Quantum chemical modelling of polarons and perovskite solid solutions

Following our previous study [J. Phys.: Condens. Matter 10 (1998) 6271] of a single Nb impurity and Nb clusters in KTaO₃, we present results of the calculations for a series of perovskite KNb_xTa_1−xO₃ (KTN) solid solutions (x=0, 0.125, 0.25, 0.75, 1). The quantum chemical method of the intermediate neglect of the differential overlap (INDO) combined with the large unit cell (LUC) periodic model is used. According to the INDO calculations, Nb impurity becomes off-center in KTaO₃ already at the lowest studied concentrations (x=0.125), in a good agreement with XAFS measurements. We compare our results with previous ab initio FP-LMTO calculations. Quantum chemical calculations confirm the existence of self-trapped electrons in KNbO₃; the corresponding lattice relaxation energy is 0.21 eV. We estimate the optical absorption energy to be 0.78 eV. An electron in the ground state occupies a t_2g orbital of the Nb⁴⁺ ion. Its orbital degeneracy is lifted by a combination of the breathing and Jahn–Teller (JT) modes when four nearest equatorial O atoms are displaced by 1.4% a_o outwards and two oxygens shift 1% inwards along the z axis.     

A theoretical study of H absorption at a Fe(110)–Pd(100) interface and Fe–Pd alloys

The electronic structure and bonding at a Fe(110)–Pd(100) interface was theoretically analyzed in the framework of semi-empirical quantum chemical calculations. The Fe–Pd interface was modeled by a Fe₇₄Pd₇₄ cluster and a Fe–Pd six layer slab.The extended Hückel tight binding (EHTB) method and its modifications, including repulsive interactions, were used to calculate the interfacial adhesion and the H-absorption energy.The energetic minimum position for H is found at the Fe–Pd interface closer to the Pd layer.The interfacial Fe–Pd distance result to be 1.73 Å where Fe–Pd develops a strong bonding interaction. An important metal–metal adhesion was also found.The changes in the Density of States (DOS) and the Crystal Orbital Overlap Population (COOP) were compared in different structures: clusters, slab and two types of Fe–Pd alloys.The H as an impurity is responsible for a Fe–Fe and Pd–Pd bond weakening.However, the H effect is much less detrimental for the Fe–Pd bonds at the interface.When H is located at interstitial sites in bulk Fe–Pd alloys, the Pd–Pd overlap population shows a notorious decrease in the case of fcc structures while for fct structures the change is only 12%. The intermetallic bonding was also weakened as compared with the pure alloys. The objective of this work is to bring a plausible explanation to the null permeability to hydrogen in Pd-coated Fe films.     

Quantum chemical modelling of point defects in KNbO3 perovskite crystals

We present results of semi-empirical quantum chemical calculations for several perovskite KNb_xTa_1−xO₃ (KTN) solid solutions, as well as point intrinsic defects – F centers and hole polarons bound to K vacancy – in KNbO₃. Method of the intermediate neglect of the differential overlap (INDO) was combined with typically 320-atom supercells and atomic geometry optimization. Analysis of the optimized atomic and electronic structure has clearly demonstrated that several nearest Nb atoms substituting for Ta in KTaO₃ – unlike Ta impurities in KNbO₃ – reveal the self-ordering effect, which probably triggers the ferroelectricity observed in KTN. We predict co-existence of one-site (atomic) and two-site (molecular) polarons with close absorption energies (≈1 eV). When available, the INDO results are compared with ab initio calculations. The relevant experimental data are discussed.     

Networks of influence and infection: parental choices and childhood disease

Clusters of unvaccinated individuals are at risk of outbreaks of infection. When an individual''s decision to choose vaccination is influenced by the choices of his social group, such clusters can readily arise. However, when the interactions that influence decision-making and those that permit the transmission of infection are different—for instance, when parents make vaccination decisions on behalf of their children—it is unclear how large the impact of this social influence will be. Here we use a modelling approach to represent social influence within a network of parents and the transmission of infection through a network of children. We show that the effect of social influence depends on the amount of overlap between the two different networks; large overlap means that clusters of parents who choose not to vaccinate are likely to have interacting children, generating clusters of unvaccinated children. Spatially local connections can further increase the impact of social influence. Outbreaks are most likely when parents who do not vaccinate have children who interact.     

Mobility of small clusters of self-interstitial atoms in dilute Fe–Cr alloy studied by means of atomistic calculations

Atomistic simulations have been used to characterize the interaction and mobility of small clusters of self-interstitial atoms (SIAs) in dilute Fe–Cr alloys. The variety of migration mechanisms for Di- and Tri-SIA clusters in the bcc Fe matrix were studied using the nudged elastic band method. The corresponding binding and migration energies for the SIA clusters interacting with isolated Cr atoms and Cr–Cr close pairs were calculated using the two-band model interatomic potential. The obtained results are discussed in the light of available experimental data for dilute Fe–Cr alloys and are compared with results obtained using ab initio calculations.     

