Formation Energies Of Point Defects Research Articles

A simple model for large-scale simulations of fcc metals with explicit treatment of electrons

The continuing advance in computational power is beginning to make accurate electronic structure calculations routine. Yet, where physics emerges through the dynamics of tens of thousands of atoms in metals, simplifications must be made to the electronic Hamiltonian. We present the simplest extension to a single s-band model [A.P. Sutton, T.N. Todorov, M.J. Cawkwell and J. Hoekstra, Phil. Mag. A 81 (2001) p.1833.] of metallic bonding, namely, the addition of a second s-band. We show that this addition yields a reasonable description of the density of states at the Fermi level, the cohesive energy, formation energies of point defects and elastic constants of some face-centred cubic (fcc) metals.

Energy calculation of point defects in plutonium by embedded atom method

Plutonium is vulnerable to aging due to α radioactive decay. The properties and behaviors of point defects in plutonium are the basis for understanding plutonium aging. We have employed a molecular dynamics technique to calculate the formation energy and binding energy of point defects and small helium-vacancy clusters in plutonium, using embedded atom method, Morse pair potential and the Lennard-Jones pair potential for describing the interactions of Pu-Pu, Pu-He and He-He, respectively. A single self-interstitial atom’s steady configuration is 〈100〉 dumb-bell. An interstitial helium atom at octahedral site is more stable than that at tetrahedral site. As a result of high binding energy of an interstitial helium atom to a vacancy, helium atoms can combine with vacancies to form helium-vacancy cluster during the process of self-radiation. The formation energy of helium-vacancy cluster increases with the increasing number of helium atoms. When the number of helium atoms equals to the number of vacancy, the helium-vacancy cluster is rather stable. Both substitutional and interstitial helium atoms are trapped at the grain boundary (GB). The binding energy of the self-interstitial atom at GB core is higher than that of helium atom and vacancy.

Effect of Nb on electronic structure of NiTi intermetallic compound: A first-principles study

The electronic structure of pure and Nb doped B2 NiTi have been calculated with the first-principle ultrasoft pseudopotential approach of the plane wave based on the density functional theory aiming at examining the effect of Nb on the electronic structure and bonding characteristic of NiTi. The point defect formation energy calculation results show that the introduction of Nb largely enhances the energy required to form the vacancies and anti-sites of both Ni and Ti sublattice. Furthermore, the calculation results on the partial density of states (PDOS) suggest that the addition of Nb increase the s-s, p-p and d-d electronic interactions between Nb and neighboring Ni and Ti atoms. The electron density of NiTi was also increased with the introduction of Nb. All these Nb-inuced results on electronic structure and bonding characteristic may hamper the hop of Ni and Ti atoms, which may facilitate to improve of oxidation resistance of NiTi intermetallic compound in the experimental findings.

First-principles density functional calculations for Mg alloys: A tool to aid in alloy development

In studying the thermodynamics and phase stability of Mg alloys, one is often confronted with the lack of accurate, quantitative experimental data. This deficiency can be partially rectified via first-principles calculations based on density functional theory. In this paper, we will illustrate the utility of first-principles energetics for Mg alloys using three case studies (i) formation energies of ordered/disordered solid phases; (ii) solute–vacancy binding energies in Mg; (iii) point defect formation energies of β-Mg 17Al 12. These first-principles calculations can provide highly accurate thermodynamic and kinetic information for Mg alloys.

Point defects and chemical potentials in D8 8–Sn 3Ti 5

The point defect formation energies in D8 8–Sn 3Ti 5 are obtained from first principles calculations. The D8 8 structure is hexagonal, hP16, P6 3/mcm, prototype Mn 5Si 3. Four sublattices are introduced to account for the D8 8 structure and for the possibility of inserting atoms in the 2b sites of the structure P6 3/mcm. The 2b sites are not occupied in the stoichiometric compound at T = 0 K. But the possibility exists that a few atoms occupy these sites at high temperature or for off-stoichiometric alloys. A statistical model based on a mean-field approximation is developed in the canonical ensemble. The defect concentrations are calculated as function of temperature and deviation from stoichiometry. For stoichiometric D8 8–Sn 3Ti 5 alloys, the dominant thermal defects are composed of Sn atoms in interstitial positions 2b of the D8 8 structure and Ti atoms in antisite position on the sites preferentially occupied by Sn atoms. In the Sn-rich D8 8–Sn 3Ti 5, the constitutional defects are Sn atoms in interstitial positions. In the Ti-rich D8 8–Sn 3Ti 5, the constitutional defects are Ti atoms in antisite position. The chemical potentials as well as the Gibbs energy are obtained as function of composition for various temperatures. The extension of the one-phase domain of D8 8–Sn 3Ti 5 in the Sn–Ti phase diagram is calculated.

