Charge distribution in structurally disordered systems

In this paper we calculate the charge distribution n(Q) for a structurally disordered system of identical atoms. The atoms have non-zero charges associated to them only because the spatial configuration around each atom is different. The systems considered are those for which an atomic basis set is adequate and an iterative tight binding scheme, where the matrix elements depend on the atomic charges, is used. We study the effect of including explicitly the electrostatic interaction among the charges associated to the atoms in the calculation of n(Q). We propose that the atomic positions of a totally random configuration be modified by amounts proportional to the electrostatic forces on the atoms. We call this a relaxation effect. We find that the new atomic configurations give a narrower n(Q) although they have practically the same energy and radial distribution function as the original configuration.     

Periodic systems of N-atom molecules

The atoms have long been classified into a periodic system, which is now based on quantum mechanics and group theory. A classification of molecules containing any number (N) of atoms is proposed. It is an extension of the periodic system of the atoms. The approach in this paper is that of group theory, although the proposed system has been subjected to exhaustive comparison with experimental and ab initio computational results for diatomic molecules, and conforms to the commonly known behaviours of molecules with larger N. Orthonormal transformations are performed so that the molecules can be arranged according to their numbers of electrons and to the differences of atomic numbers of the constituent atoms. These arrangements parallel the physical reality of atomic bonding and permit partial three-dimensional models of the systems to be constructed for molecules with as many as four atoms.     

Recent Advances in the Theoretical Methods and Computational Schemes for Investigations of Resonances in Few-Body Atomic Systems

This paper describes the research works performed in my group in recent years in the theoretical methods and computational schemes for investigations of resonances in few-body atomic systems. These methods include the complex absorbing potential method, the stabilization method, and the method of complex scaling. In addition to atomic resonances, this paper also describes some of our recent works on investigations of Borromean bindings in three-body atomic systems. By systematically changing the two-body interaction from the long range Coulomb potential to the short range screened Coulomb (Yukawa) potential, we have investigated the Borromean bindings for hydrogen molecule ion H ₂ ⁺ and the muonic molecular ions.     

The atomistic origin of the inverse piezoelectric effect in α-quartz

Ab initio calculations have been carried out using the FP-APW+lo method in order to understand the atomic origin of the inverse piezoelectric effect in α-quartz. The external electric field was modelled by a saw-like potential V_ext in order to achieve translational symmetry within a supercell (SC) containing 72 atoms. The original trigonal quartz structure was repeated along the [110] direction, which corresponds to the direction of the external field. An electric field with 550 kV/mm was applied and the atomic positions of the SC were relaxed until the forces acting on the atoms vanished. In parts of the SC, V_ext changes almost linearly and thus the relaxed atomic positions can be used to determine the structural response due to the external electric field. The calculations provide the piezoelectric modulus of the correct order of magnitude. In contrast to previous models and in agreement with recent experimental results, the atomic origin of the piezoelectric effect can be described by a rotation of slightly deformed SiO₄ tetrahedra against each other. The change of the Si-O bond lengths and the tetrahedral O-Si-O angles is one order of magnitude smaller than that of the Si-O-Si angles between neighbouring tetrahedra. The calculated changes of X-ray structure factors are in agreement with experiment when the theoretical data are extrapolated down to the much smaller field strength that is applied in the experiment (E<10 kV/mm).     

Optical switching in a Ξ system: A comparative study on DROP and EIT

Liquid Lennard-Jones clusters with magic number of atoms N = 55, 147, 309, 561 and 923 were cooled down in Monte Carlo simulations until freezing. Structural properties of the clusters, including the radial dependence of atomic concentration/density and the local regular structure in arrangement of atoms, just before freezing were analysed. Existence of spherical layers in atomic density around the centre of mass of liquid LJ clusters was confirmed. Formation of layers is explained by central net forces acting on every cluster atom and leading to positioning an atom close to the cluster centre of mass. The strong layering in small clusters of N = 55 and 147 affects atomic diffusion in radial and tangential directions inside the cluster, leading to easier movement of atoms on the layer surface. Analysis of radial profiles of four types of structural units detected in liquid clusters reveals that icosahedral units are the most numerous and are located mainly near cluster surface of all clusters and also in the centre of small clusters.     

