Density-functional calculations of defect formation energies using the supercell method-Brilliouin-zone sampling.

Using the DFT supercell method, the BZ sampling error in the formation energy and atomic structure are investigated for vacancy and interstitial defects in diamond and silicon. We find that the k-point sampling errors in the total energy vary considerably depending on the charge state and defect type without systematic cancellation, even for the same size of supercell. The error in the total energy increases with decreasing electronic perturbation of the defect system relative to the perfect bulk; this effect originates in the localization of electronic states due to the symmetry reduction induced by the presence of a defect. The error in the total energy is directly transferred to the formation energy, and consequently changes the thermodynamic stability of charge states and shifts the ionization levels. In addition, in force calculations and atomic structure determinations, the k-point sampling error is observed to increase as the charge becomes more negative. The Γ-point sampling results in erroneously large relaxation of the four atoms surrounding a vacancy in diamond. We suggest that stronger repulsions between electrons occupying degenerate defect levels at Γ-point compared to those occupying split energy levels at other k points induces larger atomic movements.Peer reviewe

A Geometry Centred Process in Airframe Design

The requirement for different abstractions of the core geometry is a key challenge in development of future design systems. In particular the fidelity of the analysis models tends to increase as more knowledge of the design is gained, but these higher fidelity models must coexist alongside coarser models and information must pass consistently and reliably between them. For example a detailed 3D solid of a joint may be embedded within a beam-shell model which ultimately obtains its loads from an aerodynamic model of the cross-section. Much of the difficulty for analysis model derivation arises due to the complexity of the master solid geometry. Shapes and configurations need to be identified, and abstracted to a suitable analysis form. An aerodynamic model may require only the exterior profile of the aircraft, but the structural model may require that stiffeners be represented as a line at the neutral axis with associated cross-sectional properties, or the skin is reduced to a 2D surface. The approach presented here is to remove the geometry as the reference source and replace it with a more abstract representation of the aircraft, and thereafter to use a common geometry generation process for the various disciplines. Model creation then becomes the central focus of the design process for all the disciplines being integrated. This then becomes an implicit part of the systems engineering process. The solid geometry, analysis, manufacturing and economic models can then be derived as required from a common design representation ensuring consistency, ease of use and reliability.</p

Interaction of double-stranded DNA inside single-walled carbon nanotubes

Deoxyribonucleic acid (DNA) is the genetic material for all living organisms, and as a nanostructure offers the means to create novel nanoscale devices. In this paper, we investigate the interaction of deoxyribonucleic acid inside single-walled carbon nanotubes. Using classical applied mathematical modeling, we derive explicit analytical expressions for the encapsulation of DNA inside single-walled carbon nanotubes. We adopt the 6–12 Lennard–Jones potential function together with the continuous approach to determine the preferred minimum energy position of the dsDNA molecule inside a single-walled carbon nanotube, so as to predict its location with reference to the cross-section of the carbon nanotube. An analytical expression is obtained in terms of hypergeometric functions which provides a computationally rapid procedure to determine critical numerical values. We observe that the double-strand DNA can be encapsulated inside a single-walled carbon nanotube with a radius larger than 12.30 Å, and we show that the optimal single-walled carbon nanotube to enclose a double-stranded DNA has radius 12.8 Å.Mansoor H. Alshehri; Barry J. Cox; James M. Hil