Overlayer stress effects on defect formation in Si and Ge

Point-defect formation energies in bulk crystalline materials such as Si and Ge are material specific quantities defined for the case of formation at a free surface, but in many cases of technological interest, point defects are formed at the interface between the crystalline substrate and a strained material overlayer. Here the energy cost of generating a bulk point defect at the overlayer/substrate interface is modified by the stress interaction during defect formation, leading to an effective supersaturation or undersaturation in the bulk, relative to the ‘equilibrium’ concentration expected for the case of a free surface. This in turn impacts on diffusion, defect formation and activation of dopant impurities in the substrate. We present current experimental evidence for this phenomenon, based on studies of B diffusion under tensile-strained nitride layers, and discuss the likely implications for dopant activation in Si and Ge.

First principles study of point defects in titanium oxycarbide

We have performed first principles density functional theory calculations to study the formation energy of point defects in TiC, TiO and TiCO compounds. The formation energy of isolated vacancies was obtained for different equilibrium conditions. For binary compounds, we have also calculated the formation energy of antisite defects. It was found that the defect formation energies strongly depend on the chemical environment. Our results show that C vacancies are easily formed in TiC and TiCO. For the TiO compound, Ti vacancies are highly probable to occur and O vacancies are also easily formed under titanium rich conditions.

Formation and properties of defects and small vacancy clusters in SiC: Ab initio calculations

Large-scale ab initio simulation methods have been employed to investigate the configurations and properties of defects in SiC. Atomic structures, formation energies and binding energies of small vacancy clusters have also been studied as a function of cluster size, and their relative stabilities are determined. The calculated formation energies of point defects are in good agreement with previously theoretical calculations. The results show that the di-vacancy cluster consists of two C vacancies located at the second nearest neighbor sites is stable up to 1300K, while a di-vacancy with two Si vacancies is not stable and may dissociate at room temperature. In general, the formation energies of small vacancy clusters increase with size, but the formation energies for clusters with a Si vacancy and nC vacancies (VSi–nVC) are much smaller than those with a C vacancy and nSi vacancies (VC–nVSi). These results demonstrate that the VSi–nVC clusters are more stable than the VC–nVSi clusters in SiC, and provide possible nucleation sites for larger vacancy clusters or voids to grow. For these small vacancy clusters, the binding energy decreases with increasing cluster size, and ranges from 2.5 to 4.6eV. These results indicate that the small vacancy clusters in SiC are stable at temperatures up to 1900K, which is consistent with experimental observations.

Influence of Nb doping on oxidation resistance of γ-TiAl:A first principles study

Nb doping is proved to be the most promising way of enhancing the oxidation resistance of TiAl alloys， yet the intrinsic mechanism is still unclear. To understand the effect of Nb doping, a first principles study of several point defects in γ-TiAl during oxidation is performed. Besides the determination of the stable defect structures it is revealed that （1） the formation energy of Nb doping increases with Nb content increasing， at the cost of degradation of the phase stability， which is a hindrance to the oxidation resistance; （2） the abilities of interstitial oxygen and titanium vacancy formation are lowered by Nb addition， thus oxygen diffusion and vacancy formation are reduced correspondingly， which enhances the oxidation resistance of the alloy; （3） the effect of Nb doping on the formation energy of point defect is rather localized， therefore the influence of Nb doping is correlated with its distribution and content in γ-TiAl.

