Vacancy Sources Research Articles

Structure Property Relationship in BaTiO3–Na0.5Bi0.5TiO3–Nb2O5–NiO X8R System

A novel BaTiO3–Na0.5Bi0.5TiO3–Nb2O5–NiO (BT‐NBT‐Nb‐Ni) system that meets the X8R specification (−55°C–150°C, ΔC/C≤±15%) of multilayer ceramic capacitors (MLCCs) was fabricated, with a maximum dielectric constant of 2350 at room temperature (25°C). Core–shell microstructure was observed by transmission electron microscopy (TEM), accounting for the good dielectric temperature stability. The role of Ni on the formation of core–shell structure and phase structure, and the subsequent relationship between structure and dielectric/ionic conduction properties were investigated. It was observed that the addition of Ni could adjust the ratio of core/shell, and significantly reduces the dielectric loss over the studied temperature range. A new Ba11(Ni, Ti)28O66+x phase with a 10‐layer close‐packed structure was identified by X‐ray diffraction (XRD), serving as a source of oxygen vacancies for ionic conduction in addition to Ba(Ni,Ti)O3. Furthermore, the impedance spectroscopy measurements demonstrated the remarkable impact of these Ni‐induced oxygen vacancies on both the grain and grain‐boundary conductivities.

Transparent-conductive-oxide (TCO) buffer layer effect on the resistive switching process in metal/TiO2/TCO/metal assemblies

The effect of a transparent conductive oxide (TCO) buffer layer on the insulator matrix and on the resistive switching process in the metal/TiO2/TCO/metal assembly was studied depending on the material of the TCO (ITO-(In2O3)0.9(SnO2)0.1 or SnO2 or ZnO). For the first time electro-physical studies and near edge x-ray absorption fine structure (NEXAFS) studies were carried out jointly and at the same point of the sample, providing direct experimental evidence that the switching process strongly influences the lowest unoccupied bands and the local atomic structure of the TiO2 layers. It was established that a TCO layer in a metal/TiO2/TCO/metal assembly is an additional source of oxygen vacancies for the TiO2 film. The RL (RH) states are achieved presumably with the formation (rupture) of the electrically conductive path of oxygen vacancies. Inserting an Al2O3 thin layer between the TiO2 and TCO layers to some extent restricts the processes of migration of the oxygen ions and vacancies, and does not allow the anti-clockwise bipolar resistive switching in a Au/TiO2/Al2O3/ITO/Au assembly. The greatest value of the ratio RH/RL is observed for the assembly with a SnO2 buffer layer that will provide the maximum set of intermediate states (recording analog data) and increase the density of information recording in this case.

Less is more. Cation exchange and the chemistry of the nanocrystal surface.

We link the extent of Pb for Cd cation exchange reactions in PbS colloidal quantum dots (QDs) to their surface chemistry. Using PbS QDs with either a full or a partial surface coverage by excess Pb, we demonstrate the central role played by vacant cation sites on the QD surface. They facilitate the adsorption of cations from solution, and they act as a source of vacancies needed for the transport of cations through the crystal lattice. This model explains our finding that the cation exchange reaction runs to completion when using a low Cd excess in the exchange bath, while it is impeded by a high Cd excess. Whereas in the latter case, the QD surface is poisoned by surface Cd, the former conditions provide the mixture of surface Cd and vacant surface sites the exchange reaction needs to proceed. This understanding provides a missing link needed to build a unifying mechanistic picture of cation exchange reactions at nanocrystals.

Effect of Surface and Grain Boundary on the Reversion of Al-Zn Alloys

Age-hardening of Al-Zn alloy after quenching develops inhomogeneously due to the effect of surface as a vacancy sink and grain boundary as an easy path. In this study, reversion of the age-hardened Al-Zn alloys, in which ellipsoidal GP zones were formed, was investigated by Vickers micro-hardness test. Ellipsoidal GP zones were reverted more quickly near the surface and grain boundary than in the interior, as spherical GP zones in Al-10%alloy did. It is considered that the surface and grain boundary plays a role of effective source for vacancies, in addition to the interior source such as dislocations, as in the case of the reversion of spherical GP zones.

