Investigation of mechanical, lattice dynamical, electronic and thermoelectric properties of half Heusler chalcogenides: A DFT study

Heusler alloys, particularly half-Heusler (HH) compounds, exhibit exceptional potential for next-generation optoelectronic and renewable energy applications. In this study, we employ advanced density functional theory (DFT) to systematically investigate the structural, electronic, optical, thermodynamic, and thermoelectric properties of LiBeZ (Z = P/As) HH alloys. The band structure analysis using the mBJ exchange–correlation functional reveals that both LiBeP and LiBeAs exhibit indirect band gaps (1.82 eV and 1.66 eV, respectively), placing them in the ideal range for optoelectronic applications. Additionally, their broad-spectrum absorption and minimal reflectivity highlight their potential for efficient solar cells and optical sensor technologies. Moreover, as temperature rises, the enthalpy and entropy of the alloys increase, while Gibbs free energy decreases, indicating thermal stability. The alloys’ heat capacity follows the Debye model, making them suitable for thermoelectric and high-temperature electronic applications. Furthermore, from the thermoelectric properties analysis, it can be conferred that these materials have a high value of ZTe and are suitable materials for thermoelectric devices. In conclusion, the predicted results strongly indicate that LiBeP and LiBeAs could serve as key materials for next-generation photonic, thermoelectric devices, and energy-harvesting devices. Future research should focus on experimental validation and device integration to fully harness their potential.Supplementary InformationThe online version contains supplementary material available at 10.1038/s41598-025-14470-6.

Previous studies have indicated that the figure of merit ($\mathit{ZT}$) of half-Heusler (HH) alloys with composition $M\mathrm{NiSn}$ ($M\phantom{\rule{0.16em}{0ex}}=\phantom{\rule{0.16em}{0ex}}\mathrm{Ti}$, Zr, or Hf) is greatly enhanced when the alloys contain a nano-scale full-Heusler (FH) $\mathrm{MN}{\mathrm{i}}_{2}\mathrm{Sn}$ second phase. However, the formation mechanism of the FHnanostructures in the HH matrix and their vibrational properties are still not well understood. We report on first-principles studies of thermodynamic phase equilibria in the MNiSn-$\mathrm{MN}{\mathrm{i}}_{2}\mathrm{Sn}$ pseudobinary system as well as HH and FH vibrational properties. Thermodynamic phase diagrams as functions of temperature and Ni concentration were developed using density functional theory (DFT) combined with a cluster expansion and Monte Carlo simulations. The phase diagrams show very low excess Ni solubility in HH alloys even at high temperatures, which indicates that any Ni excess will decompose into a two-phase mixture of HH and FH compounds. Vibrational properties of HH and FH alloys are compared. Imaginary vibrational modes in the calculated phonon dispersion diagram of $\mathrm{TiN}{\mathrm{i}}_{2}\mathrm{Sn}$ indicate a dynamical instability with respect to cubic [001] transverse acoustic modulations. Displacing atoms along unstable vibrational modes in cubic $\mathrm{TiN}{\mathrm{i}}_{2}\mathrm{Sn}$ reveals lower-energy structures with monoclinic symmetry. The energy of the monoclinic structures is found to depend strongly on the lattice parameter. The origin of the instability in cubic $\mathrm{TiN}{\mathrm{i}}_{2}\mathrm{Sn}$ and its absence in cubic $\mathrm{ZrN}{\mathrm{i}}_{2}\mathrm{Sn}$ and $\mathrm{HfN}{\mathrm{i}}_{2}\mathrm{Sn}$ is attributed to the small size of the Ti $3d$ shells compared to those of Zr and Hf atoms. Lattice constants and heat capacities calculated by DFT agree well with experiment.

