RESEARCH ARTICLE
Ab Initio Study of Novel Quaternary Heusler LiTiRhZ (Z = Si, Ge, Sn) Compounds for Thermoelectric Application
Bhoopendra Kumar Dewangan,
Lokanksha Suktel,
Sapan Mohan Saini,
Bhoopendra Kumar Dewangan
Department of Physics, National Institute of Technology Raipur, Raipur, India
Department of Physics, Government ML Shukla PG College, Bilaspur, India
Search for more papers by this authorLokanksha Suktel
Department of Physics, National Institute of Technology Raipur, Raipur, India
Search for more papers by this authorCorresponding Author
Sapan Mohan Saini
Department of Physics, National Institute of Technology Raipur, Raipur, India
Correspondence: Sapan Mohan Saini ([email protected])
Search for more papers by this authorBhoopendra Kumar Dewangan,
Lokanksha Suktel,
Sapan Mohan Saini,
Bhoopendra Kumar Dewangan
Department of Physics, National Institute of Technology Raipur, Raipur, India
Department of Physics, Government ML Shukla PG College, Bilaspur, India
Search for more papers by this authorLokanksha Suktel
Department of Physics, National Institute of Technology Raipur, Raipur, India
Search for more papers by this authorCorresponding Author
Sapan Mohan Saini
Department of Physics, National Institute of Technology Raipur, Raipur, India
Correspondence: Sapan Mohan Saini ([email protected])
Search for more papers by this authorFirst published: 07 June 2025
Funding: The authors received no specific funding for this work.
ABSTRACT
Quaternary Heusler LiTiRhZ (Z = Si, Ge, Sn) compounds are investigated for mechanical and thermodynamic stability and their suitability as potential thermoelectric materials in a high-temperature range. The density functional theory and Boltzmann transport equations have been used for the calculations of structural, electronic, phonon dynamics, elastic, and thermoelectric properties. The compounds exhibit indirect band gaps of 1.076, 1.132, and 1.032 eV in LiTiRhZ (Z = Si, Ge, Sn), respectively, confirming their semiconducting nature. The negative formation energies and high melting points (~1800 K) suggest structural stability and experimental feasibility. Elastic and phonon calculations confirm mechanical and dynamical stability, along with ductile and anisotropic behavior. For a better understanding of thermodynamic properties, free energy, entropy, and specific heat at constant volume are also investigated up to 1000 K temperature. We obtained the increasing nature of power factor in all studied compounds, indicating the high value of figure of merit (ZT), particularly in the high-temperature region, with LiTiRhSi achieving a maximum ZT ~ 0.69 at 1000 K, showing its potential for high-temperature thermoelectric applications. The higher and stable values of ZT as compared to the other reports in the high-temperature range may provide strong support for experimental research on the studied compounds.
Conflicts of Interest
The authors declare no conflicts of interest.
Open Research
Data Availability Statement
The data that support the findings of this study are available on request from the corresponding author. The data are not publicly available due to privacy or ethical restrictions.
References
- 1P. K. Rawat, B. Paul, and P. Banerji, “Thermoelectric Properties of PbSe0.5Te0.5: X (PbI2) With Endotaxial Nanostructures: A Promising n-Type Thermoelectric Material,” Nanotechnology 24 (2013): 215401, https://doi.org/10.1088/0957-4484/24/21/215401.
- 2K. Uchida, S. Takahashi, K. Harii, et al., “Observation of the Spin Seebeck Effect,” Nature 455 (2008): 778–781, https://doi.org/10.1038/nature07321.
- 3H. S. Choi, S. Yun, and K. i. Whang, “Development of a Temperature-Controlled Car-Seat System Utilizing Thermoelectric Device,” Applied Thermal Engineering 27 (2007): 2841–2849, https://doi.org/10.1016/j.applthermaleng.2006.09.004.
- 4D. Champier, “Thermoelectric Generators: A Review of Applications,” Energy Conversion and Management 140 (2017): 167–181, https://doi.org/10.1016/j.enconman.2017.02.070.
- 5B. I. Ismail and W. H. Ahmed, “Thermoelectric Power Generation Using Waste-Heat Energy as an Alternative Green Technology,” Recent Patents on Electrical Engineeringe 2 (2009): 27–39, https://doi.org/10.2174/1874476110902010027.