An interpretation of structural sorting diagrams for AB type compounds using molecular orbital ideas

The factors governing the structure adopted by a particular AB compound are investigated by deriving two parameters reflecting aspects of the interaction between A and B, using simple molecular orbital ideas, which can be quantified by use of atomic parameters derived from pseudopotential theory. A plot of the values of these two parameters, for a large database of compounds, produces a remarkable topological clustering of AB compounds with the same structure. This structural sorting can also be effected for nonoctet AB compounds if the number of electrons is taken into account. These parameters are related to other indices, R_σ, R_π, previously used by Bloch, Zunger, Phillips et al. to construct structural sorting diagrams. Hence we find a justification for the success of such displays, and shed light on the reasons underpinning structural preference, in terms of the number of valence electrons, and the relative positions of the energy levels of the constituent atoms. There appear to be strong similarities between the electronic reasons behind atomic site preferences in molecules and this site preference or coordination number problem in solids.     

Scattering of slow electrons by inert gas atoms. Effective polarization potential method

The problem of selecting the polarization-correlation potential V _pol for describing the interaction of electrons with atomic targets is examined. Based on the differential cross section for electron scattering by the hydrogen atom calculated using the partial wave method and the exact exchange operator, the optimal form of this potential is determined. It is demonstrated that the parameters of the potential V _pol can be determined from the condition of equality of the calculated and experimental values of the electron affinity of the hydrogen atom. For the interaction of slow electrons with inert gas atoms, the polarization parameter R _p is proposed to be determined from the known position of the Ramsauer minimum in the total elastic scattering cross section. In particular, calculations are performed for krypton and argon atoms. The results agree well with numerous experimental and theoretical published data.     

First-principle study of structural and electronic properties of ternary layered Ta2AlC

The structural and electronic properties of ternary layered Ta₂AlC ceramics have been studied using the first-principle method based on the density-functional theory. We have obtained the equilibrium lattice parameters and the equilibrium atomic positions in the unit cell. The equilibrium lattice parameters are computed to be a=b=3.15 Å and c=13.95 Å. The internal coordinates of Ta are determined to be (1/3, 2/3, 0.092). The band structure and density of states reveal that Ta₂AlC is an electronic conductor. The charge density distribution shows that the Ta and C atoms form a strong Ta-C-Ta covalently bonded chain.     

Thermal expansion near plane and stepped surfaces

A theory of the thermal expansion of the plane and (11n) stepped surfaces of fcc crystals is presented. The temperature dependent relaxations arise from cubic anharmonic terms in the crystal potential energy. We show that the thermal expansion depends on the positions of the atoms with respect to the steps and is greatest for the atom of the upper corner. The knowledge of these new atomic positions at each temperature allows us to calculate new atomic force constants and then new vibrational properties at this temperature. The application is made for a Ni crystal for which we give the corrections, due to the thermal expansion, on the mean square displacements of stepped surface atoms. The variation with temperature of the optical modes due to a light monolayer is also presented.     

X-ray scattering: A powerful probe of lattice strain in materials with small dimensions

X-ray diffraction was recognized from the early days as highly sensitive to atomic displacements. Indeed structural crystallography has been very successful in locating with great precision the position of atoms within an individual unit cell. In disordered systems, it is the average structure and fluctuations about it that may be determined. In the field of mechanics, diffraction may thus be used to evaluate elastic displacement fields. In this short overview, we give examples from recent work where X-ray diffraction has been used to investigate average strains in lines, films or multilayers. In small objects, the proximity of surfaces or interfaces may create very inhomogeneous displacement fields. X-ray scattering is again one of the best methods to determine such distributions. The need to characterize displacement fields in nano-structures together with the advent of third generation synchrotron radiation sources has generated new and powerful methods (anomalous diffraction, coherent diffraction, micro-diffraction, etc.). We review some of the recent and promising results in the field of strain measurements in small dimensions via X-ray diffraction.     

