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Heat to energy conversion: Unlocking high thermoelectric performance in NaMgBi-based half-Heusler compounds via Lithium alloying

This study demonstrates that alloying NaMgBi half-Heusler compounds with lithium effectively optimizes both electronic and phonon transport properties, significantly reducing lattice thermal conductivity and enhancing the thermoelectric figure-of-merit (ZT) to a maximum of approximately 1.78.

Original authors: Solomon Tahiru Tonga

Published 2026-08-27

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CC BY 4.0

Original authors: Solomon Tahiru Tonga

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine a world where the heat escaping from a car engine, a power plant, or even a human body could be captured and turned directly into electricity, without any moving parts or noisy machinery. This is the promise of thermoelectric materials, a class of substances that act as silent bridges between temperature differences and electrical power. For decades, scientists have searched for the perfect material to make this technology efficient enough for widespread use. The challenge lies in a difficult balancing act: a good thermoelectric material must be excellent at conducting electricity while simultaneously being terrible at conducting heat. If it lets heat flow through too easily, the temperature difference needed to generate power disappears. If it blocks electricity, no power is produced. The goal is to find a substance that allows electrons to zip through freely while trapping the vibrating atoms that carry heat, effectively turning waste warmth into usable energy.

In a recent study, researchers turned their attention to a specific family of crystals known as half-Heusler compounds, focusing on a material made of sodium, magnesium, and bismuth. While this combination shows promise, its ability to convert heat into electricity was not yet at its peak. The team, led by Solomon T. Tonga and colleagues, asked a simple but profound question: could they improve this material by swapping some of its sodium atoms for lithium? Lithium is a lighter, smaller cousin of sodium, and the researchers hypothesized that mixing it in might disrupt the flow of heat without hurting the flow of electricity. To test this, they did not mix chemicals in a lab flask; instead, they built a detailed digital model of the material using powerful supercomputers. They simulated the behavior of the atoms and electrons in the pure sodium-magnesium-bismuth crystal and then created virtual versions where a quarter, half, or three-quarters of the sodium atoms were replaced by lithium.

The computer simulations revealed that swapping sodium for lithium worked exactly as the researchers hoped, but through a clever mechanism of disruption. In the pure material, the atoms vibrate in a somewhat orderly fashion, allowing heat to travel quickly. When lithium atoms were introduced, their different size and mass created a kind of internal chaos. This disorder acted like a series of speed bumps for the heat-carrying vibrations, scattering them and slowing their progress. As a result, the material became much better at trapping heat. The simulations showed that the thermal conductivity dropped significantly, with the most lithium-rich version reducing heat flow by nearly two-thirds compared to the original. This is a crucial win, as it means the material can maintain the temperature difference required to generate power for longer.

However, trapping heat is only half the battle; the material must still conduct electricity well. The researchers found that the lithium substitution did not ruin the electrical performance. In fact, the electronic structure of the material changed in a way that actually helped. The mix of atoms altered the energy landscape for the electrons, making it easier for them to move in one direction while hindering their movement in the opposite direction. This asymmetry boosted a key property called the Seebeck coefficient, which measures how much voltage is generated by a temperature difference. The best-performing mixture, where one-quarter of the sodium was replaced by lithium, achieved a remarkable balance. It maintained a strong electrical current while its ability to conduct heat was significantly suppressed.

When the researchers combined these factors to calculate the overall efficiency, known as the figure of merit, the results were striking. The pure sodium-magnesium-bismuth material had a moderate efficiency score. But the optimized mixture with lithium reached a score of approximately 1.78 at high temperatures, a substantial improvement that places it among the more promising candidates for future energy harvesting devices. The study suggests that this specific recipe of atoms creates a material that is mechanically stable and robust, capable of withstanding the stresses of real-world use. While these findings come from computer simulations and have not yet been physically manufactured and tested in a lab, the data provides a clear roadmap. It demonstrates that simply tuning the atomic recipe of a known material can unlock hidden potential, turning a decent heat-to-electricity converter into a highly efficient one. This work offers a concrete path forward for developing cleaner, more efficient ways to capture the vast amounts of wasted heat that surround us every day.

Technical Summary: Unlocking High Thermoelectric Performance in NaMgBi-based Half-Heusler Compounds via Lithium Alloying

Problem Statement
Thermoelectric (TE) materials convert heat directly into electricity, offering potential for sustainable energy harvesting and waste-heat recovery. However, their efficiency, quantified by the dimensionless figure of merit ( $ZT = S^2\sigma T / \kappa$ ), is limited by the strong interdependence of transport parameters: increasing electrical conductivity ( $\sigma$ ) often reduces the Seebeck coefficient ( $S$ ), while strategies to lower thermal conductivity ( $\kappa$ ) can detrimentally affect electronic transport. While high-performance materials like Bi $_2$ Te $_3$ , PbTe, and SnSe exist, there is a need to identify and optimize environmentally benign, mechanically robust systems. Half-Heusler (HH) compounds are promising candidates due to their tunable band gaps and thermal stability, yet specific Mg-based bismuthides like NaMgBi possess semi-metallic or narrow-gap electronic structures that require precise engineering to maximize $ZT$ . The challenge lies in simultaneously optimizing electronic transport and suppressing lattice thermal conductivity ( $\kappa_l$ ) without compromising mechanical stability.

