  We combine density functional theory (DFT) within the local density
approximation (LDA), the quasiharmonic approximation (QHA), and a model
vibrational density of states (VDoS) to calculate elastic moduli and sound
velocities of gamma-[Fe_x,Mg_(1-x)]_2SiO_4 (ringwoodite), the most abundant
mineral of the lower Earth's transition zone (TZ). Comparison with experimental
values at room-temperature and high pressure or ambient-pressure and high
temperature shows good agreement with our first-principles findings. Then, we
investigate the contrasts associated with the
beta-to-gamma-[Fe_x,Mg_(1-x)]_2SiO_4 transformation at pressures and
temperatures relevant to the TZ. This information offers clearly defined
reference values to advance the understanding of the nature of the 520 km
seismic discontinuity.
