Title: Stress Analysis at the Atomic Scale Speaker: Terry Delph, Mechanical Engineering & Mechanics Department, Lehigh University Date/Time: Tuesday, August 1, 2006, 2:00 pm – 3:00 pm (PST)Location: Building 940/Auditorium, videoconferenced to Building 980, Room 95 (Sandia NM Brief Abstract: Atomistic analysis has been frequently used to calculate continuum-level quantities, stress in particular, on length scales smaller than continuum mechanics can reach. The most widely used atomic scale stress measure is the so-called “atomic stress”, a somewhat ad hoc volumetric partition of the bulk, or virial, stress. Recent developments in this area have clarified the description of atomic scale stress, and have shown how stress measures may be developed that parallel those used at the continuum level. In particular, Cormier, Rickman, and Delph [1] and Delph [2, 3] have developed general expressions for what may be termed the local Cauchy stress. This is the stress measure that satisfies the atomistic equation for conservation of linear momentum, and is analogous to the well-know continuum-level Cauchy stress. Delph [2] has moreover given a definition of the local second Piola-Kirchoff (PK2) stress as that stress measure that is work conjugate to the Lagrange strain tensor. Of particular interest is the fact that the widely used atomic stress is a particular case of the (volume averaged) local PK2 stress. Cormier, Rickman, and Delph [1] showed that these two stress measures yield numerically different predictions. Both the local Cauchy and local PK2 stresses contain some degree of arbitrariness resulting from the choice of density functions and averaging volume. However as one approaches the continuum scale, the local PK2 stress and the local Cauchy stress are related to each other in a fashion similar to that existing on the continuum level. We give a detailed example of the use of the local Cauchy stress in a fairly complicated setting: the stresses near a single atomic step on the (2x1) reconstructed surface of (001) silicon. The dimer rows are found to dominate the stress distribution near the surface and give rise to highly oscillatory stresses. Further from the surface, the stresses are found to be well described by a combination of a stress monopole resulting from the anisotropy of the dimer stresses and a stress dipole resulting from the presence of the atomic step.CSRI POC: Jonathan Zimmerman, (925) 294-6677, Jean Lee, (925) 294-2437 |