- 6G. E. Terry, M. Tritt, and M. A. Subramanian, “Thermoelectric Materials, Phenomena, and Applications: A Bird's Eye View Definition and Description of the Figure of Merit and Thermoelectric Performance,” MRS Bulletin 31 (2006): 188–198.
10.1557/mrs2006.44 Google Scholar
- 7W. Xie, A. Weidenkaff, X. Tang, Q. Zhang, J. Poon, and T. M. Tritt, “Recent Advances in Nanostructured Thermoelectric Half-Heusler Compounds,” Nanomaterials 2 (2012): 379–412, https://doi.org/10.3390/nano2040379.
- 8M. A. Karri, E. F. Thacher, and B. T. Helenbrook, “Exhaust Energy Conversion by Thermoelectric Generator: Two Case Studies,” Energy Conversion and Management 52 (2011): 1596–1611, https://doi.org/10.1016/j.enconman.2010.10.013.
- 9R. Guo, X. Wang, and B. Huang, “Thermal Conductivity of Skutterudite CoSb 3 From First Principles: Substitution and Nanoengineering Effects,” Scientific Reports 5 (2015): 1–9, https://doi.org/10.1038/srep07806.
10.1038/srep07806 Google Scholar
- 10Y. Tang, Z. M. Gibbs, L. A. Agapito, et al., “Convergence of Multi-Valley Bands as the Electronic Origin of High Thermoelectric Performance in CoSb3 Skutterudites,” Nature Materials 14 (2015): 1223–1228, https://doi.org/10.1038/nmat4430.
- 11D. Parker and D. J. Singh, “High-Temperature Thermoelectric Performance of Heavily Doped PbSe,” Physical Review B 82 (2010): 035204, https://doi.org/10.1103/PhysRevB.82.035204.
- 12S. A. Khandy, I. Islam, D. C. Gupta, R. Khenata, and A. Laref, “Lattice Dynamics, Mechanical Stability and Electronic Structure of Fe-Based Heusler Semiconductors,” Scientific Reports 9 (2019): 1–8, https://doi.org/10.1038/s41598-018-37740-y.
- 13K. Kaur and J. Kaur, “Exploration of Thermoelectricity in ScRhTe and ZrPtPb Half Heusler Compounds: A First Principle Study,” Journal of Alloys and Compounds 715 (2017): 297–303, https://doi.org/10.1016/j.jallcom.2017.05.005.
- 14K. Kaur, “TiPdSn: A Half Heusler Compound With High Thermoelectric Performance,” EPL 117 (2017): 47002, https://doi.org/10.1209/0295-5075/117/47002.
- 15K. Inomata, N. Ikeda, N. Tezuka, et al., “Highly Spin-Polarized Materials and Devices for Spintronics,” Science and Technology of Advanced Materials 9 (2008): 014101, https://doi.org/10.1088/1468-6996/9/1/014101.
- 16M. A. Hossain, M. T. Rahman, M. Khatun, and E. Haque, “Structural, Elastic, Electronic, Magnetic and Thermoelectric Properties of New Quaternary Heusler Compounds CoZrMnX (X=Al, Ga, Ge, In),” Computational Condensed Matter 15 (2018): 31–41, https://doi.org/10.1016/j.cocom.2018.03.006.
10.1016/j.cocom.2018.03.006 Google Scholar
- 17F. Casper, T. Graf, S. Chadov, B. Balke, and C. Felser, “Half-Heusler Compounds: Novel Materials for Energy and Spintronic Applications,” Semiconductor Science and Technology 27 (2012): 063001, https://doi.org/10.1088/0268-1242/27/6/063001.
- 18D. Kieven, R. Klenk, S. Naghavi, C. Felser, and T. Gruhn, “I-II-V Half-Heusler Compounds for Optoelectronics: Ab Initio Calculations,” Physical Review B: Condensed Matter 81 (2010): 1–6, https://doi.org/10.1103/PhysRevB.81.075208.
- 19J. He, S. S. Naghavi, V. I. Hegde, M. Amsler, and C. Wolverton, “Designing and Discovering a New Family of Semiconducting Quaternary Heusler Compounds Based on the 18-Electron Rule,” Chemistry of Materials 30 (2018): 4978–4985, https://doi.org/10.1021/acs.chemmater.8b01096.
