Ideal Vacancy Research Articles

Computational study of Li3BO3 and Li3BN2 I: Electrolyte properties of pure and doped crystals

Both ${\mathrm{Li}}_{3}{\mathrm{BO}}_{3}$ and ${\mathrm{Li}}_{3}{\mathrm{BN}}_{2}$ materials have promising properties for use in all-solid-state batteries and other technologies dependent on electrolytes with significant ionic conductivity. As the first of a two-part study, this paper reports the analysis of detailed simulations of Li ion diffusion in the monoclinic forms of these materials. Using both NEB and MD methods, it is clear that Li ion migration via vacancy mechanisms provides the most efficient ion transport in each material. While the results suggest that interstitial defects in these materials do not play a direct role in Li ion migration, their relative stability seems to enhance vacancy production via the formation of Frenkel-type defects. This may partially explain why the Li ion conductivities computed from MD simulations of samples initially containing a single Li ion vacancy are in reasonable agreement with measured values of this work for ${\mathrm{Li}}_{3}{\mathrm{BO}}_{3}$ and those reported in the literature for poorly crystalline samples of both materials. The possibility of increasing vacancy concentrations by substitutional doping (F for O in ${\mathrm{Li}}_{3}{\mathrm{BO}}_{3}$ and C for B in ${\mathrm{Li}}_{3}{\mathrm{BN}}_{2}$) is also examined, finding simulated conductivities comparable to those of the ideal vacancy model.

OPTIMAL LIST PRICE AND DURATION OF VACANCY IN THE HOUSING MARKET IN TOKYO

In the housing market, the advertised list price significantly influences the final sale price and the duration a property spends on the market. With the uncertainties and complexities of the housing market, the list price can be a difficult and critical decision for home sellers. This paper develops a theoretical model for an optimal list price strategy with an information learning process to ensure a maximum expected return and a discussion of the ideal vacancy rate. The optimal list price strategy is composed of factors such as the frequency of list price revisions, the best timing to revise the price, and the value of a sequence of list prices and varies according to the market situation, and patience and prior knowledge of the seller. The results of the application in Tokyo 23 wards imply that there is an excess of houses in the sale market and potential for home sellers to improve their list price strategy and the learning process in order to shorten the time a property spends on the market without losing any return.

Effects of coherency stress and vacancy sources/sinks on interdiffusion across coherent multilayer interfaces – Part II: Interface sharpening and intermixing rate

Vacancy-mediated interdiffusion in coherent Mo/V and Cu/Ni multilayers is simulated to evaluate the effects of coherency stress and vacancy sources/sinks on interface sharpening and the intermixing rate, using the phase field model developed in a previous paper for two limiting cases: ideal vacancy sources/sinks densely distributed or not present at all. Interface sharpening stems from a large diffusion coefficient asymmetry across the interface, which in turn originates from the large difference in vacancy formation and migration energies between the two constituent layers. Remarkable sharpening is found in Mo/V multilayers either with dense or without vacancy sources/sinks, but only in Cu/Ni with a high density of sources/sinks. Sharpening is suppressed by coherency stress in Cu/Ni regardless of the existence of vacancy sources/sinks, but only promoted in Mo/V with a high density of sources/sinks. The intermixing rate is suppressed in Mo/V by the introduction of a high density of vacancy sources/sinks that are parallel or perpendicular to the interfaces, or uniformly distributed in all orientations, but only promoted in Cu/Ni by the introduction of vacancy sources/sinks that are parallel to the interfaces. The intermixing rate is promoted in Mo/V by coherency stress regardless of the existence of vacancy sources/sinks, but promoted in Cu/Ni by coherency stress only when the vacancy sources/sinks are parallel to the interface or not present at all. The effects of that part of coherency stress induced by the mismatch in atomic volumes on interface sharpening and the intermixing rate are opposite to, but dominant over, those of the stress induced by lattice creation/annihilation in vacancy sources/sinks.

