K. W. Lodge

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.

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.

Theory of electric field gradients in metals

An expression for the electric field gradient (EFG) at a nucleus in a metal is obtained by constructing an antishielding theory specifically for the metallic situation. By being constructed on an energy basis the theory is able to clarify the interpretation of the conduction electron contributions to the total EFG. The expression obtained for the total EFG contains not only the familiar antishielding factors gamma infinity and gamma (r) but also a new radial dependent factor which is in a sense the dual of gamma (r). The traditional expression for the total EFG in metals is revealed as an extreme simplification and possible improvements in practical calculations are suggested.

Twist-boundary energy in aluminium an ab initio calculation

Abstract The variational method of Fletcher and Adamson is used, together with an interaction potential due to Harrison, to calculate the energy of a (100) twist boundary in aluminium as a function of twist angle. The calculated energy rises from a cusped zero for zero misfit to high-angle misfit values of about 500 to 700 erg cm−2, in reasonable agreement with the only experimental data available.

The potential drop across an imperfect diffusion bond

In the non-destructive evaluation of diffusion bonds, a possible technique is to measure the potential drop for a given current flow. Using evidence from optical and acoustic microscopy, the geometrical details of an incomplete diffusion bond are represented by an idealized mathematical approximation. This is solved exactly using conformai mapping by a Schwarz transformation. The result for the change in resistance as a function of bond development is given as an analytic expression.

Calculation of electric field gradients in metals

The electric field gradient (EFG) at a nucleus in the metals Be, Mg, Zn, Cd and In has been calculated. Pseudopotential theory is used and only conduction electrons external to the ion core at the origin are considered. The conduction electrons are found to produce an EFG which partly screens the ionic contribution. Good agreement with experiment is found for Be but the calculated values in Mg, Cd and In are smaller than the experimental values and it is concluded that the conduction electrons within the ion core at the origin make a large contribution to the EFG at the nucleus in these cases.

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.