A real space approach to electronic structure calculations has several important advantages. A regular real-space mesh produces a sparse, local, and highly structured Hamiltonian, which enables effective use of iterative numerical methods and parallel computer architectures. However, a regular real space mesh has equal resolution everywhere, while actual physical systems are inhomogeneous. To remedy this inherent inefficiency without losing the advantages of a regular mesh, we carry out computations on a regular mesh in curvilinear space. There are several choices involved in the implementation of the method. These include the choice of the coordinate transform, the form of the discretized Laplacian, the regularization of the ionic potential for all-electron calculations, and the method of calculating the forces. Of particular interest is the use of error analysis to optimize the grid for a given physical system. The adaptive grid is versatile enough to describe accurately a very wide class of systems, including ones with highly inhomogeneous electronic distributions. We report all-electron calculations for atoms and molecules with is and 2p valence electrons, and pseudopotential calculations for molecules and solids.

We have developed a set of techniques for performing large scale ab initio calculations using multigrid accelerations and a real-space grid as a basis. The multigrid methods permit efficient calculations on ill-conditioned systems with long length scales or high energy cutoffs. We discuss the design of pseudopotentials for real-space grids, and the computation of ionic forces. The technique has been applied to several systems, including an isolated C60 molecule, the wurtzite phase of GaN, a 64-atom cell of GaN with the Ga d-states in valence, and a 443-atom protein. The method has been implemented on both vector and parallel architectures. We also discuss ongoing work on O(N) implementations and solvated biomolecules.

We present an overview of the locally self-consistent multiple scattering (LSMS) method. The method is based on real space multiple scattering theory, is naturally highly parallel, and has been implemented on Intel Paragon parallel platforms within the Center for Computational Sciences at Oak Ridge National Laboratory. O(N)-scaling is demonstrated for unit cells as large as 1000-atoms. We discuss in detail how the real space convergence properties of the method can be controlled by taking advantage of the stationary properties of a finite temperature Harris-Foulkes free energy functional. We show how the LSMS method can be combined with spin-dynamics to treat non-collinear magnetic states of materials. We show some preliminary results for the ground state magnetic structure of FCC Fe0.6 5Ni 0.35 alloys that indicate the possible existence of non-collinear arranges of magnetic moments in this system.

We present the parallelization strategy adopted to perform Variational Quantum Monte Carlo calculations on solids on distributed-memory architectures and the issues involved in the development of the parallel programs. Results obtained by the calculation of total electronic energy of graphite using nonlocal pseudopotentials in conjunction with the Variational Monte Carlo approach will be shown.

Molecular dynamics simulations are performed to investigate structure, mechanical properties, and thermal transport in amorphous silicon nitride under uniform dilation. As the density is lowered, we observe the formation of pores below ρ = 2.6 g/cc and at 2.0 g/cc the largest pore percolates through the entire system. Effects of porosity on elastic constants, phonons and thermal conductivity are investigated. Thermal conductivity and Young's modulus are found to scale as ρ1.5 and ρ3.6, respectively.

We investigate early stages of sintering of silicon nitride (Si3N4) nanoclusters by molecular-dynamics (MD) simulations on parallel computers. Within 100 pico seconds, an asymmetric neck is formed between nanocrystals at 2,000K. In the neck region, there are more four-fold than three-fold coordinated Si atoms. In contrast, amorphous nanoclusters develop a symmetric neck, which has nearly the same number of three-fold and four-fold coordinated Si atoms. In the case of sintering among three nanoclusters, a chain-like structure forms in 200 pico seconds. The present study shows that sintering is driven by rapid diffusion of surface atoms and cluster rearrangement.

Implementing molecular dynamics on the IBM SP2 parallel computer, we have studied the fracture of two-dimensional notched solids under tension using million atom systems. Brittle materials are modelled through the choice of interatomic potential function and the speed of the failure process, and our interest is to learn about the dynamics of crack propagation in ideal materials. Recent laboratory findings occur in our simulation experiments, one of the most intriguing is the dynamic instability of the crack tip as it approaches a fraction of the sound speed. A detailed comparison between laboratory and computer experiments is presented, and microscopic processes are identified. In particular, an explanation for the limiting velocity of the crack being significantly less than the theoretical limit is provided.