Effects of coherency stress and vacancy sources/sinks on interdiffusion across coherent multilayer interfaces – Part I: Theory

A phase field model corresponding to vacancy-mediated interdiffusion in coherent multilayers with completely miscible constituents is developed to explore the effects of several factors on interdiffusion across coherent multilayer interfaces, such as: (1) the dependence of diffusion potentials and mobilities on coherency stress; (2) the dependence of diffusion potentials and mobilities on composition; (3) the elastic constant inhomogeneity resulting from a inhomogeneous composition distribution; and (4) the properties of vacancy sources/sinks. The Gibbs free energy of the system consists of chemical and elastic energies. The gradient energy is neglected as the multilayers under consideration can be chemically well approximated by an ideal substitutional solution model. Elastic energy is a function of the stress-free strain and inhomogeneous elastic moduli distributions, while the stress is solved by anisotropic phase field microelasticity theory. The diffusion potentials are obtained straightforwardly as functional derivatives of the free energy with respect to composition and are in keeping with previous derivations that involved many mathematical manipulations or quite advanced theories. The diffusion mobilities are affected by the stress through modification of the vacancy formation and migration energies. Two limiting cases of vacancy sources/sinks are taken into account: ideal vacancy sources/sinks are uniformly and densely distributed, or not present at all, so the vacancy concentration is in equilibrium all the times, as determined by the local stress and composition in the former case, but deviates from the equilibrium concentration in the latter. The model can be conveniently extended to consider the non-ideal activity of vacancy sources/sinks by introducing a general kinetic relation for the vacancy creation rate.

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.

Effects of Predation Threat on the Structure and Benefits from Vacancy Chains in the Hermit Crab Pagurus bernhardus

AbstractVacancy chains occur when individuals occupy discrete re‐useable resource units, which once abandoned by the current owner can then be occupied by a new owner. In order to enter the newly vacated resource the new owner must first vacate its current resource unit, such that a vacancy chain consists of a series of linked moves between resource units of different value, equivalent to different ‘strata’ in the chain. Vacancy chains may represent an important route by which resources are distributed through populations. Indeed, the arrival of a new resource has the potential to initiate a series of moves propagating beyond the individual that encounters the new resource unit. Thus, the chain participants as a whole may experience ‘aggregate benefits’ from the arrival of the new resource unit. The extent of these benefits, however, may not necessarily be evenly distributed between all chain participants; some individuals could receive greater than average benefits by moving through more than one stratum (‘skipping’) and some individuals could experience a reduction in resource value by moving to a resource unit of lower quality than that occupied initially (a ‘backward move’). Such moves represent deviations from the ‘ideal’ vacancy chains assumed by theory. Here we analyse the aggregate benefits and benefits to individuals participating in vacancy chains of empty gastropod shells in the hermit crab Pagurus bernhardus. We also investigate the effect of predation risk on these two levels of benefits and on chain structure. Adding a new shell at the top of the chain causes an overall increase in shell quality after 24 h but the distribution of benefits between strata in the chain varies with the presence and absence of the predator cue. Although there was significant concordance between chain structure in the presence and absence of the predator cue, the structure was significantly different from an ideal vacancy chain in the absence but not the presence of the predator cue.

Point defects in covalent semiconductors: A molecular cluster model

A multiple-scattering-Xα cluster model of tetrahedrally coordinated covalent semiconductors is discussed. In order to simulate the rest of the crystal at the cluster boundaries, all electrons filling dangling bonds are eliminated from the self-consistent calculations and transferred to a Watson sphere. This manner of simulating the “saturating effects” of the rest of the crystal is more practical than the usual procedure of terminating the atoms at the surface of the cluster with hydrogen atoms. The model is applied to perform the first self-consistent calculations of the electronic structure of vacancies and substitutional impurities in GaAs. The efficiency and accuracy of the model is demonstrated by calculating the well-studied states of an ideal vacancy in Si. The obtained results are in good agreement with other self-consistent calculations.

Electron States of a Vacancy in the Core of the 90° Partial Dislocation in Silicon

AbstractAn LCAO scheme (linear combination of atomic orbitals) taking into account ten atomic orbitals (s‐, p‐, and d‐type) is used to calculate the electronic structure of a vacancy present in the core of the reconstructed 90° partial dislocation in silicon. The levels in the band gap are extracted using Lanczos' algorithm and a continued fraction representation of the local density of states. The three‐fold degenerate state of the ideal vacancy is split into three levels with energies 0.26, 1.1, and 1.9 eV measured from the valence band edge.

