A comprehensive phase diagram of lowest-energy structures and compositions of the rutile TiO_2(110) surface in equilibrium with a surrounding gas phase at finite temperatures and pressures has been determined using density functional theory in combination with a thermodynamic formalism. The exchange of oxygen, hydrogen, and water molecules with the gas phase is considered. Particular attention is given to the convergence of all calculations with respect to lateral system size and slab thickness. In addition, the reliability of semilocal density functionals to describing the energetics of the reduced surfaces is critically evaluated. For ambient conditions the surface is found to be fully covered by molecularly adsorbed water. At low coverages, in the limit of single, isolated water molecules, molecular and dissociative adsorption become energetically degenerate. Oxygen vacancies form in strongly reducing, oxygen-poor environments. However, already at slightly more moderate conditions it is shown that removing full TiO_2 units from the surface is thermodynamically preferred. In agreement with recent experimental observations it is furthermore confirmed that even under extremely hydrogen-rich environments the surface cannot be fully hydroxylated, but only a maximum coverage with hydrogen of about 0.6-0.7 monolayer can be reached. Finally, calculations of migration paths strongly suggest that hydrogen prefers to diffuse into the bulk over desorbing from the surface into the gas phase.
Hydroxylation of the rutile TiO$_2$ (110) surface has attracted much attention as the excess unpaired electrons introduced by hydroxyls play a critical role in surface chemistry and photocatalysis process of this material. In this work, based on density functional theory calculations with the Hubbard U correction, the electronic structures of the hydroxylated TiO$_2$ (110) surfaces have been studied. One interesting effect is found that the hydroxylation can elevate band edges of TiO$_2$, and thus can enhance its reducing power for photocatalysis. The underlying physical mechanism for such shi…
The characterization of Pt/TiO2 (Degussa P25) catalyst system using atomic resolution Z-contrast images and electron energy loss spectroscopy in the scanning transmission electron microscope has recently revealed that Pt particles have a strong tendency to nucleate on the rutile phase of TiO2 rather than anatase. Comparative ab initio pseudopotential calculations for Pt and Pt_2 on the stoichiometric and reduced TiO2 surfaces, and oxygen vacancy (V_O) formation energies are performed to address the microscopic origin of this finding. The results, which show that Pt actually binds more strongly…
Nanoporous anatase TiO2 rods and rutile TiO2 chrysanthemums were successfully synthesized via a simple ethylene glycol-mediated synthesis route. Their morphologies, phase compositions and components were characterized by SEM, TEM, Raman and IR, respectively. The results show that a self-assembly growth takes place in the calcination under vacuum, which makes the titanium glycolate rods transform into rutile TiO2/C chrysanthemums rather than anatase TiO2 rods. It also indicates that the carbon plays an important role in the phase transition process which promotes the phase transition to rutile …
The optical properties of thermally annealed TiO2 samples depend on their preparation process, and the TiO2 thin films usually exist in the form of anatase or rutile or the mixture of the two phases. The electronic structures and optical properties of anatase and rutile TiO2 are calculated by means of First-principles generalized gradient approximation (GGA) +U approach. By Introducing the Coulomb interactions on 3d orbitals of Ti atom (Ud) and 2p orbitals of O atom (Up), we can reproduce the experimental values of the band gap. The optical properties of anatase and rutile TiO2 are obtained by…
The electronic properties of pentavalent-ion (Nb$^{5+}$, Ta$^{5+}$, and I$^{5+}$) doped anatase and rutile TiO$_2$ are studied using spin-polarized GGA+\emph{U} calculations. Our calculated results indicate that these two phases of TiO$_2$ exhibit different conductive behavior upon doping. For doped anatase TiO$_2$, some up-spin-polarized Ti 3\emph{d} states lie near the conduction band bottom and cross the Fermi level, showing an \emph{n}-type half-metallic character. For doped rutile TiO$_2$, the Fermi level is pinned between two up-spin-polarized Ti 3\emph{d} gap states, showing an insulati…
Room-temperature ferromagnetism has been recently discovered in Co-doped TiO$_2$ rutile. Our $ab$ $initio$ density-functional theory investigations show that the substitutional Co ions incorporated into TiO$_2$ rutile tend to cluster and then the neighboring interstitial sites become energetically favorable for Co to reside. This suggests that a Co-doped rutile containing only substitutional Co is not an appropriate reference bulk system in derterming the local environment of Co in polycrystalline (Ti,Co)O$_2$ rutile. We also find that the interstitial Co is in the low spin state and destroys …
