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Origin of high thermoelectric performance of FeNb 1 − x Zr/Hf x Sb 1 − y Sn y alloys: A first-principles study

View Article: PubMed Central - PubMed

ABSTRACT

The previous experimental work showed that Hf- or Zr-doping has remarkably improved the thermoelectric performance of FeNbSb. Here, the first-principles method was used to explore the possible reason for such phenomenon. The substitution of X (Zr/Hf) atoms at Nb sites increases effective hole-pockets, total density of states near the Fermi level (EF), and hole mobility to largely enhance electrical conductivity. It is mainly due to the shifting the EF to lower energy and the nearest Fe atoms around X atoms supplying more d-states to hybrid with X d-states at the vicinity of the EF. Moreover, we find that the X atoms indirectly affect the charge distribution around Nb atoms via their nearest Fe atoms, resulting in the reduced energy difference in the valence band edge, contributing to enhanced Seebeck coefficients. In addition, the further Bader charge analysis shows that the reason of more holes by Hf-doping than Zr in the experiment is most likely derived from Hf atoms losing less electrons and the stronger hybridization between Hf atoms and their nearest Fe atoms. Furthermore, we predict that Hf/Sn co-doping may be an effective strategy to further optimize the thermoelectric performance of half-Heusler (HH) compounds.

No MeSH data available.


Calculated band decomposed charge densities of 1 × 1 × 5 FeNbSb supercell (a) and FeNb0.9Hf0.1Sb (b) for the valence bands at the point M, with the isosurface value of 0.01. Color code: Fe atoms, yellow; Nb atoms, green; Sb atoms, purple; Hf atoms, light blue. Here, Sb atoms are not displayed.
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f9: Calculated band decomposed charge densities of 1 × 1 × 5 FeNbSb supercell (a) and FeNb0.9Hf0.1Sb (b) for the valence bands at the point M, with the isosurface value of 0.01. Color code: Fe atoms, yellow; Nb atoms, green; Sb atoms, purple; Hf atoms, light blue. Here, Sb atoms are not displayed.

Mentions: Besides, from Figs 3(a) and 5(d–f), we find that Zr or Hf-doping decreases the energy difference (⊿EA-M) in the valence band edge between the point A and M, and their calculated values are: for FeNbSb supercell, ⊿EA-M = 0.040 eV; for 10% Hf-doped FeNbSb, ⊿EA-M = 0.012 eV; for 15% Hf-doped FeNbSb, ⊿EA-M = 0.015 eV; for 15% Zr-doped FeNbSb, ⊿EA-M = 0.013 eV. Many previous studies showed that the bands were effectively degenerate when multiple bands have the same or comparable energy within kBT. Near the EF, the reduced ⊿EA-M makes the band degeneracy increase, and thus, results in the enhanced Stot. To investigate the reason of the decreased energy difference (⊿EA-M) in the valence band edge, we plot the calculated band decomposed charge density of 1 × 1 × 5 FeNbSb supercell and FeNb0.9Hf0.1Sb for valence bands at the high symmetry point M in Fig. 8. Compared with FeNbSb supercell, the charge distribution of FeNb0.9Hf0.1Sb is highly localized, and these charges mainly distribute around Nb2, Nb3, Nb5, and Nb6 atoms at the vicinity of Hf atoms. In fact, Fe1 (or Fe4) atoms are located in the centers of tetrahedra formed by Hf1 and Nb2 (or Nb6) atoms, and also, Fe2 (or Fe3) atoms are located in the centers of tetrahedra formed by Hf2 and Nb3 (or Nb5) atoms, suggesting that Hf atoms indirectly affect the charge distribution around Nb atoms via their nearest Fe atoms. To deeply understand the influence of Hf-doping on the charge distribution, we calculated the bond lengths and bond angles of the tetrahedra formed by Hf and Nb atoms in Fig. 9(c). From Fig. 9(c), we find that the bond lengths and bond angles of 1-tetrahedra are same as those of 2-tetrahedra, and also, 3-tetrahedra and 4-tetrahedra have the same bond lengths and bond angles. (1, 2, 3, and 4 represent Hf1-Nb1-Nb2-Nb2, Hf2-Nb3-Nb3-Nb4, Hf2-Nb4-Nb5-Nb5, and Hf1-Nb1-Nb6-Nb6, respectively). It likely leads to the similar charge distribution around Nb2 and Nb3 atoms, and also, the similar charge distribution around Nb5 and Nb6 atoms. The obvious change in charge distribution by Hf-doping will affect the energy of the valence bands at point M, and therefore, it results in the decreased energy difference in the valence band edge between the point A and M.