Investigations of mechanical and thermoelectric properties of ‘AlNiP’ novel half-Heusler alloy

In last two decades, Half Heusler (HH) alloys proved themselves as a potential candidate for thermoelectric devices. This is not only due to their structural capability for demonstrating and integrating various new concepts to enhance the thermoelectric figure of merit (ZT) but also high thermal stability which is advantageous for thermoelectric devices. However, most of the efficient HH alloys consist of expensive elements which resist their commercial application. This encouraged the development of highly efficient Fe-based Full Heusler (FH) alloys which have almost similar advantages of HH alloys along with the economical benefit. The main challenge in Fe-based FH as efficient thermoelectric as HH alloys is the reduction of lattice thermal conductivity and optimization of carrier concentration. This could be done through the use of concepts like bulk nanostructuring/bulk nanocomposite and more recently introduced Panoscopic approach or all scale hierarchical architecturing engineering and band structure engineering. In this review, we firstly discussed about the current progress on Fe-based FH alloys along with the challenges in enhancing the figure of merits. Herein, we also discussed various approaches adopted in bulk as well as nanostructured FH alloys to circumvent the interdependency of parameters in achieving higher ZT. It ends with discussion of the future trends for Fe-based FH thermoelectric materials for waste heat recovery. Through this review, we not only explain the probability of finding efficient thermoelectric in Fe-based FH alloys but also give a blueprint for enhancing ZT in many other thermoelectric materials.

First-principles investigation on the novel half-Heusler VXTe (X=Cr, Mn, Fe, and Co) alloys for spintronic and thermoelectric applications

Correlation between processing conditions, microstructure and charge transport in half-Heusler alloys

Enhancing thermoelectric properties of MCoSb-based alloys by entropy-driven energy-filtering effects and band engineering

Half-Heusler (HH) alloys constitute an important class of materials that exhibit promising potential in high-temperature thermoelectric (TE) power generation. In this work, we synthesized Zr1−x Yb x NiSn (x = 0, 0.01, 0.02, 0.04, 0.06 and 0.10) HH alloys using a time-efficient levitation melting and spark plasma sintering procedure. X-ray diffraction showed that the samples were predominantly single phased, and that the lattice constant increased systematically with increasing Yb doping ratio. The doping effects of Yb on the thermoelectric properties were studied. It was found that Yb doping consistently decreased the electrical and thermal conductivities. On the other hand, the effects of Yb doping on the Seebeck coefficient were found to be non-monotonic. The magnitude of the Seebeck coefficient (n-type) was increased upon Yb doping up to x = 0.02, above which Yb doping introduced notable p-type conduction. As a result, the room-temperature Seebeck coefficient of the x = 0.10 sample became positive although the magnitude was not high. The thermoelectric figure of merit, ZT, reached a maximum of ∼0.38 at 900 K for the x = 0.01 sample. Selective doping on the Ni and Sn sites are necessary to further optimize the TE performance of Zr1−x Yb x NiSn alloys.

Half-Heusler (HH) alloys are potential thermoelectric materials for use at elevated temperatures due to their high Seebeck coefficient and superior mechanical and thermal stability. However, their enhanced lattice thermal conductivity is detrimental to thermoelectric applications. One way to circumvent this problem is to introduce mass disorder at lattice sites by mixing the components of two or more alloys. Such systems are typically stabilized by the entropy of mixing. In this work, using computational tools, we propose a mixed HH, namely, ZrHfCoNiSnSb, which can be formed by the elemental compositions of the parent half-Heuslers ZrNiSn/HfNiSn and HfCoSb/ZrCoSb. We propose that this new compound can be synthesized at elevated temperatures, as its Gibbs free energy is reduced due to higher configurational entropy, making it more thermodynamically stable than the parent compounds under such conditions. Our calculations indicate that it is a dynamically stable semiconductor with a band gap of 0.61 eV. Its lattice thermal conductivity at room temperature is 5.40 W m-1 K-1, which is significantly lower than those of the parent compounds. The peak value of this alloy's figure of merit (ZT) is 1.00 for the n-type carriers at 1100 K, which is 27% more than the best figure of merit obtained for the parent compounds.