The relative energies of the low-pressure rutile, anatase, and brookite polymorphs and the high-pressure columbite polymorph of TiO$_2$ have been calculated as a function of temperature using the diffusion quantum Monte Carlo (DMC) method and density functional theory (DFT). The vibrational energies are found to be important on the scale of interest and significant quartic anharmonicity is found in the rutile phase. Static-lattice DFT calculations predict that anatase is lower in energy than rutile, in disagreement with experiment. The accurate description of electronic correlations afforded b…
The availability of low-index rutile TiO2 single crystal substrates with atomically flat surfaces is essential for enabling epitaxial growth of rutile transition metal oxide films. The high surface energy of the rutile (001) surface often leads to surface faceting, which precludes the sputter and annealing treatment commonly used for the preparation of clean and atomically flat TiO2(110) substrate surfaces. In this work, we reveal that stable and atomically flat rutile TiO2(001) surfaces can be prepared with an atomically ordered reconstructed surface already during a furnace annealing treatme…
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 a…
Rutile CrO2 is the most important half-metallic material with nearly 100% spin polarization at the Fermi level, and rutile TiO2 is a wide-gap semiconductor with many applications. Here we show through first-principles investigation that a single-unit-cell CrO2 layer on rutile TiO2 (001) surface is ferromagnetic and semiconductive with a gap of 0.54 eV, and its electronic state transits abruptly to a typical metallic state when an electrical field is applied. Consequently, this makes an interesting electrical switching effect which may be useful in designing spintronic devices.
Present study investigates the photoabsorption properties of single crystal rutile TiO2 (110) surfaces after they have been implanted with low fluence of Cobalt ions. The surfaces, after implantation, demonstrate fabrication of nanostructures and anisotropic nano-ripple patterns. Creation of oxygen vacancies (Ti3+ states) as well as band gap modification for these samples is also observed. Results presented here demonstrate that fabrication of self organized nanostructures and development of oxygen vacancies, upon cobalt implantation, promote the enhancement of photoabsorbance in both UV (2 ti…
We revisited ab initio evaluations of the energy barriers along the possible diffusion paths of the defects in rutile TiO$_2$. By using a method carefully considering the cancellation of the self-interaction, Ti interstitials hopping along $c$-axis are identified as the major diffusion directing to [001] surface. The conclusion is contradicting to any of previous theoretical works, and the discrepancy is explained by the overestimation of the radius of defects due to the poor cancellations in the previous works. The updated prediction here can explain the superior photocatalysis activity in [0…
We use first principles density functional theory to investigate the softening of polar phonon modes in rutile TiO$_2$ under tensile (110)-oriented strain. We show that the system becomes unstable against a ferroelectric distortion with polarization along (110) for experimentally accessible strain values. The resulting polarization, estimated from the Born effective charges, even exceeds the bulk polarization of BaTiO$_3$. Our calculations demonstrate the different strain dependence of polar modes polarized along (110) and (001) directions, and we discuss the possibility of strain engineering …
The ferroelectric trends of rutile (TiO$_2$) in bulk and at the (110) surface are investigated by means of ab initio density functional theory. We discuss the underlying mechanism of the incipient ferroelectric behavior of rutile in terms of Born effective charges, which we decompose in individual contributions by means of maximally localized Wannier functions. We show that a ferroelectric phase can be stabilized for a variety of different lattice distortions which all enlarge the shortest Ti-O distance, even if the longer apical Ti-O bond is simultaneously shortened. At the (110) surface, the…
Magnetic circular dichroism (MCD) of rutile Ti1-xCoxO2-d is systematically examined with various x and d to reveal a phase diagram for the appearance of ferromagnetism at higher carrier concentration and Co content. The phase diagram exactly matches with that determined from anomalous Hall effect (AHE). The magnetic field dependence of MCD also shows good coincidence with those of the magnetization and AHE. The coincidence of these independent measurements strongly suggests single and intrinsic ferromagnetic origin.
