Energetics Of Point Defects Research Articles

Energetics of charged point defects in rutile TiO 2 by density functional theory

The defect formation energies of all possible charge states of point defects in TiO 2, including titanium interstitials, titanium vacancies and oxygen vacancies, are calculated in the phase space of temperature, oxygen partial pressure and Fermi level by combining density functional theory (DFT) and thermodynamic calculations. The point defect phase diagram illustrates that fully charged defects dominate in most regimes. The calculations not only give reasonable defect formation energies compared with prior experimental measurements, but also predict n-type TiO 2 at high T and low P O 2 , and p-type TiO 2 at low T and high P O 2 , which agrees well with experimental data. In addition, we evaluate methods for correcting the effects of artificial electrostatic interactions caused by periodic boundary conditions in the DFT calculations, including the electrostatic potential alignment correction (Δ V correction) and the Makov–Payne correction.

Simulating radiation damage in δ-plutonium

Radiation events in δ-Pu (fcc) have been simulated in an attempt to understand the fundamental mechanisms that contribute to the Pu ageing process. The Pu interactions are modelled using a potential based on the modified embedded atom method (MEAM). The energetics of point defects have been investigated using static calculations together with molecular dynamics (MD) to simulate radiation events. All MD simulations were carried out with Pu initially in the face-centred-cubic (fcc) structure, although this is not the lowest energy configuration for the pure metal.The point defect study suggests that the mono-vacancy has the lowest formation energy (0.46eV), with interstitial defects favouring the 〈100〉 – split orientation over occupation of the native fcc octahedral site. Displacement threshold energy calculations at room temperature give a minimum value of between 5 and 6eV, increasing to 8–14eV along the major crystallographic directions.Low energy collision cascades, initiated with energies in the range of 0.4–1keV, show that the cascades form in a similar manner to other fcc metals with a vacancy rich zone at the cascade core, surrounded by isolated interstitial defects. Higher energy cascades show similar features but with occasional channelling of energetic atoms and sub-cascade branching which significantly reduces defect production. A common trait observed across all the cascades was the relatively slow annealing period, compared to cascades in other fcc metals, with simulations at energies above 5keV requiring many 10’s of picoseconds before the ballistic phase was completed.

Energetics of defects in β-SiC under irradiation

Energetics of point defects in β-SiC have been investigated using atomistic calculations with the empirical interatomic potential, where a simple static relaxation method and a dynamic relaxation method are separately employed. In addition to formation energy of isolated silicon interstitials, migration energies for interstitials and vacancies obtained from the dynamic relaxation method are much lower than those obtained from the simple static relaxation method. It indicates that the dynamic relaxation method possibly can provide more relaxed defect configuration than the simple static relaxation method.

Intercalation of Al into MC ( M = Ti, V, Cr)

The energetics of point defects and twins in MC x ( x < 1, M = Ti, V, Cr, space group F m 3 ¯ m ) was studied using density functional theory. Our goal is to contribute towards understanding the underlying atomic mechanisms enabling the Al intercalation into MC x . As the valence electron concentration is increased by substituting Ti in TiC x with V and further with Cr, the energy of formation for C vacancies is decreased. This may be understood based on the electronic structure. Upon increasing the valence electron concentration, the bonding becomes less ionic and more covalent. In covalent crystals, directional bonding may be rearranged and local relaxation is observed upon vacancy creation, while this gives rise to repulsive Coulomb forces in ionic crystals, and hence the energy of formation is expected to decrease as the valence electron concentration of M is increased. The difference between the energy of formation for an Al substitution at a C site and a C vacancy, the migration energy for Al, the point defect ordering energy, and the twin boundary energy may be overcome, for instance, during vapor phase condensation. These results may be of general relevance for the formation of MAX phases (space group P6 3/ mmc) at low temperatures.

Energetics of intrinsic point defects in uranium dioxide from electronic-structure calculations

The stability range of intrinsic point defects in uranium dioxide is determined as a function of temperature, oxygen partial pressure, and non-stoichiometry. The computational approach integrates high accuracy ab initio electronic-structure calculations and thermodynamic analysis supported by experimental data. In particular, the density functional theory calculations are performed at the level of the spin polarized, generalized gradient approximation and includes the Hubbard U term; as a result they predict the correct anti-ferromagnetic insulating ground state of uranium oxide. The thermodynamic calculations enable the effects of system temperature and partial pressure of oxygen on defect formation energy to be determined. The predicted equilibrium properties and defect formation energies for neutral defect complexes match trends in the experimental literature quite well. In contrast, the predicted values for charged complexes are lower than the measured values. The calculations predict that the formation of oxygen interstitials becomes increasingly difficult as higher temperatures and reducing conditions are approached.

