Atomic Cluster Calculations Research Articles

Bond Energetics at Intergranular Interfaces in Alumina-Doped Silicon Nitride

In Si 3 N 4 ceramics sintered with Al 2 O 3 , the interfacial strength between the intergranular glass and the reinforcing grains has been observed to increase with increases in the aluminum and oxygen content of the epitaxial β-Si 6-z Al z O z N 8-z layer that forms on the Si 3 N 4 grains. This has been attributed to the formation of a network of strong bonds (cross bonds) that span the glass-crystalline interface. This proposed mechanism is considered further in light of first-principles atomic cluster calculations of the relative stabilities of bridge and threefold-bonded atomic fragments chosen to represent compositional changes at the glass/Si 3 N 4 grain interface. Calculated binding energies indicate Al-N binding is favorable at the Si 3 N 4 grain surface, where aluminum occupancy can promote the growth of SiAION, further enhancing the cross-bonding mechanism of interfacial strengthening.

The importance of amorphous intergranular films in self-reinforced Si3N4 ceramics

High-fracture-strength and high-toughness β-Si3N4 ceramics can be obtained by tailoring the size and number of the elongated bridging grains. However, these bridging mechanisms rely on debonding of the reinforcing grains from the matrix to increase toughness. Interfacial debonding is shown to be influenced by sintering aids incorporated in the amorphous intergranular films. In one case, the interface strength between the intergranular glass and the reinforcing grains increases with the aluminum and oxygen content of an interfacial epitaxial β-SiAlON layer. In another, the incorporation of fluorine in the intergranular film allows the crack to circumvent the grains. Atomic cluster calculations reveal that these two debonding processes are related to (1) strong Si–O and Al–O bonding across the glass/crystalline interface with an epitaxial SiAlON layer and (2) a weakening of the amorphous network of the intergranular film when difluorine substitutes for bridging oxygen.

Determining point charge arrays that produce accurate ionic crystal fields for atomic cluster calculations

In performing atomic cluster calculations of local electronic structure defects in ionic crystals, the crystal is often modeled as a central cluster of 5–50 ions embedded in an array of point charges. For most crystals, however, a finite three-dimensional repeated array of unit cells generates electrostatic potentials that are in significant disagreement with the Madelung (infinite crystal) potentials computed by the Ewald method. This is illustrated for the cubic crystal CaF2. We present a novel algorithm for solving this problem for any crystal whose unit cell information is known: (1) the unit cell is used to generate a neutral array containing typically 10 000 point charges at their normal crystallographic positions; (2) the array is divided into zone 1 (a volume defined by the atomic cluster of interest), zone 2 (several hundred additional point charges that together with zone 1 fill a spherical volume), and zone 3 (all other point charges); (3) the Ewald formula is used to compute the site potentials at all point charges in zones 1 and 2; (4) a system of simultaneous linear equations is solved to find the zone 3 charge values that make the zone 1 and zone 2 site potentials exactly equal to their Ewald values and the total charge and dipole moments equal to zero, and (5) the solution is checked at 1000 additional points randomly chosen in zone 1. The method is applied to 33 different crystal types with 50–71 ions in zone 1. In all cases the accuracy determined in step 5 steadily improves as the sizes of zones 2 and 3 are increased, reaching a typical rms error of 1 μV in zone 1 for 500 point charges in zone 2 and 10 000 in zone 3.

Role of Intergranular Films in Toughened Ceramics

Self-reinforced silicon nitride ceramics rely the generation of elongated grains that act as reinforcing elements to gain increases in fracture toughness. However, the size and number of the reinforcing grains must be controlled, along with the matrix grain size, to optimize the fracture toughness and strength. Furthermore, the toughening processes of crack bridging are dependent upon retention of these reinforcing grains during crack extension by an interfacial debonding process. Both the debonding process and the resultant toughening effects are found to be influenced by the composition of the sintering aids which typical are incorporated into the amorphous intergranular films found in these ceramics. Specifically, it is shown that the interface between the intergranular glass and the reinforcing grains is strengthened in the presence of an epitaxial SiAlON layer. In addition, the interface strength increases with the Al and 0 content of the SiAlON layer. Micromechanics modeling indicates that stresses associated with thermal expansion mismatch are a secondary factor in interfacial debonding in these specific systems. On the other hand, first principles atomic cluster calculations reveal that the debonding behavior is consistent with the formation of strong Si-0 and Al-O bonds across the glass-crystalline interface.