We present ab initio time-dependent-density-functional calculations and non-resonant inelastic x-ray scattering measurements of the dynamical structure factor of rutile TiO2. Our calculations are in good agreement with experiment and prove the presence of large crystal local-field effects below the Ti M-edge, which yield a sharp loss peak at 14 eV whose intensity features a remarkable non-monotonic dependence on the wave vector. These effects, which impact the excitation spectra in the oxide more dramatically than in transition metals, provide a signature of the underlying electronic structure…
The results of a comprehensive and systematic ab-initio based ground-state search for the structural arrangement of oxygen vacancies in rutile phase TiO$_2$ provide new insights into their memristive properties. We find that O vacancies tend to form planar arrangements which relax into structures exhibiting metallic behavior. These meta-stable arrangements are structurally akin to, yet distinguishable from the Magnéli phase. They exhibit a more pronounced metallic nature, but are energetically less favorable. Our results confirm a clear structure-property relationship between segregated oxygen…
Band alignment effects of anatase and rutile nanocrystals in TiO$_2$ powders lead to an electron hole separation, increasing the photo catalytic efficiency of these powders. While size effects and types of possible alignments have been extensively studied, the effect of interface geometries of bonded nanocrystal structures on the alignment is poorly understood. In order to allow conclusive studies of a vast variety of bonded systems in different orientations, we have developed a new density functional tight binding parameter set to properly describe quantum confinement in nanocrystals. Applyin…
Transition metal oxides are considered promising thermoelectric materials for harvesting high-temperature waste heat due to their stability, abundance and low toxicity. Despite their typically strong ionic character, they can exhibit surprisingly high power factors $σS^2$, as in n-type SrTiO$_3$ for instance. Thus, it is worth examining other transition metal oxides that might surpass the performances of SrTiO$_3$. This theoretical paper investigates the thermoelectric properties of n-type rutile TiO$_2$, which is the most stable phase of titanium oxide up to 2000 K. The electronic structure i…
We perform full-potential screened-hybrid density-functional theory (DFT) calculations to compare the thermodynamic stability of neutral and charged states of the surface oxygen vacancy at the rutile TiO$_2$(110) surface. Solid-state (QM/MM) embedded-cluster calculations are employed to account for the strong TiO$_2$ polarization response to the charged defect states. Similar to the situation for the bulk O vacancy, the +2 charge state $V_{\rm O}^{2+}$ is found to be energetically by far most stable. Only for Fermi-level positions very close to the conduction band, small polarons may at best b…
We present theoretical evidence for local magnetic moments on Ti3+ ions in oxygen-deficient anatase and rutile TiO2 observed in a recent experiment [S. Zhou, et al., Phys. Rev. B 79, 113201 (2009)]. Results of our first-principles GGA+U calculations reveal that an oxygen vacancy converts two Ti4+ ions to two Ti3+ ions in anatase phase, which results in a local magnetic moment of 1.0 $μ_B$ per Ti3+. The two Ti3+ ions, however, form a stable antiferromagnetic state, and similar antiferromagnetism is also observed in oxygen-deficient rutile phase TiO2. The calculated results are in good agreement…
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 adsorbate's highest occupied molecular orbital (HOMO) levels relative to the substrate's 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 projec…
Polaron formation plays a major role in determining the structural, electrical and chemical properties of ionic crystals. Using a combination of first principles calculations and scanning tunneling microscpoy/atomic force microscopy (STM/AFM), we analyze the interaction of polarons with CO molecules adsorbed on the rutile TiO$_2$(110) surface. Adsorbed CO shows attractive coupling with polarons in the surface layer, and repulsive interaction with polarons in the subsurface layer. As a result, CO adsorption depends on the reduction state of the sample. For slightly reduced surfaces, many adsorp…
