Energetics Of Defect Formation Research Articles

Pyrochlore-type lanthanide titanates and zirconates: Synthesis, structural peculiarities, and properties

This contribution provides a thorough examination of the structural characteristics of pyrochlore-type lanthanide titanates and zirconates Ln2Ti2O7 and Ln2Zr2O7, across various length scales. This paper also examines their processing, interesting physical properties (electrical, magnetic, and thermal characteristics), and responses to high pressure and ion irradiation. Brief sections on the elemental oxides' crystal chemistry, pertinent phase diagrams, and energetics of defect formation are also provided. Pyrochlore-type Ln2Ti2O7 and Ln2Zr2O7 stand out as truly multifunctional materials. Moreover, they have emerged as fascinating materials due to magnetic geometrical frustration, arising from the ordering of magnetic Ln3+ and non-magnetic Ti4+ (or Zr4+) cations into separate, interpenetrating lattices of corner-sharing tetrahedra. This results in a diverse array of exotic magnetic ground states, such as spin-ice (e.g., Dy2Ti2O7 or Ho2Ti2O7) or quantum spin ice (e.g., Tb2Ti2O7), observed at both low and room temperatures. They also exhibit varied electrical and electrochemical characteristics. Some members such as Gd2Zr2O7, function as fast ion conductors with a conductivity (σ) of ≈10−2 S·cm−1 at 800 °C and activation energy (Ea) ranging from 0.85 to 1.52 eV, depending on the degree of structural disorder. Others, such as Gd2TiMoO7, are mixed ionic-electronic conductors with σ ≈ 25 S·cm−1 at 1000 °C, making them promising candidate materials for applications in energy conversion and storage devices and oxygen separation membranes. Their exceptionally low thermal conductivity (e.g., κ ∼ 1.1–1.7 W·m−1·K−1 between 700 and 1200 °C for Ln2Zr2O7), close to the glass-like lower limit of highly disordered solids, positions them as valuable materials for thermal barrier coatings. They can also effectively accommodate actinides (e.g., Pu, Np, Cm, Am) in solid solutions and sustain prolonged exposure to radiation due to alpha-decay events, while preserving the integrity of the periodic atomic structure. Proposed as major components in actinide-bearing ceramics, they contribute to the long-term immobilization and disposal of long-lived waste radionuclides from nuclear programs. Some of these properties are displayed simultaneously, opening avenues for new applications. Despite the wealth of data available in the literature, this review highlights the need for a better understanding of order/disorder processes in pyrochlore-type materials and the influence of the structural length scale on their physical and chemical properties. Recent experimental evidence has revealed that pyrochlore short-range structure is far more complex than originally thought. Moreover, pyrochlore local structure is now believed to include short-range, lower symmetry, ordered domains, such as the orthorhombic weberite-type of structure. Notably, short- and long-range structures appear decoupled across different length scales and temperature regimes, and these differences persist even in well-ordered samples. We believe that the pyrochlore structure offers a unique opportunity for examining the interplay between chemical composition, defect chemistry, and properties. In Memoriam: Rodney C. Ewing, Fondly Remembered.

Oxide Ion Conduction, Defect Chemistry, and the Conducting Mechanism in Ruddlesden–Popper La2–xMxBaIn2O7–0.5x (M = Ca, Sr, Ba)

Tetragonal La2BaIn2O7 belongs to the stoichiometric n = 2 members of the Ruddlesden–Popper (RP) structure, with La3+ and Ba2+ cations ordered in the rock salt and octahedral layers, respectively. Herein, a series of alkaline-earth-metal-doped materials La2–xMxBaIn2O7–0.5x (M = Ca, Sr, Ba) were prepared by the traditional solid-state reaction method. The results revealed that the substitutions of Ca/Sr/Ba for La introduced oxygen vacancies and led to good oxide ion conduction, e.g., ∼1.21 × 10–3–1.38 × 10–2 S/cm within 600–900 °C for the specimen La1.7Ba1.3In2O6.85, which was more than 2 orders of magnitude higher than the parent material. However, both the parent and acceptor-doped La2BaIn2O7 showed very limited proton conductions. The energetics of defect formation and oxygen vacancy migrations in La2BaIn2O7-based materials was studied through the static lattice and molecular dynamics (MD) atomistic simulations based on the interatomic potential approach. The defect formation energy calculations for the electrons and holes in La2BaIn2O7 rationalized the experimentally observed pure ionic conduction under low pO2 and mixed ionic and p-type electronic conductions under high pO2, respectively. The MD simulations indicated two-dimensional oxygen vacancy migration within the perovskite slab for the acceptor-doped La2BaIn2O7.