Methodology
This study employs a comprehensive computational framework based on Density Functional Theory (DFT) combined with semiclassical Boltzmann transport theory.

Electronic Structure: Calculations were performed using the Quantum-ESPRESSO package with the Generalized Gradient Approximation (GGA-PBE) functional. Crucially, Spin-Orbit Coupling (SOC) was explicitly included to account for relativistic effects in the heavy Bismuth (Bi) element.
Structural Models: The study investigates pristine NaMgBi and Lithium (Li)-alloyed variants with stoichiometries Na $_{1-x}$ Li $_x$ MgBi ( $x = 0.25, 0.50, 0.75$ ). The cubic half-Heusler structure (space group $F\bar{4}3m$ ) was adopted, consistent with previous theoretical studies, though the author acknowledges recent experimental findings of a tetragonal phase.
Transport Properties: Electronic transport coefficients (Seebeck coefficient $S$ , electrical conductivity $\sigma$ , electronic thermal conductivity $\kappa_e$ ) were calculated using the BoltzTraP2 code under the Constant Relaxation Time Approximation (CRTA) with a fixed relaxation time of 10 fs over a temperature range of 100–1000 K.
Thermal Conductivity: Lattice thermal conductivity ( $\kappa_l$ ) was estimated using the semi-empirical Slack model, derived from calculated elastic constants, Debye temperatures, and Grüneisen parameters.
Stability Analysis: Mechanical stability was assessed via Born stability criteria using calculated elastic constants ( $C_{ij}$ ), and thermodynamic stability was evaluated through formation energy calculations.

Key Contributions and Results
The study demonstrates that Li alloying effectively decouples the trade-offs between electronic and phonon transport in NaMgBi-based half-Heuslers:

Structural and Mechanical Stability: All investigated compositions (pristine and Li-doped) retain the cubic half-Heusler structure and satisfy mechanical stability criteria. Li substitution induces lattice softening (reduced elastic moduli) but maintains ductile behavior, which is favorable for device fabrication. While formation energies for some doped systems are small or slightly positive (suggesting metastability), they are considered accessible under non-equilibrium synthesis conditions.
Electronic Structure Modifications: Li substitution acts primarily as a band structure modulator rather than a direct carrier dopant. The alloying modifies the dispersion of Bi-p orbitals near the Fermi level, suppressing electron-hole compensation and enhancing band asymmetry. This leads to an increase in the density-of-states effective mass, which boosts the Seebeck coefficient.
Thermal Conductivity Reduction: A significant reduction in lattice thermal conductivity is observed with increasing Li content. The large mass contrast between Na and Li atoms introduces strong mass-disorder scattering, while lattice softening enhances anharmonicity. $\kappa_l$ decreases by approximately 66% from pristine NaMgBi to the Li-rich Na $_{0.25}$ Li $_{0.75}$ MgBi.
Thermoelectric Performance:
- Power Factor: The power factor ( $S^2\sigma$ ) is optimized at intermediate Li concentrations. Specifically, Na $_{0.75}$ Li $_{0.25}$ MgBi achieves the highest electrical conductivity ( $1.4 \times 10^{19}$ S/m) while maintaining a substantial Seebeck coefficient (234 $\mu$ V/K).
- Figure of Merit (ZT): The combined optimization results in a marked improvement in $ZT$ . While pristine NaMgBi reaches a $ZT \approx 0.92$ at 1000 K, the Li-alloyed systems show superior performance. Na $_{0.75}$ Li $_{0.25}$ MgBi achieves a maximum $ZT \approx 1.78$ at 1000 K. Even Li-rich compositions (e.g., Na $_{0.25}$ Li $_{0.75}$ MgBi) maintain high $ZT$ values (~1.64) despite reduced electrical conductivity, due to extremely low thermal conductivity.

Significance and Claims
The author claims that this study establishes alkali-metal alloying as a viable and effective strategy for optimizing semi-metallic half-Heusler thermoelectrics. The research highlights that:

Li alloying in NaMgBi successfully balances the enhancement of the Seebeck coefficient and electrical conductivity while drastically reducing lattice thermal conductivity through phonon scattering.
The predicted $ZT$ of ~1.78 for Na $_{0.75}$ Li $_{0.25}$ MgBi is competitive with established high-performance systems like FeNbSb-based alloys and optimized Mg $_3$ Sb $_2$ compounds.
The work bridges the gap between theoretical predictions and practical application by providing a consistent structural motif (cubic HH) for rational design, suggesting that simple chemical substitution can yield high-efficiency, environmentally friendly thermoelectric materials.

The author maintains modesty regarding their quantitative predictions, noting that the study relies on the Slack model for thermal conductivity and CRTA for electronic transport. They explicitly state that future work involving anharmonic phonon calculations (e.g., Phono3py), deformation potential-based relaxation times, and convex-hull stability analysis is necessary for rigorous quantitative validation.

Technical Summary: Unlocking High Thermoelectric Performance in NaMgBi-based Half-Heusler Compounds via Lithium Alloying

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