Row of Dislocation loops as a Vacancy Source in Ultrahigh-Purity Aluminum Single Crystals with a Low Dislocation Density

Row of Dislocation loops as a Vacancy Source in Ultrahigh-Purity Aluminum Single Crystals with a Low Dislocation Density

Evolution of the shape of the conducting channel in complementary resistive switching transition metal oxides

Ultimate control of the defect distribution and local conduction path in a bipolar resistive switching (BRS) Pt/TiO2/Pt sample, which was in a unipolar reset state, is provided by means of voltage pulsing and the resulting time-transient current analysis. The limited amount of oxygen vacancies in this system allowed reversibly switching-diode-like current-voltage curves, which was also confirmed in another Magnéli-phase-containing Pt/WO3/Pt sample. Such careful control of the defect distribution allowed the achievement of a complementary resistive switching (CRS) curve even from a single switching layer. The unlimited vacancy source in the Pt/TiO2/TiO2-x/Pt sample did not allow the switching-diode type and the CRS behavior. The data retention of the on-state in the BRS was critically dependent on the shape of the rejuvenated conduction channel. The required time to lead to the rejuvenation of the conducting channel was ∼70-100 ns when the threshold voltage for the BRS set of ∼-1 V was applied.

Irreversible thermodynamics of creep in crystalline solids

We develop an irreversible thermodynamics framework for the description of creep deformation in crystalline solids by mechanisms that involve vacancy diffusion and lattice site generation and annihilation. The material undergoing the creep deformation is treated as a non-hydrostatically stressed multi-component solid medium with non-conserved lattice sites and inhomogeneities handled by employing gradient thermodynamics. Phase fields describe microstructure evolution which gives rise to redistribution of vacancy sinks and sources in the material during the creep process. We derive a general expression for the entropy production rate and use it to identify of the relevant fluxes and driving forces and to formulate phenomenological relations among them taking into account symmetry properties of the material. As a simple application, we analyze a one-dimensional model of a bicrystal in which the grain boundary acts as a sink and source of vacancies. The kinetic equations of the model describe a creep deformation process accompanied by grain boundary migration and relative rigid translations of the grains. They also demonstrate the effect of grain boundary migration induced by a vacancy concentration gradient across the boundary.

First-principles study of point defects in Ni3Al

The energetics and structural properties of native, substitutional and interstitial defects in NiAl have been investigated by first-principles methods. In particular, we have determined the formation energies of composition conserving defects and established that the so-called penta defect, which consists of four vacancies on Ni sublattice and Ni antisite on the Al sublattice, is the main source of vacancies in NiAl. We show that this is due to the strong Ni-site preference of vacancies in NiAl. We have also calculated the site substitution behaviour of Cu, Pd, Pt, Si, Ti, Cr, V, Nb, Ta and Mo and their effect on the concentration expansion coefficient. We show the latter information can used for an indirect estimate of the site substitution behaviour of the alloying elements. The solution energy of carbon and its effect on the lattice constant of NiAl have been obtained in the dilute limit in the first-principles calculations. We have also determined the chemical and strain-induced carbon–carbon interactions in the interstitial positions of NiAl. These interactions have been subsequently used in the statistical thermodynamic simulations of carbon ordering in NiAl.

On the diffusion of NV defects in diamond

AbstractBesides their importance for quantum information processing, NV defects are crucial agents for the diffusion and aggregation of nitrogen in diamond. In the absence of transition metals, it is thought that the first stage of nitrogen aggregation, where close neighbour nitrogen pairs are formed, is mediated by NV defects. Here we use density functional theory to explore the barriers to NV diffusion. We conclude that the barrier is around 5 eV when there is a ready source of vacancies and that this barrier is weakly dependent on pressure.

Confinement of vacancies during annealing of H implanted GaN sandwiched between two {InGaN/GaN} superlattices

Using transmission electron microscopy techniques, we identify the extended defects of interstitial and vacancy types found after H implantation and annealing in GaN. We statistically analyze the effect of boarding or sandwiching GaN between strained superlattices on these populations of defects. We finally demonstrate the possibility to use compressively strained layers to localize and favour the precipitation of vacancy type defects in GaN. The source of excess vacancies, the mechanism responsible for the cavity localization, and the drastic increase of their volume fraction are discussed.

