Some applications of the generalised Peierls-Nabarro model for screw dislocations
Abstract of thesis entitled
Some Applications of the Generalised Peierls-Nabarro Model for Screw Dislocations
Leung Siu Ho
for the degree of Master of Philosophy
at the University of Hong Kong
in August 1998
It is important to realize that the mechanical properties of a certain material depend on the mobility of the dislocations under stress. The configuration of the atoms in the strained region around the dislocation centre is believed to be a determining factor for such mobility. The core is defined as the region with mismatch displacement up to only a certain fraction of the Burgers vector (the unit vector for dislocation) and it can be said that the motion of the dislocation is relatively easy if the dissociation causes less hindrance from the lattice within the core.
A lot of observations from experiments can be found from the literature and these form the background for the development of theories on the dislocation core. In particular, we are interested in the continuum Peierls-Nabarro model which was devised originally to investigate and formulate analytically the planar dissociation of dislocations (i.e. the core spreading occurring in the same plane).
The original Peierls-Nabarro model focuses on dislocations situated in an infinite medium but other geometries are also possible. Although geometries like multi-fold dissociation have already been studied by generalising the model, there is little work on dislocation cores situated in a thin film.
In this work, the Peierls-Nabarro model is generalised to thin films of different geometries through conformal-mapping the Peierls-Nabarro equation. The respective governing equations are solved numerically to give the displacement and strain fields. These generalised models are then compared with the original Peierls-Nabarro model to reveal the properties of screw dislocations in different situations.
It is found that the distribution of the displacement and strain fields in the thin film situation is similar to that of the original model. However, the dislocation core is less spread and the maximum strain near the dislocation centre increases as the thickness of the film decreases. Also, when the screw dislocation is placed away from the line of symmetry of the film, the configuration along the two sides of the cut deviates from symmetry. The thicker slab is less strained whilst the thinner slab is more severely strained.
These results may help to understand the behaviour of screw dislocations in materials used in the thin-film industry such as protective films and semiconductors.
School:The University of Hong Kong
School Location:China - Hong Kong SAR
Source Type:Master's Thesis
Keywords:thin films mechanical properties dislocations in crystals screws
Date of Publication:01/01/1999