Destabilization of pseudo-Jahn–Teller distortion in cesium-doped hexagonal tungsten bronzes

Abstract

In Cs-doped hexagonal tungsten bronzes (Cs-HTBs), X-ray diffraction–Rietveld analysis has revealed that an increase in the alkali dopant and oxygen vacancies (VO) elongate the c-axis, contract the a-axis, and decrease the deviations of the W–O distance and W coordinates from those of a regular WO6 octahedron. These structural changes are interpreted as a destabilization of pseudo-Jahn–Teller (PJT) distortion by electron donation from Cs+ and VO. A dramatic difference is observed in the destabilization efficiency between the donated electrons from Cs+ and VO, suggesting that the former and latter electrons should be delocalized and localized, respectively. First-principles density functional theory calculations using optB86b-vdW functionals reproduced the behavior of c-axis elongation and a-axis contraction by Cs doping. The projected orbital density of states indicates that the Cs-derived electrons are donated to W-5dyz and W-5dzx orbitals to extend along the c-axis, whereas the VO-derived electrons are donated to W-5dxy and W-5dx2−y2 orbitals to strongly localize in the a–b plane. In HTBs, an anisotropic increase and decrease in the t2g* antibonding electrons from the doped alkali are concluded to induce the anisotropic structural change in PJT distortions.

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 …”

“…Here, the distortion is shown relaxed largely in a linear fashion within each space group except Pc . The decreasing distortion is interpreted as caused by the donated electrons that reduce the hybridization of W–5 d /O–2 p orbitals . Therefore, it is naturally expected to occur in the WO 6 octahedra in Cs‐HTB as well, although no experimental confirmations have been previously reported.…”

“…The decreasing distortion is interpreted as caused by the donated electrons that reduce the hybridization of W-5d/O-2p orbitals. 51 Therefore, it is naturally expected to occur in the WO 6 octahedra in Cs-HTB as well, although no experimental confirmations have been previously reported. Thus, we have plotted various structural parameters related to the distortions of WO 6 with respect to x and y, as shown in Figures 10 and 11.…”

“…This outcome is in complete agreement with our detailed first-principles analyses reported separately. 40,51…”