Modelling of fission gas release from irradiated UO2 fuel under high-temperature annealing conditions

The new model for the vacancy field evolution in grains during annealing of irradiated fuel was developed and implemented in the MFPR code. The model simulates time and spatial variation of the vacancy concentration in the presence of extended vacancy sources (grain boundaries and dislocations) and sinks (growing intragranular bubbles). Being combined with the models for dislocation creep and for bubbles biased migration in the vacancy gradient, the new model self-consistently describes the processes of gas release and microstructure evolution observed in the annealing tests.

First-principles study of defect behavior in irradiated uranium monocarbide

Ab initio electron theory based on the projector-augmented-wave method in the generalized gradient approximation of the density functional theory is used for calculating formation and migration energies of point defects in uranium monocarbide (UC). The use of the Hubbard term to describe the 5$f$ electrons of uranium is discussed on the basis of the density of states and cohesive energies. A formalism allowing the ``raw'' calculated energies to be normalized is proposed to take into account the compositional dependence of defective crystals. Such formation energies are then used to determine the population of predominant defects as a function of nonstoichiometry. We identify the most stable defects as uranium antisites and carbon vacancies for UC${}_{1\ensuremath{-}x}$, and dimers ${\mathrm{C}}_{2}$ for UC${}_{1+x}$. The most stable thermal defects are obtained, in turn, by formation of complex defects associating dimer ${\mathrm{C}}_{2}$ and carbon vacancies whereas carbon Frenkel pairs and Schottky defects require larger formation energies. The migration energies are also calculated for different mechanisms, using as diffusion vectors both thermal vacancy sources and preexisting constitutional defects in the case of off-stoichiometric alloys. We compare the calculated diffusion paths with available experimental data proposed by Matzke [J. Less-Common Met. 121, 537 (1986)].

Vacancy clustering and diffusion in heavily P doped Si

A kinetic Monte Carlo (KMC) algorithm with a vacancy source and sink has been developed to determine the equilibrium vacancy concentration (CVe) in Si1−xPx alloys. KMC results for CVe exhibit good agreement with the Lomer formula with added entropic terms to account for high P concentrations. They also highlight the role of CVe and clustering on self and impurity diffusion during thermal aging.

Modelling of the influence of the vacancy source and sink activity and the stress state on diffusion in crystalline solids

Diffusion in solids is a well-known phenomenon that has many consequences in technology and material science. Modelling of diffusion-controlled processes requires both a reliable theory of diffusion and reliable kinetic coefficients, as well as other thermodynamic data. Often the classical Darken theory, valid for stress-free systems with ideal vacancy source and sink activity, is generalized to multicomponent systems with ideal vacancy source and sink activity. Nazarov and Gurov presented a theory for stress-free systems with no vacancy source and sink activity. Recently we published a general theory of diffusion that accounted for the role of non-ideal vacancy source and sink activity, as well as the stress state. Since diffusion theories are tested and diffusion coefficients measured usually on diffusion couples, this paper presents evolution equations based on that general theory for a diffusion couple. In the limit, the equations of the Darken theory and the Nazarov and Gurov theory are valid for ideal vacancy source and sink activity and no vacancy source and sink activity, respectively. Simulations for binary and ternary diffusion couples demonstrate the influence of the vacancy source and sink activity and the stress state on evolution of site fraction profiles of components and vacancies, and on the Kirkendall effect.

Substitutional diffusion in multicomponent solids with non-ideal sources and sinks for vacancies

Based on previous work by the authors the diffusion equations for a multicomponent solid are derived. Generation and annihilation of vacancies are described by an evolution law which is directly coupled with an eigenstrain rate. Manning’s correlation factor f is used in the kinetic factor for diffusion of vacancies. In addition to presentation of the diffusion equations, a rigorous treatment of the boundary conditions, assuming no or an ideal source and sink for vacancies at the surface, is presented. As an instructive example development of the site fractions of the components and the eigenstress state are demonstrated for a multicomponent chemically inhomogeneous layer on a substrate. Both the role of nonlinear terms and the correlation factor f in the diffusion equations are studied. Computational procedures to calculate to the proper boundary conditions are also outlined.

