Vacancy-suppressed lattice conductivity of high-$\mathit{ZT}$ In${}_4$Se${}_{3-x}$

Anomalous, vacancy-induced anisotropic thermal conductivity is one of the important properties in the recently discovered high-$ZT$ In${}_4$Se${}_{3-x}$ compound. In this work, the lattice thermal conductivity of In${}_4$Se${}_{3-x}$ is investigated using equilibrium molecular dynamics simulation, the point-defect model, and ab initio calculations. The charge density distribution shows highly anisotropic structure with strong bonding along In-Se-In chain direction. Se vacancy strongly suppresses the phonon propagation along the chain direction, with little change in other directions. We show that suppressed long-range acoustic phonon transport caused by the vacancy results in anisotropic change of lattice conductivity. We suggest controlling of vacancy in intrinsic low-dimensional compounds is critical in achieving optimal lattice thermal conductivity and other thermoelectric properties.

Figure 1

Crystal structure of In${}_4$Se${}_3$. (a) Perspective view of the $a$-$b$ plane. Gray and yellow spheres represent In and Se atoms, respectively. (b) The structure contains three distinct In-Se-In chains along the $c$ axis; blue, black, and red lines indicate In1-Se1, In2-Se2, and In3-Se3 chains, respectively. (c) Crystal structure of In${}_4$Se${}_{3-x}$, containing Se3 vacancy.

Figure 2

(a) Variation of the directional lattice conductivity as a function of temperature for In${}_4$Se${}_3$ ($x=0$, solid lines) and In${}_4$Se${}_{2.5}$ ($x=0.5$, dashed lines). (b) The calculated a-b and b-c plane lattice conductivities and comparison to experiment.[1] (c) The decomposition of lattice conductivity and comparison to the Slack relation for In${}_4$Se${}_3$ ($x=0$). (d) The decomposition of lattice conductivity for In${}_4$Se${}_{2.5}$ ($x=0.5$).

Figure 3

Variation of the directional lattice conductivity of In${}_4$Se${}_{3-x}$ as a function of vacancy at 300 K. The calculated MD results (solid lines) are compared with the point-defect model (dashed lines).

Figure 4

Phonon dispersion curves and density of state of (a) In${}_4$Se${}_3$ and (b) In${}_4$Se${}_{2.75}$. [1,0,0], [0,1,0], and [0,0,1] indicate the $a$-, $b$-, and $c$-directions in the structure, respectively.

Figure 5

Charge density distributions in the (a) In${}_4$Se${}_3$ and (b) In${}_4$Se${}_{2.9}$ lattice.