First-principles investigation of diffusion and defect properties of Fe and Ni in Cr2O3

Diffusion of Fe and Ni and the energetics of Fe- and Ni-related defects in chromium oxide (α–Cr2O3) are investigated using first-principles Density Functional Theory calculations in combination with the climbing-image nudged elastic band method. The orientations of the spin magnetic moments of the migrating ions are taken into account and their effects on migration barriers are examined. Several possible diffusion pathways were explored through interstitial and vacancy mechanisms, and it was found that the principal mode of ion transport in Cr2O3 is via vacancies. Both interstitial- and vacancy-mediated diffusions are anisotropic, with diffusion being faster in the z-direction. The energetics of defect formation indicates that the Ni-related defects are less stable than the Fe-related ones. This is consistent with Ni-diffusion being faster than Fe-diffusion. The results are compared with previous theoretical and experimental data and possible implications in corrosion control are discussed.

Acceptor Doping and Oxygen Vacancy Migration in Layered Perovskite NdBaInO4-Based Mixed Conductors

The Ca2+ and Ba2+ solubility on Nd3+ sites in new layered perovskite NdBaInO4 mixed oxide ionic and hole conductor and their effect on the oxide ion conductivity of NdBaInO4 were investigated. Among the alkaline earth metal cations Ca2+, Sr2+, and Ba2+, Ca2+ was shown to be the optimum acceptor–dopant for Nd3+ in NdBaInO4 showing the largest substitution for Nd3+ up to 20% and leading to oxide ion conductivities ∼3 × 10–4–1.3 × 10–3 s/cm within 600–800 °C on Nd0.8Ca0.2BaInO3.9 composition, exceeding the most-conducting Nd0.9Sr0.1BaInO3.95 in the Sr-doped NdBaInO4. Energetics of defect formation and oxygen vacancy migration in NdBaInO4 were computed through the atomistic static-lattice simulation. The solution energies of Ca2+/Sr2+/Ba2+ on the Nd3+ site in NdBaInO4 for creating the oxygen vacancies confirm the predominance of Ca2+ on the substitution for Nd3+ and enhancement of the oxygen vacancy conductivity over the larger Sr2+ and Ba2+. The electronic defect formation energies indicate that the p-type c...

Point defects in twisted bilayer graphene: A density functional theory study

We have used ab initio density functional theory, incorporating van der Waals corrections, to study twisted bilayer graphene (TBLG) where Stone-Wales defects or monovacancies are introduced in one of the layers. We compare these results to those for defects in single layer graphene or Bernal stacked graphene. The energetics of defect formation is not very sensitive to the stacking of the layers or the specific site at which the defect is created, suggesting a weak interlayer coupling. However signatures of the interlayer coupling are manifested clearly in the electronic band structure. For the "$\gamma\gamma$" Stone Wales defect in TBLG, we observe two Dirac cones that are shifted in both momentum space and energy. This up/down shift in energy results from the combined effect of a charge transfer between the two graphene layers, and a chemical interaction between the layers, which mimics the effects of a transverse electric field. Charge density plots show that states near the Dirac points have significant admixture between the two layers. For Stone Wales defects at other sites in TBLG, this basic structure is modified by the creation of mini gaps at energy crossings. For a monovacancy, the Dirac cone of the pristine layer is shifted up in energy by $\sim0.25$ eV due to a combination of the requirements of the equilibration of Fermi energy between the two layers with different numbers of electrons, charge transfer, and chemical interactions. Both kinds of defects increase the density of states at the Fermi level. The monovacancy also results in spin polarization, with magnetic moments on the defect of 1.2 - 1.8 $\mu_B$.

Ion irradiation of the TiO2 polymorphs and cassiterite

Thin crystals of rutile, brookite, anatase, and cassiterite were irradiated in situ in the transmission electron microscope using 1.0 MeV Kr ions at 50-300 K. Synthetic rutile and natural cassiterite, with 0.1-0.2 wt% impurities, remain crystalline up to a fluence of 5 x 10{sup 15} ions cm{sup -2} without evidence for amorphization at 50 K. Natural brookite and anatase, with 0.3-0.5 wt% impurities, become amorphous at fluences of 8.1 x 10{sup 14} and 2.3 x 10{sup 14} ions cm{sup -2}, respectively. We have also studied two natural rutile samples containing {approx}1.7 and 1.2 wt% impurities. These samples became amorphous at 9.2 x 10{sup 14} and 8.6 x 10{sup 14} ions cm{sup -2} at 50 K, respectively. Further analyses of the fluence-temperature data for natural brookite, rutile, and anatase give critical amorphization temperatures of 168 {+-} 11, 209 {+-} 8, and 242 {+-} 6 K, respectively. Results are briefly discussed with respect to several criteria for radiation resistance, including aspects of the structure, bonding, and energetics of defect formation and migration.

