Metavalent bonding induced abnormal phonon transport in diamondlike structures: Beyond conventional theory

A phenomenon appears in a few examples of the chalcopyrites (space group $I$-42 $d$) where heavier atoms do not necessarily lead to lower lattice thermal conductivity, in contradiction with Keyes expression that formulates an inverse relation of thermal conductivity with mean atomic mass. Herewith, the thermal conductivity of $\mathrm{CuIn}{\mathrm{Se}}_2, \mathrm{CuIn}{\mathrm{Te}}_2, \mathrm{AgIn}{\mathrm{Se}}_2$, and $\mathrm{AgIn}{\mathrm{Te}}_2$ was calculated and compared at room temperature from the linearized Boltzmann transport equation using ab initio density functional theory. $\mathrm{CuIn}{\mathrm{Se}}_2$ and $\mathrm{AgIn}{\mathrm{Se}}_2$ solids exhibit lower lattice thermal conductivity than that of $\mathrm{CuIn}{\mathrm{Te}}_2$ and $\mathrm{AgIn}{\mathrm{Te}}_2$, respectively, despite the fact that Te atoms are significantly heavier than Se. A comparison between dispersion relation, the Grüneisen parameter, and projected density of states leads to the conclusion that anharmonic transverse acoustic modes in the form of anomalous vibrations of Cu and Ag cause the lower values of the thermal conductivity. By analyzing the electronic structure, the compounds under study fit perfectly into a recently defined region of the metavalent bonding well known for its pronounced anharmonicity. The insight gained from the current results deepens our understanding of the unusual heat transfer phenomenon related to the metavalent bonding and sheds light on design and discovery of thermally functional materials that break the prediction by the conventional theory.

Figure 1

Temperature dependent thermal conductivity of $\mathrm{CuIn}{\mathrm{Se}}_2, \mathrm{CuIn}{\mathrm{Te}}_2, \mathrm{AgIn}{\mathrm{Se}}_2$, and $\mathrm{AgIn}{\mathrm{Te}}_2$.

Figure 2

Phonon dispersion relation and Grüneisen parameter of (a) $\mathrm{CuIn}{\mathrm{Se}}_2$, (b) $\mathrm{CuIn}{\mathrm{Te}}_2$, (c) $\mathrm{AgIn}{\mathrm{Se}}_2$, and (d) $\mathrm{AgIn}{\mathrm{Te}}_2$. The different color in the phonon dispersion indicates different Grüneisen parameter (from negative to positive) as indicated by the bar code.

Figure 3

Comparison of frequency dependent normalized accumlative thermal conductivity for $\mathrm{CuIn}{\mathrm{Se}}_2$ and $\mathrm{CuIn}{\mathrm{Te}}_2$ (left) and $\mathrm{AgIn}{\mathrm{Se}}_2$ and $\mathrm{AgIn}{\mathrm{Te}}_2$ (right).

Figure 4

Comparison of frequency dependent squared group velocity for $\mathrm{CuIn}{\mathrm{Se}}_2$ and $\mathrm{CuIn}{\mathrm{Te}}_2$ (left) and $\mathrm{AgIn}{\mathrm{Se}}_2$ and $\mathrm{AgIn}{\mathrm{Te}}_2$ (right). The tellurides generally have lower group velocities than selenides, which cannot explain the lower lattice thermal conductivity of selenides than tellurides.

Figure 5

Comparison of frequency dependent weighted phase space for $\mathrm{CuIn}{\mathrm{Se}}_2$ and $\mathrm{CuIn}{\mathrm{Te}}_2$ (left) and $\mathrm{AgIn}{\mathrm{Se}}_2$ and $\mathrm{AgIn}{\mathrm{Te}}_2$ (right). The tellurides generally have larger phase space than selenides, which cannot explain the stronger phonon anharmonicity of selenides than tellurides.

Figure 6

Comparison of frequency dependent phonon relaxation time for $\mathrm{CuIn}{\mathrm{Se}}_2$ and $\mathrm{CuIn}{\mathrm{Te}}_2$ (left) and $\mathrm{AgIn}{\mathrm{Se}}_2$ and $\mathrm{AgIn}{\mathrm{Te}}_2$ (right).

Figure 7

Vibrational density of states for $\mathrm{CuIn}{\mathrm{Se}}_2, \mathrm{CuIn}{\mathrm{Te}}_2, \mathrm{AgIn}{\mathrm{Se}}_2$, and $\mathrm{AgIn}{\mathrm{Te}}_2$ projected on each atom.

Figure 8

Charge sharing vs charge transfer map where $\mathrm{CuIn}{\mathrm{Se}}_2, \mathrm{CuIn}{\mathrm{Te}}_2, \mathrm{AgIn}{\mathrm{Se}}_2$, and $\mathrm{AgIn}{\mathrm{Te}}_2$ studied herein belong to the metavalent bonding category, leading to strong intrinsic phonon anharmonicity. The data for materials other than $A^{\mathrm{I}}\mathrm{In}{{\mathrm{C}}_2}^{\mathrm{VI}}$ ($A^{\mathrm{I}}=\mathrm{Cu},\mathrm{Ag}$; ${\mathrm{C}}^{\mathrm{VI}}=\mathrm{Se},\mathrm{Te}$) are taken from Ref [15]. Symbols labeled “PD” refer to the Peierls distorted structures of the same compound.