Debonding behavior between β-Si 3N 4 whiskers and oxynitride glasses with or without an epitaxial β-SiAlON interfacial layer

In order to gain insight on the influence of intergranular glass on the fracture toughness of silicon nitride, the debonding behavior of the interface between the prismatic faces of β-Si 3N 4 whiskers and oxynitride glasses was investigated in model systems based on various Si–(Al)–Y(Ln)–O–N (Ln: rare-earth) oxynitride glasses. It was found that while the interfacial debonding strength increased when an epitaxial β′-SiAlON layer grew on the β-Si 3N 4 whiskers, the critical angle for debonding was lowered with increasing Al and O concentrations in the SiAlON layer. Only in the absence of a SiAlON epitaxial layer, were debonding conditions altered by residual stresses imposed on the interface due to thermal–mechanical mismatch. A possible explanation for the effect of SiAlON formation and its composition on the debonding behavior is suggested by first-principles atomic cluster calculations. It is concluded that by tailoring the densification additives and hence the chemistry of the intergranular glass, it is possible to improve the fracture resistance of silicon nitride.

First-principles atomic cluster study of boron interactions in Ni3Al

First-principles atomic cluster calculations have been carried out in the local density approximation to understand the segregation behavior and strengthening effects of boron in Ni3Al. The binding energy of boron is calculated in lattice fragment clusters representing the perfect crystal, as well as various defect sites. The agreement between trends in energetics determined for small clusters and periodic supercells indicates the dominant role of boron’s interaction with nearest-neighbors of the host. The stereochemical factor underlying boron’s preferential bonding to nickel atoms in four-fold planar coordination (i.e., sp3 hybridization) suggests a mechanism for the boron-effect in Ni3Al: increased cohesion provides a driving force for B segregation to open sites, such as at Ni-enriched grain boundary sites, and the strengthening is a result of strong localized Ni–B covalent bond formation.

Surface resistivity induced by isolated atoms and atomic clusters on metallic surfaces.

We investigate the surface resistivity induced by isolated atoms and atomic clusters adsorbed on semi-infinite flat jellium substrates by a first-principles density-functional calculation. For this purpose, the original expression of the surface resistivity derived in a recent work [Phys. Rev. B 52, 10 819 (1995)] is recast in a form suitable for surface Green function calculations based on the Dyson equation. For single atoms and diatomic molecules, we study the dependence of the adsorbate-induced resistivity on the adatom-substrate bond length and the adatom-adatom bond length. In addition, we perform extensive resistivity calculations for atomic clusters consisting of n atoms in various atomic configurations (n\ensuremath{\leqslant}5) in order to clarify the dependence of the adsorbate-induced resistivity on the size and shape of atomic clusters. \textcopyright{} 1996 The American Physical Society.

Calculation of edge and vertex energies of diamond microcrystals

Preferential crystallographic growth planes are influenced to a large extent by the shape of the microcrystals that nucleate the growth. In contrast with macroscopic crystals, for nanometer scale microcrystals the energies associated with edges and vertices play a crucial role in determining an energetically favourable shape. We present a model for the computation of edge and vertex energies within the framework of semi-empirical quantum chemical calculations for atomic clusters. For two diamond crystallite shapes, both terminated by hydrogen saturated (111) surfaces, energy coefficients for the bulk and surface as well as two types of edges and vertices are obtained. The values are consistent with measurements. Size dependent effects are investigated by calculating the energy per atom for arbitrary sizes of a given shape, from the coefficients. It is found that even for this simple example, there is an energy cross-over at small crystallite size.

