Majid Karimi

MODELS FOR ADATOM DIFFUSION ON FCC (001) METAL SURFACES

We present a class of models that describe self-diffusion on fcc (001) metal substrates within a common framework. The models are tested for Cu(001), Ag(001), Au(001), Ni(001), and Pd(001), and found to apply well for all of them. For each of these metals the models can be used to estimate the activation energy of any diffusion process using a few basic parameters that may be obtained from experiments, ab initio or semiempirical calculations. To demonstrate the approach, the parameters of the models are optimized to describe self- diffusion on the (001) surface, by comparing the energy barriers to a full set of barriers obtained from semiempirical potentials via the embedded atom method (EAM). It is found that these models with at most four parameters, provide a good description of the full landscape of hopping energy barriers on fcc (001) surfaces. The main features of the diffusion processes revealed by EAM calculations are quantitatively reproducible by the models.

Electromigration-induced flow of islands and voids on the Cu(001) surface

Electromigration-induced flow of islands and voids on the Cu(001) surface is studied at the atomic scale. The basic drift mechanisms are identified using a complete set of energy barriers for adatom hopping on the Cu(001) surface, combined with kinetic Monte Carlo simulations. The energy barriers are calculated by the embedded atom method, and parameterized using a simple model. The dependence of the flow on the temperature, the size of the clusters, and the strength of the applied field is obtained. For both islands and voids it is found that edge diffusion is the dominant mass-transport mechanism. The rate limiting steps are identified. For both islands and voids they involve detachment of atoms from corners into the adjacent edge. The energy barriers for these moves are found to be in good agreement with the activation energy for island/void drift obtained from Arrhenius analysis of the simulation results. The relevance of the results to other FCC(001) metal surfaces and their experimental implications are discussed.

Molecular dynamics simulations of crack propagation in Ni with defects

A series of molecular dynamics simulations using the embedded atom method is conducted to investigate crack propagation under mode I loading in a Ni single crystal with and without defects. The crack system (0 0 1)[1 0 0] in a slab of 160 000 atoms was studied. Defects consisting of lines of vacancies were introduced near the crack tip. Critical loads and strain energy distributions around the crack tip are obtained. Our results indicate that the critical strain necessary for crack propagation is dependent on the defect configuration and can either increase or decrease relative to the defect-free system.

Diffusion, adsorption, and desorption of molecular hydrogen on graphene and in graphite.

The diffusion of molecular hydrogen (H2) on a layer of graphene and in the interlayer space between the layers of graphite is studied using molecular dynamics computer simulations. The interatomic interactions were modeled by an Adaptive Intermolecular Reactive Empirical Bond Order (AIREBO) potential. Molecular statics calculations of H2 on graphene indicate binding energies ranging from 41 meV to 54 meV and migration barriers ranging from 3 meV to 12 meV. The potential energy surface of an H2 molecule on graphene, with the full relaxations of molecular hydrogen and carbon atoms is calculated. Barriers for the formation of H2 through the Langmuir-Hinshelwood mechanism are calculated. Molecular dynamics calculations of mean square displacements and average surface lifetimes of H2 on graphene at various temperatures indicate a diffusion barrier of 9.8 meV and a desorption barrier of 28.7 meV. Similar calculations for the diffusion of H2 in the interlayer space between the graphite sheets indicate high and low temperature regimes for the diffusion with barriers of 51.2 meV and 11.5 meV. Our results are compared with those of first principles.

Temperature dependence of the elastic constants of Ni: reliability of EAM in predicting thermal properties

The temperature dependence of the elastic constants of Ni is calculated using molecular dynamics (MD) simulations in conjunction with the embedded atom method (EAM). The Parrinello - Rahman version of molecular dynamics is employed along with the fluctuation formulae in the and EhN ensembles at various temperatures from 0 K to somewhat below the melting point (experimental value 1725 K). The calculated results for the elastic constants, compressibility, linear coefficient of thermal expansion, specific heat and the melting temperature compare reasonably well to experiment.

An atomic beam diffraction study of a rare gas monolayer of square symmetry : Kr on (100) NaCl

Using cold helium atomic beam diffraction and atomic beam overlayer deposition, we have measured the structure of krypton physisorbed on the (100) face of NaCl crystals at temperatures below 50 K. Our data show that this system provides the first example of a rare gas overlayer growing with fourfold nearest neighbor coordination up to a complete monolayer coverage and beyond. The lattice mismatch with the substrate is 1.65%, resulting in the formation of coherent patches of about 30 atoms in diameter as derived from the width of the diffraction peaks. By means of close coupling intensity calculations, we have also determined the average location of the atoms in the direction perpendicular to the substrate. Because of the lattice mismatch this distance results to be equal to the position of the minimum of the laterally averaged Kr-substrate potential (3.4 A) as opposed to the position of the absolute minimum of the potential which is located 2.7 A above the center of the unit cell.