Phase transition from anatase to rutile for the 70nm TiO2 crystallite has been investigated by annealing at different temperatures followed by TDPAC measurement of these TiO2 crystallites adsorbed with 181Hf tracer. The width of the peaks in XRD spectra for TiO2 crystallites annealed at different temperatures indicates the growth of the crystallites with temperature. The samples annealed upto 823K for 4hrs showed no phase transition, except the growth of the crystallites. However, it showed phase transition at the same temperature (823K), when annealed for longer duration. Annealing for shorte…
We perform first-principles calculations of the quasiparticle defect states, charge transition levels, and formation energies of oxygen vacancies in rutile titanium dioxide. The calculations are done within the recently developed combined DFT+GW formalism, including the necessary electrostatic corrections for the supercells with charged defects. We find the oxygen vacancy to be a negative U defect, where U is the defect electron addition energy. For the values of Fermi level below 2.8 eV (relative to the valence band maximum) we find the +2 charge state of the vacancy to be the most stable, wh…
The lattice dynamics of TiO$_2$ in the rutile crystal structure was studied by a combination of thermal diffuse scattering, inelastic x-ray scattering and density functional perturbation theory. We experimentally confirm the existence of an anomalous soft transverse acoustic mode with energy minimum at q = (1/2 1/2 1/4). The phonon energy landscape of this particular branch is reported and compared to the calculation. The harmonic calculation underestimates the phonon energies but despite this the shape of both the energy landscape and the scattering intensities are well reproduced. We find a …
Water absorption and dissociation processes on pristine low-index TiO$_2$ interfaces are important but poorly understood outside the well-studied anatase (101) and rutile (110). To understand these, we construct three sets of machine learning potentials that are simultaneously applicable to various TiO$_2$ surfaces, based on three density-functional-theory approximations. We compute the water dissociation free energies on seven pristine TiO$_2$ surfaces, and predict that anatase (100), anatase (110), rutile (001), and rutile (011) surfaces favor water dissociation, anatase (101) and rutile (10…
We calculate the lattice dielectric function of strongly anharmonic rutile $\mathrm{TiO}_2$ from ab initio anharmonic lattice dynamics methods. Since an accurate calculation of the $Γ$ point phonons is essential for determining optical properties, we employ the modified self-consistent approach, including third-order anharmonicity as well as fourth-order anharmonicity. The resulting optical phonon frequencies and linewidths at the $Γ$ point much better agree with experimental measurements than those from a perturbative approach. We show that the four-phonon scattering process contributes as mu…
A first-principles atomic orbital-based electronic structure method is used to investigate the low index surfaces of rutile Titanium Dioxide. The method is relatively cheap in computational terms, making it attractive for the study of oxide surfaces, many of which undergo large reconstructions, and may be governed by the presence of Oxygen vacancy defects. Calculated surface charge densities are presented for low-index surfaces of TiO$_2$, and the relation of these results to experimental STM images is discussed. Atomic resolution images at these surfaces tend to be produced at positive bias, …
We present a detailed investigation of the structure and activity of extended defects namely monoatomic steps on (1x1)-TiO2(110). Specifically, the two most stable <001> and <1-11> step edges are considered. Employing an automated genetic algorithm that samples a large number of candidates for each step edge, more stable, reconstructed structures were found for the <1-11> step edge, while the bulk truncated structures were recovered for the <001> step edge. We demonstrate how oxygen vacancies along these defects have lower formation energies than on flat terraces and how water and methanol mol…
