Q. M. Hu

The effect of electron localization on the electronic structure and migration barrier of oxygen vacancies in rutile

By applying the on-site Coulomb interaction (Hubbard term U) to the Ti d orbital, the influence of electron localization on the electronic structure as well as the transport of oxygen vacancies (VO) in rutile was investigated. With U = 4.5 eV, the positions of defect states in the bandgap were correctly reproduced. The unbonded electrons generated by taking out one neutral oxygen atom are spin parallel and mainly localized on the Ti atoms near VO, giving rise to a magnetic moment of 2 μB, in agreement with the experimental finding. With regard to the migration barrier of VO, surprisingly, we found that U = 4.5 eV only changed the value of the energy barrier by ±0.15 eV, depending on the diffusion path. The most probable diffusion path (along [110]) is the same as that calculated by using the traditional GGA functional. To validate the GGA + U method itself, a hybrid functional with a smaller supercell was used, and the trend of the more probable diffusion path was not changed. In this regard, the traditional GGA functional might still be reliable in the study of intrinsic-defect transportation in rutile. Analyzing the atomic distortion and density of states of the transition states for different diffusion paths, we found that the anisotropy of the diffusion could be rationalized according to the various atomic relaxations and the different positions of the valence bands relative to the Fermi level of the transition states.

Binding of an oxide layer to a metal: The Case of Ti(101̅0)/TiO2(100)

We study the chemical nature of the bonding of an oxide layer to the parent metal. In order to disentangle chemical effects from strain/misfit, the Ti(1012(100) interface has been chosen. We use the density functional pseudopotential method which gives good agreement with experiment for known properties of bulk and surface Ti and TiO2. Two geometries, a film-like model (with free surface in the structure) and a bulk-like model (with no free surface in the structure), are used to simulate the interface, in each case with different terminations of Ti and TiO2. For the single- oxygen interfaces, the interface energies obtained using these two models agree with each other; however, for the double-oxygen ones, the relative stability is quite different. The disturbance to the electronic structure is confined within a few atomic layers of the interface. The interfacial bonding is mainly ionic, and surprisingly, there is more charge transfer from Ti to O in the interface than in the bulk. In consequence, the Ti/TiO2 interface has stronger binding than the bulk of either material. This helps to explain why the oxide forms a stable, protective layer on Ti and Ti alloys.

Theoretical study of oxygen sorption and diffusion in the volume and on the surface of a γ-TiAl alloy

The oxygen sorption on the low-index (001), (100), and (110) surfaces of a γ-TiAl alloy is studied by the pseudopotential method with the generalized gradient approximation for the exchange-correlation functional. The most preferred sites for oxygen sorption in the bulk and on the surface of the alloy are determined. The titanium-rich octahedral site is shown to be preferred for oxygen sorption in the bulk material. The effect of the oxygen concentration on the atomic and electronic structures of the stoichiometric TiAl(100) surface is studied. It is shown that, at the first stage of oxidation, oxygen prefers to form bonds with titanium. The energy barriers for oxygen diffusion on the stoichiometric (100) surface and in the bulk of the material are calculated. The energy barriers are shown to depend substantially on the local environments of oxygen and to increase during diffusion from titanium-rich sites. The most possible mechanism of oxygen diffusion from the (100) surface to the bulk of the material is oxygen migration through tetrahedral sites.

First-principles investigations of ordering in binary α-Ti solid solutions

The ordering tendency in binary f-Ti solid solution containing 3sp or 4sp simple-metal (SM) or 3d transition-metal (TM) solute is investigated systematically by the linear muffin-tin orbital (LMTO) method within the atomic sphere approximation (ASA). We demonstrated that the effective pairwise interaction (EPI) energy in a solid solution is equal to half the solute-solute interaction energies and can be evaluated by a supercell total energy approach. The calculations of EPI energy both with and without volume relaxation of the supercells and local density of states (LDOS) show that the EPI energies of Ti-SM and Ti-TM solutions are dominated by different factors. For Ti-SM solutions, the EPI energies are of large absolute values with a negative sign, indicating strong ordering tendency in these solutions. The volume relaxation does not alter the EPI energy substantially. The calculated LDOS shows that the ordering tendency in Ti-SM solutions may be related to the hybridization between the electrons of the SM atoms when they are close to each other. For most Ti-TM solutions, if calculated without relaxation, the absolute EPI energies are very small; however, if calculated with relaxation, they are of relatively large positive values, indicating a clustering tendency in these solutions. By combining the calculated EPI energy and Flinns model for short-range order (SRO) strengthening, the increase in critical shear stress sro due to SRO is estimated for Ti-SM alloys, and the results qualitatively agree with experiment.