First-principles study of site occupancy of dilute 3d, 4d and 5d transition metal solutes in L1 0 TiAl

Using a statistical-mechanical Wagner–Schottky model parametrized by first-principles density-functional (DFT-GGA) calculations on 32-atom supercells, we predict the lattice site occupancy of 3d (Ti–Cu), 4d (Zr–Ag) and 5d (Hf–Au) transition-metal elements in L1 0 TiAl intermetallic compound as a function of both alloy composition and temperature. The effects of local atomic relaxations, anisotropic lattice distortions, as well as magnetism on point defect energetics are fully taken into account. Our calculations show that, at all alloy compositions and temperatures, Zr and Hf consistently show a preference for the Ti sublattice, while Co, Ru, Rh, Pd, Ag, Re, Os, Ir, Pt and Au consistently show a preference for the Al sublattice. In contrast, the site preference of V, Cr, Mn, Fe, Ni, Cu, Nb, Mo, Tc, Ta and W strongly depend on both alloy stoichiometry and temperature. Our calculated results compare favorably with the existing theoretical and experimental studies in the literature.

Energetics of point defects in TiC

Density functional theory was used to evaluate the energetics of point defects in TiC x ( x < 1): C vacancies and Al substitution at a C site. Our ambition is to contribute towards understanding the underlying atomic mechanisms enabling the Al intercalation into TiC x and the subsequent formation of Ti 3AlC 2. The difference between the energy of formation for an Al substitution at a C site and a bulk C vacancy is 0.224 eV. Furthermore, only 49 meV/vacancy is required to order the existing bulk C vacancies. Surface effects were also considered: the energy of formation for Al on TiC(1 0 0) at a vacant surface C site is smaller by 2.779 eV than in the case of the C surface vacancy, indicating that Al is likely to be incorporated. Based on these energy differences, it is reasonable to assume that Ti 3AlC 2 is formed by Al surface ingress into TiC x and that vacancy ordering takes place.

Electronic, Energetic, and Chemical Effects of Intrinsic Defects and Fe-Doping of CoAl2O4: A DFT+UStudy

The spinel cobalt aluminate has gained interest as a potential photoelectrochemical catalyst for the renewable production of hydrogen. Using band structure theory, we determine the energetics of possible intrinsic point defects in spinel CoAl2O4 and analyze their effect on its electronic and chemical properties. Extrinsic Fe-doping is also examined. Cation vacancies are found to be shallow acceptors, but their formation energy is sensitive to the growth conditions; an oxygen rich environment is required to enhance the p-type conductivity. Fe is an isovalent substituent on the Co (Al) site, exhibiting a preference for octahedral coordination, and forms a deep donor (acceptor) level near the center of the band gap, corresponding to a Fe(II) to Fe(III) transition.

Diffusion in a Single Crystal within a Stressed Environment

The energetics of point defects and diffusion in a single crystal is analyzed with respect to stress in overlying or encapsulating layers. The resulting theory subsumes previous formulations of pressure and stress effects on diffusion. A key prediction is that stress on the overlayer side of the crystal boundary perturbs point defect concentrations in the underlying crystal. The effect can occur without significant strain in the crystal itself. The theory is compared with available published data on diffusion in silicon under thin strained overlayers.

Correlation effects and energetics of point defects in uranium dioxide: a first principle investigation

Density functional (DFT) calculations have been used to investigate the stability of point defects in uranium dioxide. Correlation effects are taken into account within the DFT + U approach as implemented in the Vienna ab initio simulation package (VASP). More particularly, the formation energies of both intrinsic and extrinsic point defects, i.e. vacancies, interstitials, Frenkel pairs and Schottky trio defects, are calculated. Our results are compared with available experimental data and are also discussed in relation to previous calculations based on conventional functionals, such as the local spin-density approximation and generalized gradient approximations.