A combination of Scanning Tunneling Microscopy/Spectroscopy and Density Functional Theory (DFT+U) is used to characterize excess electrons in TiO$_2$ rutile and anatase, two prototypical materials with identical chemical composition but different crystal lattices. In rutile, excess electrons can localize at any lattice Ti atom, forming a small polaron, which can easily hop to neighboring sites. In contrast, electrons in anatase prefer a free-carrier state, and can only be trapped near oxygen vacancies or form shallow donor states bound to Nb dopants. The present study conclusively explains the…
Defects in the surface region of a reducible oxide, as TiO2, have a profound effect on applications, while their nature is very much influenced by the possibility of small polaron formation. Here, we probe rutile (110) and anatase (101) single crystals via high-resolution ultraviolet photoelectron spectroscopy and resolve multiple components of the well-known defect state in the band gap. In rutile, we find two at VBM+2.1 eV and VBM+1.4 eV, which we assign to subsurface polaron traps and vacancy-bound states, respectively, confirming the predicted partial suppression of polaron formation at hi…
In this paper, I demonstrate a density functional theory plus dynamical mean field theory study on the electronic properties of doped $TiO_2$ rutile as well as another tetragonal phase anatase with oxygen vacancy. The density of states and optical properties have been obtained from the electronic structure applying screened hybrid exchange correlation density functionals. All the single-particle excitations are treated within the dynamical mean field theory for independent quasiparticles. For optical properties, excitations are considered by solving the Bethe-Salpeter equation for Coulomb corr…
This topical review focuses on the recently active debate on the band alignment between two polymorphs of TiO$_2$, rutile and anatase. A summary is given to the popular methods for measurement and calculation of band alignment between materials. We point out, through examination of recently experimental and theoretical reports, that the outstanding discrepancy in the band alignment between two TiO$_2$ phases is attributed to factors that influence band alignment rather than needs a definite answer of which band alignment is right. According to an important factor, the presence of an interface,…
In a quest of enriching the area of d0 magnetism in oxide materials, we have undertaken to study Mg-doped TiO2 compounds. The Ti1-xMgxO2 (x=0, 0.02, 0.04 and 0.06) nanoparticles were prepared by solid-state reaction route. The X-ray diffractions (XRD) patterns of these samples indicate single phase of tetragonal rutile-structure of TiO2. The refinement of the XRD patterns reveals no change in the crystallographic lattice parameters in comparison to pure TiO2 upon Mg doping and it indicates that Mg2+ ions do not enter core grains and form core/shell structure. SEM observations reveal the unifor…
Adsorption of Fe on the rutile (110)-surface is investigated by means of {\it ab initio} density functional theory calculations. We discuss the deposition of single Fe atoms, an increasing Fe coverage, as well as the adsorption of small Fe clusters. It is shown that the different interface structures found in experiment can be understood in terms of the adsorption of the Fe atoms landing first on the rutile surface. On the one hand, strong interface bonds form if single Fe atoms are deposited. On the other hand, the Fe-Fe bonds in deposited Fe clusters lead to a three-dimensional growth mode. …
We report on structural, magnetic and electronic properties of Co-implanted TiO2 rutile single crystals for different implantation doses. Strong ferromagnetism at room temperature and above is observed in TiO2 rutile plates after cobalt ion implantation, with magnetic parameters depending on the cobalt implantation dose. While the structural data indicate the presence of metallic cobalt clusters, the multiplet structure of the Co L3 edge in the XAS spectra gives clear evidence for a substitutional Co 2+ state. The detailed analysis of the structural and magnetic properties indicates that there…
Brookite TiO2 as an active photocatalyst for photoconversion of plastic wastes to acetic acid and simultaneous hydrogen production: Comparison with anatase and rutile
Pure rutile Co-doped TiO$_2$ films were fabricated successfully by the conventional pulsed laser deposition technique on silicon substrates from a ceramic target. Under the right fabrication conditions, Co concentration in the films could be almost the same as in the synthesized target, and films under various conditions all are ferromagnetic well above room temperature. Even though Rutherford backscattering spectroscopy measurements show that Co atoms seem to be mostly localized near the surface of the films and less exist in deeper levels, other experimental evidences show that the ferromagn…
