Anharmonicity Driven by Vacancy Ordering Unlocks High-performance Thermoelectric Conversion in Defective Chalcopyrites II-III$_2$-VI$_4$

Abstract

Defective chalcopyrites have recently emerged as promising thermoelectric materials because their ordered intrinsic vacancies can profoundly reshape both lattice dynamics and electronic structure. Here, we present a comprehensive first-principles investigation of the thermal and carrier transport properties of II-III$_2$-VI$_4$ defective chalcopyrites. We show that vacancy ordering serves as a structural amplifier of lattice distortion, giving rise to strong lattice anharmonicity and metavalent-bonding character. In combination with soft low-frequency phonons, strongly negative Grüneisen parameters, and substantially enlarged four-phonon scattering phase space, this leads to four-phonon scattering-dominated heat transport and suppresses the lattice thermal conductivity to ultralow values. Meanwhile, systematic anion substitution at the VI-site provides an effective route to tune the electronic structure: decreasing anion electronegativity weakens metal-anion hybridization, shifts anion $p$ states upward, narrows the band gap, and thereby improves electrical transport. Benefiting from this synergy between vacancy-induced phonon suppression and anion-regulated electronic optimization, CdGa$_2$Te$_4$ exhibits an ultralow lattice thermal conductivity of 0.19 W$\cdot$m$^{-1}$K$^{-1}$ and a high room-temperature $ZT$ of 0.957. These results establish a microscopic framework linking vacancy ordering, higher-order phonon scattering, and anion-dependent band engineering, and highlight defective chalcopyrites as a promising platform for high-performance thermoelectrics.

Figures (4)

