Lattice Dynamics of Molybdenum at High Pressure

We have determined the lattice dynamics of molybdenum at high pressure to 37 GPa using high-resolution inelastic x-ray scattering. Over the investigated pressure range, we find a significant decrease in the $H$-point phonon anomaly. We also present calculations based on density functional theory that accurately predict this pressure dependence. Based on these results, we infer that the likely explanation for the $H$-point anomaly in molybdenum is strong electron-phonon coupling, which decreases upon compression due to the shift of the Fermi level with respect to the relevant electronic bands.

Figure 1

Representative inelastic x-ray scattering data collected at 17 GPa. The data show the dispersion for the longitudinal acoustic mode along $[001]$. Note the softening in the spectra above $q=0.6$.

Figure 2

Phonon dispersions in molybdenum. The filled symbols are IXS data collected at 17 GPa; the open symbols are inelastic neutron scattering results at 1 atm [9]. Circles are longitudinal acoustic modes; squares transverse acoustic modes. Along $[\xi \xi 0]$ the triangles and squares show the two nondegenerate transverse acoustic modes $\mathrm{TA}[110]⟨-110⟩$ and $\mathrm{TA}[110]⟨001⟩$, respectively. The dashed lines show the calculations performed at 105.1 a.u. (one atmosphere), and the solid lines the calculations at 99.2 a.u. (17 GPa).

Figure 3

Phonon dispersions along $[001]$ as a function of pressure. Filled symbols are IXS data (circles, 17 GPa; triangles, 37 GPa); the unfilled squares are inelastic neutron scattering data (one atmosphere). Our calculations are shown as solid lines. The inset shows the Gruneisen parameter as a function of density for a $q\sim 0.65$, corresponding to the maximum in the dispersion, and at the $H$ point ($q=1.0$).