Waste heat is everywhere in modern energy systems, from industrial furnaces and engines to power plants and manufacturing lines. Thermoelectric materials offer an appealing way to recover some of that otherwise lost energy because they can convert a temperature difference directly into electricity without moving parts. The difficulty is finding materials that combine strong electrical performance with sufficiently low thermal conductivity, remain stable at high temperatures, and avoid problematic elements.
A new peer-reviewed computational study published in Scientific Reports on 2 October 2026 identifies the lead-free quaternary chalcogenide NaZrCuS3 as a potentially useful candidate for high-temperature thermoelectric energy conversion. The calculations predict a maximum thermoelectric figure of merit, known as ZT, of about 0.78 at 1000 K along one crystallographic direction. The material also reached a calculated power factor of 17.17 × 10−3 W m−1 K−2.
Why thermoelectric performance is difficult to optimise
A good thermoelectric must perform several competing jobs at once. It needs a large Seebeck coefficient, which describes the voltage generated by a temperature difference, and high electrical conductivity so that charge can move efficiently. At the same time, it should conduct as little heat as possible through its crystal lattice. Improving one property can easily worsen another.
Researchers often summarise this balance using the dimensionless figure of merit ZT. Higher values indicate a more favourable combination of electrical conductivity, Seebeck response and thermal conductivity at a given temperature. The new work does not report the performance of a manufactured device. Instead, it asks whether the underlying physics of NaZrCuS3 makes the compound worth pursuing experimentally.
The researchers modelled the material from first principles
M. M. Rabbi of the University of Rajshahi and Mst. A. Khatun of Hajee Mohammad Danesh Science and Technology University used density functional theory to calculate the material’s structural, mechanical and electronic properties. They then combined those calculations with semiclassical Boltzmann transport modelling to estimate thermoelectric behaviour across temperature and charge-carrier conditions.
The analysis predicted a stable orthorhombic crystal phase with substantial lattice rigidity and thermal stability. Electronic-structure calculations produced a direct semiconductor band gap of approximately 0.92 eV. This moderate gap matters because the authors argue that it should help suppress bipolar conduction at elevated temperatures, a process that can undermine thermoelectric performance when both electrons and holes contribute to transport.
The orbital calculations also indicated different microscopic origins for electron and hole transport. Cu-S hybridised states dominated hole transport, while Zr-S states were more important for electron transport. That difference contributed to pronounced directional, or anisotropic, transport properties rather than identical performance along every crystal axis.
The strongest prediction emerged at high temperature
The transport calculations produced large Seebeck coefficients and strong power factors, particularly under n-type doping, where electrons are the dominant charge carriers. The highest reported power factor was 17.17 × 10−3 W m−1 K−2.
Most importantly, the researchers calculated a maximum ZT of approximately 0.78 at 1000 K along the material’s a-axis. The result emerged within a constant relaxation-time treatment of electronic transport and a semi-empirical Slack model used to estimate lattice thermal conductivity.
The temperature dependence is central to the proposed application. NaZrCuS3 was predicted to have relatively high lattice thermal conductivity around room temperature, which is not ideal for thermoelectric conversion. The model, however, showed that lattice thermal conductivity decreases substantially as temperature rises. That decline improves the overall thermoelectric balance and helps explain why the predicted ZT becomes more attractive in the high-temperature regime.
A lead-free candidate for waste-heat recovery
The findings are potentially important because thermoelectric research is not concerned only with maximum efficiency. Composition, environmental impact, stability and operating temperature also influence whether a material can eventually become practical. The authors describe NaZrCuS3 as an environmentally preferable lead-free candidate and argue that its calculated properties justify further investigation for high-temperature waste-heat recovery.
The directional behaviour may also be useful rather than merely inconvenient. If future experiments confirm the anisotropy, crystal orientation and processing could become part of the optimisation strategy. The strong n-type predictions similarly indicate that controlling carrier concentration may be crucial to obtaining the best performance.
The numbers are predictions, not device measurements
The study’s biggest limitation is also essential to interpreting its headline result. NaZrCuS3 was evaluated computationally. The reported ZT of about 0.78 is a theoretical prediction, not a measured efficiency from a synthesised thermoelectric module.
Several modelling assumptions can influence the final estimate. The electronic transport calculations use the constant relaxation-time approximation, while lattice thermal conductivity is estimated with the Slack model rather than measured directly. Real materials can contain defects, grain boundaries, impurities and phase instabilities that alter both electrical and thermal transport. Manufacturing constraints can introduce additional differences between an ideal crystal and a working device.
Experimental synthesis and characterisation are therefore the critical next steps. Researchers would need to confirm the proposed crystal structure and stability, measure the band gap and transport coefficients, determine actual thermal conductivity across temperature, and test whether appropriate n-type carrier concentrations can be achieved reproducibly. Only then can the predicted ZT be compared with real-world performance.
Even with those caveats, computational screening can narrow an enormous materials search space. A material that combines a roughly 0.92 eV direct band gap, favourable high-temperature transport and a predicted ZT approaching 0.8 provides a concrete target for experimental materials scientists rather than a guarantee of a future commercial technology.
Source Information
Study: Rabbi, M. M. & Khatun, M. A. “Lead-free quaternary chalcogenide NaZrCuS3 for efficient thermoelectric energy conversion: insights from first-principles and Boltzmann transport.” Scientific Reports (2026).
Published: 2 October 2026
DOI: 10.1038/s41598-026-74222-y