We present a simulation procedure for fracture that self-consistently accounts for dislocation emission, dislocation migration and crack growth. We find that the dislocation microstructure in front of the crack tip is highly organized and shows a complex temporal-spatial evolution. The final dislocation microstructure and the number of emitted dislocations immediately proceeding fracture varies rapidly with the loading rate. For high loading rates, fracture occurs at smaller loads with increasing loading rate. However, the load at fracture shows a maximum with respect to loading rates.

Multiresolution molecular dynamics approach on parallel computers has been used to investigate fracture in ceramic materials. In microporous silica, critical behavior at fracture is analyzed in terms of pore percolation and kinetic roughening of fracture surfaces. Crack propagation in amorphous silicon nitride films is investigated, and a correlation between the speed of crack propagation and the morphology of fracture surfaces is observed. In crystalline silicon nitride films, temperature-assisted void formation in front of a crack tip slows down crack propagation.

The elastic displacement field solution of a semi-infinite crack in an anisotropic body, calculated using a complex variable approach due to Sih and Liebowitz, is usually used by atomistic simulations of fracture. The corresponding expression for the displacement field of a finite crack is numerically cumbersome since it involves multiple square roots of complex numbers. In this study, displacement field of the crack is calculated by superposing the displacements of dislocations in an equivalent double pileup, equilibrated under mode I conditions. An advantage of this method is its extensibility to atomistic studies of more complex systems containing multiple cracks or interfaces. The pileup representation of the finite crack is demonstrated as being equivalent to its corresponding continuum description using the example of a double ended crack in α-Fe, loaded in mode I. In these examples, the interatomic interaction in α-Fe is described by an empirical embedded atom (EAM) potential.

We use atomistic Monte-Carlo simulations to investigate the dynamics of cracks which sizes are smaller than the Griffith length. We demonstrate that such cracks can irreversibly grow proviso their size is larger than a certain critical length which is smaller than the Griffith length, as recently suggested [ L. Golubović and A. Peredera, Phys. Rev. E51, 2799 (1995)]. We show here that this thermally assisted creep crack growth is dominated by irreversible changes in the region of the crack tip, primarily in the form of dislocation emissions and nucleation of microcavities and voids. These processes act together during the crack growth: the crack tip region acts as a source for emissions of dislocations which subsequently serve as seeds for creation of vacancy clusters in a region away but still close to the crack tip. Eventually, passages between these vacancy clusters and the mother crack are formed and the crack thus increases in size. As this process repeats, the crack grows.

This paper presents a synopsis of already published work for cracks on interfaces and new results on the effect of changing the chemistry of the atoms at the interface. Once the appropriate cut-off for the oscillatory singularity in the interface analysis is determined, the physics of the crack is determined in terms of an appropriate driving force for a particular event of interest, and a lattice resistance to the event. Analytic approximations are available for the driving forces, and the lattice resistance is determined on the basis of a block construction for the lattice. We show that for the case where the chemical bonding at the interface is different from that in the matrix, the same ideas are applicable, provided the different chemistry is incorporated correctly in the lattice resistance construction.

Theories of toughness of materials depend on an understanding of the characteristic instabilities of the crack tip, and their possible interactions. In this paper we examine the effect of dislocation emission on subsequent cleavage of a crack and on further dislocation emission. The work is an extension of the previously published Lattice Greens Function methodology[l, 2, 3]. We have developed a Cavity Greens Function describing a blunt crack and used it to study the effect of crack blunting under a range of different force laws. As the crack is blunted, we find a small but noticeable increase in the crack loading needed to propagate the crack. This effect may be of importance in materials where a dislocation source near the crack tip in a brittle material causes the crack to absorb anti-shielding dislocations, and thus cause a blunting of the crack. It is obviously also relevant to cracks in more ductile materials where the crack itself may emit dislocations.