Effects of trace elements on transition metal cohesion

First-principles atomic cluster calculations of the effects of trace elements on transition metal cohesion have identified different mechanisms of cohesive enhancement and decohesion. This study of Li-row interstitial atoms in a Ni6 octahedral host shows that elements which form covalent bonds with host atoms without leading to much strain (e.g. B and C) increase the cohesive strength of the host. Decohesion, a lowering of the cohesive strength of the host, is promoted by trace elements which favor the formation of ionic bonds (e.g. Li and F). In this case, decohesion occurs by mechanisms involving metal-metal bond density reduction (by charge transfer and/or Pauli exclusion) and/or by incomplete screening of the impurity nucleus. These mechanisms are identified through directly calculated restoring forces in the cluster and analysis of deformation densities which detail the charge density rearrangements in the host in the presence of Li-row interstitial atoms.

Quantum chemical modeling of the scanning tunneling microscope

An approach to the calculation of the tunneling current in STS and STM experiments from the results of quantum chemical atomic cluster calculations, is presented. Essential features of the model are that the final states involved in the expression derived by Tersoff and Hamann, are excited states rather than ionised states, and furthermore these states have to be calculated from multiconfiguration Cl wavefunctions. The method is applied to measurements on the clean and hydrogenated Si(100) surface. Good agreement with measured STS curves is obtained, but only when the dimer geometry is allowed to respond to the biasing voltage to give a zero buckling of the dimer when a positive bias voltage is applied to the surface, and a buckling of 0.41 Å for a negative bias. For the hydrogenated surface the tunneling is found to drastically weaken the dimer bond. Good qualitative agreement is also found for calculated and measured topography curves for an STM tip scanning over the dimer in the dimer plane.

Crystal binding energies from atomic-cluster calculations.

A parameter-free technique is proposed to estimate the binding energy of a crystal from the knowledge of the binding energy of suitably chosen small atomic clusters, the latter being computed by an all-electron discrete variational method within local-density-functional theory. Test calculations of the equilibrium static properties of several metals and semiconductors, including the third-row elements from Na to Si and the group-IV semiconductors from C to Sn, will be compared with previous experimental and theoretical results.

Ternary Compounds Binding Energies from Atomic Cluster Calculations

A recently proposed method for obtaining a priori reliable estimates of bulk binding energies from LDA calculations on small atomic clusters is here extended to chalcopyrites. The results appear in very good agreement with experimental data, thus commending the method to anyone interested in systematic studies on these compounds.

Interface structures for epitaxy of diamond on Si(100)

Two new models for the atomic structure at the interface between a diamond (100) epitaxial overlayer in a (1/√2×1/√2)R45 configuration on a Si(100) substrate are proposed. Quantum chemical atomic cluster calculations are reported to find optimised geometries for these models and to compare them energetically with a bulk-like interface model. It is found that the model with C-C dimer bridges in the first two atomic layers of the epitaxial film is most favourable and bonds strongly enough to the substrate to sustain epitaxial stretching up to a film thickness of seven atomic layers.

First-principles simulation of intrinsic collision cascades in KCl and NaCl to test interatomic potentials at energies between 5 and 350 eV.

Theoretical interatomic potentials for KCl and NaCl are tested at energies 5--350 eV against experimental data from intrinsic collision cascades. The collisional scattering of Cl with Cl, K, and Na atoms was observed from Doppler-shifted \ensuremath{\gamma} rays depopulating an excited state in recoiling $^{36}\mathrm{Cl}$ produced through the thermal neutron capture $^{35}\mathrm{Cl}$(n,\ensuremath{\gamma}${)}^{36}$Cl. The collisional scattering was simulated with molecular dynamics. Interatomic potentials from the present Iab initioP atomic cluster calculations are proposed for the Cl-Cl, Cl-K, and Cl-Na interactions in KCl and NaCl.

