Isolated hydrogen configurations in zirconia as seen by muon spin spectroscopy and ab initio calculations

We present a systematic study of isolated hydrogen in diverse forms of ${\mathrm{ZrO}}_2$ (zirconia), both undoped and stabilized in the cubic phase by additions of transition-metal oxides $({\mathrm{Y}}_2{\mathrm{O}}_3,{\mathrm{Sc}}_2{\mathrm{O}}_3$, 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 $[A_{\mathrm{iso}}=3.02\left(8\right)$ GHz], but slightly anisotropic in the nanograin yttria-doped zirconia $[A_{\mathrm{iso}}=2.1\left(1\right)$ GHz, $D=0.13\left(2\right)$ GHz] probably due to muons stopping close to the interface regions between the nanograins in the latter case.

Figure 1

Schematic of a portion of the undistorted fluorite cubic lattice of zirconia, showing the alternance between cubes with and without a Zr cation. Blue spheres represent oxygen anions and the dark brown sphere represents the zirconium cation.

Figure 2

Muon spin asymmetry as a function of time, in transverse geometry $(B=10$ mT), at $T=7.8$ K, for the ScSZ sample. The maximum instrumental asymmetry is indicated (horizontal dashed lines), showing the existence of an unobserved fraction of muon spin polarization (missing fraction). A rapidly decaying component is prominent in the first $6\mu \mathrm{s}$, superimposed on a slowly relaxing component dominant for higher times.

Figure 3

Formation-energy plot of the different charge states of hydrogen as a function of the Fermi-level position in the gap. The plot shows the results obtained by the hybrid-functional (HSE06) approach. The thermodynamic charge-transition levels, $E(q/q^{\prime })$, are denoted by the vertical lines. The valence-band (VB) edge defines the reference energy for the Fermi level which spans the band gap up to the conduction-band minimum $\left(E_C\right)$. The plot depicts the formation energies of the lowest-energy structures that hydrogen forms in the ScSZ cell for each of its charge states.

Figure 4

Atomistic structure of a neutral oxygen-bound hydrogen configuration in ScSZ obtained from the hybrid (HSE06) calculations. The spin-density isosurface reveals the localization of the excess electron (shown in yellow). The chemical elements are represented as H (very small red sphere), Zr (small dark brown spheres), O (large blue spheres), Sc (medium-sized light-gray spheres).

Figure 5

Temperature dependence of the slowly relaxing paramagnetic relaxation ${\lambda }_{p1}$ for the ScSZ sample. The line is a fit as detailed in the text.

Figure 6

$\mu \mathrm{SR}$ Fourier spectrum of YSZ at $T=8.5$ K in an external magnetic field of $B=10$ mT.

Figure 7

Repolarization curve for ${\mathrm{ZrO}}_2$:Ca (monoclinic) at $T=300$ K. The red line is a fit assuming an isotropic hyperfine interaction $A=3.02\left(8\right)$ GHz.

Figure 8

Repolarization curve for YSZ at $T=300$ K. The red line is a fit assuming an axially symmetric anisotropic hyperfine interaction with $A_{\mathrm{iso}}=2.1\left(1\right)$ GHz and $D=0.13\left(2\right)$ GHz.

Figure 9

Observed fraction of muon spin polarization as a function of temperature, in transverse geometry $(B=10$ mT), for the ScSZ sample. The line is a fit to a Boltzmann model with an activation energy $E_a=0.14\left(3\right)$ eV, which we associate with the barrier between the atom-like interstitial configuration and the oxygen-bound configuration.