Defective Structure of BN Nanotubes: From Single Vacancies to Dislocation Lines

A combination of electron microscopy and theoretical calculations provides new insights into the structure, electronics, and energetics of point defects and vacancy lines in BN single-wall nanotubes (SWNT). We show that the point defects forming under electron irradiation in the BN SWNTs are primarily divacancies. Due to the partially ionic character of the BN bonding, divacancies behave like an associated Schottky pair, with a dissociation energy of around 8 eV. Clustering of multiple vacancies is energetically favorable and leads to extended defects which locally change the nanotube diameter and chirality. Nevertheless these defects do not alter significantly the band gap energy, and all of them have electronic structure similar to that of BN divacancies. We thus conclude that under irradiation BN SWNT may have a very stable alteration of its electronic and optical properties.

Mechanism of oxide deformation during silicon thermal oxidation

Mechanisms of oxide deformation during silicon thermal oxidation are studied by investigating the energetics of intrinsic point defects in the bulk silicon oxide and in the oxide film of the silicon oxide/silicon interface with first-principles calculations. The results suggest that the SiO 2 and the SiO interstitials are thought to relate to the deformation of the silicon oxide. Especially, during the silicon oxidation, the SiO interstitial is suggested to be important because it can be formed in the oxide film neighboring to the interface and can enhance the deformation of the oxide films.

Point defects and mechanical behavior of titanium alloys and intermetallic compounds

First principles calculations were carried out to investigate the energetics of point defects, including solute atoms, vacancies, and antisite defects, in titanium solid solution and intermetallics. Their influence on the mechanical behavior of titanium alloys and intermetallic compounds were discussed. The self consistent procedure proposed by the authors was applied to TiAl intermetallic compounds. The ordering parameter was redefined to include the contribution of vacancies to the disordering of intermetallic compounds, so that the new approach can be applied to both strongly and weakly ordered compounds. Concentrations of point defects of various kinds can be estimated for intermetallics of different composition at different temperature. The solid solution strengthening of alloying elements through short range ordering was studied for titanium alloys and the solid solution hardening rate was estimated for various alloying elements. The solute-vacancy interaction in titanium alloys was calculated and its influence on the diffusion and creep behavior was discussed. These calculations provided some useful information for the selection of alloying elements in designing new titanium alloys.

Schottky defect formation energy in MgO calculated by diffusion Monte Carlo

The energetics of point defects in oxide materials plays a major role in determining their high-temperature properties, but experimental measurements are difficult, and calculations based on density functional theory (DFT) are not necessarily reliable. We report quantum Monte Carlo calculations of the formation energy ${E}_{\mathrm{S}}$ of Schottky defects in MgO, which demonstrate the feasibility of using this approach to overcome the deficiencies of DFT. In order to investigate system-size errors, we also report DFT calculations of ${E}_{\mathrm{S}}$ on repeating cells of up to $\ensuremath{\sim}1000$ atoms, which indicate that QMC calculations on systems of only 54 atoms should yield high precision. The DFT calculations also provide the relaxed structures used in the variational and diffusion Monte Carlo calculations. For MgO, we find ${E}_{\mathrm{S}}$ to be in close agreement with results from DFT and from model interaction potentials, and consistent with the scattered experimental values. The prospects for applying the same approach to transition metal oxides such as FeO are indicated.

The effects of space charge, dopants, and strain fields on surfaces and grain boundaries inYBCO compounds

Statistical thermodynamical and kinetically-limited models are applied to study the origin andevolution of space charges and band-bending effects at low-angle [001] tilt grain boundaries inYBa2Cu3O7 and the effects of Ca doping upon them. Atomistic simulations, using shell models ofinteratomic forces, are used to calculate the energetics of various relevant point defects. Theintrinsic space charge profiles at ideal surfaces are calculated for two limits of oxygen contents,i.e. YBa2Cu3O6 andYBa2Cu3O7. At one limit,O6, the system is aninsulator, while at O7 it is a metal. This is analogous to the intrinsic and doping cases of semiconductors. The siteselections for doping calcium and creating holes are also investigated by calculating theheat of solution. In a continuum treatment, the volume of formation of doping calcium atY-sites is computed. It is then applied to study the segregation of calcium ions to grainboundaries in the Y-123 compound. The influences of the segregation of calcium ions onspace charge profiles are finally studied to provide one guide for understanding theimprovement of transport properties by doping calcium at grain boundaries in the Y-123compound.

