Simon L. Altmann

Core structure and electronic bands of the 90° partial dislocation in silicon

Abstract The core structure of the 90° partial dislocation in silicon is obtained by energy minimization of a cluster with respect to a Lifson-Warshel valence force field. Both the reconstructed and unreconstructed topologies are considered, and the reconstructed structure is favoured by 2·66 eV per lattice vector. Comparison of these structures with the one resulting from the anisotropic elastic approximation shows that the latter introduces a spurious bond length alternation. Electronic dislocation bands are determined by the extended Huckel theory, the parameters of which are obtained by calculation and fitting of the perfect silicon lattice. For the reconstructed structure, the lower dislocation band dips by more than 1 eV below the top of the valence band (E v) and the upper band—unoccupied, of width 1·2 eV—lies in the gap, extending from about 0·4eV above E v until it overlaps the bottom of the conduction band. Comparison of the bands for the elastic and unreconstructed structures indicates that the...

Force field treatment of an amorphous germanium model

A continuous random network model of amorphous germanium has been generated by computer. A relaxation process for this model has been performed by using a Lifson-Warshel force field parametrized by reproducing the phonon dispersion curves of crystalline germanium. The diffraction and radial distribution functions, computed on using the generated model, are in good agreement with those obtained experimentally by means of both neutron and X-ray diffraction, although the present model is entirely independent of them. The relative density of the model is 1.005 in good agreement with some experimental results.

A valence force field for the silicon crystal

A Lifson-Warshel force field (1968), which goes beyond the harmonic approximation and is well adapted for calculations in defect structures, has been developed for the silicon crystal. The parameters of this field have been determined by least-squares fitting of the phonon dispersion curves, which are reproduced with an accuracy comparable with that of harmonic valence force fields. Several of these parameters were kept constant during this fitting at values derived from silicon molecular data. The stacking fault energy, which vanishes for harmonic valence force fields, is calculated in reasonable agreement with experiment.

The 90° partial dislocation in silicon: Geometry and electronic structure

Abstract The core structure of the reconstructed 90° partial dislocation in silicon is obtained by energy minimization with respect to the Lifson—Warshel valence force field using periodic boundary conditions. A low strain energy attests to the stability of the reconstructed geometry. The electronic structure is calculated using a local pseudo-potential approach in an improved peripheral orbital treatment. The silicon indirect gap is found to be completely clear of dislocation levels, in agreement with experiment. Stacking-fault levels are found in the gap near the valence band edge in agreement with specialized stacking-fault energy level calculations.

Force field treatment of an amorphous-silicon model

Abstract A continuous random network model for amorphous silicon has been generated by computer. A relaxation process for this model has been simulated by using two different force fields, one of which, the Keating, is well-known, whereas the other, the Lifson-Warshel has only recently been used in this type of solid. Comparison of the final results obtained by the use of these two fields shows that it is only with the Lifson-Warshel field that good agreement is obtained for the computed average microscopic properties of the generated clusters. The success of this field is due to its inclusion of four-body and long-range interactions, which are absent in the Keating potential.

The stacking-fault energy in diamond

Abstract A Lifson-Warshel force field of the type recently used by the authors to study defect structures in silicon has now been developed for diamond. The parameters of this field are determined mostly by least-squares fitting of the phonon dispersion curves, but some experimental values must also be used. The crucial term is the torsional parameter, for which values differing by a factor of two or so have been proposed, leading to stacking-fault energies ranging from 992 to 340 mJ m−2. The latter value derives from a better-based value of the torsional parameter and agrees well with a recent experimental value of 279 ± 41 mJ m−2. The possibility of lattice relaxation in the stacking fault is also discussed.

Molecular cluster studies of defects in tetrahedral lattices: Dangling bonds reconstruction at the core of a 90° partial dislocation in diamond

Abstract The energetics of bond reconstruction at the core of a 90° partial dislocation in diamond has been studied by means of HFR-MO-LCAO-SCF computations on C5H10 and C10H18 model molecular clusters. The results obtained agree with previous VFF investigations and they confirm that the reconstructed geometry is energetically favoured with respect to the unreconstructed one.

A note on the force field treatment of an amorphous silicon model

The diffraction function for amorphous silicon, computed for a Continuous Random Network is calculated and compared with experiment.

The Illusion of Mirrors: Velázquez's Las Meninas

There have been dozens of interpretations of Las Meninas but most critics assume that either the Royal couple, or their portrait in the Velazquezs large canvas shown in the picture, is actually reflected on a back mirror. I shall provide evidence, however, to support the view that this mirror never existed. And there is no evidence whatsoever that the double portrait was ever painted. In view of these facts I shall make a new proposal about the way the picture was painted and about the painters intentions. I shall show evidence that the king was adamant that he did not want his portrait painted, since he did not want to show his age (he was more than double the age of his queen). It is thus reasonable to assume that Velazquez, in order to assuage the Kings qualms, created the mirror, thus allowing him to produce a very diffuse picture of the royal couple, where no evidence of aging could possibly be discerned.

Right and Left in Art: The Annunciation:

Since the early study by Wölfflin, the question of right and left in pictures has been exhaustively discussed. The early speculative studies and the more recent empirical evidence are reviewed here. The main thrust of the article concerns the Annunciation in the iconography that was standard roughly from the 13th to the 17th centuries. Three major effects have been discussed in the literature in order to understand the positioning of the Virgin on the right. They are the direction of motion and the agency effect, both concerning the archangel, and the presentation of the Virgins left cheek. It is proposed here that a fourth effect, the power of the first diagonal, is worthy of consideration, largely because it is the only effect that may obtain for variant Annunciations, in which the Virgin is on the left. Preliminary evidence from actual examples, albeit in a reduced sample, is discussed both in standard and variant Annunciations. In the final section, a preliminary experiment is presented, the results of which are consistent with the use of this rule in composition.