Local Defect Structures and Ion Transport Mechanisms in the Oxygen-Excess Apatite La9.67(SiO4)6O2.5

Apatite-type oxides of general formula La9.33+x(SiO4)6O2 + 3x/2 have been attracting considerable interest recently because of their observed high oxide-ion conductivity and potential use in solid oxide fuel cells (SOFCs), oxygen sensors, and ceramic membranes. In this paper, computer modeling techniques are used to investigate, at the atomic level, the energetics of defect formation, oxide-ion migration, and cation migration in the oxygen-excess apatite silicate, La9.67(SiO4)6O2.5. Recent research has suggested that oxide-ion conduction in these apatite systems proceeds by an interstitial mechanism. Our results support this view and have revealed how the flexibility of the SiO4 substructure plays a crucial role in facilitating oxide-ion migration: the presence of interstitial oxide ions creates pseudo-“SiO5” units, which can effectively pass along the c direction by oxygen transfer. La vacancy migration is also examined and, as expected, found to have a high energy barrier.

Changes of local electronic structure of perfect (VO) 2P 2O 7( [formula omitted]) surface in response to oxygen vacancy formation: effect of electron trapping

This paper reports theoretical calculations based on density functional theory applied to investigate how the formation of oxygen vacancies modify the catalytic properties of the (VO) 2P 2O 7(1 0 0) surface. Although a detailed understanding of the structure of the perfect surface is crucial, it must be stressed that in most practical cases oxide surfaces are defective and irregular. Among the various defects occurring in the metal oxides, the oxygen vacancy at the surface has received particular attention from both experimentalists and theoreticians. In spite of its simplicity this relatively common defect has very interesting properties. In this work one type of surface oxygen monovacancy is considered––the neutral F s 0 center i.e. vacancy with two trapped electrons. Electronic structures of vacancies at the (VO) 2P 2O 7(1 0 0) surface are studied using a cluster model. The energetics of defect formation and the effect of electron trapping on the atomic arrangement is discussed. It is shown that the vacancies significantly modify the physical and chemical properties of the (VO) 2P 2O 7(1 0 0) surface, thus influencing its catalytic behavior. A link between the sensitivity of the reactivity of the chemical system and the perturbation in the electronic density of the system due to the point anionic defects is demonstrated.

Electron spin localisation and correlation effects for point defects in semi-ionic solids

Point defects strongly influence the electrical, catalytic and optical properties of important industrial materials such as silica, aluminosilicates and aluminophosphates. We concentrate here on the predictive ability of modern ab initio solid-state tools to describe electron localised states in these materials. We apply a periodic boundary conditions approach to investigate equilibrium configurations and electronic structures of oxygen vacancies in the form of diamagnetic VO and paramagnetic E′ centres. Localisation of the electronic states at the defect is studied using both Hartree–Fock (HF) and Density Functional theories. Thus, we are able to characterise the effect of electron correlation on spin polarisation and electron trapping. Geometries and energetics of defect formation are investigated, along with the one-electron spectra and spin/charge density distributions, which allow us to gather a comprehensive representation of the defect ground state.

Cation Coordination At Σ Grain Boundaries in TiO2 and SrTiO3, and its Effect on the Local Electronic Properties

Grain boundaries have long been known to have a dominant effect on the electronic properties of polycrystalline materials. In the case of electroceramic oxides, the thermodynamics of defect formation (vacancies or interstitials, cations or anions) are usually invoked to predict the presence of a space charge potential at the grain boundaries. The relative energetics for the formation of each type of defect determines the size and sign of this potential barrier and thus, the effect that boundaries have on the overall electronic properties of the materials. However, a limitation to this continuum thermodynamics approach is that it does not consider the effect of the grain boundary structure.To investigate whether the grain boundary atomic structure can have an effect on the energetics of defect formation and hence the electronic properties, here we examine the structure of Σ5 boundaries in two systems, SrTiO3 (perovskite) and TiO2(rutile).

