Structure and formation energy of carbon nanotube caps

We present a detailed study of the geometry, structure and energetics of carbon nanotube caps. We show that the structure of a cap uniquely determines the chirality of the nanotube that can be attached to it. The structure of the cap is specified in a geometrical way by defining the position of six pentagons on a hexagonal lattice. Moving one (or more) pentagons systematically creates caps for other nanotube chiralities. For the example of the (10,0) tube we study the formation energy of different nanotube caps using ab-initio calculations. The caps with isolated pentagons have an average formation energy 0.29+/-0.01eV/atom. A pair of adjacent pentagons requires a much larger formation energy of 1.5eV. We show that the formation energy of adjacent pentagon pairs explains the diameter distribution in small-diameter nanotube samples grown by chemical vapor deposition.Comment: 8 pages, 8 figures (gray scale only due to space); submitted to Phys. Rev.

Temperature driven α\alpha to β\beta phase-transformation in Ti, Zr and Hf from first principles theory combined with lattice dynamics

Lattice dynamical methods used to predict phase transformations in crystals typically deal with harmonic phonon spectra and are therefore not applicable in important situations where one of the competing crystal structures is unstable in the harmonic approximation, such as the bcc structure involved in the hcp to bcc martensitic phase transformation in Ti, Zr and Hf. Here we present an expression for the free energy that does not suffer from such shortcomings, and we show by self consistent {\it ab initio} lattice dynamical calculations (SCAILD), that the critical temperature for the hcp to bcc phase transformation in Ti, Zr and Hf, can be effectively calculated from the free energy difference between the two phases. This opens up the possibility to study quantitatively, from first principles theory, temperature induced phase transitions.Comment: 4 pages, 3 figure

First-principles calculation of intrinsic defect formation volumes in silicon

We present an extensive first-principles study of the pressure dependence of the formation enthalpies of all the know vacancy and self-interstitial configurations in silicon, in each charge state from -2 through +2. The neutral vacancy is found to have a formation volume that varies markedly with pressure, leading to a remarkably large negative value (-0.68 atomic volumes) for the zero-pressure formation volume of a Frenkel pair (V + I). The interaction of volume and charge was examined, leading to pressure--Fermi level stability diagrams of the defects. Finally, we quantify the anisotropic nature of the lattice relaxation around the neutral defects.Comment: 9 pages, 9 figure

Thermally activated reorientation of di-interstitial defects in silicon

We propose a di-interstitial model for the P6 center commonly observed in ion implanted silicon. The di-interstitial structure and transition paths between different defect orientations can explain the thermally activated transition of the P6 center from low-temperature C1h to room-temperature D2d symmetry. The activation energy for the defect reorientation determined by ab initio calculations is 0.5 eV in agreement with the experiment. Our di-interstitial model establishes a link between point defects and extended defects, di-interstitials providing the nuclei for the growth.Comment: 12 pages, REVTeX, Four figures, submitted to Phys. Rev. Let

Electronic structure of periodic curved surfaces -- topological band structure

Electronic band structure for electrons bound on periodic minimal surfaces is differential-geometrically formulated and numerically calculated. We focus on minimal surfaces because they are not only mathematically elegant (with the surface characterized completely in terms of "navels") but represent the topology of real systems such as zeolites and negative-curvature fullerene. The band structure turns out to be primarily determined by the topology of the surface, i.e., how the wavefunction interferes on a multiply-connected surface, so that the bands are little affected by the way in which we confine the electrons on the surface (thin-slab limit or zero thickness from the outset). Another curiosity is that different minimal surfaces connected by the Bonnet transformation (such as Schwarz's P- and D-surfaces) possess one-to-one correspondence in their band energies at Brillouin zone boundaries.Comment: 6 pages, 8 figures, eps files will be sent on request to [email protected]

A fourfold coordinated point defect in silicon

Due to their technological importance, point defects in silicon are among the best studied physical systems. The experimental examination of point defects buried in bulk is difficult and evidence for the various defects usually indirect. Simulations of defects in silicon have been performed at various levels of sophistication ranging from fast force fields to accurate density functional calculations. The generally accepted viewpoint from all these studies is that vacancies and self interstitials are the basic point defects in silicon. We challenge this point of view by presenting density functional calculations that show that there is a new fourfold coordinated point defect in silicon that is lower in energy

Atomic scale models of Ion implantation and dopant diffusion in silicon

We review our recent work on an atomistic approach to the development of predictive process simulation tools. First principles methods, molecular dynamics simulations, and experimental results are used to construct a database of defect and dopant energetics in Si. This is used as input for kinetic Monte Carlo simulations. C and B trapping of the Si self- interstitial is shown to help explain the enormous disparity in its measured diffusivity. Excellent agreement is found between experiments and simulations of transient enhanced diffusion following 20-80 keV B implants into Si, and with those of 50 keV Si implants into complex B-doped structures. Our simulations predict novel behavior of the time evolution of the electrically active B fraction during annealing

The strain energy and Young's Moduli of single-wall Carbon nanotubules calculated from the electronic energy-band theory

The strain energies in straight and bent single-walled carbon nanotubes (SWNTs) are calculated by taking account of the total energy of all the occupied band electrons. The obtained results are in good agreement with previous theoretical studies and experimental observations. The Young's modulus and the effective wall thickness of SWNT are obtained from the bending strain energies of SWNTs with various cross-sectional radii. The repulsion potential between ions contributes the main part of the Young's modulus of SWNT. The wall thickness of SWNT comes completely from the overlap of electronic orbits, and is approximately of the extension of $\pi$ orbit of carbon atom. Both the Young's modulus and the wall thickness are independent of the radius and the helicity of SWNT, and insensitive to the fitting parameters. The results show that continuum elasticity theory can serve well to describe the mechanical properties of SWNTs.Comment: 12 pages, 2 figure

Coil Formation in Multishell Carbon Nanotubes: Competition between Curvature Elasticity and Interlayer Adhesion

To study the shape formation process of carbon nanotubes, a string equation describing the possible existing shapes of the axis-curve of multishell carbon tubes (MCTs) is obtained in the continuum limit by minimizing the shape energy, that is the difference between the MCT energy and the energy of the carbonaceous mesophase (CM). It is shown that there exists a threshold relation of the outmost and inmost radii, that gives a parameter regime in which a straight MCT will be bent or twisted. Among the deformed shapes, the regular coiled MCTs are shown being one of the solutions of the string equation. In particular,the optimal ratio of pitch $p$ and radius $r_0$ for such a coil is found to be equal to $2\pi$, which is in good agreement with recent observation of coil formation in MCTs by Zhang et al.Comment: RevTeX, no figure, 12 pages, to appear in Phys. Rev. Let