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Register a new userBi-Arrhenius diffusion and surface trapping of $^{8}$Li$^{+}$ in rutile TiO$_2$
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Aris Chatzichristos
Publication date
2018
fields
Physics
and research's language is
English
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We report measurements of the diffusion rate of isolated ion-implanted $^{8}$Li$^{+}$ within $sim$120 nm of the surface of oriented single-crystal rutile TiO$_2$ using a radiotracer technique. The $alpha$-particles from the $^{8}$Li decay provide a sensitive monitor of the distance from the surface and how the depth profile of $^{8}$Li evolves with time. The main findings are that the implanted Li$^{+}$ diffuses and traps at the (001) surface. The T-dependence of the diffusivity is described by a bi-Arrhenius expression with activation energies of 0.3341(21) eV above 200 K, whereas at lower temperatures it has a much smaller barrier of 0.0313(15) eV. We consider possible origins for the surface trapping, as well the nature of the low-T barrier.
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We report measurements of the dynamics of isolated $^{8}$Li$^{+}$ in single crystal rutile TiO$_{2}$ using $beta$-detected NMR. From spin-lattice relaxation and motional narrowing, we find two sets of thermally activated dynamics: one below 100 K; and one at higher temperatures. At low temperature, the activation barrier is $26.8(6)$ meV with prefactor $1.23(5) times 10^{10}$ s$^{-1}$. We suggest this is unrelated to Li$^{+}$ motion, and rather is a consequence of electron polarons in the vicinity of the implanted $^{8}$Li$^{+}$ that are known to become mobile in this temperature range. Above 100 K, Li$^{+}$ undergoes long-range diffusion as an isolated uncomplexed cation, characterized by an activation energy and prefactor of $0.32(2)$ eV and $1.0(5) times 10^{16}$ s$^{-1}$, in agreement with macroscopic diffusion measurements. These results in the dilute limit from a microscopic probe indicate that Li$^{+}$ concentration does not limit the diffusivity even up to high concentrations, but that some key ingredient is missing in the calculations of the migration barrier. The anomalous prefactors provide further insight into both Li$^{+}$ and polaron motion.
Small polaron formation in transition metal oxides, like the prototypical material rutile TiO$_2$, remains a puzzle and a challenge to simple theoretical treatment. In our combined experimental and theoretical study, we examine this problem using Raman spectroscopy of photo-excited samples and real-time time-dependent density functional theory (RT-TDDFT), which employs Ehrenfest dynamics to couple the electronic and ionic subsystems. We observe experimentally the unexpected stiffening of the $A_{1g}$ phonon mode under UV illumination and provide a theoretical explanation for this effect. Our analysis also reveals a possible reason for the observed anomalous temperature-dependence of the Hall mobility. Small polaron formation in rutile TiO$_2$ is a strongly non-adiabatic process and is adequately described by Ehrenfest dynamics at time scales of polaron formation.
The hyperfine structure of the interstitial muonium (Mu) in rutile (TiO$_2$, weakly $n$-type) has been identified by means of a muon spin rotation technique. The angle-resolved hyperfine parameters exhibit a tetragonal anisotropy within the $ab$ plane and axial anisotropy with respect to the $langle 001rangle$ ($hat{c}$) axis. This strongly suggests that the Mu is bound to O (forming an OH bond) at an off-center site within a channel along the $hat{c}$ axis, while the unpaired Mu electron is localized around the neighboring Ti site. The hyperfine parameters are quantitatively explained by a model that considers spin polarization of the unpaired electron at both the Ti and O sites, providing evidence for the formation of Mu as a Ti-O-Mu complex paramagnetic state. The disappearance of the Mu signal above $sim$10 K suggests that the energy necessary for the promotion of the unpaired electron to the conduction band by thermal activation is of the order of $10^1$ meV. These observations suggest that, while the electronic structure of Mu (and hence H) differs considerably from that of the conventional shallow level donor described by the effective mass model, Mu supplies a loosely bound electron, and thus, serves as a donor in rutile.
Knowledge of the molecular frontier levels alignment in the ground state can be used to predict the photocatalytic activity of an interface. The position of the adsorbates highest occupied molecular orbital (HOMO) levels relative to the substrates valence band maximum (VBM) in the interface describes the favorability of photogenerated hole transfer from the VBM to the adsorbed molecule. This is a key quantity for assessing and comparing H$_2$O photooxidation activities on two prototypical photocatalytic TiO$_2$ surfaces: anatase (A)-TiO$_2$(101) and rutile (R)-TiO$_2$(110). Using the projected density of states (DOS) from state-of-the-art quasiparticle (QP) $G_0W_0$ calculations, we assess the relative photocatalytic activity of intact and dissociated H$_2$O on coordinately unsaturated (Ti$_{textit{cus}}$) sites of idealized stoichiometric A-TiO$_2$(101)/R-TiO$_2$(110) and bridging O vacancies (O$_{textit{br}}^{textit{vac}}$) of defective A-TiO$_{2-x}$(101)/R-TiO$_{2-x}$(110) surfaces ($x=frac{1}{4},frac{1}{8}$) for various coverages. Such a many-body treatment is necessary to correctly describe the anisotropic screening of electron-electron interactions at a photocatalytic interface, and hence obtain accurate interfacial level alignments. The more favorable ground state HOMO level alignment for A-TiO$_2$(101) may explain why the anatase polymorph shows higher photocatalytic activities than the rutile polymorph. Our results indicate that (1) hole trapping is more favored on A-TiO$_2$(101) than R-TiO$_2$(110) and (2) HO@Ti$_{textit{cus}}$ is more photocatalytically active than intact H$_2$O@Ti$_{textit{cus}}$.
The hyperfine structure of the interstitial muonium (Mu) center in rutile (TiO$_2$, weakly $n$-type) has been identified by means of muon spin rotation technique. The angle-resolved hyperfine parameter has a tetragonal anisotropy within the $ab$ plane and axial anisotropy along the $c$ axis, strongly suggesting that Mu simulates the known local structure of interstitial hydrogen (H) located at an off-center position within a channel along $c$ axis, and the electron wave function bound to Mu is highly delocalized (~1.5 nm along $c$ axis, ~0.8 nm for $a$ axis). The ionization energy of Mu ($rightarrow mu^+ + e^-$) due to thermal activation is deduced to be 1.2(4) meV, as is directly inferred from the disappearance of Mu signal above ~8 K. These observations suggest that electronic level associated with Mu (as well as H) is situated near the bottom of the conduction band, serving as a shallow donor state in rutile.
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