Water-related defects and oxygen diffusion in albite: a computer simulation study

Computer simulation techniques have been used to investigate the energetics of defect formation in Albite and to calculate O and (OH) migration activation energies. We find that the Na Frenkel defect has the lowest formation energy, whilst interstitials associated with impurities are the most favourable O defects. Water can be accommodated in the albite structure as both OH groups and as H2O molecules with solution energy of 0.73 eV and 0.9 eV respectively. The activation energies for O migration is reduced by up to 50% when the O is migrating as part of an (OH) group. In addition, we find a marked diffusional anisotropy for both O and (OH) in albite.

Ground state structural anomalies in cuprous halides: CuCl.

We have examined structural instabilities and elastic anomalies in CuCl via first-principles calculations and find that its crystal structure is not ideal zinc blende but that correlated displacements of groups of four Cu atoms lead to a more stable configuration. About 20% of the Cu atoms are estimated to be affected. The Cu-Cu distance in the C${\mathrm{u}}_{4}$ complex shrinks from 3.82 to 2.72 \AA{}, close to that of metallic Cu. The energetics of defect formation are examined also for CuBr and CuI.

Point defects and ion migration in PbFCl

Atomistic simulation techniques have been applied to PbFCI in order to calculate the energetics ofdefect formation and ion transport mechanisms in the undoped material. Schottky-like disorder is computed to be the dominant ionic defect. The activation energies for a variety of anion vacancy migration mechanisms are calculated and found to be in good agreement with experiment. The results support the models in which the low temperature ionic conductivity is attributed to an interplanar Cl vacancy mechanism. We predict that the out-of-plane configuration of the Cl2− species is the most stable self-trapped hole (Vk center). Interatomic separations of the Vk centers following lattice relaxation are also discussed.

Effect of Bias on Recovery Rates of Stressed Amorphous Silicon Mis Structures

ABSTRACTThe effect of Fermi level position on the annealing of defects created by electron accumulation is investigated. Results indicate that holes accelerate the annealing of defects created by electrons confirming the theoretical understanding of the proximity compensated layer. Capacitance-voltage curves indicate that hole accumulation tends to create defect states located closer to the conduction band than electron accumulation–a result in agreement with energetics of defect formation.

Pressure and Strain Effects on Diffusion

AbstractWe have investigated, via parameter-free calculations, the effects of hydrostatic and nonhydrostatic strains on the energetics of defect formation and self-diffusion in silicon. The three microscopic mechanisms, vacancy, interstitial, and concerted exchange, have very similar activation enthalpies at zero pressure but exhibit different behavior with hydrostatic pressure. Our results suggest that experiments performed at different pressures can determine the relative contributions of each of these mechanisms. The calculations also show that the neutral Si vacancy has a negative relaxation volume, with the nearest neighbors of the vacancy relaxing inwards, in contrast to the Si (111) surface. Large nonhydrostatic strains, which are present in e.g. Si/GexSi1-x pseudomorphic heterostractures, substantially reduce the formation energy of the tetrahedral interstitial, but do not affect the formation energy of the vacancy. These findings suggest that, aside from being another useful tool for the investigation of self-diffusion in Si, nonhydrostatic strain may significantly affect annealing and impurity diffusion in strained heterostructures. In particular, the interstitial-assisted impurity diffusion may proceed more rapidly in Si lattice-matched to GexSi1-x, but be slowed down in GexSi1-x lattice-matched to Si. The compressed GexSi1-x layers may thus act as diffusion barriers for impurities diffusing with help of native interstitials, such as B or P.

Defect Structure and Ion Transport in PbFCI

AbstractTheoretical techniques are used to examine the energetics of defect formation and ion transport mechanisms in PbFCI. Schottky disorder is found to be the dominant intrinsic defect. The calculated formation energy is in good agreement with experiment. Activation energies for the migration of anion vacancies are presented.

Energetics of defect formation and interaction in pyrrhotite Fe 1− xS and its homogeneity range

Sulphur fugacities in equilibrium with Fe 1− x S (pyrrhotite) were measured at different temperatures in the range 820–1374 K by direct (silica gauges) and indirect (H 2S/H 2) methods. The results give direct evidence of the boundaries of the homogeneity range and can be interpreted in terms of iron vacancy formation and interaction and of an additional defect, e.g. iron on sulphur sites. The homogeneity range of Fe 1− x S is calculated as a function of temperature from the energetic parameters of the defects and the sulphur fugacities limiting the existence region of this phase. Fe 1− x S exists with positive values of x except at the eutectic with iron (1261 K) where x is 0±0.0001.