A Simple Shell Model for Quantum Dots in a Tilted Magnetic Field

A model for quantum dots is proposed, in which the motion of a few electrons in a three-dimensional harmonic oscillator potential under the influence of a homogeneous magnetic field of arbitrary direction is studied. The spectrum and the wave functions are obtained by solving the classical problem. The ground state of the Fermi-system is obtained by minimizing the total energy with regard to the confining frequencies. From this a dependence of the equilibrium shape of the quantum dot on the electron number, the magnetic field parameters and the slab thickness is found.Comment: 15 pages (Latex), 3 epsi figures, to appear in PhysRev B, 55 Nr. 20 (1997

The evolution of grain boundary character during superplastic deformation of an Al-6 pct Cu-0.4 pct Zr alloy

The evolution of microstructure, texture, and microtexture in an Al-6 pct Cu-0.4 pct Zr alloy was studied during mechanical testing at 480 °C and a strain rate of 5·10−4 s−1. The as-processed material had an elongated, banded microstructure and a deformation texture with orientation distribution along the β-orientation fiber. The true strain vs true stress curve exhibited three stages: I, II, and III. Work hardening occurred in stages I and III, whereas nearly steady-state behavior was observed in stage II. A bimodal distribution of boundary disorientation angles was evident in as-processed material and persisted into stage I, with peaks at 5–15 deg in the low-angle boundary (LAB) regime and at 45–60 deg in the high-angle boundary (HAB) regime. An increase in strain rate sensitivity coefficient, m, in stage I was accompanied by fragmentation of the initial microstructure, leading to the formation of new grains. During stage II the strain rate sensitivity coefficient, m, attained a value of 0.5, which is consistent with the onset of grain boundary sliding. In stage III, the texture and the grain boundary disorientation distribution became randomized while the m value decreased. Grain elongation and cavity formation at second-phase particles and along grain boundaries were seen in samples deformed to failure. The as-processed microstructure is described in terms of deformation banding, and a model for the evolution of such a structure during superplastic deformation is proposed.Peer reviewe