Dumbbell Rattling in Thermoelectric Zinc Antimony

Inelastic neutron scattering measurements on thermoelectric ${\mathrm{Zn}}_4{\mathrm{Sb}}_3$ reveal a dominant soft local phonon mode at 5.3(1) meV. The form factor of this local mode is characteristic for dumbbells vibrating preferably along the dumbbell axis and can be related to a vibration of Sb dimers along the $c$ axis. The Lorentzian width of the mode corresponds to short phonon lifetimes of 0.39(2) ps and yields an estimate of the thermal conductivity that agrees quantitatively with recent steady state measurements. Heat capacity measurements are consistent with an Einstein mode model describing the local Sb-dimer rattling mode with an Einstein temperature of 62(1) K. Our study suggests that soft localized phonon modes in crystalline solids are not restricted to cagelike structures and are likely to be a universal feature of good thermoelectric materials.

Figure 1

The idealized crystal structure of the ${\mathrm{Zn}}_4{\mathrm{Sb}}_3$ site forms dimers, i.e., $d<d^{\prime }$, oriented along the $c$ axis in channels of distorted hexagonal layers of Sb and Zn, on the $18e$ and $36f$ sites, respectively.

Figure 2

The heat capacity of ${\mathrm{Zn}}_4{\mathrm{Sb}}_3$. The sum of a Debye contribution with a Debye temperature of 240 K and a soft 62 K or 5.3 meV Einstein mode accurately describes the measured heat capacity.

Figure 3

Inelastic neutron time-of-flight data (iv) compared to calculations with a damped harmonic oscillator (Lorentzian) with a dumbbell form factor, and multiphonon contribution (Gaussian) at 200 and 300 K: (i) an isotropic dumbbell mode, (ii) a longitudinal dumbbell mode, (iii) a weakly correlated longitudinal dumbbell mode.