On the Cluster Structure of a Circulating Fluidized Bed

A model of a bottom fluidized bed has been developed, in which the latter is represented as an ensemble of uniformly distributed spherical clusters. Using Ergun’s formula, we obtained the dependence for calculating the diameter of a cluster. The results were compared with experimental data on the sizes of clusters in the transport zone of a circulating fluidized bed. In the framework of this model, a correlation to calculate the rate of filtration at which the bottom layer disappears has been obtained.__________Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 78, No. 2, pp. 104–110, March–April, 2005.     

The Nucleation of a Nanoparticle of Silicon Dioxide in a Closed Domain. Computer Experiment

The method of molecular dynamics is used to study SiO₂ clusters located in cavities of spherical, cylindrical, and cubic shape. The effect of the elastically stressed state of the cell boundaries on the physical properties of nanoparticles contained in them is investigated. Given the same pattern of application of external forces, a nanoparticle in a spherical cell experiences a stronger compression than in clusters surrounded by envelopes of other geometries. The clusters assume the shape of the cavity in which they were contained. The effect of compressive forces results in the breakage of Si–O bonds and in the subsequent oxygen enrichment of the cluster surface. The behavior of nanoparticles after the elimination of the stimulation by the cavity boundaries is treated. It is only for a cluster of spherical geometry that a significant number of Si–O bonds is restored. For other clusters, the evaporation of oxygen atoms is observed.     

Fabrication of fluorescent hollow capsule with CdS–polyelectrolyte composite films

CdS–polyelectrolyte (CdS–PE) clusters were synthesized by using polyelectrolyte as the stabilizing agent in the aqueous solution. The blue shift of UV–Vis and Fluorescent spectra, the TEM images show the formation of nanoparticles within the polyelectrolyte chains. Using the normal polyelectrolyte hollow capsules as template, the CdS–PE clusters as functional layer materials, the uniform organic–inorganic hollow microspheres have been produced by layer-by-layer (LbL) self-assembly technology.     

Quantum-chemical simulation of Al- and Sc-bound hole polarons in BaTiO3 crystal

Quantum-chemical modelling of impurity-bound hole polarons in BaTiO₃ crystal was carried out employing the semi-empirical method of intermediate neglect of differential overlap (INDO) modified for crystals. Two-site hole has been found to be the most common configuration in the BaTiO₃ crystal doped with Al or Sc atoms. The automated geometry optimisation was carried out to obtain the polaron spatial configuration and atomic displacements in the defective region. The ΔSCF calculated absorption energy for the aluminium-bound polaron was found to be equal to 0.27 eV and the corresponding absorption energies for scandium-bound polaron were computed to be 1.92 and 0.62 eV.     

Hermite–Cloud: a novel true meshless method

In this paper, a novel true meshless numerical technique – the Hermite–Cloud method, is developed. This method uses the Hermite interpolation theorem for the construction of the interpolation functions, and the point collocation technique for discretization of the partial differential equations. This technique is based on the classical reproducing kernel particle method except that a fixed reproducing kernel approximation is employed instead. As a true meshless technique, the present method constructs the Hermite-type interpolation functions to directly compute the approximate solutions of both the unknown functions and the first-order derivatives. The necessary auxiliary conditions are also constructed to generate a complete set of partial differential equations with mixed Dirichlet and Neumann boundary conditions. The point collocation technique is then used for discretization of the governing partial differential equations. Numerical results show that the computational accuracy of the Hermite–Cloud method at scattered discrete points in the domain is much refined not only for approximate solutions, but also for the first-order derivative of these solutions.     

Metal dissolution in aqueous electrolyte: Semi-empirical Hartree-Fock and ab initio MD calculations

The semi-empirical Hartree-Fock intermediate neglect of differential overlap (INDO) method and ab initio molecular dynamics (MD) were used to model complementary aspects of the dissolution of metal in aqueous electrolyte. The INDO calculations were used to explore the potential energy surface of adsorbed water molecules and the reaction path followed by metal ions leaving the cluster. The MD calculations showed how the hydration shell formed around the metal ion as it left the surface, starting with one top site adsorbed water and ending with a five waters surrounding the ion.     

A method for the numerical investigation of nonstationary processes in multisectional installations for separating multicomponent isotope mixtures

On the basis of the Dufort-Frankel method for the integration of differential equations of parabolic type, we develop a method for the numerical calculation of nonstationary processes.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 43, No. 3, pp. 456–462, September, 1982.     

Kinetics of distillation with vapor (gas) in a layer

Based on an analysis of the solution of the differential equation of diffusion and experimental data on the kinetics of distillation, we investigate the problem of the intensity of turbulence in a boundary layer under conditions of bubbling of vapor through a layer of liquid (vegetable oil).Scientific-Industrial Association of Fatty Oil Industry, St. Petersburg. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 67, Nos. 3–4, pp. 255–257, September–October, 1994.     

