PHONONIC FILTER EFFECT IN THE BA-GE-NI CLATHRATE SYSTEM
Intermetallic clathrates are so called cage compounds. Their structure can be described by a host framework, consisting of large cages, which enclose heavy guest atoms (see Fig. 1). While clathrates exhibit a crystal-like electrical conductivity, their thermal conductivity is strongly reduced making them promising materials for thermoelectric application. So far, the microscopic mechanisms responsible for their reduced thermal conductivity have not been understood. In particular the respective roles played by encapsulated guest atoms and the structural complexity of the host framework are ambiguous.
A widespread idea to explain the low lattice thermal conductivity in clathrates was that encaged atoms, oscillating at a rattling frequency, would scatter heat carrying phonons, reducing lifetime and velocity of sound of the latter ones, thus decreasing lattice thermal conductivity *). In a different approach, low-energy phonon branches were proposed as source of Umklapp scattering, meaning collisions of phonons with each other, what would also result in a reduction of phonon lifetimes and thus lattice thermal conductivity.
With high resolution inelastic neutron scattering (INS) measurements on a Ba-Ge-Ni single crystal we could now demonstrate that the observed lifetimes of acoustic phonons are by far not small enough to explain the low κ in clathrates. The experimentally measured phonon linewidths in the investigated Ba-Ge-Ni clathrate were indeed found to be very narrow, such that strong Umklapp scattering could be ruled out as the origin of the low κ in clathrates. In addition a transfer of scattering intensity from modes that are dominated by Ba motions to modes that are rather motions of the framework was evidenced. This now points to coherent motion of guest and host framework, meaning that the two subsystems are coupled with each other, thus indeed breaking down the picture of isolated oscillators since for an isolated oscillator neither such intensity change nor the also evidenced energy dispersion would be expected. These findings therefore contradict the above discussed scenarios. The intensity transfer from acoustic phonon branch to the Ba dominated phonon branches occurs without a strong energy broadening of the acoustic phonon profile and therefore without a significant decrease of their lifetime. Thus phonon lifetimes are not efficiently reduced by guest atom vibrations and therefore scattering processes, including Umklapp scattering, can be ruled out as the main mechanism for the suppression of the heat transport in these materials. Our INS results, however, contain further striking information. From the determined dispersion curves (see Figure 2) it is evident that the acoustic phonon branch is interrupted at low energies, even before it encounters the guest dominated optical branch at about 6 meV. Thus we do not observe any acoustic-like phonons above 6 meV and therefore the acoustic phonon branch does not cross or anti-cross the 6 meV branch. Instead the acoustic branch simply fades away (red dots in Figure 2).
Taking this observation into account, we proposea new mechanism to explain the low lattice thermal conductivity in clathrates - a phononic low-pass filtering of acoustic phonon modes, having its origin in both guest and host structure. In a first order approximation the lattice thermal conductivity in clathrates can be then be described by a modified Debye model ***). Instead of assuming acoustic phonons and thus heat transport up to the Debye frequency, a cutoff frequency is introduced which corresponds to the energy of the first Ba dominated phonon mode (first blue branch in Figure 2). To fully calculate the thermal properties of a material all phonon modes would have to be taken into account. Our simple approach is, yet, justified, since the main contribution to heat transport can be attributed to acoustic phonons, while the optical modes above the introduced cutoff frequency can in first order be negelected due to smaller lifetimes and group velocities.
Finally a computational comparison of a model Ge46 framework system with pure Ge shows that the cage structure itself is significantly decreasing the lattice thermal conductivity. An additional reduction of κ in the Ba8Ge40Ni6 clathtrate arises then from the Ba dominated phonons which lower the cutoff energy of the modified Debye model, i.e. the energy above which no acoustic phonons are evidenced. Thus it indeed is the combination of structural complexity and low energy Ba modes that results in a filtering of acoustic phonons, such that above the cutoff frequency almost no contributions to thermal conduction can be expected.
The lattice dynamics of the Ba-Ge-Ni clathrate evidences unconventional dynamics, resulting from the combined effects of unit cell complexity and guest-host interaction. A possible explanation for the low lattice thermal conductivity in clathrates was presented with a phononic filter effect that strongly hinders the heat transport above the lowest guest phonon energy. Furthermore we want to emphasize that the thermal conductivity in complex materials cannot be explained by simple models derived for systems with low structural complexity. To conclude, this points out that materials of high structural complexity clearly show potential for extraordinary physical properties.
*) In a simple picture the lattice thermal conductivity results from acoustic phonons that transport heat throughout a crystal. The lifetime of a phonon and its velocity determine how far it is able to transport the energy (or heat) it is carrying.
**) The linewidth of a phonon is inversely proportional to its lifetime, such that a narrow linewidth means a large lifetime and vice versa.
***) The Debye model assumes that a crystal only evidences acoustic phonon modes (i.e. modes that are capable to transport heat), up to elevated frequencies (the maximum frequency is called Debye frequency).
Euchner H, Pailhes S, Nguyen L, Assmus W, Ritter F, Haghighirad A, Grin Y, Paschen S, de Boissieu M, Phys. Rev. B