Plenary talks

abstract: 1.a
Non-Planar Dislocations: 3-D Models and Thermally-Activated Glide Processes
A.H.W. NGAN, Department of Mechanical Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong, P.R. China.
In recent years, there has been a renewed interest in studying the cross-slip of screw dislocations in the simple face-centered cubic (FCC) structure. As has been reviewed by a number of authors, new developments in both linear elastic semi-continuum modeling within the Peierls-Nabarro framework as well as in the application of atomistic simulation have been made in the past decade or so to investigate the 3-D problem of cross-slip of screw dislocations in the simple FCC structure. This paper serves to address parallel developments, both in semi-continuum approaches and in 3-D atomistic simulations, in modeling the cross slip of screw dislocations in the body-centered cubic (BCC) structure and the ordered L12 structure. In the latter two cases, the dislocation cores have non-planar spreading offering high intrinsic Peierls stress, and hence the flow behaviours of these materials, such as the non-Schmid behaviour, temperature-dependence of flow stress, etc., are largely due to the behaviours of single dislocations. The non-planar spreading of cores poses extra challenges in the semi-continuum modeling, and models describing the non-planar situation within a generalised Peierls-Nabarro framework will be discussed. These models were found to provide useful insight into the characteristic features of the glide of screw dislocations in these materials. 3-D atomistic modeling of the minimum-energy path for the glide processes will also be investigated with an aim to reconcile with experimentally determined activation energies for slip.


abstract: 1.b
The Peierls Model: Progress and Limitations
G. SCHOECK, Institute of Materials Physics, University of Vienna, Boltzmanng.5,1090 Vienna, Austria.
The velocity of moving dislocations is generally controlled by thermal activation events on atomic scale. Therefore detailed information on the atomic structure of dislocation cores is required. This cannot be obtained with the ``usual'' concept of Volterra dislocations which contain an elastic singularity in the core.

With the availability of high-speed computing it has become possible to perform atomistic modelling of the dislocation core. An attractive alternative is given by the Peierls model, originally proposed by Orowan in 1940 and elaborated by Peierls and Nabarro. Compared with simulations it is computationally much less expensive and combines the atomic description of the dislocation core in the glide plane with the long-range elastic displacement field of the dislocation.

The original treatment was on the stress level and considered the balance of elastic surface stresses acting at the two linear elastic half spaces above and below the glide plane by the atomic interaction across the glide plane. This lead to the so-called Peierls-Nabarro integral-equation, whose solution describes the displacement profile of the Peierls dislocation with a finite core width. Except for a simple sine force law for the atomic interaction across the glide plane (and some minor modifications) only numerical solutions can be obtained. If the atomic misfit energy $E_{A}$ is calculated by summing the atomic energy density $\gamma$ in the glide plane at the position of the atoms, the dislocation energy depends on the exact position of the core-centre within the lattice cell. Upon displacing the dislocation there result then periodic variations in the energy with amplitude $\Delta E_{P}$ called the Peierls energy.

Within the past decades a large number of improvements have been made on the model. The original treatment on the stress level has however only heuristic value. It has some serious drawbacks, which are of fundamental nature and prevent applications in realistic crystal structures: It can only handle displacements in 1D, whereas generally the displacement vector in the glide plane has both edge and screw components and deviates from the direction of the crystallographic Burgersvector. Furthermore it does not allow to take account of variations in the elastic energy, which occur in the lattice when the centre of the dislocation is displaced.

An important contribution to overcome these limitations was made by Leibfried and Dietze in 1951, who proposed a treatment on the energy level. The total energy (i.e. the elastic energy of the two elastic half spaces and the atomic misfit energy in the glide plane) can be expressed as functional of the (still unknown) displacement profile, which then can be determined as solution of a variational problem. Since their paper was in German, it went widely unnoticed.

