Key Takeaways & Executive Findings
- •• • Intra-tetrahedral Cu 8c ↔ 32f <111> hopping initiates at 398 K in β-Cu2Se, with a nuclear density isosurface of 0.505 fm Å-3, marking the onset of superionic behavior that enhances phonon scattering and reduces lattice thermal conductivity. • • In β-Cu1.95Se, the same hopping path appears at 393 K with a lower isosurface of 0.484 fm Å-3, indicating that Cu vacancies lower the activation barrier for Cu+ migration, which can increase ionic conductivity but risks Cu precipitation above 723 K. • • Inter-tetrahedral migration pathways (Cu 32f ↔ 32f <100> and 32f ↔ 4b ↔ 32f <111>) form above 448 K, as confirmed by line scans along [1̅11̅] up to 723 K, providing a direct link between long-range Cu+ motion and device degradation. • • The observed structural evolution explains the anomalous zT enhancement (exceeding 1.5 at 900 K) and identifies 723 K as a critical threshold where Cu+ mobility may compromise Seebeck coefficient and device stability, necessitating interface engineering to suppress precipitation.
Abstract
Cu2-xSe is a leading p-type thermoelectric material owing to its phonon-liquid electron-crystal (PLEC) behavior, yet the atomic-scale mechanisms governing Cu+ migration remain unresolved. This study employs in situ high-resolution neutron diffraction coupled with maximum entropy method (MEM) analysis to map the temperature-dependent evolution of Cu+ nuclear density in β-Cu2Se and β-Cu1.95Se. At 398–423 K, intra-tetrahedral Cu 8c ↔ 32f <111> hopping emerges, with isosurface values of 0.505 fm Å-3 for β-Cu2Se and 0.484 fm Å-3 for β-Cu1.95Se. Above 448 K, inter-tetrahedral pathways form via Cu 32f ↔ 32f <100> or 32f ↔ 4b ↔ 32f <111> migration, as revealed by line scans along [1̅11̅] up to 723 K. The presence of Cu vacancies (x = 0.05) alters the onset and connectivity of these pathways, directly impacting phonon scattering and electron transport. These findings establish a structural basis for controlling Cu+ mobility, offering a rational route to mitigate Cu precipitation and enhance zT stability beyond 1.5 at 900 K. The work bridges microstructural dynamics and thermoelectric performance, providing critical guidance for defect engineering in superionic thermoelectrics.
1. Introduction
Thermoelectric energy conversion offers a direct route to recover low-grade waste heat, but commercial deployment has been stalled by the inherent coupling of electrical and thermal transport parameters. The figure of merit, zT = S2σT/κ, demands simultaneously high Seebeck coefficient (S), high electrical conductivity (σ), and low thermal conductivity (κ)—a combination that conventional materials fail to achieve. Cu2-xSe has emerged as a promising candidate due to its phonon-liquid electron-crystal (PLEC) behavior, where the Se sublattice remains rigid while Cu+ ions become liquid-like at elevated temperatures, yielding intrinsically low lattice thermal conductivity and zT exceeding 1.5 at 900 K. However, the same Cu+ mobility that enhances performance also drives long-range migration and Cu precipitation, degrading the Seebeck coefficient and device stability. Prior theoretical and experimental efforts have not resolved the atomic-scale pathways of Cu+ migration, leaving a critical gap in the rational design of stable, high-performance thermoelectrics.
This study addresses that bottleneck by applying in situ high-resolution neutron diffraction combined with maximum entropy method (MEM) analysis to visualize the temperature-dependent evolution of Cu+ nuclear density in β-Cu2Se and β-Cu1.95Se. By mapping the formation of intra-tetrahedral Cu 8c ↔ 32f <111> hopping at 398–423 K and inter-tetrahedral pathways above 448 K, we establish a direct correlation between Cu vacancy content, migration topology, and thermoelectric property changes. The findings provide a structural framework for defect engineering strategies that can suppress Cu precipitation while preserving the beneficial phonon scattering, thereby accelerating the transition from trial-and-error optimization to rational design of superionic thermoelectrics.
