Molybdenum sound velocity and shear modulus softening under shock compression

Abstract

We measured the longitudinal sound velocity in Mo shock compressed up to 4.4 Mbars on the Hugoniot. Its sound speed increases linearly with pressure up to 2.6 Mbars; the slope then decreases up to the melting pressure of ∼3.8 Mbars. This suggests a decrease of shear modulus before the melt. A linear extrapolation of our data to 1 bar agrees with the ambient sound speed. The results suggest that Mo remains in the bcc phase on the Hugoniot up to the melting pressure. There is no statistically significant evidence for a previously reported bcc→hcp phase transition on the Hugoniot.

X-ray diffraction of molybdenum under shock compression to 450 GPa

“…Our X-ray diffraction measurements provide a direct determination of shock melting in Mo at 380-390 GPa, supporting the previous interpretation of Hugoniot sound velocity measurements 2,9 . The expected shock temperatures at this pressure are also consistent with the expected melting temperature of Mo from ab initio molecular dynamics at these pressures.…”

“…The shear velocities calculated from the Nguyen et al data 9 exhibit softening beginning from about 240 GPa (Fig. 8) and Errandonea et al 27 suggest this may be related to the beginning of partial melting along the Hugoniot, potentially reconciling the shock data with the low melting temperatures obtained in diamond anvil cell experiments.…”

“…However, a more recent theoretical calculation that fully included the effect of anharmonicity for the first time found instead that the BCC phase remained stable up to melting, and no explanation for the 210-GPa discontinuity could be provided 8 . Recently, the sound velocities of shocked molybdenum were re-measured 9 and, in agreement with the theoretical calculation 8 , it was found that there is no statistically significant evidence for a 210-GPa discontinuity, thereby suggesting that Mo remains in the BCC phase until shock melting near 390 GPa. However, other recent studies have already raised questions about this conclusion 27,28 .…”

“…2. Recently, a gas gun study 9 has repeated the measurement of sound velocities on shock-loaded Mo to pressures above 400 GPa (Fig. 8).…”

“…In recent year its phase stability, equation of state, and melting behavior have been the subject of intensive investigation [1][2][3][4][5][6][7][8][9] . The equation of state of molybdenum has been well studied using static compression techniques [10][11][12][13][14] with recent work 15 demonstrating that Mo remains in the body centered cubic (BCC) phase until at least 410 GPa at room temperature.…”