Why is it so difficult to realize Dy ⁴⁺ in as‐synthesized BaZrO ₃ ?

Rare-earth doped barium zirconate (BaZrO$_3$) ceramics are of interest as proton-conducting and luminescent materials. Here, we report a study dysprosium (Dy) other relevant point defects in BaZrO$_3$ using hybrid density-functional defect calculations. The tetravalent Dy$^{4+}$ is found to be structurally electronically stable at the Zr lattice site (i.e., Dy$_{\rm Zr}^0$), but most often energetically less favorable than trivalent Dy$^{3+}$ Zr}^-$) as-synthesized BaZrO$_3$, due formation low-energy, positively charged oxygen vacancies mixed-site occupancy Dy host lattice. Dy$^{4+}$/Dy$^{3+}$ ratio can, principle, increased by preparing material under highly oxidizing Ba-rich conditions co-doping with acceptor-like impurities; however, post-synthesis treatment may still needed realize non-negligible concentration. We also find that certain unoccupied $4f$ states O $2p$ {\it strongly hybridized}, feature not seen rare-earth-containing materials, isolated Zr}$ might source broad blue emission band-to-defect ("charge-transfer") luminescence.