A study of low-energy guest phonon modes in clathrate-II Na_xSi₁₃₆(x= 3, 23, and 24)

Abstract

Single-crystal x-ray diffraction from clathrate-II Na x Si 136 (x = 24) prepared by a new technique reveals the exceptionally large Na@Si 28 atomic displacement parameter (U eq ) is strongly temperature dependent, and can be attributed to low-energy rattling modes associated with the Na guest. Inelastic neutron scattering (INS) spectra collected from Na x Si 136 powder specimens (x = 3, 23) confirm the presence of low-energy guest-derived phonon modes for Na@Si 28 and Na@Si 20 . The lower energy Na@Si 28 rattler mode falls in the frequency range of the silicon host acoustic phonons, indicating the possibility for interaction with these phonons. The presence of these low-energy modes combined with the ability to controllably vary the guest content presents a unique opportunity for exploring the influence of guest-framework interactions on the lattice dynamics in intermetallic clathrates.

Synthesis and Structural Characterization of Single-Crystal K7.5Si46 and K17.8Si136 Clathrates

“…K@Si 28 in K 17.8 Si 136 is best refined at the center of the polyhedron, that is, with no positional disorder, in contrast to the case of Na x Si 136 where Na@Si 28 may be "off-center". 24, 45,51,52 Characteristic interatomic distances for clathrate-I and II NaÀSi and KÀSi derived from single-crystal X-ray diffraction data are given in Table 3. The alkaliÀSi and SiÀSi atomic distances for K 7.5 Si 136 are similar to those reported previously for polycrystalline K 7.6 Si 136 .…”

Effect of Guest Atom Composition on the Structural and Vibrational Properties of the Type II Clathrate-Based Materials AxSi136, AxGe136 and AxSn136 (A = Na, K, Rb, Cs; 0 ≤ x ≤ 24)

“…The predicted vibrational modes for Na 4 Si 136 , Na 4 Ge 136 , and Na 4 Sn 136 are shown in Figure 3 a – c , respectively. The number in parentheses is for the Na guest associated modes in Na 4 Si 136 , and was obtained from inelastic neutron scattering (INS) experiments [15]. …”

“…Recently, binary Type II clathrate based compounds with cubic space group symmetry $Pm\overline{3}n$ have attracted considerable attention [14,15,16,17,18,19]. The 136 atom unit cell of these materials contains two different sized cages: dodecahedra (20-atom cages) and hexakaidecahedra (28-atom cages).…”

“…Among the experimental techniques which have been used are temperature-dependent single-crystal XRD (which measures mean square atomic displacement amplitudes U eq ), temperature-dependent heat capacity (C p ) studies, and inelastic neutron scattering (INS) studies [15]. The results of our first principles calculations show reasonable agreement with the experimental data when comparing our calculated vibrational energy of 6.2 meV (at x = 4) for Na in the Si 28 cages with the experimentally determined Na atom rattler frequency of 6.5 meV in Na 3 Si 136 .…”

Phonon engineering through crystal chemistry

“…67,[79][80][81][82][83] The flatness of the guest mode can be deduced from the width of the heat capacity or phonon DOS peak. For example, in the germanium-clathrates, broad peaks observed in the phonon DOS reveal strong coupling between the guest and host modes.…”