boundary of Fe-Si alloys is observed to be dependent on pressure but weakly dependent on temperature. Our results, coupled with literature data on liquid equations of state, yield an estimation of the density contrast between B2 solid and liquid under Mercury’s core conditions, which directly relates to the buoyancy of the crystallizing material. While the density contrast may be large enough to form a solid inner core by the gravitational sinking of B2 alloys in a Si-rich core, the density of the B2 solid is close to that of the liquid at solidus conditions for Si concentration approaching ~10 wt% Si.

Picosecond acoustics combined with a diamond anvil cell is used to study liquid indium and to determine with high accuracy both the sound velocity and the melting curve over an extended pressure and temperature range. The sound velocities, determined by phonon surface imaging, complement previous inelastic x-ray scattering determinations and are in good agreement with estimations according to a thermodynamic model. Based on exact thermodynamic relations, the equation of state of the liquid phase is obtained using the isothermal bulk modulus B-T,B- 0 and its first pressure derivative B'(T). These quantities are derived from the precise experimental determination of the variation of the sound velocity as a function of pressure. Melting is determined via the detection of abrupt changes in the elastic properties between solid and liquid phases and through the monitoring of the solid-liquid coexistence. The melting curve constrained up to 6 GPa and 673 K is shown to be well described by the Simon-Glatzel equation in the full (p, T) range explored.

Picosecond acoustics is an optical pump-probe technique allowing to access thermoelastic properties and sound velocities of a large variety of materials under extreme conditions. Coupled with diamond anvil cells and laser heating, picosecond acoustics measurements offer the possibility to probe materials over a pressure and temperature range directly pertinent for the deep planetary interiors. In this paper we highlight the capabilities and versatility of this technique by presenting some recent applications on materials of geophysical interest. All the independent components of the elastic tensor of MgO are simultaneously determined by measurements on a single crystal at ambient conditions. Compressional sound velocity is measured at high pressure on an iron-carbon alloy and on polycrystalline argon. First laser heating test measurements performed on molybdenum at high pressure are also presented. These examples demonstrate that picosecond acoustics is a valuable alternative to already existing techniques for determining the physical properties of samples under extreme pressure and temperature conditions.

Knowledge of the elastic properties and equations of state of iron and iron alloys are of fundamental interest in Earth and planetary sciences as they are the main constituents of telluric planetary cores. Here, we present results of X-ray diffraction measurements on a ternary Fe–Ni–Si alloy with 5 wt% Ni and 5 wt% Si, quasi-hydrostatically compressed at ambient temperature up to 56 GPa, and under simultaneous high pressure and high temperature conditions, up to 74 GPa and 1750 K. The established pressure dependence of the c/a axial ratio at ambient temperature and the pressure–volume–temperature (P–V–T) equation of state are compared with previous work and literature studies. Our results show that Ni addition does not affect the compressibility and axial compressibility of Fe–Si alloys at ambient temperature, but we suggest that ternary Fe–Ni–Si alloys might have a reduced thermal expansion in respect to pure Fe and binary Fe–Si alloys. In particular, once the thermal equations of state are considered together with velocity measurements, we conclude that elements other than Si and Ni have to be present in the Earth’s inner core to account for both density and seismic velocities.

An electronic-driven liquid-liquid phase transition in rubidium is revealed by picosecond acoustic measurements combined with ab initio calculations. Picosecond acoustics were used to measure the melting line up to 10 GPa, finding the maximum in the melting curve at 7 GPa and 555 K. We observe the onset of a continuous liquid-liquid phase transition beginning around the melting maxima through until 16 GPa. Sound velocity shows a softening similar to that reported for liquid caesium, caused by a change in the bulk modulus during a crossover from the low-density to the high-density liquid. Guided by the ab initio calculations, we relate the changes in the thermoelastic properties to the progressive localization of the valence electrons in the pressure range of 6-16 GPa. At high pressure rubidium forms an electride liquid quantified by the appearance of interstitial quasiatoms localized in the valence electron density.