Interaction of dissolved atoms and relaxation due to interstitial atoms in hcp metals

The literature data on the mechanism of internal friction maxima induced by O, N, and C in α-Ti, α-Zr, and α-Hf, are contradictory. They do not answer the question which kind of complexes induces relaxation: interstitial atoms or interstitial atoms with substitutional atoms. To clarify this question, modeling of the short-range order and atomic displacement fields around the solute atom clusters was carried out by the Monte-Carlo technique for typical Ti–O–Zr alloys. The energies of strain-induced (elastic) O–O and O–Zr interactions and displacement fields of host atoms around the solute atoms were calculated and used in modelling. The concentration dependence of relaxation strength due to diffusion under stress of oxygen atoms was evaluated using the values of local displacement around the solute atom complexes. It is shown that the developing short-range order cannot be described by the single O–O or O–Zr pair and the associated relaxation, as simple reorientation of any specific atomic pairs. It seems likely that in many cases the internal friction is caused by more complicated clusters constituted by interstitial and substitutional atoms.     

On One Method of Solving Nonstationary Heat-Conduction Problems for Multilayer Structures

As applied to the solution of the heat-conduction problem for a two-layer structure, the Fourier method is used jointly with the orthogonal Bubnov-Galerkin method. An important feature is the introduction of additional boundary conditions, the need for which is explained by the appearance of an additional parameter μ after the separation of the variables in the input differential equation. The additional boundary conditions are derived from the basic differential equation by differentiating it at the boundary points.__________Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 78, No. 2, pp. 24–28, March–April, 2005.     

Analytic Solution of the Plane Problem of the Theory of Elasticity for a Nonuniform Strip

We construct the analytic solution of the plane problem of the theory of elasticity in stresses for a strip nonuniform across the width. To deduce the key equations, we perform the direct integration of the original differential balance and continuity equations. In the space of Fourier transforms, the key equations are reduced to an integral Volterra equation of the second kind, which is solved by the method of successive approximations.__________Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 41, No. 1, pp. 114–116, January–February, 2005.     

Computational investigation of GanAl (n = 1–15) clusters by the density-functional theory

Low-lying equilibrium geometric structures of aluminum-doped gallium cluster Ga_nAl (n = 1–15) clusters obtained by an all-electron linear combination of atomic orbital approach, within spin-polarized density functional theory, are reported. The binding energy, dissociation energy, and stability of these clusters are studied with the three-parameter hybrid generalized gradient approximation (GGA) due to Becke-Lee–Yang–Parr (B3LYP). Ionization potentials, electron affinities, hardness, and static polarizabilities are calculated for the ground-state structures within the same method. The growth pattern for Ga_nAl (n = 1–15) clusters is Al-substituted Ga_n + 1 clusters and it keeps the similar frameworks of the most stable Ga_n + 1 clusters except for Ga₈Al and Ga₁₃ Al clusters. The Al atom substituted the surface atom of the Ga_n + 1 clusters for n < 12. Starting from n = 12, the Al atom completely falls into the center of the Ga-frame. The Al atom substituted the center atom of the Ga_n + 1 clusters to form the Al-encapsulated Ga_n geometries for n > 12. The odd−even oscillations from Ga_nAl (n = 5) in the dissociation energy, the second-order energy differences, the HOMO–LUMO gaps, the ionization potential, the electron affinity, and the hardness are more pronounced. The stability analysis based on the energies clearly shows the clusters from n = 5 with an even number of valence electrons are more stable than clusters with odd number of valence electrons.     

Solution of a direct problem of heat exchange between a cooled turbine blade and a gas by the pivot method

Using the pivot method we solve a third-order differential equation that describes the heat exchange of a gas with a cooled turbine blade.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 21, No. 3, pp. 531–536, September, 1971.     

Surface Phenomena in the Hydrodynamics of an Incompressible Fluid

By taking as an example the outflow of an incompressible fluid through a hole with small geometric parameters under the conditions of supersmall pressures, we attempted to evaluate the effect of surface phenomena on its flow by the similarity method. The Navier–Stokes differential equation was supplemented by parameters allowing for the effect of surface forces. The modified Navier–Stokes equation was subjected to similarity conversion. This yielded a dimensionless group that includes the whole range of variable parameters affecting the fluid flow, namely, the generalized criterion Pv. The graphic dependence of the coefficient of the fluid flow rate on the generalized criterion Pv is presented on the basis of experimental data.     

Small Cluster Studies of the Lattice Coupling of the Emery Model

Small copper–oxygen clusters as parts of the copper–oxygen planes are diagonalized numerically. The dependence on in plane oxygen displacements simulated by varying the transfer integrals is studied for different dislocation patterns. Energy eigenvalues, correlation functions, and adiabatic potentials are given.