Energetics of native point defects in cubic silicon carbide

In this work we present a detailed investigation of native point defects energetics in cubic SiC, using state-of-the-art first principles computational method. We find that, the carbon vacancy is the dominant defect in p-type SiC, regardless the growth conditions. Silicon and carbon antisites are the most common defects in n-type material in Si-rich and C-rich conditions respectively. Interstitial defects and silicon vacancy are less favorite from the energetic point of view. The silicon vacancy tends to transform into a carbon vacancy-antisite complex and the carbon interstitial atom prefers to pair to a carbon antisite. The dumbbell structure is the lowest-energy configuration for the isolated carbon interstitial defect, and the tetrahedral interstitial silicon is a stable structure in p-type and intrinsic conditions, while in n-type material the dumbbell configuration is the stable one. Our results suggest that, in samples grown in Si-rich stoichiometric conditions, native defects are a source of n-doping and of compositional unbalance of nominally intrinsic SiC, in accord with experimental evidence.

First-principles calculations for defects and impurities: Applications to III-nitrides

First-principles calculations have evolved from mere aids in explaining and supporting experiments to powerful tools for predicting new materials and their properties. In the first part of this review we describe the state-of-the-art computational methodology for calculating the structure and energetics of point defects and impurities in semiconductors. We will pay particular attention to computational aspects which are unique to defects or impurities, such as how to deal with charge states and how to describe and interpret transition levels. In the second part of the review we will illustrate these capabilities with examples for defects and impurities in nitride semiconductors. Point defects have traditionally been considered to play a major role in wide-band-gap semiconductors, and first-principles calculations have been particularly helpful in elucidating the issues. Specifically, calculations have shown that the unintentional n-type conductivity that has often been observed in as-grown GaN cannot be attributed to nitrogen vacancies, but is due to unintentional incorporation of donor impurities. Native point defects may play a role in compensation and in phenomena such as the yellow luminescence, which can be attributed to gallium vacancies. In the section on impurities, specific attention will be focused on dopants. Oxygen, which is commonly present as a contaminant, is a shallow donor in GaN but becomes a deep level in AlGaN due to a DX transition. Magnesium is almost universally used as the p-type dopant, but hole concentrations are still limited. Reasons for this behavior are discussed, and alternative acceptors are examined. Hydrogen plays an important role in p-type GaN, and the mechanisms that underlie its behavior are explained. Incorporating hydrogen along with acceptors is an example of codoping; a critical discussion of codoping is presented. Most of the information available to date for defects and impurities in nitrides has been generated for GaN, but we will also discuss AlN and InN where appropriate. We conclude by summarizing the main points and looking towards the future.

First-principles study of defect energetics in titanium-doped alumina

First-principles plane-wave pseudopotential calculations were performed to study electronic structures, structural relaxation, and energetics of point defects in Ti-doped ${\mathrm{Al}}_{2}{\mathrm{O}}_{3}.$ Substitutional and interstitial Ti ions with charge compensating intrinsic defects were considered, and their formation energies were evaluated under various atomic chemical potentials. It was found that substitutional ${\mathrm{Ti}}^{4+}$ ions with charge compensating Al vacancies were most stable in the oxidized condition. In contrast, as oxygen chemical potentials decreased, the formation energy of substitutional ${\mathrm{Ti}}^{3+}$ decreased to have the smallest value in the relatively reduced conditions. However, in the intermediate range of oxygen potentials, substitutional ${\mathrm{Ti}}^{3+}$ and ${\mathrm{Ti}}^{4+}$ exhibited similar formation energies, indicating that these Ti defects can coexist in a particular reduction environment.

Free-energy calculations of intrinsic point defects in silicon

We study the energetics of various point defects in silicon using ab initio density-functional methods. The formation free energies are calculated from the harmonic phonon frequencies, which are determined from ab initio density-functional perturbation theory calculations. We deduce the concentrations of defects as a function of temperature and compare them with experimental estimates. The localized vibrational modes associated with the various defects are described.

Structure, point defects and ion migration in LaInO 3

This article deals with the energetics of point defects, oxygen migration and proton incorporation in LaInO 3. We have used atomistic simulation methods to determine the most possible structure for this oxide and compare this result with Rietveld analysis of a sample. Defect energy calculations show that substitution of La by Sr is conducive to the production of oxygen vacancies. We have calculated the energy of oxygen migration between different oxygen sites that takes place through various paths. With the methods utilised, we also found that the incorporation of water into a LaInO 3 cell is favourable being this a necessary condition for the occurrence of proton conduction in this system. These results are compared to both experimental and previous calculations and their validity is discussed.