Localization of Propagative Phonons in a Perfectly Crystalline Solid

Perfectly crystalline solids are excellent heat conductors. Prominent counterexamples are intermetallic clathrates, guest-host systems with a high potential for thermoelectric applications due to their ultralow thermal conductivities. Our combined experimental and theoretical investigation of the lattice dynamics of a particularly simple binary representative, ${\mathrm{Ba}}_8{\mathrm{Si}}_{46}$, identifies the mechanism responsible for the reduction of lattice thermal conductivity intrinsic to the perfect crystal structure. Above a critical wave vector, the purely harmonic guest-host interaction leads to a drastic transfer of spectral weight to the guest atoms, corresponding to a localization of the propagative phonons.

Figure 1

(a) ${\mathrm{Ba}}_8{\mathrm{Si}}_{46}$ microcrystal grown at 5 GPa and $1000°\mathrm{C}$. (b) Representation of face sharing ${\mathrm{BaSi}}_{20}$ and ${\mathrm{BaSi}}_{24}$ cages as building units of type-I clathrates. Atoms are represented by their atomic displacement ellipsoids obtained from single crystal x-ray diffraction.

Figure 2

Mapping of the simulated IXS intensities for (a) longitudinal phonons (${\mathrm{LA}}_{001},$) and (c) transverse phonons (${\mathrm{TA}}_{110}^{001}$). Black dots represent the fitted experimental positions. White vertical lines labeled from $q_1$ to $q_8$ in (a) indicate the cuts shown in Fig. 3. The $\mathbf{q}$ dependences of the phonon DSF of the ${\mathrm{LA}}_{001}$ and ${\mathrm{TA}}_{110}^{001}$ (filled red squares) is depicted in (b) and (d), respectively, together with the guest optical phonons at $E_1$ (blue circles). The solid black line stands for the DSF of the acoustic branch extracted from the simulated spectra.

Figure 3

(a)–(h) Constant $Q$ scans for ${\mathrm{LA}}_{001}$. Phonon wave vectors ${\mathbf{q}}_{00h}$ are labeled from $q_1$ to $q_8$ corresponding to cuts through the dispersion as depicted by the vertical white lines in Fig. 2. Orange lines are fits as described in the Supplemental Material [14]. Blue profiles correspond to the ab inito simulated IXS spectra, convoluted with the instrumental resolution. The blue vertical lines indicate the simulated phonon energies without the convolution.

Figure 4

Simulated dispersions (left) and participation ratios (right) for phonons propagating in the [$6+h,0,0$] direction in ${\mathrm{Si}}_{46}$ [top panels (a),(b)] and ${\mathrm{Ba}}_8{\mathrm{Si}}_{46}$ [bottom panels (c),(d)]. Modes in (a),(c) are color coded with respect to their PR. Green means a high PR; red and black correspond to intermediate and low PR, respectively.

Figure 5

(a) Atomic participation ratio, as defined in Eq. (2), obtained for a powder average of phonon modes in ${\mathrm{Ba}}_8{\mathrm{Si}}_{46}$, with each color representing a given Wyckoff site. (b),(c) show the projection of the average atom distribution of atoms in the large ${\mathrm{BaSi}}_{24}$ cluster resulting from phonon motions in different frequency intervals as determined for the powder average of modes whose APR is depicted in (a). (b) Corresponds to modes with acoustic character in the range 0–2 meV; (c) Depicts modes in the range from 6 to 8 meV.