The self-consistent phonon (SCP) theory is used to study the mechanical stability of crystals to vibration as temperature is increased. The temperature at which instability occurs, TI, depends sensitively on the approximation made to the SCP theory. In the self-consistent harmonic approximation, TI is-10-200 times the observed melting temperature T~, depending on the crystal considered. In higher approximations Tl is reduced to-. (3-4)T~in all cases. Although the exphcit character of the instability depends somewhat on the approximation, the instability is sudden, and takes place at a critical vibrational amplitude reminiscent of the Lindemann model of melting.
We show that the recently measured kinetic energy of atoms in solid helium is substantially larger than expected for even a moderately anharmonic solid. The large kinetic energy is rather an explicit measure of the highly anharmonic nature of solid helium. An explanation is proposed here in terms of the anharmonic one-phonon response functions which have large, high-frequency tails that contribute significantly to the kinetic energy.
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