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 ($\rig…
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 $α$-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 tempe…
A comparative first principles pseudopotential study of the adsorption and migration profiles of single Pt and Au atoms on the stoichiometric and reduced TiO2 rutile (110) surfaces is presented. Pt and Au behave similarly with respect to (i) most favorable adsorption sites, which are found to be the hollow and substitutional sites on the stoichiometric and reduced surfaces, respectively, (ii) the large increase in their binding energy (by ~1.7 eV) when the surface is reduced, and (iii) their low migration barrier near 0.15 eV on the stoichiometric surface. Pt, on the other hand, binds more str…
Although the rutile structure of TiO$_2$ is stable at high temperatures, the conventional quasiharmonic approximation predicts that several acoustic phonons decrease anomalously to zero frequency with thermal expansion, incorrectly predicting a structural collapse at temperatures well below 1000\,K. Inelastic neutron scattering was used to measure the temperature dependence of the phonon density of states (DOS) of rutile TiO$_2$ from 300 to 1373\,K. Surprisingly, these anomalous acoustic phonons were found to increase in frequency with temperature. First-principles calculations showed that wit…
Surface fluorination of TiO$_2$ (F-TiO$_2$) has complicate photocatalytic behavior in degradation of organic compounds. This work attempts to establish an elegant scenario based on the band model to understand this behavior. Density functional theory (DFT) calculations show that fluorination of the rutile TiO$_2$(110) surface (F-TiO$_2$${110}$) results in the falling of band edges. The falling of valence band edge (VBE) facilitates production of free $\cdot$OH radicals, whereas the falling of conduction band edge (CBE) lowers the reducing power of photo-electrons and inhibits reductive reactio…
The formation energies of the oxygen vacancy and titanium interstitial in rutile TiO2 were calculated by the screened exchange (sX) hybrid density functional method, which gives a band gap of 3.1 eV, close to the experimental value. The O vacancy gives rise to a gap state lying 0.7 eV below the conduction band edge, whose charge density is localised around the two of three Ti atoms next to the vacancy. The Ti interstitial generates four defect states in the gap, whose unpaired electrons lie on the interstitial and the adjacent Ti 3d orbitals. The formation energy for the neutral O vacancy is 1…
Ab-initio density functional theory (DFT) calculations of the relative stability of anatase and rutile polymorphs of TiO2 were carried using all-electron atomic orbitals methods with local density approximation (LDA). The rutile phase exhibited a moderate margin of stability of ~ 3 meV relative to the anatase phase in pristine material. From computational analysis of the formation energies of Si, Al, Fe and F dopants of various charge states across different Fermi level energies in anatase and in rutile, it was found that the cationic dopants are most stable in Ti substitutional lattice positi…
Far from being conclusively understood, the reactive interaction of water with rutile does still present a challenge to atomistic modelling techniques rooted on quantum mechanics. We show that static geometries of stoichiometric TiO$_2$/water interfaces can be described well by Density Functional Tight Binding (DFTB). However, this method needs further improvements to reproduce the low dissociation propensity of H$_2$O after adsorption predicted by Density Functional Theory (DFT). A reliable description of the surface reactivity of water is fundamental to investigate the non-stoichiometric rec…
Based on a dipolar-elastic model for oxygen vacancies on rutile (110), we evaluated analytically the overall energy of a periodic array of two vacancies and extracted the interaction parameters from total-energy density functional theory (DFT) calculations. Our calculations show that the dipole model holds for next-nearest neighbor vacancies and beyond. The elastic-dipolar interaction vanishes for adjacent vacancies, but they still experience an electrostatic repulsion. The proposed interaction model predicts a vacancy separation distribution that agrees well with that determined in our ultra-…