Electronic energy levels of an ideal vacancy in II 3–V 2 compounds

The electronic properties of neutral ideal vacancies in some II–V compounds have been studied in the Green's-function framework and using the tight-binding method. It was shown that deep levels in the fundamental energy gap are created only for cation T 2 levels in phosphides and anion A 1 level for Zn 3As 2. The cation T 2 level for arsenides is degenerate (or nearly degenerate) with the top of the valence bands.

Electronic structure of a single oxygen vacancy in rutile TiO2

I report calculations of the electronic structure of an ideal (undistorted) oxygen vacancy in rutile TiO2 using the equation-of-motion method. I use a full phenomenological tight-binding Hamiltonian due to Vos to describe the electronic structure. The bulk band structure is also discussed in detail using the traditional Green’s-function method. I illustrate an efficient way to calculate the perfect-crystal Green’s-function matrix elements for any structure, including those that belong to non-symmorphic space groups. The results show that the oxygen vacancy in rutile TiO2 results in deeply localized states in its vicinty.

Electromigration-induced void growth in bamboo structures

A novel resistometric technique enables the investigation of single void nucleation and growth induced by electromigration (EM) for aluminum (Al) lines having a perfect bamboo structure in comparison with single-crystal Al lines. Fine tungsten (W) voltage probes were fabricated at every 4 μm along the Al line with grain sizes of 10 μm or more. Local electrical resistance changes have confirmed that a void nucleated only at the grain boundary and no damage appeared within the grains. The measured values of the local electrical resistance changes were converted to EM-induced void growth rates. The vacancy flux was deduced from the void growth rate under the assumption that a vacancy volume is equal to the atomic volume. It has been clarified that the vacancy fluxes for a bamboo-structured Al line were about one order magnitude smaller than the ideal vacancy fluxes in the Al lattice derived from the Nernst–Einstein relation. The vacancy fluxes for single-crystal Al lines were also quantified under an accelerated test at a high electric current density with a temperature gradient. These results suggest that the bamboo grain boundaries have a blocking effect on vacancy flow. This blocking produces vacancy supersaturation near the grain boundary, and the reduction in vacancy flux is well explained by the back-diffusion due to the corresponding concentration gradient.

The Ideal Vacancy States in α-Sn

The Ideal Vacancy States in α-Sn

Electronic Structure of the Ideal Vacancies in (Hg, Cd)Te

AbstractThe localized orbital method (LOM) based upon an atomic‐like basis set and empirical pseudopotential Hamiltonian in conjunction with the Green's function method is employed for the study of electron states of ideal vacancies in (Hg, Cd)Te. This method is used for the first time for a calculation of ideal vacancies in (Hg, Cd)Te. Bloch sums are formed from Gaussian orbitals of s and p symmetry on each atomic site. A systematic study shows that an accurate description of band energies and density of states can be obtained, with the use of a minimal Gaussian set. Since the relativistic terms are neglected the weighted average of the spin splitted levels of HgTe and CdTe are used for the calculation of band energies and densities of states. The calculated ideal vacancy states are in general agreement with what is known about defect levels in (Hg, Cd)Te.

Electronic structure of neutral and charged vacancies in Ga-related III-V compound semiconductors

Self-consistent semiempirical tight-binding theory is used to study the neutral and charged states of the ideal vacancies in GaP and GaSb. For the neutral states, the diagonal elements of the defect potential on the first and second nearest neighbors of a vacancy are obtained by a charge-neutrality condition, while for the charged states, these matrix elements are determined self-consistently. The theory also takes the off-diagonal matrix elements corresponding to atoms adjacent to a vacancy into account. The defect energy levels and the localizations of the levels are computed using the Lanczos–Haydock recursion method. The general character of the electronic structure of vacancies in the Ga-related III-V compound semiconductors has been extracted from these calculations and from the similar calculations we performed for vacancies in GaAs. We analyze the defect states of the vacancies in terms of chemical bondings of the crystals. It is shown that, for the cation vacancies (the Ga vacancies) in the three semiconductors, both the a1 resonances at the top of the valence band and the t2 bound states in the fundamental gap consist mainly of the atomiclike p orbitals centered on the four nearest neighbors, whereas for the anion vacancies, the a1 states at the top of the valence band contain mainly the atomiclike p orbitals of the four neighboring atoms and the t2 bound states in the fundamental gap contain both the atomiclike s and the atomiclike p orbitals of the four neighboring atoms. We also find that the t2 gap levels of the charged cation (anion) vacancies in the three semiconductors are all located in the lower (upper) half of the fundamental gap. The calculated results are in agreement with available results from local density calculations and support the identifications of the vacancy defects by the positron-annihilation technique.

