Tunneling and rattling in clathrate crystal

Abstract

We present tunneling and rattling motions of an off-center guest atom in a cage referring to a clathrate crystal La3Pd20Ge 6. The elastic constant C44 of La3Pd 20Ge6 shows a Debye-type dispersion of around 20 K obeying a relaxation time τ=τ0 exp(E/kBT) with an attempt time of τ0=2.0 × 10-12 s and an activation energy E=197 K. At low temperatures below 3 K down to 20 mK, the C44 shows a softening of C44=C440(T -T C0)/(T-Θ) with TC0=-337.970 mK and Θ=-338.044 mK. These facts are attributed to two different types of off-center motions with Γ5 symmetry in the 4α-site cage of LE3Pd20Ge6, a thermally activated rattling motion over the potential hill, and a tunneling motion through the potential hill at low temperatures.