Colloquium Fall 2002
Labor Day, University Holiday
In this talk we present the general structure for the explicit equations of motion for general mechanical systems subjected to holonomic and nonholonomic equality constraints. The constraints considered here need not satisfy D'Alembert's principle, and our derivation is not based on the principle of virtual work. Therefore the equations obtained here have general applicability. They show that in the presence of such constraints, the constraint force acting on the system can always be viewed as made up of the sum of two components. The explicit form for each of the two components is provided. The first of these components is the constraint force that would have existed were all the constraints ideal; the second is caused by the non-ideal nature of the constraints, and though it needs specification by the mechanician and depends on the particular situation at hand, this component nonetheless has a specific form. The paper also provides a generalized form of D'Alembert's principle which is then used to obtain the explicit equations of motion for constrained mechanical systems where the constraints may be nonideal. We show an example where the new general, explicit equations of motion obtained in this paper are used to directly write the equations of motion for describing a nonholonomically constrained system with non-ideal constraints.
The Peierls-Nabarro (PN) model provides an ideal framework for a multiscale study of dislocation core properties. The strength of the model, when combined with ab initio calculations for the energetics, is that it produces essentially an atomistic simulation for dislocation core properties without suffering from the uncertainties associated with empirical potentials. Therefore, this method is particularly useful in providing insight into alloy design when empirical potentials are not available or not reliable for such multi-element systems. Various core properties, including the core width, dissociation behavior, core energetics, and Peierls stress for different dislocations have been investigated. The correlation between the core energetics and the Peierls stress with the dislocation character has been explored. The effect of hydrogen on the dislocation core properties of aluminum will be discussed. We find that H not only facilitates dislocation emission from the crack tip but also enhances dislocation mobility dramatically, leading to macroscopically softening of the material ahead of the crack tip. We observe strong binding between H and dislocation cores, with the binding energy depending on dislocation character. This dependence can directly affect the mechanical properties of Al by inhibiting dislocation cross-slip and developing slip planarity. Finally, I will discuss extension of the original planar PN model to study dislocation spreading at more than one slip planes, such dislocation cross-slip and junctions. The model is applied to study the external stress assisted dislocation cross-slip and constriction process in two fcc metals, Al and Ag, exhibiting different deformation properties. We find that the screw dislocation in Al can cross-slip spontaneously in contrast with that in Ag, where the screw dislocation splits into two partials that cannot cross-slip without first being constricted. The dislocation response to an external stress is examined in detail. The dislocation constriction energy and the critical stress for cross-slip are determined, and from the latter, we estimate the cross-slip energy barrier for straight screw dislocations.
by: Gang Lu [1,2], Nicholas Kioussis , E. Kaxiras  and V. Bulatov 
 Department of Applied Physics, Harvard University
 Department of Physics, California State University Northridge
 Chemistry & Materials Science, Lawrence Livermore National Laboratory.
Much of the success in understanding the properties of electrons in solid materials has been based on taking advantage of the symmetry and periodicity of a crystalline structure. However, it is well known that amorphous materials with non-periodic structures can also be metals, insulators, and semiconductors. The disorder of the amorphous structure causes some moderately well understood localization phenomena. Adding magnetic ions to an amorphous system results in dramatic and not yet understood effects, due to an interaction between the conduction electrons and the local magnetic moments. These local magnetic moments cause a shift in the metal-insulator transition that can be reversed by application of a magnetic field. The result is that very large negative magnetoresistance (many orders of magnitude) occurs in amorphous Si doped with magnetic rare earth ions (a-RExSi1-x) for x<0.15. In zero applied magnetic field, these alloys are strongly insulating. Applying a magnetic field aligns the RE moments and delocalizes the electrons. We use magnetotransport, magnetic susceptibility, tunneling spectroscopy, IR absorption spectroscopy, and heat capacity measurements to understand the effect of magnetic moments on electrical transport in semiconductors and the effect of the semiconducting matrix on the magnetic moments.