Adsorption of oxygen on low-index surfaces of the TiAl3 alloy

Method of the projector augmented waves in the plane-wave basis within the generalized-gradient approximation for the exchange-correlation functional has been used to study oxygen adsorption on (001), (100), and (110) low-index surfaces of the TiAl3 alloy. It has been established that the sites that are most energetically preferred for the adsorption of oxygen are hollow (H) positions on the (001) surface and bridge (B) positions on the (110) and (100) surfaces. Structural and electronic factors that define their energy preference have been discussed. Changes in the atomic and electronic structure of subsurface layers that occur as the oxygen concentration increases to three monolayers have been analyzed. It has been shown that the formation of chemical bonds of oxygen with both components of the alloy leads to the appearance of states that are split-off from the bottoms of their valence bands, which is accompanied by the formation of a forbidden gap at the Fermi level and by a weakening of the Ti–Al metallic bonds in the alloy. On the Al-terminated (001) and (110) surfaces, the oxidation of aluminum dominates over that of titanium. On the whole, the binding energy of oxygen on the low-index surfaces with a mixed termination is higher than that at the aluminum-terminated surface. The calculation of the diffusion of oxygen in the TiAl3 alloy has shown that the lowest barriers correspond to the diffusion between tetrahedral positions in the (001) plane; the diffusion of oxygen in the [001] direction occurs through octahedral and tetrahedral positions. An increase in the concentration of aluminum in the alloy favors a reduction in the height of the energy barriers as compared to the corresponding barriers in the γ-TiAl alloy.

Trapping of interstitial defects: filling the gap between the experimental measurements and DFT calculations

We show that any impurity will slow the diffusion of oxygen in Nb. Using a first-principles plane-wave pseudopotential method and the supercell model, we calculated the interaction energies between substitutional atoms (SA) (X = Ti, V, Ta, Zr, and Hf) and interstitial oxygen in a Nb matrix. All impurities act as traps for oxygen: undersized SA (Ti and V) have strongest binding at the nearest octahedral interstice, while for oversized SA (Zr and Hf), the strongest trapping site is the second-nearest octahedral interstice. We evaluated the diffusion coefficients of O in the Nb-X alloys using kinetic Monte Carlo (KMC) modeling based in the transition state theory, using our calculated oxygen migration energies. From this, the effective (average) X-O interaction energies were extracted using the Oriani model (Oriani 1970 Acta Metall. 18 147-57). The effective X-O interaction energies are close to the strongest interaction energies between X and O obtained from the direct supercell calculations. The phenomenological effective diffusion barrier obtained from the KMC modeling is close to the energy difference between the most stable configuration and the highest saddle point along the diffusion path. Both results demonstrate that the weaker trapping site has negligible influence on the diffusion of O.

Origin of the abnormal diffusion of transition metal atoms in rutile

Diffusion of dopant in rutile is the fundamental process that determines the performance of many devices in which rutile is used. The diffusion behavior is known to be highly sample-dependent, but the reasons for this are less well understood. Here, rutile is studied by using first-principles calculations, in order to unravel the microscopic origins of the diverse diffusion behaviors for different doping elements. Anomalous diffusion behavior in the open channel along the [001] direction is found: larger atoms including Sc and Zr have lower energy barrier for diffusion via interstitial mechanism, apparently contradicting their known slow diffusion rate. To resolve this, we present an alternate model for the overall diffusion rate of the large-size dopants in rutile, showing that parallel to the [001] channel, it is limited by the formation of the interstitial states, whereas in the direction perpendicular to [001], it proceeds via a kick-out mechanism. By contrast, Co and Ni prefer to stay in the interstitial site of rutile, and have conventional diffusion with a very small migration barrier in the [001] channel. This leads to highly anisotropic and fast diffusion. The diffusion mechanisms found in the present study can explain the diffusion data measured by experiments.

Structure of Bergman-type W-TiZrNi approximants to quasicrystal, analyzed by lattice inversion method

The combined interatomic pair potentials of TiZrNi, including Morse and Inversion Gaussian, are successfully built by the lattice inversion method. Some experimental controversies on atomic occupancies of sites 6-8 in W-TiZrNi are analyzed and settled with these inverted potentials. According to the characteristics of composition and site preference occupancy of W-TiZrNi, two stable structural models of W-TiZrNi are proposed and the possibilities are partly confirmed by experimental data. The stabilities of W-TiZrNi mostly result from the contribution of Zr atoms to the phonon densities of states in lower frequencies.