Origin of high thermoelectric performance of FeNb 1 − x Zr/Hf x Sb 1 − y Sn y alloys: A first-principles study
Calculated band decomposed charge densities of 1 × 1 × 5 FeNbSb supercell (a) and FeNb0.9Hf0.1Sb (b) for the valence bands at the point M, with the isosurface value of 0.01. Color code: Fe atoms, yellow; Nb atoms, green; Sb atoms, purple; Hf atoms, light blue. Here, Sb atoms are not displayed.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC5015081&req=5

f9: Calculated band decomposed charge densities of 1 × 1 × 5 FeNbSb supercell (a) and FeNb0.9Hf0.1Sb (b) for the valence bands at the point M, with the isosurface value of 0.01. Color code: Fe atoms, yellow; Nb atoms, green; Sb atoms, purple; Hf atoms, light blue. Here, Sb atoms are not displayed.
Mentions: Besides, from Figs 3(a) and 5(d–f), we find that Zr or Hf-doping decreases the energy difference (⊿EA-M) in the valence band edge between the point A and M, and their calculated values are: for FeNbSb supercell, ⊿EA-M = 0.040 eV; for 10% Hf-doped FeNbSb, ⊿EA-M = 0.012 eV; for 15% Hf-doped FeNbSb, ⊿EA-M = 0.015 eV; for 15% Zr-doped FeNbSb, ⊿EA-M = 0.013 eV. Many previous studies showed that the bands were effectively degenerate when multiple bands have the same or comparable energy within kBT. Near the EF, the reduced ⊿EA-M makes the band degeneracy increase, and thus, results in the enhanced Stot. To investigate the reason of the decreased energy difference (⊿EA-M) in the valence band edge, we plot the calculated band decomposed charge density of 1 × 1 × 5 FeNbSb supercell and FeNb0.9Hf0.1Sb for valence bands at the high symmetry point M in Fig. 8. Compared with FeNbSb supercell, the charge distribution of FeNb0.9Hf0.1Sb is highly localized, and these charges mainly distribute around Nb2, Nb3, Nb5, and Nb6 atoms at the vicinity of Hf atoms. In fact, Fe1 (or Fe4) atoms are located in the centers of tetrahedra formed by Hf1 and Nb2 (or Nb6) atoms, and also, Fe2 (or Fe3) atoms are located in the centers of tetrahedra formed by Hf2 and Nb3 (or Nb5) atoms, suggesting that Hf atoms indirectly affect the charge distribution around Nb atoms via their nearest Fe atoms. To deeply understand the influence of Hf-doping on the charge distribution, we calculated the bond lengths and bond angles of the tetrahedra formed by Hf and Nb atoms in Fig. 9(c). From Fig. 9(c), we find that the bond lengths and bond angles of 1-tetrahedra are same as those of 2-tetrahedra, and also, 3-tetrahedra and 4-tetrahedra have the same bond lengths and bond angles. (1, 2, 3, and 4 represent Hf1-Nb1-Nb2-Nb2, Hf2-Nb3-Nb3-Nb4, Hf2-Nb4-Nb5-Nb5, and Hf1-Nb1-Nb6-Nb6, respectively). It likely leads to the similar charge distribution around Nb2 and Nb3 atoms, and also, the similar charge distribution around Nb5 and Nb6 atoms. The obvious change in charge distribution by Hf-doping will affect the energy of the valence bands at point M, and therefore, it results in the decreased energy difference in the valence band edge between the point A and M.

View Article: PubMed Central - PubMed

ABSTRACT

The previous experimental work showed that Hf- or Zr-doping has remarkably improved the thermoelectric performance of FeNbSb. Here, the first-principles method was used to explore the possible reason for such phenomenon. The substitution of X (Zr/Hf) atoms at Nb sites increases effective hole-pockets, total density of states near the Fermi level (EF), and hole mobility to largely enhance electrical conductivity. It is mainly due to the shifting the EF to lower energy and the nearest Fe atoms around X atoms supplying more d-states to hybrid with X d-states at the vicinity of the EF. Moreover, we find that the X atoms indirectly affect the charge distribution around Nb atoms via their nearest Fe atoms, resulting in the reduced energy difference in the valence band edge, contributing to enhanced Seebeck coefficients. In addition, the further Bader charge analysis shows that the reason of more holes by Hf-doping than Zr in the experiment is most likely derived from Hf atoms losing less electrons and the stronger hybridization between Hf atoms and their nearest Fe atoms. Furthermore, we predict that Hf/Sn co-doping may be an effective strategy to further optimize the thermoelectric performance of half-Heusler (HH) compounds.

No MeSH data available.