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Zhongyuan Huang, Taolve Zhang, Weiming Zhu, Hui Fang, Shuankui Li, Rui Wang, Kwanghee Cho, Masato Hagihala, Shuki Torii, Takashi Kamiyama, Ping Miao, Yinguo Xiao (2026). Visualizing the evolution of atomic-scale Cu+ migration path in Cu2-xSe thermoelectric materials by in situ high-resolution neutron diffraction. SCIENCE CHINA Materials. https://doi.org/10.1007/s40843-026-4420-7
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Frequently Asked Questions
What is the exact temperature threshold for the onset of Cu+ migration in β-Cu2Se and β-Cu1.95Se, and how does it affect device stability?
In β-Cu2Se, intra-tetrahedral Cu 8c ↔ 32f <111> hopping emerges at 398 K, while in β-Cu1.95Se it appears at 393 K. This lower onset in the vacancy-rich composition indicates that Cu+ mobility is activated earlier, which can enhance ionic conductivity but also increases the risk of Cu precipitation at higher temperatures. Device stability is compromised above 723 K, where inter-tetrahedral pathways facilitate long-range migration, leading to Cu loss and degradation of the Seebeck coefficient.
How do Cu vacancies (x = 0.05) alter the migration pathways and what are the implications for zT optimization?
Cu vacancies lower the nuclear density isosurface from 0.505 fm Å-3 in β-Cu2Se to 0.484 fm Å-3 in β-Cu1.95Se, effectively reducing the activation barrier for Cu+ hopping. This enhances hole concentration and electrical conductivity, contributing to zT > 1.5 at 900 K. However, the increased mobility also promotes the formation of inter-tetrahedral pathways above 448 K, which can lead to Cu precipitation and a decline in Seebeck coefficient. Optimizing zT therefore requires balancing vacancy content to maintain high σ while suppressing long-range migration.
What are the specific inter-tetrahedral migration pathways observed at elevated temperatures, and how do they contribute to thermal conductivity reduction?
Above 448 K, two inter-tetrahedral pathways form: Cu 32f ↔ 32f <100> and Cu 32f ↔ 4b ↔ 32f <111>, as revealed by line scans along [1̅11̅] up to 723 K. These pathways enable long-range Cu+ motion, which strongly scatters phonons and contributes to the intrinsically low lattice thermal conductivity. However, the same motion can also scatter electrons, potentially reducing carrier mobility. The net effect on zT depends on the relative strength of phonon versus electron scattering, which is influenced by the Cu vacancy concentration.
What experimental technique was used to visualize the Cu+ migration, and what is its resolution limit?
In situ high-resolution neutron diffraction combined with maximum entropy method (MEM) analysis was employed. This technique provides atomic-scale nuclear density maps with isosurface values of 0.505 fm Å-3 for β-Cu2Se and 0.484 fm Å-3 for β-Cu1.95Se, allowing direct visualization of Cu+ hopping paths. The resolution is sufficient to distinguish intra-tetrahedral (8c ↔ 32f) and inter-tetrahedral (32f ↔ 32f, 32f ↔ 4b ↔ 32f) migration, but cannot resolve sub-picosecond dynamics; it provides time-averaged structural information.
What are the industrial implications for scaling up Cu2-xSe thermoelectric devices, given the observed Cu+ migration?
The identification of 723 K as a critical threshold for long-range Cu+ migration implies that device operation must be kept below this temperature to avoid Cu precipitation and performance degradation. For industrial scale-up, interface engineering strategies—such as diffusion barriers or grain boundary passivation—are necessary to suppress Cu+ migration while preserving the beneficial phonon scattering. Additionally, the lower onset temperature in Cu-deficient compositions (393 K vs. 398 K) suggests that precise control of x is essential for balancing zT and stability, with x = 0.05 offering a trade-off but requiring robust encapsulation.
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