Electronic structures of point defects in III-V compound semiconductors

The self-consistent electronic structures of ideal vacancies in nine III-V compound semiconductors and in Si and Ge have been calculated using the spin-unrestricted density-functional theory and the linear muffin-tin-orbital Green function method. Moreover, anti-site defects in these compound semiconductors have been investigated. The ionisation levels in the band gap have been determined from the total energies for all types of vacancies in different charge states. The trends in the ionisation level positions are studied when the width of the band gap and the 'size' of the vacancy are varying from one host to another. The results are compared with previous calculations and experiments, and the effects due to lattice relaxation are discussed.

Atomistic Computer Modelling in Advanced Materials R & D

Abstract One way to model the behaviour of advanced materials is to use ab initio total energy calculations. Because these are normally limited in practice to 20–100 atoms either a small supercell or a small fragment of the solid is used. We have chosen a small fragment of silicon with a hydrogenated surface (comprising 26 atoms) to evaluate the formation energy of an ideal vacancy and the activation energy for concerted exchange of atoms. The preliminary results reported here are in reasonable agreement with solid state calculations.

Study of the ideal vacancies in a IV-VI compound

The Green's function scattering-theoretic method is used to study the ideal vacancies in the SnTe. The diagonal matrix elements of the Green's function are calculated using the Linear Combination of Atomic Orbitals method with the minimal basis set, all nearest-neighbor interactions and a second neighbor interaction. A good description of the valence and the conduction bands is obtained. The Sn vacancy is found to induce two holes in the valence bands and the Te vacancy two electrons in the conduction bands, in accord with the known experimental and theoretical results. Using the calculated Green's function and the specifics of the electronic structure of the IV-VI compounds, the changes in the electronic structure due to a substitutional impurity and the implications of the vacancies to the structural stability of SnTe and the other IV-VI compounds are discussed.

Electron density and atomic relaxation around a vacancy in a small metal particle

The electron density in an ideal vacancy placed at the center of a small Aluminium microparticle has been studied as a function of the number of atoms in the microparticle. In these circumstances one can conclude that the perturbation of the density is localized in the close neighborhood of the vacancy and is nearly independent of the particle size. Then relaxation of the nearest neighbours of the vacancy was allowed. This relaxation was found to be small, but its sign depends on particle size. For particles larger than ∼100 atoms the relaxation is towards the vacancy, as for a vacancy in bulk Aluminium. But for smaller particles, the relaxation is away from the vacancy. This relaxation suggests a nontrivial size dependence of the energy of vacancy formation.

The Research of Electronic Properties of Hydrogenated a-Si

We first used Bethe lattice method and coherent potential approximation method to calculate the densities of bulk and surface states for a–Si, a–Si:H. The ideal vacancies were also studied. The results agree with experiments and other works. Dihedral disorder contributes to the submerging of a peak and sp peak of the valence band. In hydrogenated case, extra structure appears in the spectrum of densities of surface states. Doped hydrogen affects the densities of bulk states in the gap in principle, but hydrogen is not important for densities of surface states in the gap. Finally, we obtained self-energies which are in good agreement with the empirical results from experiments and other methods[1].

Local density of states of the Si(111) surface with vacancies and its reconstruction

Abstract The local density of states on and near an ideal vacancy on the unreconstructed and unrelaxed ideal (111) surface of silicon is calculated by means of a new generalized cluster-Bethe-lattice method, introduced recently by the present authors. The essence of the method is shortly described and illustrated on this particular example. The results compare well with photoemission experiments and calculations of other authors. They are discussed within the context of the existing ‘vacancy’ models of the Si(111)7 × 7 reconstruction.