Polarons in reduced cesium tungsten bronzes studied using the DFT + U method

Oxygen vacancies and pseudo Jahn‐Teller destabilization in cesium‐doped hexagonal tungsten bronzes

“…Thus, the electrons donated from V O s are conjectured as localized in W–5 d to affect only a limited number of W–O bonds near V O . This outcome is in complete agreement with our detailed first‐principles analyses reported separately …”

“…A remarkably less magnitude of the dimensional change, 1/18, is observed for electrons emitted from oxygen vacancies to modify lattice parameters, as compared with that for electrons emitted from Cs + , suggesting that most electrons emitted from oxygen vacancies should be localized in the W–5 d orbital. This conclusion is supported by the theoretical calculations reported separately …”

“…In WO 3− x , V O s are introduced not randomly but via planar defects called the CS plane, which are experimentally verified by TEM . Similarly, our recent first‐principle calculations on Cs 0.33 WO 3− y suggest that V O s are not introduced randomly but could be condensed in linear loops . The presence of these W‐rich defects could modify the XRD intensity distribution, although crystallographic details of these defects are unclarified.…”

“…Wang et al have shown by DFT hybrid functional calculations that V O s introduce W 4+ and W 5+ polarons according to their configurations in WO 3− x . In Cs 0.33 WO 2.67 , Yoshio et al have calculated using the DFT+U method and visualized the electron localization around V O with the average W valency of +5. Therefore, the W valency was examined by XPS.…”

“…25,26 Similarly, our recent first-principle calculations on Cs 0.33 WO 3−y suggest that V O s are not introduced randomly but could be condensed in linear loops. 40 The presence of these W-rich defects could modify the XRD intensity distribution, although crystallographic details of these defects are unclarified. Therefore, the effect of the local relaxations was bypassed in the next analysis in Section 3.5.…”