The recent revival of the interest in the Peierls model was prompted by the possibility to obtain the atomic misfit energy in crystallographic glide planes in 2D, the so-called ?-surface, with ab-initio methods using density functional theory. This allows to obtain reliably core configurations of dissociated dislocations. Due to the simplifying assumptions inherent in the model, calculations of the Peierls energy and the Peierls stress must be considered however to be only order of magnitude estimates.


abstract: 1.c
Dislocations and plasticity of icosahedral AlPdMn quasicrystals
F. MOMPIOU, D. CAILLARD, CEMES-CNRS, Toulouse, France.
The plasticity of quasicrystals is more simple than what could be anticipated from their rather exotic structure. Indeed, it proceeds as in crystals by the motion of dislocations with well-defined Burgers vectors, which can be observed by TEM. In the same respect, quasicrystals are much more brittle than usual metallic alloys but their mechanical properties are similar to those of semiconductors.

In this talk, the plasticity mechanisms of icosahedral AlPdMn will be described and compared with those of normal crystals. Simple descriptions of quasicrystals will be given in terms of a 2-dimensional aperiodic tiling obtained by the cut and projection of a 3-dimensional periodic cubic lattice along an irrational plane. Perfect (retiled) and imperfect (non-retiled) dislocations will be defined in this 2-dimensional quasicrystal.

Different examples will be given of the TEM contrast of dislocations and stacking faults (also called ``phason walls'') trailed by imperfect dislocations. The contrast of perfect dislocations can be interpreted only when the phase shifts due to both phason field (local chemical disorder) and elastic strain field are taken into account. Since the phason field can be described by a displacement in the ``perpendicular space'' lost during the cut and projection process, rules of contrast are the same as in normal crystals provided the scalar products G.B are computed in the higher dimensional periodic space.

Dislocation densities, Burgers vectors and planes of motion determined by several groups will be reviewed, with emphasis on recent results showing that climb is the dominant dislocation motion mechanism. In particular, an in situ experiment shows that glide is at least 1000 times slower than climb, at high temperature and under comparable stresses. Mechanical properties will be tentatively explained by a high-stress climb model involving a difficult jog-pair nucleation.


abstract: 1.d
First Principles Simulation of Dislocation Cores in Metals
CHRISTOPHER WOODWARD, Air Force Research Laboratory, USA.
In order to understand the ``chemistry of deformation'' an adequate description of the strain field near the center of dislocations (i.e. the core) is required. While continuum elasticity methods have been very successful in describing long-range stress fields of dislocations these methods diverge in the core region. Atomistic methods have shown that the forces produced at the dislocation core and their coupling to the applied stress can have a dramatic effect on plasticity. However, atomistic methods are limited by the fidelity of the assumed interaction model and for this reason are at best semi-empirical. Several methods, based on first principles calculations, have emerged in the last few years for modeling dislocations in metals. These techniques employ a variety of approximations of either the local or the long-range strain field. One such method uses a 2-dimensional Peierls-Nabarro model in combination with the generalized stacking fault (i.e. the gamma surface) derived from first principles reference calculations. This method has been used to study the spacing of Shockley partial dislocations, to approximate the Peierls stress and to study solid solution effects. We have developed an alternative technique, the First-Principles Greens Function Boundary Condition method, based on a flexible boundary-condition method where the local dislocation strain field is self-consistently coupled to the long-range elastic field. The problem is divided into two parts: a solution for the nonlinear dislocation-core region and a solution for the long-range elastic response. Solving these individual problems is straightforward and by iteratively coupling the two solutions we can efficiently solve for the strain field in all space. While this technique has the advantage of modeling the actual electronic structure of the dislocation core it can be computationally challenging. We have used this method to study dislocations cores and the Peierls stress in: bcc Mo and Ta, L10 TiAl, and in fcc Al. Solid solution hardening/softening effects in Mo and Al alloys are currently being investigated. We will review several methods that have been applied to this class of problem, and summarize the advantages and disadvantages of these approaches.