Adatom-based (2 × 2 n) reconstruction on Ge(111)

Atomic cluster calculations are reported which model adatom generated (2 × 2) and c(2 × 8) reconstruction on the germanium (111) surface, for both the T4 and H3 adsorption sites. The clusters are four atomic layers deep and the positions of atoms in the first three atomic layers are found by minimising the total energy calculated with the MNDO quantum chemical Hamiltonian, according to the prevailing symmetry. Both closed and open shell wavefunctions are considered. We find at least four different electronic states with similar energies but different geometries. The lowest energy is found for the c(2 × 8)H3 configuration with a p-like dangling bond on the rest atom, while for the (2 × 2) structure an s-like dangling bond orbital on the adatom is most favourable.

Forces and Geometry Optimization in First-Principles Atomic Cluster Calculations

ABSTRACTWe make use of the existing formalism for calculating atomic forces within the local density approximation (LDA) to determine forces in all-electron, local orbital electronic structure calculations. The forces are calculated as the proper total energy derivatives, including the necessary basis-set corrections. Our technique evaluates the LDA potential exactly on a variationally determined integration mesh which allows all integrals relevant to the electronic structure problem to be computed to any desired accuracy. We demonstrate the high accuracy of forces calculated using our method with an application to the molybdenum dimer. Several issues concerning the accuracy of the forces are discussed, including self-consistency effects, and the effects of integration error. We discuss the use of the forces in dynamical routines for geometry optimizations.

Vibrational Properties of Hydrogen in Proton‐Implanted Silicon

AbstractSome aspects of the infrared absorption spectra of crystalline silicon containing implanted hydrogen or deuterium are interpreted on the basis of simple atomic cluster calculations. It is shown that the vibrational properties of the implanted ions can be understood solely by taking into account the effect of the host silicon network on the local impurity vibrations.

Augmented Gaussian-orbital basis for atomic-cluster calculations within the density-functional formalism: Application toCu2

The principle of augmentation, used to introduce inner-atom core structure into slowly varying basis functions, is applied to Gaussian orbitals to define a new basis set for highly accurate total-energy calculations for atomic clusters within the density-functional formalism. Diffuse Gaussian-orbital tails are matched continuously and differentiably to inner-atom numeric radial functions at the atomic-sphere radius. Major advantages of Gaussian-orbital basis sets are acquired without the need for numerous Gaussians of large exponent for the core region. The numeric functions used inside the atom permit essentially exact solutions for that region. Procedures are described which recover use of the efficient integral algorithms for the Gaussian-orbital-tail matrix elements. The interactions over the structured inner-atom region are treated by efficient integrand smoothing and integration procedures for the sphere. The new augmented Gaussian basis removes the primary limitations on the use of Gaussian orbitals for heavy atoms. As an illustration the method is applied to the copper dimer in an all-electron framework within the local-spin-density approximation (LSDA). The calculated binding energy, equilibrium separation, and first ionization potential of ${\mathrm{Cu}}_{2}$ are within 2% of experiment within the $X\ensuremath{\alpha}$ model. Excitation energies are better described within more recent refined exchange-correlation functionals. These all-electron results show the LSDA model predicts a slightly contracted bond length for ${\mathrm{Cu}}_{2}$, consistent with bulk LSDA calculations for the $3d$ transition-metal series.

A linear approximation in self-consistent density functional calculations for atomic clusters

Self-consistent density functional calculations for atomic clusters are considered using a localized basis. A procedure is developed in which the change in the exchange-correlation potential at some stage of the iterative process is approximated as linearly proportional to the change in charge density. The computer time required for an iteration can be reduced substantially. As a test case, the method is applied to the H 2 molecule.

Theoretical models of the electronic structure at surface irregularities

It is widely recognized that structure sensitivity of surface processes is a reflection of the electronic structure of the surface and is thus coupled to the geometrical arrangement of surface atoms. The interactions which take place between the surface and an adsorbate species are dependent upon the bonding among the atoms of the surface, and this in turn is determined by the structural arrangement of the surface atoms. Surface irregularities which alter the coordination number of a surface atom are particularly effective in altering the bonding properties of that atom. Theoretical electronic structure calculations for atomic clusters and thin films chosen to represent surface irregularities are summarized in this presentation. Emphasis is placed on discussion of the changes in features of the local densities-of-states and the surface orbitals, as compared with those corresponding to the bulk and low index surface planes.