Huge attention has been shifted to thermoelectric properties of half-Heusler compounds because of the ability of these compounds to convert heat into electricity. The calculations of thermoelectric properties of these compounds are necessitated by the search for alternatives to fossil fuel. This report presents ab initio calculations of electronic and thermoelectric properties of the most stable phase of hafnium–rhodium-based arsenic, antimony and bismuth (HfRhZ(Z = As, Sb and Bi)) half-Heusler compounds by density functional theory based on projector augmented wave pseudopotential method with Perdew–Burke–Ernzerhof generalized gradient approximation used for exchange–correlation functional. The properties calculated in this work are the equilibrium lattice constant, the density of states, band structures, Seebeck coefficients, electrical conductivity, power factor and electronic fitness function (EFF). EFF is calculated to overcome the problem of optimizing Seebeck coefficient and electrical conductivity because of inverse proportion relationship between Seebeck coefficient and electrical conductivity. The $$\gamma$$ γ phase of these compounds is found to be most stable, and thus, electronic and thermoelectric properties of this phase are obtained for the p-type HfRhZ( Z = As, Sb and Bi). The p-type HfRhZ(Z = As, Sb and Bi) is a better thermoelectric material than the n-type HfRhZ(Z = As, Sb and Bi). The Seebeck coefficients of these compounds are 272.01 $$\upmu$$ μ V/K, 555.75 $$\upmu$$ μ V/K and 244.92 $$\upmu$$ μ V/K for HfRhAs, HfRhSb and HfRhBi, respectively, and EFF of HfRhAs, HfRhSb and HfRhBi is 1.21 $$\times10^{-19}\,\mathrm{W}^{5/3}\,\mathrm{ms}^{-1/3}\,\mathrm{K}^{-2}$$ × 10 - 19 W 5 / 3 ms - 1 / 3 K - 2 at 1.75 $$\times 10^{20}\,{\text{cm}}^{-3}$$ × 10 20 cm - 3 , 1.55 $$\times10^{-19}\,\mathrm{W}^{5/3}\,\mathrm{ms}^{-1/3}\,\mathrm{K}^{-2}$$ × 10 - 19 W 5 / 3 ms - 1 / 3 K - 2 at 1.64 $$\times 10^{20}\,{\text{cm}}^{-3}$$ × 10 20 cm - 3 and 1.07 $$\times10^{-19}\,\mathrm{W}^{5/3}\,\mathrm{ms}^{-1/3}\,\mathrm{K}^{-2}$$ × 10 - 19 W 5 / 3 ms - 1 / 3 K - 2 at 4.50 $$\times{10^{20}}\mathrm{cm}^{-3}$$ × 10 20 cm - 3 , respectively. The results obtained in this work show that HfRhSb and HfRhAs are better potential thermoelectric materials than some known high-performance thermoelectric materials.

中文翻译：

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HfRhZ(Z = As, Sb and Bi)半赫斯勒化合物的电子结构和热电性质

由于半赫斯勒化合物具有将热转化为电能的能力，人们的注意力已经转移到这些化合物的热电特性上。为了寻找化石燃料的替代品，需要计算这些化合物的热电特性。本报告介绍了基于投影仪的密度泛函理论，从头计算铪-铑基砷、锑和铋（HfRhZ（Z = As、Sb 和 Bi））半赫斯勒化合物的最稳定相的电子和热电特性使用 Perdew-Burke-Ernzerhof 广义梯度近似的增强波赝势方法用于交换相关函数。在这项工作中计算的属性是平衡晶格常数、状态密度、能带结构、塞贝克系数、电导率、功率因数和电子适应度函数 (EFF)。计算EFF是为了克服塞贝克系数和电导率成反比关系而优化塞贝克系数和电导率的问题。发现这些化合物的 $$\gamma$$ γ 相是最稳定的，因此，对于 p 型 HfRhZ(Z = As、Sb 和 Bi)，获得了该相的电子和热电性质。p 型 HfRhZ（Z = As、Sb 和 Bi）是比 n 型 HfRhZ（Z = As、Sb 和 Bi）更好的热电材料。这些化合物的塞贝克系数分别为 HfRhAs、HfRhSb 和 HfRhBi 的 272.01 $$\upmu$$ μ V/K、555.75 $$\upmu$$ μ V/K 和 244.92 $$\upmu$$ μ V/K , HfRhAs、HfRhSb 和 HfRhBi 的 EFF 为 1.21 $$\times10^{-19}\,\mathrm{W}^{5/3}\,\mathrm{ms}^{-1/3}\, \mathrm{K}^{-2}$$ × 10 - 19 W 5 / 3 ms - 1 / 3 K - 2 at 1.75 $$\times 10^{20}\,{\text{cm}}^{ -3}$$ × 10 20 cm - 3 , 1.55 $$\times10^{-19}\,\mathrm{W}^{5/3}\,\mathrm{ms}^{-1/3}\ ,\mathrm{K}^{-2}$$ × 10 - 19 W 5 / 3 ms - 1 / 3 K - 2 at 1.64 $$\times 10^{20}\,{\text{cm}}^ {-3}$$ × 10 20 cm - 3 and 1.07 $$\times10^{-19}\,\mathrm{W}^{5/3}\,\mathrm{ms}^{-1/3} \,\mathrm{K}^{-2}$$ × 10 - 19 W 5 / 3 ms - 1 / 3 K - 2 在 4.50 $$\times{10^{20}}\mathrm{cm}^{ -3}$$ × 10 20 cm - 3 。在这项工作中获得的结果表明，HfRhSb 和 HfRhAs 是比一些已知的高性能热电材料更好的潜在热电材料。\mathrm{K}^{-2}$$ × 10 - 19 W 5 / 3 ms - 1 / 3 K - 2 at 1.64 $$\times 10^{20}\,{\text{cm}}^{ -3}$$ × 10 20 cm - 3 和 1.07 $$\times10^{-19}\,\mathrm{W}^{5/3}\,\mathrm{ms}^{-1/3}\ ,\mathrm{K}^{-2}$$ × 10 - 19 W 5 / 3 ms - 1 / 3 K - 2 at 4.50 $$\times{10^{20}}\mathrm{cm}^{- 3}$$ × 10 20 cm - 3 。在这项工作中获得的结果表明，HfRhSb 和 HfRhAs 是比一些已知的高性能热电材料更好的潜在热电材料。\mathrm{K}^{-2}$$ × 10 - 19 W 5 / 3 ms - 1 / 3 K - 2 at 1.64 $$\times 10^{20}\,{\text{cm}}^{ -3}$$ × 10 20 cm - 3 和 1.07 $$\times10^{-19}\,\mathrm{W}^{5/3}\,\mathrm{ms}^{-1/3}\ ,\mathrm{K}^{-2}$$ × 10 - 19 W 5 / 3 ms - 1 / 3 K - 2 at 4.50 $$\times{10^{20}}\mathrm{cm}^{- 3}$$ × 10 20 cm - 3 。在这项工作中获得的结果表明，HfRhSb 和 HfRhAs 是比一些已知的高性能热电材料更好的潜在热电材料。