Continuum simulations of the formation of Kirkendall-effect-induced hollow cylinders in a binary substitutional alloy

We examine binary substitutional diffusion in cylindrical diffusion couples in which free surfaces are considered explicit vacancy sources and sinks. The central region of the cylinder is initially occupied by an atomic species with a larger hop frequency, while the outer region is occupied by another atomic species with a smaller hop frequency. Equilibrium vacancy concentration is maintained at free surfaces that serve as vacancy sources and sinks. In the crystal, diffusion is governed by the standard diffusion equations with analytically evaluated diffusion coefficients. The void growth dynamics and hollow cylinder formation stemming from the Kirkendall effect are simulated. Our results show that the Kirkendall void growth involves two competing factors. One is the net inward vacancy flux that favors void growth. The other is the Gibbs–Thomson effect that favors void shrinkage. We compute the critical initial radius for void growth above which the Kirkendall effect dominates over the Gibbs–Thomson effect. The fully grown void radius and the elapsed time to the fully grown size are also predicted for different fast-diffuser volume fractions and fast-to-slow diffuser atomic hop frequency ratios.

Vacancy-driven stress relaxation in layers

The role of vacancies together with their generally non-ideal sources and sinks has been investigated previously in the context of multi-component diffusion. This concept is applied to a thin layer on a substrate subjected to an initial eigenstress state. The surface of the layer is assumed to act as an ideal source and sink for vacancies. The interface may act either as an ideal or as no source and sink for vacancies. Non-ideal sources and sinks are supposed in the bulk. The formation of a vacancy site fraction profile across the layer due to active sources and sinks and due to diffusion is studied, provoking a relaxation of the residual eigenstress state. A set of two nonlinear partial differential equations for both the vacancy site fraction and the eigenstress distributions is developed. The problem is reformulated in dimension-free quantities. The relation between the diffusivity and the activity of sources and sinks for vacancies in the bulk is characterized by a vacancy intensity parameter k. Numerical solutions are presented, and the influence of nonlinear terms in the evolution equations is evaluated. The simulations provide the evolution of the vacancy site fraction and of the hydrostatic stress profiles in the layer. The development of a film of newly deposited or removed atoms at the layer surface and of the total thickness of the layer is also calculated. The results of simulations are discussed.

Lattice Strain Due to an Atomic Vacancy

Volumetric strain can be divided into two parts: strain due to bond distance change and strain due to vacancy sources and sinks. In this paper, efforts are focused on studying the atomic lattice strain due to a vacancy in an FCC metal lattice with molecular dynamics simulation (MDS). The result has been compared with that from a continuum mechanics method. It is shown that using a continuum mechanics approach yields constitutive results similar to the ones obtained based purely on molecular dynamics considerations.

Grain-boundary source/sink behavior for point defects: An atomistic simulation study

Abstract The grain-boundary source and sink strengths for both vacancies and self-interstitials have been determined for columnar nanocrystalline structures of Mo using molecular-dynamics simulation. The microstructures, which are initialized to contain either an over-saturation or under-saturation of one particular point defect species (either vacancies or self-interstitials), are subjected to isothermal annealing at high homologous temperatures (T > 0.75Tm) while the point-defect concentrations are monitored throughout. We clearly observe an exponential approach of the point-defect concentrations to equilibrium, in agreement with classical rate theory. These observed approaches to equilibrium yield grain-boundary source/sink strengths that correlate with analytical solutions that depend solely on the grain size. Finally, we find that grain boundary sinks have an approximately equal affinity, or bias, to vacancies and self-interstitials.

Hydrogen vacancies facilitate hydrogen transport kinetics in sodium hydride nanocrystallites

We report ab initio calculations based on density-functional theory, of the vacancy-mediated hydrogen migration energy in bulk NaH and near the NaH(001) surface. The estimated rate of the vacancy mediated hydrogen transport, obtained within a hopping diffusion model, is consistent with the reaction rates of H-D exchange in nano-NaH at the relatively low temperatures observed in recent neutron studies on TiCl3-doped NaAlH4. We further obtained the formation energy for hydrogen vacancies and interstitials in NaH in all relevant charged states. These formation energies are too high to lead to the abundant hydrogen concentrations seen experimentally. Ab initio calculations on the NaCl//NaH interface are presented to provide an insight into the mechanism which may lead to high hydrogen concentrations. We show that the formation of an fcc-Na interlayer during the growth of NaH on top of NaCl is plausible, providing a source of vacancies and leading to fast hydrogen transport. The low interface energies for NaCl//NaH are consistent with an easy growth of NaH crystallites on NaCl nucleation centers, which may, therefore, act as grain refiners.