Thus for a pressure variation of GPa and a typical

Thus, for a pressure variation of 100GPa and a typical value of bulk modulus for a solid (say 150GPa), a calculation gives around 3eV, say almost 3 order of magnitude higher than a corresponding energy shift for at ambient pressure (i.e. 90meV).
To focus on the acoustic properties, the measurement of sound velocity v versus pressure (and thus of the elastic moduli , considering the Christoffel equation) enables to probe with a high sensitivity the repulsive part of the interatomic potential, i.e. the most unknown part of the internal energy U. In the adiabatic case (ΔS=0), the Maxwell definition of an elastic constant gives:where is the strain tensor. This last equation illustrates why acoustic properties of solids and liquids are very sensitive to subtle changes in local or long-range order, and why measurements of phonons velocity under high pressure are considered as one of the most useful probe of interatomic potentials variations.
Elasticity of stressed material also provides crucial insight in the thermodynamics of condensed matter through the determination of the structural stability, the pressure dependence of the density, the melting curve, the piezoelectric properties, or the mechanical properties as few examples. However, for many years, inherent problems of carrying out elastic measurements in high pressure and high temperature GDC0449 have prevented acoustics experiments under extreme thermodynamic conditions. Consequently, little is still known about acoustic properties of liquids and solids at high density, data of major interest for physics, chemistry and planetology (Fig. 1). For what concerns the last case, the argument is straightforward: taking into account that the deepest core sampling has been extracted at a depth of only few kilometers, more than 99% of the Earth interior remains to be investigated by reproducing the thermodynamic conditions in the laboratory. For example, knowledge of the Earth interior composition involves the comparison of velocity-depth models derived from seismic data with sound velocities measured under extreme conditions (hundreds of GPa) in the laboratory.

Measuring techniques

Data analysis and sound velocity measurements
This section will be concerned primarily with the problem of determining the sound velocity of liquids and solids at extreme conditions by means of travel time acoustic wave measurements. Two types of measurements will here be emphasized. The so-called “temporal method”, GDC0449 where v is determined using a similar technique as the pulse echoes one. Note that here, the knowledge of the sample thickness e is requested. This technique being one of the most frequently used methods in ultrasonics community, it will not be considered at length in the present paper. The “imagery method” will however be described in more details. Mainly inspired by the acoustic wavefronts imaging technique developed in the 1990s [17], we would here particularly stress our development of a new type of analysis, which enables the determination of both v and e at the same time and for each pressure.

Measurement of sound wave velocity of polycrystalline iron at high pressure
Experiments at conditions of planetary’s core are still extremely challenging and important topics addressed include the density, the magnetism, and of course the sound velocity at ultrahigh pressures. Among all, the elastic properties of iron, particularly reference to get a better understanding of the Earth’s core, have been the subject of several papers. However, a huge discrepancy exists between shock waves non-equilibrium experiments [29] and indirect measurements of sound velocity under static compression [30].
In this study [31], the diamond anvil cell device combined with the technique of picosecond ultrasonics is demonstrated to be an adequate tool to measure the acoustic properties of iron up to 152GPa, i.e. one order of magnitude higher than previously published ultrasonic data. A disk of iron with 10m of diameter has been deposited on a platelet of silica 5m thick (see right part of Fig. 3). Loaded in a DAC (diamonds with culet of 100m and bevel of 300m), the quality of the iron sample has been first checked through X-ray diffraction, giving rise to homogeneous diffraction rings (i.e. excellent polycristallinity) and the expected density =7.85(1)gcm−3). The grain size of the polycristalline iron sample was less that 1m–.