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 $\langle 001\rangle$ ($\hat{c}$) 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 …
Black TiO2 with/without noble metal has been proposed for visible photocatalyst, still leaving poor catalyst efficiency. Alternatively, phase-mixed TiO2 such as anatase and rutile has been commonly used for visible catalysts with the inevitable inclusion of noble metal. Here, we perform a noble metal-free visible photocatalyst blue TiO2 with type-II band-aligned ordered anatase/disordered rutile structure, via phase-selective reduction with alkali metals. The changed band alignment in this heterostructure was identified by absorption and ultraviolet photoemission spectroscopy, which was furthe…
Electron $g$-value comparison of paramagnetic muonium and hydrogen centers in rutile TiO$_2$
Advanced Science Research Center, Japan Atomic Energy Agency（日本原子能机构先进科学研究中心）；Department of Physics, Institute of Science Tokyo（东京科学大学物理系）；Institute of Materials Structure Science, High Energy Accelerator Research Organization (KEK)（高能加速器研究机构物质结构科学研究所）
We study the electronic and magnetic structure of carbon and nitrogen impurities and interstitials in rutile TiO${_2}$. To this end we perform \textit{ab-initio} calculations of a 48-atom supercell employing the VASP code. In order to obtain a realistic description of the electronic and magnetic structure, exchange and correlation are treated with the HSE06 hybrid functional. Both, atomic positions and cell dimensions are fully relaxed. Substitutional carbon and nitrogen are found to have a magnetic moment of 2 and 1$μ{_B}$, respectively, with a tendency for anti-ferromagnetic long range order…
The adsorption profiles and electronic structures of Pt$_n$ (n = 1--4) clusters on stoichiometric, reduced and reconstructed rutile TiO$_2$(110) surfaces were systematically studied using on site d-d Coulomb interaction corrected hybrid density functional theory calculations. The atomic structure of small Pt cluster adsorbates mainly depend on the stoichiometry of the corresponding titania support. The cluster shapes on the bulk terminated ideal surface look like their gas phase low energy structures. However, for instance, they get significantly distorted on the reduced surfaces with increasi…
Quasiparticle excitation energies and optical properties of TiO$_{2}$ in the rutile and anatase structures are calculated using many-body perturbation theory methods. Calculations are performed for a frozen crystal lattice; electron-phonon coupling is not explicitly considered. In the GW method, several approximations are compared and it is found that inclusion of the full frequency dependence as well as explicit treatment of the Ti semicore states are essential for accurate calculation of the quasiparticle energy band gap. The calculated quasiparticle energies are in good agreement with avail…
Oxygen-deficient TiO$_2$ in the rutile structure as well as the Ti$_3$O$_5$ Magn{é}li phase is investigated within the charge self-consistent combination of density functional theory (DFT) with dynamical mean-field theory (DMFT). It is shown that an isolated oxygen vacancy (V$_{\rm O}$) in titanium dioxide is not sufficient to metallize the system at low temperatures. In a semiconducting phase, an in-gap state is identified at $\varepsilon_{\rm IG}^{\hfill}\sim -0.75\,$eV\, in excellent agreement with experimental data. Band-like impurity levels, resulting from a threefold V$_{\rm O}$-Ti coord…
Titanium dioxide (TiO$_2$) presents a long-standing challenge for approximate Kohn-Sham density-functional theory (KS-DFT), as well as to its Hubbard-corrected extension, DFT+$U$. We find that a previously proposed extension of first-principles DFT+$U$ to incorporate a Hund's $J$ correction, termed DFT+$U$+$J$, in combination with parameters calculated using a recently proposed linear-response theory, predicts fundamental band-gaps accurate to well within the experimental uncertainty in rutile and anatase TiO$_2$. Our approach builds upon established findings that Hubbard correction to both ti…
We report measurements of the dynamics of isolated $^{8}$Li$^{+}$ in single crystal rutile TiO$_{2}$ using $β$-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 10…