Atomic charges in Mg2SiO4 (forsterite), fitted to thermoelastic and structural properties

First and second derivatives of cohesion energy of forsterite with respect to cell edges (generalized Born-Mayer model) are related to thermoelastic tensors; first derivatives with respect to five structural parameters (rotation angle of the SiO₄ tetrahedron, translations of Si and Mg(2) atoms) are set equal to zero by the zero-force principle. All differentiations are performed by keeping constant the internal geometry of the SiO₄ group. Fourteen equations are then obtained and solved numerically in the magnesium and oxygen atomic charges, and in three repulsive parameters, considered as unknowns. The best fitting charge distribution is: z_Mg = 1.38, z_o = ?1.05, z_si = l.44 e. Elastic constants are reproduced with an average relative deviation of 4%, and calculated atomic positions show an average shift of 0.014 A from experimental values. Results are discussed and compared with atomic charges determined from X-ray electron density measurements and vibrational spectroseopy data.     

An atomistic study of grain boundary segregation and cracking

A Monte Carlo model is applied to study a Σ = 5 (310) fcc tilt boundary structure and impurity segregation to this boundary. The Johnson-type potential functions are used to express atomic interactions for two binary alloys of NiCu and CuSb systems. Through atomic relaxation near absolute zero, the basic structural unit of the Σ = 5 CSL boundary is found to dissociate into two subunits. For the NiCu system, copper segregation to the boundary follows the Gibbsian equilibrium segregation behavior in which the segregation is localized on a few atomic layers, its amount increases with increase in the bulk concentration but decreases with increase in temperature. For the CuSb system, an assumption of the CuCu bond weakening due to the strong, adjacent CuSb bonds is also incorporated to realize the embrittling effect of Sb atoms. The preferential site for the large Sb atoms is the vertex of a pentagonal bipyramid in the Σ = 5 grain boundary. Without bond weakening, the Sb-segregated grain boundary maintains a structure combined with a distorted pentagonal bipyramid and a capped trigonal prism. However, with bond weakening some bonds of the trigonal prisms are disrupted in order to form new pentagonal bipyramids. When a uniaxial strain is applied in the direction perpendicular to the grain boundary plane, the weakened copper bonds become the source of microcracks thus enhancing brittle fracture along the Sb-segregated grain boundary.     

Electronic transport properties of graphene/Al2O3 (0001) interface

The electronic structure and transport properties of a single layer of graphene (Gr) on α-Al₂O₃ surface are studied using the density functional theory (DFT). We present three models that take into account the atom at the termination of the alumina surface: a) Al atoms, with the center of the Gr hexagon directly over an Al atom; b) Al atoms, with a carbon directly positioned above an Al atom; c) oxygen atoms. Two processes of geometric optimization were used: (i) All the atoms of the supercell were allowed to move in accordance with the BFGS quasi-Newton algorithm; (ii) The atoms of the three topmost layers of the α-Al₂O₃ (0001) slab, including the C atoms, were allowed to move, whereas the atoms of the remaining layers were frozen in their respective atomic bulk positions. The first two models preserve qualitatively the electronic structure of the pristine Gr using the geometric optimization process (i) whereas, in the third model this structure was lost due to a significant charge transfer between the carbon and oxygen atoms irrespective of the optimization procedure. However, models (a) and (b) with the optimization (ii) reveal a p-type semiconducting behavior.     

Coherent emission of a photon by many atoms

The theory ofWeisskopf andWigner of the natural line width is extended to a case where many atoms at given positions interact with one common quantized radiation field. At timet=0, one quantum of radiation energy is stored by the atoms, which however does not mean necessarily that exactly one of the atoms must be excited. We study the process of the creation of a photon in dependence on the positions of the atoms and on the state of the system of atoms att=0. The dimensions of the emitted wave train and the decay time of this excited atomic state depend sensitively on these parameters.     

Mechanism of chemisorption and interface penetration in reactive systems at low temperatures

In the transport mechanism discussed it is demonstrated that in the large gradients of the chemical potential that exist in reactive systems gas atoms should be able to migrate in a perpendicular direction up to several atomic distances below the surface by non-activated processes. The exponential decrease in the sticking probability s observed after an initial stage with a constant s value of about unity is correlated with the increase of the activation energy barrier between molecules in the gas phase and in the chemisorbed state on the surface. Quantitative experimental results of the kinetic of chemisorption processes recently obtained for oxygen and nitrogen systems support the qualitative and semiquantitative statements of the mechanism proposed.     

