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Effect of co-doping on the thermodynamic properties of ternary antimonides Zr₃Ni₃Sb₄: A first-principles study
Shao-Bo Chen, Jia-Hao Wang and Lu Zhang

The DFT calculations were performed to investigate the electronic structure, elastic moduli, and thermal transport behavior of Zr₁₂CoNi₁₁Sb₁₆ derived from Zr₃Ni₃Sb₄. For the ternary antimonide Zr₃Ni₃Sb₄ and its derivatives, structural stability was assessed by analyzing phonon spectra and formation energy. All calculated elastic moduli met the requirements for mechanical stability. Band structure calculations reveal that both Zr₃Ni₃Sb₄ and its derivative Zr₁₂CoNi₁₁Sb₁₆ exhibit semiconducting characteristics, displaying energy gaps of 0.432 eV and 0.410 eV, respectively. To analyze electronic structures and chemical bonding mechanisms, the atomic orbital projections in band structures were studied to understand material properties and electron transfer behaviors. Elastic analysis revealed Zr₃Ni₃Sb₄‘s brittleness with hardness, while its derivative Zr₁₂CoNi₁₁Sb₁₆ demonstrates ductility while maintaining hardness. Based on the derived elastic parameters and Slack’s theoretical framework, the room-temperature (300 K) lattice thermal conductivity values for Zr₃Ni₃Sb₄ and its derivative Zr₁₂CoNi₁₁Sb₁₆ were determined as 24.50 W·m^-1·K^-1 and 14.82 W·m^-1·K^-1. Following cobalt doping, significant suppression of lattice thermal transport is observed in Zr₃Ni₃Sb₄-based alloys, offering fundamental insights for their thermoelectric applications.

Keywords: band structure, density of states, elastic constants, thermal transport properties, doping