The self-trapping attractor neural network-part II: properties of a sparsely connected model storing multiple memories

In a previous paper, the self-trapping network (STN) was introduced as more biologically realistic than attractor neural networks (ANNs) based on the Ising model. This paper extends the previous analysis of a one-dimensional (1-D) STN storing a single memory to a model that stores multiple memories and that possesses generalized sparse connectivity. The energy, Lyapunov function, and partition function derived for the 1-D model are generalized to the case of an attractor network with only near-neighbor synapses, coupled to a system that computes memory overlaps. Simulations reveal that 1) the STN dramatically reduces intra-ANN connectivity without severly affecting the size of basins of attraction, with fast self-trapping able to sustain attractors even in the absence of intra-ANN synapses; 2) the basins of attraction can be controlled by a single free parameter, providing natural attention-like effects; 3) the same parameter determines the memory capacity of the network, and the latter is much less dependent than a standard ANN on the noise level of the system; 4) the STN serves as a useful memory for some correlated memory patterns for which the standard ANN totally fails; 5) the STN can store a large number of sparse patterns; and 6) a Monte Carlo procedure, a competitive neural network, and binary neurons with thresholds can be used to induce self-trapping.

Self-trapping in an attractor neural network with nearest neighbor synapses mimics full connectivity

A means of providing the feedback necessary for an associative memory is suggested by self-trapping, the development of localization phenomena and order in coupled physical systems. Following the lead of Hopfield (1982, 1984) who exploited the formal analogy of a fully-connected ANN to an infinite ranged interaction Ising model, we have carried through a similar development to demonstrate that self-trapping networks (STNs) with only near-neighbor synapses develop attractor states through localization of a self-trapping input. The attractor states of the STN are the stored memories of this system, and are analogous to the magnetization developed in a self-trapping 1D Ising system. Post-synaptic potentials for each stored memory become trapped at non-zero valves and a sparsely-connected network evolves to the corresponding state. Both analytic and computational studies of the STN show that this model mimics a fully-connected ANN.

Wandering mind: a self-trapping network can converge to attractors far from the initial state

The self-trapping attractor neural network (STN) is a naturally sparsely-connected dynamical attractor network that models short- and long-term associative memory. Long-term storage is modeled with sparse Hebbian synapses. Unlike homogeneous dynamical models of associative memory, the STN also includes back-projections from a coupled system that computes overlaps with stored memories. The coupled system sends one output for each stored memory to the sparsely-connected network, modeling hippocampal cortical pathways. Each output increases monotonically with the magnitude of the overlap of the system state with an individual stored memory, cooperating with Hebbian synaptic influences to produce ordered activity patterns that correspond to short-term storage. The research reported here tests the hypothesis that slow dynamics in the coupled system allow the sparsely-connected network to wander to the vicinity of attractors far from the initial state. Results confirm this hypothesis for the case of strong recurrent inputs and incomplete learning (weak synapses) in the attractor network.

Formation of H2 on graphene using Eley-Rideal and Langmuir-Hinshelwood processes

A hydrogen atom can either physisorb or chemisorb onto a graphene surface. To describe the interaction of H with graphene, we trained the C-C, H-H, and C-H interactions of the ReaxFF CHO bond order potential to reproduce Density Functional Theory (DFT) generated values of graphene cohesive energy and lattice constant, H2 dissociation energy, H on graphene adsorption potentials, and H2 formation on graphene using the Eley-Rideal (ER) and Langmuir-Hinshelwood (LH) processes. The results, generated from the trained H-graphene potentials, are in close agreement with the corresponding results from DFT. The advantage of using optimized CH potentials is, for example, the inclusion of physisorption interactions and quantum mechanical features of chemical bonding in the functional forms of the potentials. The trained CH potentials are utilized to study the energetics of formation of an H2 molecule on graphene using the Eley-Rideal and Langmuir-Hinshelwood processes. Potential energy surfaces for the formation of H2 through ER are generated for the collinear and oblique approach of the second hydrogen atom. Energetics of the formation of H2 through LH is studied for a variety of cases such as when hydrogen atoms are chemisorbed or physisorbed and when hydrogen occupies ortho, meta, or para chemisorption sites. The likelihood of H2 formation through LH for various configurations is discussed. Furthermore, the tunneling probability of an atom through a continuous symmetric/asymmetric barrier is calculated and applied to an adsorbed hydrogen atom on graphene.