Surface diffusion of Pb clusters on Cu(1 1 1) influenced by size dependent cluster-substrate misfit: Monte Carlo tight binding simulation model

The migration of two-dimensional Pb clusters on Cu(1 1 1) surface is studied in the framework of three-dimensional (3D) continuum space tight binding (TB) computational model. Monte Carlo simulations based on many-body TB interactions reveal significant influence of cluster-substrate misfit on diffusion behavior of two-dimensional (2D) clusters. The analysis of pair distribution function (PDF) demonstrates that cluster lattice constant depends on the number of atoms N for 1 < N < 10. The observed effect is more pronounced for heteroepitaxial than homoepitaxial systems. It can be explained in the framework of model accounting for enhanced charge transfer in heteroepitaxy and strong influence of surface potential on cluster atomic arrangement. The variation of lattice constant leads to variable misfit which affects the island migration behavior. The results are discussed in a physical model that implies cluster diffusion with size dependent cluster-substrate misfit.     

Energy bands of atomic monolayers of various materials: Possibility of energy gap engineering

The mobility of graphene is very high because the quantum Hall effects can be observed even at room temperature. Graphene has the potential of the material for novel devices because of this high mobility. But the energy gap of graphene is zero, so graphene cannot be applied to semiconductor devices such as transistors, LEDs, etc. In order to control the energy gaps, we propose atomic monolayers which consist of various materials besides carbon atoms.To examine the energy dispersions of atomic monolayers of various materials, we calculated the electronic states of these atomic monolayers using density functional theory with structural optimizations. The quantum chemical calculation software Gaussian 03 was used under periodic boundary conditions. The calculation method is LSDA/6-311G(d,p), B3LYP/6-31G(d), or B3LYP/6-311G(d,p).The calculated materials are C (graphene), Si (silicene), Ge, SiC, GeC, GeSi, BN, BP, BAs, AlP, AlAs, GaP, and GaAs. These atomic monolayers can exist in the flat honeycomb shapes. The energy gaps of these atomic monolayers take various values. Ge is a semimetal; AlP, AlAs, GaP, and GaAs are indirect semiconductors; and others are direct semiconductors.We also calculated the change of energy dispersions accompanied by the substitution of the atoms. Our results suggest that the substitution of impurity atoms for monolayer materials can control the energy gaps of the atomic monolayers.We conclude that atomic monolayers of various materials have the potential for novel devices.     

Atomic structure of a 1<Emphasis Type="Italic">T</Emphasis>-TiSe<Subscript>2</Subscript> surface layer from photoelectron and Auger electron holography data

A three-dimensional (3D) reconstruction of the atomic structure of the (100) surface of a 1T-TiSe₂ layered dichalcogenide crystal has been performed from X-ray photoelectron and Auger electron diffraction data. The diffraction patterns of the emission of Auger electrons of Se(LMM) selenium and photoelectrons of Ti2p titanium have been considered as holographic diagrams. Being processed with the scattering pattern extraction algorithm using the maximum entropy method (SPEA-MEM), they provide individual 3D images of the nearest environment of selenium and titanium atoms in the TiSe₂ lattice. Using reconstructed 3D images, the positions of 128 atoms in the 2 × 2 × 1.5-nm region of the surface layer of TiSe₂ have been determined. The structure of the surface has a 1T polytype. Interatomic distances in the layer and van der Waals gap are larger than the respective parameters in the bulk of the crystal. It is assumed that titanium layers in two Se-Ti-Se upper surface structural units are displaced along the [001] axis. The structure of the surface layer can be described by a unit cell of the P3 space group with the parameters a = 3.85 Å and c = 14.4 Å.     

Study on the oscillatory behaviour of the lattice parameter in ternary iron–nitrogen compounds

The structural properties of the XFe₃N (X=Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu and Zn) cubic ternary iron based nitrides as well as the preferential occupation site of X in the structure were studied using Full Potential Linearized Augmented Plane Wave method, within the Density Functional Theory formalism, Wien2k code, the exchange-correlation potential described with the Perdew–Burke–Ernzerhof expression, based in the Local Spin Density Approximation and Generalized Gradient Approximation. According the calculations, the Sc, Co, Ni, Cu and Zn, atoms preferred the corner sites of the cubes, while Ti, V, Cr and Mn occupy the centre of the faces of the equilibrium structures. The equilibrium structure lattice parameters have an oscillatory behaviour with the atomic number of X, with decreasing amplitude as the atomic number of X increases. This trend do not correlated with the atomic radii of X.