First-principles study on defect chemistry and migration of oxide ions in ceria doped with rare-earth cations

Oxygen transport in rare-earth oxide (RE(2)O(3)) doped CeO(2) with fluorite structure has attracted considerable attention owing to both the range of practical usage (e.g., fuel cells, sensors, etc.) and the fundamental fascination of fast oxide ion transport in crystalline solids. Using density-functional theory, we have calculated the formation energies of point defects and their migration properties in RE(2)O(3) doped CeO(2)(RE = Sc, Y, La, Nd, Sm, Gd, Dy, and Lu). The calculated results show that oxygen vacancies are the dominant defect species obtained by RE(3+) doping. They form associates with the RE(3+) ions, and the corresponding defect association energy is a strong function of the ionic radii of the RE(3+) dopants. The migration of an oxygen vacancy was investigated using the nudged elastic band method. The lowest activation energy for oxygen vacancy hopping is obtained for a straightforward migration path between two adjacent oxygen sites. The migration energy of an oxygen vacancy also strongly depends on the ionic radii of the neighbouring dopant cations. Accordingly, we have identified two factors that affect the oxygen vacancy migration; (1) trapping (or repelling) of an oxygen vacancy at the NN site of the RE(3+) dopant, and (2) reduction (or enlargement) of the migration barrier by RE(3+) doping. These findings provide insight for atomistic level understanding of ionic conductivity in doped ceria and would be beneficial for optimizing ionic conductivity.

Molecular dynamics simulation of radiation damage in bcc tungsten

Molecular dynamics simulations of collision cascades in pure tungsten are performed to assess the primary damage due to irradiation. For short-range interaction the universal potential is used [J.F. Ziegler, J.P. Biersack, U. Littmark, The Stopping and Range of Ions in Solids, Pergamon Press, 1985, p. 41], while for long-range interaction, three different embedded atom method potentials [M.W. Finnis, J.E. Sinclair, Phil. Mag. A 50 (1984) 45; G.J. Ackland, R. Thetford, Phil. Mag. A 56 (1987) 15; P.M. Derlet, D. Nguyen-Manh, S.L. Dudarev, Phys. Rev. B 76 (2007) 054107] are used, namely, Finnis–Sinclair, Ackland–Thetford and Derlet–Nguyen–Manh–Dudarev, the latter providing a more accurate formation energy for the 〈1 1 0〉 interstitial. The short-range and long-range potentials are smoothly connected. A new approach improving the reliability of such potential fits at short distances is presented. These potentials are then evaluated on the basis of displacement threshold, point defect formation and migration energies, thermal expansion and temperature of melting. Differences in the damage resulting from collision cascades are discussed.

Correlation between the optical quality and the Fermi level position in GaInNAs alloys

It is shown that the Fermi level-stabilization energy, EFS, lies inside the conduction band for GaInNAs with the band gap energy smaller than ∼0.6 eV. Since the formation energy of native point defect varies with the Fermi energy and is very small if the Fermi level is located inside the conduction (or valence) band, the Fermi level pinning at the EFS can be the main obstacle for the growth of good quality GaInNAs-based lasers for long wavelength applications. An engineering of the Fermi level position in GaInNAs can be a promising way to improve the optical quality of GaInNAs alloys.

Ab-initio Simulation of Formation and Diffusion Energies of Intrinsic Point Defects in Ge

Density functional theory with local density approximation including on-site Coulomb interaction has been used to calculate the formation and migration energy of the neutral and charged vacancy and self-interstitial in germanium.

Ab-initio Simulation of Formation and Diffusion Energies of Intrinsic Point Defects in Ge

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Point defect thermodynamics and diffusion in Fe 3C: A first-principles study

The point defect structure of cementite (Fe 3C) is investigated using a combination of the statistical mechanical Wagner–Schottky model and first-principles calculations within the generalized gradient approximation. Large 128-atom supercells are employed to obtain fully converged point defect formation energies. The present study unambiguously shows that carbon vacancies and octahedral carbon interstitials are the structural defects in C-depleted and C-rich cementite, respectively. The dominant thermal defects in C-depleted and stoichiometric cementite are found to be carbon Frenkel pairs. In C-rich cementite, however, the primary thermal excitations are strongly temperature-dependent: interbranch, Schottky and Frenkel defects dominate successively with increasing temperature. Using the nudged elastic band technique, the migration barriers of major point defects in cementite are also determined and compared with available experiments in the literature.

