K. Shintani

Low-Reynolds-number flow past an elliptic cylinder

The primary objective of this paper is to obtain the detailed description of the flow field near an elliptic cylinder that is placed perpendicularly in a uniform stream at low Reynolds number. Attention is paid to the shape effects due to the flattening of the cylinder and to the inertial effects of the fluid. The analysis resorts to the method of matched asymptotic expansions. The main part of the inner expansion describes the near flow field as a Stokes flow, which is characterized by the singularities arranged at the two foci of the ellipse. The first three terms

Molecular dynamics study of energetics of graphene flakes

O({\mathbb R}) ({\mathbb R}

Atomistic study of strain dependence of Poisson’s ratio of single-walled carbon nanotubes

= Reynolds number) in the inner expansion are developed, and the flow aspects under the influence of the fluid inertia are investigated. The streamline patterns with one or two vortices round a finite flat plate of zero thickness, which is a special case of the elliptic cylinder, are presented.

Directional dependence of surface morphological stability of heteroepitaxial layers

Molecular dynamics simulations for graphene flakes of various shapes are performed. The equilibrium structures of graphene flakes are obtained. Round, hexagonal, and rectangular graphene flakes are dealt with, and their sizes are varied from a few angstroms to 200 A. It is shown that for round and hexagonal graphene flakes of small size, the edge configuration influences their energy in equilibrium. Graphene nanoribbons (GNRs) of various aspect ratios are equilibrated at low temperature. The energies of the equilibrated graphene flakes with zigzag (ZZ) edges are lower than the energies of the equilibrated graphene flakes with armchair (AC) edges. This result corresponds to the scanning tunneling microscopy observations in the literature. The atomic bonds on the edges of graphene flakes with both edge configurations are reconstructed. The bond lengths of such reconstructed edges are smaller than the lengths of the atomic bonds inside them. Therefore, free graphene flakes undergo compressive edge stress and...

Critical thickness of a heteroepitaxial film on a twist-bonded compliant substrate

The Poisson ratio of single-walled carbon nanotubes is calculated by the molecular-dynamics simulations. The result shows that the Poisson ratio depends on both the imposed strain and the chirality. Such dependences are addressed from the viewpoint of mechanics of the honeycomb lattice of nanotubes. It is shown that the changes of bond angles of the honeycomb lattice of nanotubes due to deformation tend to decrease the Poisson ratio. On the other hand, the increase of the chiral angle would tend to increase the Poisson ratio if it was not for deformation of the honeycomb lattice. In the simulation results, the Poisson ratio decreases with the increase of strain and chiral angle, which implies that the changes of bond angles in the honeycomb lattice dominantly determine the Poisson ratio of single-walled carbon nanotubes.

Morphology of a graphene nanoribbon encapsulated in a carbon nanotube

Surface morphological stability in coherent heteroepitaxial layers is analyzed focusing on the directional dependence of surface undulations created by surface diffusion. The critical stability condition is defined in terms of the free energy of the system which is assumed to be the sum of the elastic strain energy and the surface free energy. The displacement and stress fields of the semi-infinite anisotropic solid with the slightly undulating surface are calculated by using the surface admittance tensor and the vector complex potential function. Numerical results for the Si1−xGex/Si systems show that the critical wavelength of the 〈100〉 surface undulations is smaller than that of the 〈110〉 surface undulations, which means that surface undulations are likely to be formed in the 〈100〉 directions. It is also found that the critical wavelength decreases with the increase of Ge fraction. These tendencies are in good agreement with the observations in annealing experiments for the Si1−xGex/Si systems in the l...

Molecular-dynamics analysis of morphological evolution of softly deposited Au nanoclusters

The critical thickness for misfit dislocation formation in a heteroepitaxial film on a twist-bonded compliant substrate is calculated. The boundary between the twist-bonded compliant substrate and the supporting bulk substrate with a low twist angle is assumed to be represented by a cross grid of straight dislocations. The critical thickness is determined by the zero of that formation energy of a misfit dislocation which consists of the self-energy of the dislocation, the interaction energy between the dislocation and the dislocation arrays in the twist boundary, and the interaction energy between the dislocation and the mismatch strain. Numerical results for the InxGa1−xP film on a twist-bonded GaAs compliant substrate show that the critical thickness of the film on a twist-bonded compliant substrate is considerably larger than that of the film on a free-standing compliant substrate. This difference in critical thicknesses for the twist-bonded compliant substrate and the free-standing substrate is due to...

Morphology of a columnar stack of coronene molecules encapsulated in a single-walled carbon nanotube

The morphologies of graphene nanoribbons (GNRs) encapsulated in single-walled carbon nanotubes (SWNTs) are investigated using molecular-dynamics (MD) simulation. The GNRs are assumed to be hydrogen-terminated and formed by connecting polycyclic aromatic hydrocarbons, perylene or coronene molecules. The combined structures consisting of a GNR and an encapsulating SWNT are equilibrated at room temperature. It is shown that if the diameter of a SWNT is larger than the sum of the width of the GNR and twice the length of a C-H bond, a twisted GNR is obtained, whereas if the diameter of a SWNT is smaller than the sum of the two, the cross section of the SWNT cannot maintain its original circular shape and elliptically distorts, and a non-twisted GNR or a twisted GNR of long pitch is obtained. The estimated pitch of a regularly-twisted GNR agrees with the experimentally observed one in order of magnitude.

Effect of anisotropy on the excess stress and critical thickness of capped Si1−xGex strained layers

The initial period following deposition of soft-landing Au clusters is investigated by classical molecular-dynamics simulation. The embedded-atom method potential is adopted for the interaction between Au atoms. Clusters of specified sizes are cut out of the bulk crystal structure. Whether a cluster equilibrated at a given temperature is in a solid state or in a liquid state is judged by tracking the trajectory of an atom in the cluster and by examining the radial distribution function. The deposition simulation reveals that there is an energy barrier in the morphological accommodation of a cluster to the substrate if the cluster is crystalline before deposition, and is equilibrated at a temperature different from that of the substrate. On the other hand, there is no energy barrier in the morphological accommodation of a cluster that is in a liquid state before deposition. Exceptionally, a crystalline cluster that is nearly at a melting temperature can accommodate itself smoothly to the substrate maintain...

Atomistic model of limited-thickness Si(001) epitaxy at low temperatures

The morphology of stacked coronene molecules encapsulated in a single-walled carbon nanotube (SWCNT) is investigated using atomistic simulation. First, the minimum energy configuration of coronene molecules in a SWCNT is sought by means of conjugate gradient (CG) minimization. Secondly, encapsulation of coronene molecules into a SWCNT existing in a coronene atmosphere is simulated by means of molecular dynamics (MD). In both of the simulations, the diameter of the SWCNT ranges from 1.35 to 1.69 nm, and the final configurations of coronene molecules within a SWCNT are examined. In a thin SWCNT, coronene molecules tilt against the radial direction of the SWCNT and slide relative to each other, whereas in a thick SWCNT, they do not tilt but rotate relative to each other. In a SWCNT of the intermediate diameter, they tilt, slide, and rotate. For the SWCNT diameter less than or equal to 1.52 nm, the mean tilt angle of the stacked coronene molecules almost linearly decreases with increasing the diameter, whereas for the diameter above 1.52 nm, it is approximately 0∘. To check the validity of the results, the MD simulations are performed changing the density of the coronene atmosphere and the length of the SWCNT; the results prove to be valid. Finally, the effects of temperature on the mean tilt angle and mean intermolecular distance of stacked coronene molecules are examined by a rather simplified simulation, which shows that both of them increase with increasing temperature.