The incorporation of interstitial hydrogen in yttria was studied by means of ab initio calculations based on density-functional theory (DFT) and muonium spin polarization spectroscopy (μSR). The density-functional calculations, based on a semilocal functional within the GGA-PBE and a hybrid functional, uncovered multiple geometrical configurations for the neutral, H 0 , and the negatively charged, H − , states of hydrogen, thus demonstrating the existence of metastable minimum-energy sites. It was observed that the low-energy configurations for H 0 and H − are similar: they prefer to relax in deep, interstitial sites, whereas the equilibrium configurations for the positively charged state, H + , were bond-type configurations with the hydrogen forming a covalent O-H bond with an O anion. For all neutral and negative configurations, localized defect levels were found inside the gap. Overall, the results for the formation energies obtained by the two different functionals are qualitatively similar; an amphoteric behavior was found for hydrogen after considering the lowest-energy structures for each charge state. The calculated acceptor transition level, obtained by the hybrid functional and seen near midgap, is consistent with μSR data from literature. The results are consistent with the present μSR data, where the observed diamagnetic signal is attributed to a donor-like muonium at the oxygen-bonded configurations and the paramagnetic signal to an acceptor-like deep muonium at the interstitial sites.

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We present a systematic study of isolated hydrogen in diverse forms of ZrO 2 (zirconia), both undoped and stabilized in the cubic phase by additions of transition-metal oxides (Y 2 O 3 , Sc 2 O 3 , MgO, CaO). Hydrogen is modeled by using muonium as a pseudoisotope in muon-spin spectroscopy experiments. The muon study is also supplemented with first-principles calculations of the hydrogen states in scandia-stabilized zirconia by conventional density-functional theory (DFT) as well as a hybrid-functional approach which admixes a portion of exact exchange to the semilocal DFT exchange. The experimentally observable metastable states accessible by means of the muon implantation allowed us to probe two distinct hydrogen configurations predicted theoretically: an oxygen-bound configuration and a quasiatomic interstitial one with a large isotropic hyperfine constant. The neutral-oxygen-bound configuration is characterized by an electron spreading over the neighboring zirconium cations, forming a polaronic state with a vanishingly small hyperfine interaction at the muon. The atom-like interstitial muonium is observed also in all samples but with different fractions. The hyperfine interaction is isotropic in calcia-doped zirconia [A iso = 3.02(8) GHz], but slightly anisotropic in the nanograin yttria-doped zirconia [A iso = 2.1(1) GHz, D = 0.13(2) GHz] probably due to muons stopping close to the interface regions between the nanograins in the latter case.

The electronic structure of hydrogen impurity in Lu 2 O 3 was studied by first-principles calculations and muonium spectroscopy. The computational scheme was based on two methods which are well suited to treat defect calculations in f-electron systems: first, a semilocal functional of conventional density-functional theory (DFT) and secondly a DFT+U approach which accounts for the on-site correlation of the 4f electrons via an effective Hubbard-type interaction. Three different types of stable configurations were found for hydrogen depending upon its charge state. In its negatively charged and neutral states, hydrogen favors interstitial configurations residing either at the unoccupied sites of the oxygen sublattice or at the empty cube centers surrounded by the lanthanide ions. In contrast, the positively charged state stabilized only as a bond configuration, where hydrogen binds to oxygen ions. Overall, the results between the two methods agree in the ordering of the formation energies of the different impurity configurations, though within DFT+U the charge-transition (electrical) levels are found at Fermi-level positions with higher energies. Both methods predict that hydrogen is an amphoteric defect in Lu 2 O 3 if the lowest-energy configurations are used to obtain the charge-transition, thermodynamic levels. The calculations of hyperfine constants for the neutral interstitial configurations show a predominantly isotropic hyperfine interaction with two distinct values of 926 MHz and 1061 MHz for the Fermi-contact term originating from the two corresponding interstitial positions of hydrogen in the lattice. These high values are consistent with the muonium spectroscopy measurements which also reveal a strongly isotropic hyperfine signature for the neutral muonium fraction with a magnitude slightly larger (1130 MHz) from the ab initio results (after scaling with the magnetic moments of the respective nuclei).

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