Supercompliant and Soft ${({\mathrm{CH}}_3{\mathrm{NH}}_3)}_3{\mathrm{Bi}}_2{\mathrm{I}}_9$ Crystal with Ultralow Thermal Conductivity

In this Letter, we show the phonon dispersion of ${({\mathrm{CH}}_3{\mathrm{NH}}_3)}_3{\mathrm{Bi}}_2{\mathrm{I}}_9$ single crystals at 300 K measured by inelastic x-ray scattering. The frequencies of acoustic phonons are among the lowest of crystals. Nanoindentation measurements verified that these crystals are very compliant and considerably soft. The frequency overlap between acoustic and optical phonons results in strong acoustic-optical scattering. All these features lead to an ultralow thermal conductivity. The fundamental knowledge obtained from this study will accelerate the design of novel hybrid materials for energy applications.

Figure 1

Phonon dispersion of ${({\mathrm{CH}}_3{\mathrm{NH}}_3)}_3{\mathrm{Bi}}_2{\mathrm{I}}_9$ single crystals measured by IXS at 300 K. The high symmetry points are chosen based on first Brillouin zone of hexagonal unit cell: Γ (0 0 0), $A$ (0 0 0.5), $K$ (0 0.33 0.33 0), and $M$ (0.5 0 0) in units of (${\mathbf{b}}_1,{\mathbf{b}}_2,{\mathbf{b}}_3$), where ${\mathbf{b}}_1=[(2\pi /a),(2\pi /\sqrt{3}a),0]$, ${\mathbf{b}}_2=[0,(4\pi /\sqrt{3}a),0]$, and ${\mathbf{b}}_3=[0,0,(2\pi /c)]$ in Cartesian coordinate system. The inset is the first Brillouin zone of ${({\mathrm{CH}}_3{\mathrm{NH}}_3)}_3{\mathrm{Bi}}_2{\mathrm{I}}_9$ single crystal. Green squares, yellow squares, blue circles, and blue triangles denote longitudinal acoustic (LA) modes, transverse acoustic (TA) modes, longitudinal-optical (LO) modes, and transverse-optical (TO) modes, respectively. The green and yellow lines were drawn based on the markers.

Figure 2

(a) Comparison of acoustic phonon frequencies of different materials measured experimentally: $M{A}_3{\mathrm{Bi}}_2{\mathrm{I}}_9$ single crystals, tetragonal $MA{\mathrm{PbI}}_3$ single crystals [46] ($MA$ denotes ${\mathrm{CH}}_3{\mathrm{NH}}_3^{+}$), C60 (fcc) [54], argon (Ar) (fcc) [55], h-BN [56], and graphite [57] (cross-plane acoustic modes only), NaCl [63]. $M{A}_3{\mathrm{Bi}}_2{\mathrm{I}}_9$ and $MA{\mathrm{PbI}}_3$ are hybrid organic-inorganic single crystals; C60, argon, h-BN, and graphite are van der Waals crystals; NaCl is the ionic crystal. (b) Comparison of indentation modulus of different materials measured experimentally: $M{A}_3{\mathrm{Bi}}_2{\mathrm{I}}_9$ single crystals, $MA{\mathrm{PbI}}_3$ polycrystals [64], tetragonal $MA{\mathrm{PbI}}_3$ single crystals [32, 33, 34], $MA{\mathrm{PbBr}}_3$ single crystals [32, 33, 34]. Round brackets denote the orientation of the indented crystals. (c) Comparison of thermal conductivity of different materials measured experimentally at 300 K: $M{A}_3{\mathrm{Bi}}_2{\mathrm{I}}_9$ polycrystals, $MA{\mathrm{PbI}}_3$ polycrystals [35, 36], $MA{\mathrm{PbI}}_3$ single crystals [34, 35, 37, 38, 39], $MA{\mathrm{PbBr}}_3$ single crystals [34, 37, 38]. Pink denotes the experimental results of this work.