- 20H. Kara, M. Upadhyay Kahaly, and K. Özdoğan, “Thermoelectric Response of Quaternary Heusler Compound CrVNbZn,” Journal of Alloys and Compounds 735 (2018): 950–958, https://doi.org/10.1016/j.jallcom.2017.11.022.
- 21R. Zosiamliana, L. Kima, Z. Mawia, L. Zuala, G. Abdurakhmanov, and D. P. Rai, “First-Principles Investigation of the Electronics, Optical, Mechanical, Thermodynamics and Thermoelectric Properties of Na Based Quaternary Heusler Alloys (QHAs) NaHfXGe (X = Co, Rh, Ir),” Journal of Physics. Condensed Matter 36 (2024): 065501, https://doi.org/10.1088/1361-648X/ad0676.
- 22T. Kaur, J. Singh, M. Goyal, et al., “First Principles Calculations to Investigate Li-Based Quaternary Heusler Compounds LiHfCoX (X = Ge, Sn) for Thermoelectric Applications,” Physica Scripta 97 (2022): 105706, https://doi.org/10.1088/1402-4896/ac8c70.
- 23J. Singh, T. Kaur, A. P. Singh, et al., “LiNbCoX (X = Al, Ga) Quaternary Heusler Compounds for High-Temperature Thermoelectric Properties: A Computational Approach,” Bulletin of Materials Science 46 (2023): 103, https://doi.org/10.1007/s12034-023-02945-z.
- 24Y. Gupta, M. M. Sinha, and S. S. Verma, “Exploring the Structural, Elastic, Lattice Dynamical Stability and Thermoelectric Properties of Semiconducting Novel Quaternary Heusler Alloy LiScPdPb,” Journal of Solid State Chemistry 304 (2021): 122601, https://doi.org/10.1016/j.jssc.2021.122601.
- 25J. Singh, K. Kaur, S. A. Khandy, S. Dhiman, M. Goyal, and S. S. Verma, “Structural, Electronic, Mechanical, and Thermoelectric Properties of LiTiCoX (X = Si, Ge) Compounds,” International Journal of Energy Research 45 (2021): 16891–16900, https://doi.org/10.1002/er.6851.
- 26L. Suktel and S. M. Saini, “Comprehensive Investigation of Li-Based Novel Quaternary Heusler LiTiPdZ (Z = Al, Ga, in) Compounds for Thermoelectric Performance,” Physica Scripta 99 (2024): 55945, https://doi.org/10.1088/1402-4896/ad39b3.
- 27R. Muhammad, M. A. Uqaili, Y. Shuai, M. A. Mahar, and I. Ahmed, “Ab-Initio Investigations on the Physical Properties of 3d and 5d Transition Metal Atom Substituted Divacancy Monolayer h-BN,” Applied Surface Science 458 (2018): 145–156, https://doi.org/10.1016/j.apsusc.2018.07.057.
- 28M. Rafique, M. A. Uqaili, N. H. Mirjat, M. A. Tunio, and Y. Shuai, “Ab-Initio Investigations on Titanium (Ti) Atom-Doped Divacancy Monolayer h-BN System for Hydrogen Storage Systems,” Physics E: Low-Dimensional Systems and Nanostructures 109 (2019): 169–178, https://doi.org/10.1016/j.physe.2019.01.015.
- 29S. A. Khandy, I. Islam, D. C. Gupta, et al., “A Case Study of Fe2TaZ (Z = Al, Ga, In) Heusler Alloys: Hunt for Half-Metallic Behavior and Thermoelectricity,” RSC Advances 8 (2018): 40996–41002, https://doi.org/10.1039/c8ra04433c.
- 30J. P. Perdew, K. Burke, and M. Ernzerhof, “Generalized Gradient Approximation Made Simple,” Physical Review Letters 77 (1996): 3865–3868, https://doi.org/10.1103/PhysRevLett.77.3865.
- 31J. D. Pack and H. J. Monkhorst, ““Special Points for Brillouin-Zone Integrations”—a Reply,” Physical Review B 16 (1977): 1748–1749, https://doi.org/10.1103/PhysRevB.16.1748.
10.1103/PhysRevB.16.1748 Google Scholar
- 32A. Togo and I. Tanaka, “First Principles Phonon Calculations in Materials Science,” Scripta Materialia 108 (2015): 1–5, https://doi.org/10.1016/j.scriptamat.2015.07.021.
