  We measured the complex dynamic elastic modulus of MgB2 between 1.3 and 650 K
at frequencies included between 5 and 70 kHz. The main purpose of this work is
to search for possible lattice instabilities, which could contribute to enhance
the electron-phonon coupling. The Young's modulus indeed presents an anomalous
softening on cooling below 400 K, and hysteresis between cooling and heating.
Such anomalies, however, can be accounted for by intense relaxation processes
with maxima between 50 and 150 K, whose nature is not yet clarified, and by
geometric defects generated by the anisotropic thermal expansion between the
grains during thermal cycling. Additional intense relaxation processes are
observed above room temperature, and their possible origin is discussed. The
influence of the highly anharmonic in-plane vibration modes of the B atoms on
the elastic and anelastic properties of MgB2 is discussed in detail.