• Figure 1: (a) The crystal structure of zincblende ($F\bar{4}3m$, No.216), chalcopyrite ($I\bar{4}2d$, No.122), and defective chalcopyrites ($I\bar{4}$, No.82). The tetrahedra represent the coordination environments. The ideal bond angle of a perfect tetrahedron ($a = b = c$) is $109.47^\circ$. The arrow represents a decrease in the space group. The blue and pink represent cations, while the yellow denotes anions. (b) The relationship between the $\eta$ and the $\kappa_L$ of different compounds. The related zincblende and chalcopyrite data are available in ref. xie2022hidden. (c) The $\kappa_L$ evaluated by including both 3ph and 4ph scattering processes ($\kappa_L^{3,4ph}$) and by accounting for only 3ph scattering processes ($\kappa_L^{3ph}$). The color scale represents the $\kappa_L$. To calculate the relative reduction in the $\kappa_L$, subtract $\kappa_L^{3,4ph}$ from $\kappa_L^{3ph}$, then divide by the latter and multiply by 100%. (d) The $\kappa_L$ as a function of the lattice anharmonicity measure $\sigma^A$ at 300 K. The red hexagon represents defective chalcopyrites, with data for other compounds given in ref. knoop2023anharmonicity. With the purple line in the figure as the boundary, the materials in the upper region have a $\overline{M} < 50$ amu, while those in the lower region have a $\overline{M} > 50$ amu. (e) The quantum mechanics diagram of bonding in solids, with coordinates representing the number of electrons shared and transferred between adjacent atoms. The green triangle represents defective chalcopyrites, and data for other compounds can be found in ref. raty2019quantum.
• Figure 2: Calculation of the thermal transport properties of CdGa$_2$Te$_4$ and ZnGa$_2$S$_4$. (a) Phonon dispersion relations at 300 K in the $0–4$ THz frequency range. Along the $\Gamma–$M direction, the red line represents the linear fit to the acoustic branch, with its slope corresponding to the phonon group velocity. (b) The phonon density of states. In CdGa$_2$Te$_4$, the yellow, blue, and green curves represent the contributions of Cd, Te, and Ga atoms, respectively. In ZnGa$_2$S$_{4}$, the yellow, blue, and green curves represent the contributions of Zn, S, and Ga atoms, respectively. (c) The Grüneisen parameters $\gamma$. Green corresponds to CdGa$_2$Te$_4$, and blue corresponds to ZnGa$_2$S$_4$. (d) Phonon lifetimes $\tau_{3,4ph}$ including 3ph and 4ph scattering processes, as well as the 3ph ($SRs_{3ph}$) and 4ph ($SRs_{4ph}$) scattering rates of ZnGa$_2$S$_{4}$ and CdGa$_2$Te$_4$. Green and orange denote CdGa$_2$Te$_4$, blue and red denote ZnGa$_2$S$_{4}$. The red solid line indicates the Ioffe-Regel limit. (e) The spectral/cumulative thermal conductivity. $\kappa_L^{3ph}$ represents only 3ph processes. $\kappa_L^{3,4ph}$ represents both 3ph and 4ph processes. The direction of the arrow points to the cumulative thermal conductivity. (f) Three- and four-phonon weighted phase space. Hexagons denote WP3 and triangles denote WP4; orange and green symbols correspond to CdGa$_2$Te$_4$, whereas red and azure blue symbols correspond to ZnGa$_2$S$_{4}$. (g) The calculated $\kappa_C$($\omega_{q j}$,$\omega_{q j^{\prime}}$) for CdGa$_2$Te$_4$ at 300 K. The diagonal data points ($\omega_{q j}=\omega_{q j^{\prime}}$) indicate phonon degenerate eigenstates.
• Figure 3: (a) Calculation results of bond lengths, electronic band gaps (PBE/HSE), and structural parameter $\eta$ for defective chalcopyrites. Line graphs visualize parameter trends. To visualize the variation of $\eta = |2 - c/a|$ in the figure, c/2a is used here instead. (b) The atom-projected band structure of CdGa$_2$Te$_4$. Bubble sizes (all with a scaling factor of 15) represent the electronic state contributions from Te, Ga, and Cd. (c) Schematic DOS with Cd-anion antibonding as the valence band edge and Ga-anion antibonding states as the conduction band edge. (d) Schematic molecular-orbital diagram. The Cd 4d atomic orbitals and the anion p‑states form antibonding states that are expected to reside near the valence band edge. The Ga 4s atomic orbitals and the anion p‑states form antibonding states that are expected to appear at the conduction band edge. (e) Crystal Orbital Hamilton Population. The left represents the total interactions of Te–Cd and Te–Ga. The middle and right show the interactions for Cd-4d/Te-5p and Ga-4s/Te-5p, respectively. Green circles mark the energy positions of the corresponding antibonding states. Positive values correspond to bonding states, while negative values correspond to antibonding states.
• Figure 4: The scattering rates of ADP, IMP, and POP mechanisms for (a) ZnGa$_2$S$_4$ and (b) CdGa$_2$Te$_4$ at 300 K and a carrier concentration of $10^{21}$ cm$^{-3}$. The carrier mobilities of ADP, IMP, and POP mechanisms for (a) ZnGa$_2$S$_4$ and (b) CdGa$_2$Te$_4$ as a function of carrier concentration. The scatter points represent the scattering rates, and the lines represent the mobilities. The colors red, orange, and blue represent ADP, IMP, and POP, respectively. (c) The calculated results of $\sigma$, $S$, $\kappa_e$, and $PF$ of ZnGa$_2$S$_4$ and CdGa$_2$Te$_4$ with varying carrier concentrations. Blue represents ZnGa$_2$S$_4$, and red represents CdGa$_2$Te$_4$. (d) The variation of $ZT_{3ph}$ of ZnGa$_2$S$_4$ and CdGa$_2$Te$_4$ with carrier concentration considering. The illustration shows the maximum $ZT_{3ph}$ for defective chalcopyrites. (e) The variation of $ZT_{3,4ph}$ of ZnGa$_2$S$_4$ and CdGa$_2$Te$_4$ with carrier concentration. The illustration shows the maximum $ZT_{3,4ph}$ for defective chalcopyrites. (f) Comparison of ZT between CdGa$_2$Te$_4$ and other typical thermoelectric compounds at 300 K, where the specific compounds corresponding to the labels are detailed in the ref. chen2018highliang2019flexiblezhang2022defectli2024silverliu2024effortswang2011reduction.