Though atomistic simulation of 3D dislocation configurations is an important objective for the analysis of problems ranging from point defect condensation to the operation of Frank-Read sources such calculations pose new challenges. In particular, use of finite sized simulation cells produce additional stresses due to the presence of fixed boundaries in the far field which can contaminate the interpretation of these simulations. This paper discusses an approximate scheme for accounting for such boundary stresses, and is illustrated via consideration of the lattice resistance encountered by straight dislocations and simulations of 3D bow out of pinned dislocation segments. These results allow for a reevaluation of the concepts of the Peierls stress and the line tension from the atomistic perspective.

A simulation of structure and motion of edge dislocations in ordered Ni3Al was performed by atomic stiffness matrix method. In this method the equilibrium positions of the atoms were obtained by solving a set of linear equations formed by a stiffness matrix, whose terms consisted of derivatives of the interaction potential of EAM (embedded atom method) type. The superpartial dislocations, separated by an antiphase boundary (APB) on (111), dissociated into Shockley partials with complex stacking faults (CSF) on (111) plane. The core structure, represented by the Burgers vector density distribution and iso-strain contours, changed under applied stresses as well as upon addition of boron. The separation between the superpartials changed with the addition of B and antisite Ni. As one Shockley partial moved out to the surface. a Shockley partial in the interior moved a large distance to join the lone one near the surface, leaving behind a long CSF strip. The decrease in the width of the APB upon addition of B and antisite Ni has been explained by a reduction of the strength of directional bonding between Ni and Al as well as by the dragging of B atmosphere by the superpartials.

Total-Energy pseudopotential calculations are used to study both the onset and development of plasticity in nanoindentation experiments and the contrast mechanism in non-contact AFM images on Si (111) surfaces. As regards nanoindentation, plastic flow of atoms towards interstitial positions and extrusion of material towards the tip walls, stabilized by the adhesive interactions with the tip, are the dominant mechanisms. These plastic deformations are triggered by the delocalization of the charge induced by the stress in the elastically compressed structure. Atomic resolution contrast in AFM is shown to be clearly enhanced by the partial covalent chemical interaction between the dangling bonds of the adatoms in the surface and the apex atom in the tip. The contrast mechanism can be understood in terms of the coupling between the tip and the charge transfer modes among the different dangling bonds in the surface.

The results of recent ab-initio, relaxed, computations for the energy barrier to the motion of a kink on a 30° partial dislocation in silicon are summarised. The electronic structure and charge density are given. We suggest that the shearing motions involved with ductility and kink motion are controlled by the band structure energy involving valence electrons, whereas the tensile forces involved in fracture depend on both ion-ion and valence forces. Experimental atomic resolution TEM images of dissociated dislocation lines in silicon are discussed. These are formed using “forbidden reflections” with the dislocation lines lying on (111), normal to the electron beam. For images of samples at 600 C recorded at video rates, differences between successive frames reveal the motion of individual kinks, from which the kink velocity and migration energy can be estimated.

We have used ab initio total energy plane wave pseudopotential methods to perform the first completely ab initio investigation of the atomic and electronic structure of a grain boundary in a transition metal oxide. The ∑ = 15 (210)[001] tilt boundary in rutile TiG2 is studied using the conjugate gradients iterative minimisation technique for performing total energy calculations within the LDA and pseudopotential approximations. The stability of the experimentally observed translation state of the boundary is confirmed, and some insight is gained into its electronic structure.

We have performed total energy density functional theory calculations to investigate the sliding process at the ∑ = 5 (001) twist grain boundary in germanium. The accurate quantum mechanical description of the interatomic bonding provides valuable insights into the mechanisms of bond breaking and remaking that occur during the sliding.

In this paper we show how total energy calculations can be used to describe finite temperature and strain rate effects in this grain boundary.

We are using total energy pseudopotential calculations to carry out an extensive investigation into grain boundary sliding in a number of different systems, in order to understand, at microscopic level, the fundamental mechanisms responsible for this process.

In this paper we present results for the sliding process at the ∑ = 5(001) twist grain boundary in germanium, chosen as a typical covalently bonded material, and contrast them with preliminary results obtained for the ∑ = 5 (001) twist grain boundary in aluminium, a typical metal.