First-principles investigation on the electronic, mechanical and lattice dynamical properties of novel AlNiX (X = As and Sb) half-Heusler alloys

Intrinsically high lattice thermal conductivity has remained a major bottleneck for achieving a high thermoelectric figure of merit (zT) in state-of-the-art ternary half-Heusler (HH) alloys. In this work, we report a stable n-type biphasic-quaternary (Ti,V)CoSb HH alloy with a low lattice thermal conductivity κL ≈ 2 W m-1 K-1 within a wide temperature range (300-873 K), which is comparable to the reported nanostructured HH alloys. A solid-state transformation driven by spinodal decomposition upon annealing is observed in Ti0.5V0.5CoSb HH alloy, which remarkably enhances phonon scattering, while electrical properties correlate well with the altering electronic band structure and valence electron count (VEC). A maximum zT ≈ 0.4 (±0.05) at 873 K was attained by substantial lowering of κL and synergistic enhancement of the power factor. We perform first-principles density functional theory calculations to investigate the structure, stability, electronic structure, and transport properties of the synthesized alloy, which rationalize the reduction in the lattice thermal conductivity to the increase in anharmonicity due to the alloying. This study upholds the new possibilities of finding biphasic-quaternary HH compositions with intrinsically reduced κL for prospective thermoelectric applications.

This study thoroughly examines the structural, mechanical, thermal, electronic, optical, and thermoelectric properties of RhMnZ (Z = Si, Ge) half-Heusler compounds, which feature 18 valence electrons. Using density functional theory (DFT) within the WIEN2k computational framework, the ground-state properties of these compounds were determined to establish a foundational understanding of their physical characteristics. To further assess their thermoelectric potential, the Boltzmann transport equation was applied with the constant relaxation time approximation, allowing for precise calculations of thermal and electrical conductivity. Results indicate that the lattice constants of RhMnSi and RhMnGe span from 5.6394 Å to 5.7447 Å, highlighting consistent crystalline structures that lack band gaps, confirming their metallic nature. Detailed elastic and thermodynamic evaluations demonstrate that these compounds are mechanically stable, displaying ductile and anisotropic behavior. The study further reveals that thermal properties, including specific heat and entropy, tend to increase with the atomic number of Z, suggesting that RhMnGe may have a slightly higher heat capacity compared to RhMnSi. For thermal conductivity estimation, Slack's model was employed, indicating that these compounds possess high lattice thermal conductivity-a crucial factor for thermoelectric materials. The substantial figure of merit (ZT) observed in these compounds, especially at elevated temperatures, points to their potential efficiency in thermoelectric applications. The combination of high thermal conductivity, favorable mechanical stability, and robust thermoelectric properties identifies RhMnZ compounds as promising candidates for use in energy conversion technologies, particularly where efficient heat-to-electricity conversion is needed. This study thus lays the groundwork for future applications of RhMnSi and RhMnGe in thermoelectric devices.

Maximizing the scattering of multiwavelength phonons in novel biphasic high-entropy ZrCoSb-based half-Heusler alloys

We have performed a broad computational study of two half-Heusler (HH) alloys CrXPb (X = Sc, Ti) by systematically investigating their structural, mechanical, electronic, magnetic, thermoelectric, and optical properties by means of spin polarized ab initio simulations using density functional theory. Their relaxed structures indicated that they attain cubic structure in ground state. We have used PBE-GGA method for optimizations and for attaining the most accurate results of all properties, the mBJ-GGA approach is applied. Both these compounds are ductile in nature and have anisotropic elastic behavior and high stiffness. CrScPb is observed to acquire metallic nature for both spins, whereas CrTiPb is observed to have half-metallic nature (narrow band gap of 0.96 eV) with a magnetic moment of 5 μB and 4 μB for CrScPb and CrTiPb respectively. Furthermore, the thermoelectric properties showed that CrScPb has comparable but better quantity of figure of merit (ZT~0.25 for spin-up and ~ 0.5 for spin-down at room temperature) for both spins and CrTiPb has improved response for spin-up, since ZT is close to 1 at room temperature. Such values showed the efficiency of these alloys for energy conversion and power generation. Moreover, the optical properties showed variable and remarkable optical behavior in visible and UV ranges. We observed fascinating optical applications such as energy storage, reshaping of phases in optical antennas and magentaoptical devices. In nutshell, we comprehend the various properties of two potential HH alloys targeting for various applications.

Investigation of GaBi1-xSbx based highly mismatched alloys: Potential thermoelectric materials for renewable energy devices and applications