Morphology and Composition of Selected High-k Materials and Their Relevance to Dielectric Properties of Thin Films

We discuss some of the issues associated with the relation between the leakage current and the dielectric constant on the one hand, and the crystallographic structure and the chemical composition of the film on the other. Our focus is on dielectrics containing Pr oxides. Starting with the binary , we investigate electronic properties and formation energies of point defects as revealed by ab initio calculations and we attempt to associate this data with the experimental information on the influence of processing on the dielectric quality of the film. We then consider Pr silicates on Si for metal-oxide-semiconductor field effect transistors and on TiN for metal–insulator–metal front-end applications. In the latter case, annealing above about , needed to noticeably increase the effective dielectric constant, causes an increased leakage. Investigating this effect, in particular we discuss the diffusion mechanism for Ti and the influence of Ti on the leakage current, taking into account the stoichiometry dependence of defect formation energies and the position of electron transition states obtained from ab initio data.

Defect structures in the silver halides

We report a state of the art density functional theory study of the intrinsic defects within the rocksalt-structured silver halides. These materials are well known to favor Frenkel defect pairs over Schottky pairs---a key factor in their use as photographic materials. We report the defect structures and formation energies of the elementary point defects obtained using the supercell approximation. In agreement with recent experimental results, we find that the interstitial cation adopts a split-interstitial configuration, centered on a lattice site. The effects of electron or hole trapping on the defect centers in $\mathrm{AgCl}$ and $\mathrm{AgBr}$ are reported, including the formation energetics, structures, and spin localizations. Although limitations in the supercell method are evident, we have nevertheless obtained valuable new insights into the properties of these fascinating materials.

A Comparison of Intrinsic Point Defect Properties in Si and Ge

ABSTRACTIntrinsic point defects determine to a large extent the semiconductor crystal quality both mechanically and electrically not only during crystal growth or when tuning polished wafer properties by thermal treatments, but also and not the least during device processing. Point defects play e.g. a crucial role in dopant diffusion and activation, in gettering processes and in extended lattice defect formation.Available experimental data and results of numerical calculation of the formation energy and diffusivity of the intrinsic point defects in Si and Ge are compared and discussed. Intrinsic point defect clustering is illustrated by defect formation during Czochralski crystal growth.

Magnetic origin of nano-clustering and point defect interaction in Fe–Cr alloys: an ab-initio study

To understand the behaviour of point defects generated in irradiated FeCr ferritic/martensitic steels and to identify the kinetic pathways of micro-structural evolution of binary model Fe–Cr alloys, we use a combination of density functional theory (DFT) with statistical approaches involving cluster expansion and Monte Carlo simulations. This makes it possible to generate in a systematic way the low-energy configurations required for the subsequent DFT study of intrinsic defects (vacancies, interstitials) and impurity-defect interactions over the entire range of Fe–Cr alloy compositions. In the limit of low Cr concentration, DFT calculations predict that an intermetallic compound Fe15Cr has the lowest negative heat of formation. At higher Cr concentrations, simulations performed using a 4 × 4 × 4 super-cell show that magnetism is responsible for the nano-segregation of the ferromagnetic Fe15Cr and anti-ferromagnetic (α′-Cr) phases giving rise to the formation of clusters characterised by a very low positive heat of formation. We perform a systematic investigation of formation energies of point defects and their energies of interaction with Cr atoms. Further investigation of interaction of interstitial and vacancy defects with impurities (V, Nb, Ta, Mo, W, Al, Si, P, S) also shows a complex picture of interplay between magnetism and short-range ordering that affects the interaction between defects and impurities in the presence of chromium in Fe-rich alloys.

First Principles Calculations of the Formation Energy of the Neutral Vacancy in Germanium

Density functional theory (DFT) with local density approximation has been used to calculate the formation energy (EF) of the neutral vacancy in germanium single crystal. It was shown that careful checking of convergence with respect to the number of k-points is necessary when calculating the formation energy of the intrinsic point defects in Ge. The formation energy of the single neutral vacancy was estimated at 2.35 eV which is in excellent agreement with published experimental data.