We describe here a time resolved pump-probe laser technique-picosecond interferometry-which has been combined with diamond anvil cells (DAC). This method enables the measurement of the longitudinal sound velocity up to Mbar pressure for any kind of material (solids, liquids, metals, insulators). We also provide a description of picosecond acoustics data analysis in order to determine the complete set of elastic constants for single crystals. To illustrate such capabilities, results are given on the pressure dependence of the acoustic properties for prototypical cases: polycrystal (hcp-Fe-5 wt% Si up to 115 GPa) and single-crystal (Si up to 10 GPa).

Using a combination of picosecond acoustics and synchrotron x-ray diffraction, the sound velocities and equations of state of Fe-Si alloys have been determined over a wide range of compositions (10-29 at. % Si) and pressures (up to 65 GPa) under quasihydrostatic conditions. We observe marked variation in the elastic properties of the alloys depending on synthesis method and degree of Si ordering. In particular, it is observed that there is a sharp change in the density dependence of the sound velocities which coincides with the observation of long-range ordering by diffraction methods. This change in elasticity is probably due to a change in bond character of the Fe-Si alloy. Furthermore, the bcc-hcp transition in these alloys has been mapped to high pressures and Si contents. We observed that the onset of the transition changes by more than 6 GPa per at. % for alloys containing more than similar to 15 at. % Si.

Lauric acid is commonly used as a coating agent which efficiently protects against oxidation and/or coalescence a set of inorganic nanocrystals obtained by chemical process. Its stability under pressure is likely to be informative on the stability and ordering of compressed supercrystals of nanocrystals. Therefore the elastic behaviour of lauric acid submitted to high pressures up to 25 GPa is studied. This elastic behavior has been probed by two complementary in situ techniques at high pressure: Raman spectroscopy and picosecond acoustics. Comparison between pressure-induced transformations as observed with the two techniques suggests that the lauric acid remains elastically stable above 2 GPa up to 25 GPa.

The elasticity of hcp‐Fe‐5wt%Si has been investigated by synchrotron X‐ray diffraction up to 110 GPa and 2,100 K and by picosecond acoustics measurements at ambient temperature up to 115 GPa. The established Pressure‐Volume‐Temperature equation of state shows that the density of the Earth's inner core can be matched by an Fe‐Si alloy with 5wt% Si for all reasonable core temperatures, but that its compressional and shear velocities remain too high with respect to seismological observations. On the other hand, Fe‐Si alloys whose velocities are expected to get close to seismological observations are too dense at relevant temperatures. Thus, based on these combined velocity‐density measurements, silicon is not likely to be the sole light element in the inner core.

Liquid cesium (l-Cs) sound velocity at high densities was investigated along a 500-K isotherm using high-pressure picosecond acoustics measurements. At 2.0 GPa, the liquid sound velocity goes through a maximum versus pressure without any change on the reflectivity and interferometry acoustic signals. Upon further compression, a softening of the l-Cs viscoelastic properties is observed from 2.0 up to 4.0 GPa, pressure at which the reflectometric signal is abruptly reversed whereas the interferometric signal remains qualitatively the same. This anomalous behavior could be related to an electronic transformation within the l-Cs state, which here again could reflect what happens at lower temperature within the solid state. If so, such liquid-liquid transition may be driven by the progressive collapse of the $6s$ electronic orbital onto the $5d$ ones. Above 4.0 GPa, the l-Cs sound velocity starts again to increase as commonly expected upon compression.

