Search

Plastic deformation of micron-scale crystalline materials differ considerably from bulk ones, because it is characterized by random strain bursts. To obtain a detailed picture about this stochastic phenomenon, micron sized pillars have been fabricated and compressed in the chamber of a SEM. An improved FIB fabrication method is proposed to get non-tapered micro-pillars with a maximum control over their shape. The in-situ compression device developed allows high accuracy sample positioning and force/displacement measurements with high data sampling rate. The collective avalanche-like motion of dislocations appears as stress drops on the stress-strain curve. To confirm that these stress drops are directly related to dislocation activity, and not to some other effect, an acoustic emission transducer has been mounted under the sample to record emitted acoustic activity during strain-controlled compression tests of Al-5\% Mg micro-pillars. The correlation between the stress drops and the acoustic emission signals indicates that indeed dislocation avalanches are responsible for the stochastic character of the deformation process., Comment: 10 pages, 3 figures

We study numerically the Coulomb interacting two-particle stationary states of the Schr\"odinger equation, where the particles are confined in a two-dimensional infinite square well. Inside the domain the particles are subjected to a steeply increasing isotropic harmonic potential, resembling that in a nucleus. For these circumstances we have developed a fully discretized finite difference method of the Numerov-type that approximates the four-dimensional Laplace operator, and thus the whole Schr\"odinger equation, with a local truncation error of $\mathcal{O}(h^6)$, with $h$ being the uniform step size. The method is built on a 89-point central difference scheme in the four-dimensional grid. As expected from the general theorem by Keller [Num.\ Math. \textbf{7}, 412 (1965)], the error of eigenvalues so obtained are found to be the same order of magnitude which we have proved analytically as well., Comment: 44 pages, 28 figures