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A search for incipient lattice instabilities in MgB$_{2}$ by anelastic spectroscopy

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.