- 33R. Gaillac, P. Pullumbi, and F. X. Coudert, “ELATE: An Open-Source Online Application for Analysis and Visualization of Elastic Tensors,” Journal of Physics. Condensed Matter 28 (2016): 275201, https://doi.org/10.1088/0953-8984/28/27/275201.
- 34G. K. H. Madsen and D. J. Singh, “BoltzTraP. A Code for Calculating Band-Structure Dependent Quantities,” Computer Physics Communications 175 (2006): 67–71, https://doi.org/10.1016/j.cpc.2006.03.007.
- 35J. E. Saal, S. Kirklin, M. Aykol, B. Meredig, and C. Wolverton, “Materials Design and Discovery With High-Throughput Density Functional Theory: The Open Quantum Materials Database (OQMD),” JOM 65 (2013): 1501–1509, https://doi.org/10.1007/s11837-013-0755-4.
- 36F. D. Murgnaghan, “The Compressibility of Media Under Extreme Pressures,” Journal of the Franklin Institute 197 (1924): 98, https://doi.org/10.1016/s0016-0032(24)90498-4.
10.1016/s0016?0032(24)90498?4 Google Scholar
- 37S. Hebri, A. B. Abdelli, N. Belfedal, and D. Bensaid, “Investigating the Structural, Electronic, and Elastic Properties of Li-Based Quaternary Heusler Alloy Semiconductors Using Hybrid Functional – HSE06 Bandgap Recalculations,” Inorganic Chemistry Communications 150 (2023): 110479, https://doi.org/10.1016/j.inoche.2023.110479.
- 38B. B. Karki, G. J. Ackland, and J. Crain, “Elastic Instabilities in Crystals From Ab Initio Stress-Strain Relations,” Journal of Physics. Condensed Matter 9, no. 41 (1997): 8579–8589, https://doi.org/10.1088/0953-8984/9/41/005.
- 39D. G. Pettifor, “Theoretical Predictions of Structure and Related Properties of Intermetallics,” Materials Science and Technology 8 (1992): 345–349, https://doi.org/10.1179/mst.1992.8.4.345.
- 40J. Haines, J. Leger, and G. Bocquillon, “Synthesis and Design of Super Hard Materials,” Annual Review of Materials Research 31 (2001): 1–23.
- 41N. Kaur, R. Sharma, V. Srivastava, and S. Chowdhury, “Thermodynamic and Thermoelectric Properties of FeCrTiZ (Z = Si, Ge) Quaternary Heusler Compounds,” Journal of Chemical Thermodynamics 184 (2023): 107089, https://doi.org/10.1016/j.jct.2023.107089.
- 42S. Sâad Essaoud and A. S. Jbara, “Electronic-Structural, Thermo-Electric, and Thermo-Mechanical Properties of M2AC and M2AB (M = Nb or Mo, A = Al or Ga) Compounds,” Indian Journal of Physics 97 (2023): 105–114, https://doi.org/10.1007/s12648-022-02386-0.
- 43P. Debye, “Zur Theorie der spezifischen Wärmen,” Annalen der Physik 344 (1912): 789–839, https://doi.org/10.1002/andp.19123441404.
10.1002/andp.19123441404 Google Scholar
- 44C. Kittel, Introduction to Solid State Physics, 8th ed. (Wiley, 2005).
- 45H. B. Callen, Thermodynamics and an Introduction to Thermostatistics, 2nd ed. (Wiley, 1985).
- 46E. S. R. Gopal, Epecific Heat at Low Temperature (Springer US, 1966).
10.1007/978-1-4684-9081-7 Google Scholar
- 47T. Graf, C. Felser, and S. S. P. Parkin, “Simple Rules for the Understanding of Heusler Compounds,” Progress in Solid State Chemistry 39 (2011): 1–50, https://doi.org/10.1016/j.progsolidstchem.2011.02.001.
- 48K. Jia, C. L. Yang, M. S. Wang, X. G. Ma, and Y. G. Yi, “First-Principles Insight on Elastic, Electronic, and Thermoelectric Transport Properties of BAgX (X = Ti, Zr, Hf),” Results in Physics 15 (2019): 102563, https://doi.org/10.1016/j.rinp.2019.102563.