We carried out sound velocity and density measurements on solid hcp-Fe and an hcp-Fe-Si alloy with 9 wt.% Si at 300 K up to similar to 170 and similar to 140 GPa, respectively. The results allow us to assess the density (rho) dependence of the compressional sound velocity (V-p) and of the shear sound velocity (V-s) for pure Fe and the Fe-Si alloy. The established V-p-rho and V-s-rho relations are used to address the effect of Si on the velocities in the Fe-FeSi system in the range of Si concentrations 0 to 9 wt.% applicable to the Earth's core. Assuming an ideal linear mixing model, velocities vary with respect to those of pure Fe by similar to+80 m/s for V-p and similar to-80 m/s for Vs for each wt.% of Si at the inner core density of 13 000 kg/m(3). The possible presence of Si in the inner core and the quantification of its amount strongly depend on anharmonic effects at high temperature and on actual core temperature. (C) 2017 Elsevier B.V. All rights reserved.

Based on the original combination of picosecond acoustics and diamond anvils cell, hypersonic sound velocities of liquids and solids under extreme conditions can be accurately measured [1]. Picosecond acoustics is a time-resolved optical pump-probe technique, contactless and non-destructive, analogous in many aspects to the classical ultrasonic pulse-echo technique. It permits the study of ultrafast phenomena in micrometric samples or thin films. In addition to time of flight measurements in the ps range, it can provide phonon surface imaging as a function of time, or time-resolved stimulated Brillouin scattering. This laser acoustic technique can be applied to many materials and enables the determination over and extended pressure and temperature range of the melting curve and phase diagram, the equation of state for liquids, the complete set of elastic constants for single crystals.

Alkali metals are very intriguing materials : they are considered as simple liquids at ambient conditions, but at high pressures their properties become more complex. Their phase diagrams exhibit some maxima in the melting curve at high pressure [1], [2], and some minima, meaning the material become liquid under strong compression. They can exhibit also a considerable variety of crystalline phases [3], transparency (at approximately 200 GPa in the case of Na [4]), and some liquid-liquid phase transitions (LLPT), for example a LLPT was reported in Rb at 12 GPa and 300°C [5]. Thermodynamic and elastics properties of liquid alkali metals are difficult to determine at extreme conditions with ultrasonic classical techniques, due to their high reactivity and the large sample size required. To overcome these difficulties, we combined diamond anvil cell with the picoseconds acoustics technique [6], which is an optical pump-probe technique similar to pulse-echo ultrasonic technique, non-destructive and contactless. Little is known about the phase diagram of Rb above 8 GPa (see Fig.1). On the contrary, the phase diagram of Cs is best known, including two maxima in the melting line and a deep minimum at 4.8 GPa and 370°C [2]. We report the phase diagrams and the sound velocities in liquid heavy alkali metals Cs and Rb measured by picoseconds acoustics. In these two liquid metals, the evolution of the sound velocity is complicated. The sound velocity in liquid Cs shows similarities with the underlying solid phase. No LLPT was found in the P-T range considered here (0-15 GPa, 300°C) for liquid Rb. These measurements open the way to determine the equation of state and the thermodynamic properties of liquid Rb and Cs [7].

The elasticity at high pressure of solid hydrogen in hexagonal close-packed (hcp) phase I has been examined experimentally by laser acoustics technique in a diamond anvil cell, up to 55 GPa at 296 K, and theoretically using pair and three-body semiempirical potentials, up to 160 GPa. In the experiments on H-2 and D-2, the compressional sound velocity has been measured; the Poisson's ratio has been determined by combining these data with the previously reported equation of state. At room temperature, the difference between the adiabatic and isothermal processes vanishes above 25 GPa but cannot be neglected at lower pressure. Theoretically, all five elastic constants of hcp hydrogen have been calculated, and various derived elastic quantities are presented. The elastic anisotropy of hcp hydrogen was found to be significant, with Delta P approximate to 1.2, Delta S-1 Delta approximate to 1.7, and Delta S-2 approximate to 1. Calculations suggest the Poisson's ratio to decrease with pressure reaching a minimum value of 0.28 at 145 GPa. In the experiment, the Poisson's ratio is also found to decrease with pressure. Theoretical calculations show that the inclusion of zero-point vibrations on the elastic properties of H-2 does not result in any drastic changes of the behavior of the elastic quantities.