These local strengths were combined to model the behavior of the whole sphere, a process called finite element analysis, or FEA. When simulated by a computer, the strain at each point in a sphere of specific dimensions, subjected to the applied compression, could be calculated and visualized. The simulations revealed that as displacement increased, the sphere's shape served to transfer stress to certain regions experiencing maximum shear regions corresponding to the top and bottom of the sphere where it contacted the substrate and the diamond anvil. This is where the spheres were usually observed to fail in the actual experiments. Indeed, the experimental results generally followed the predictions of the FEA model.
"The model incorporates the actual experimental conditions as well as possible," says Minor, "including the 'glue' we use to hold the nanosphere on the substrate. This is just a little of the carbonaceous material left over from the chemical process used to create the cadmium sulfide nanospheres. Originally we cleaned this away, but after we experienced a couple of instances of the spheres slipping away when they were squeezed, we stopped cleaning them so they would stay attached to the surface. The FEA model had to take this carbonaceous material into account."
The FEA model showed that the stresses within the FEA model at the point of fracture were indeed quite high. For example, a nanosphere 450 nanometers in diameter with a shell about 69 nanometers thick, deformed by compression to some eight percent of its original diameter, experiences local shear stresses approaching the ideal shear strength of cadmium sulfide. A 'fracture criterion,' derived by the researchers from their model, accurately predicts that a typical nanosphere experiences some 70 percent of the ideal shear strength at its point of failure.
"These are the most complete analyses of the mechanical properties of single nanoparticle
|Contact: Paul Preuss|
DOE/Lawrence Berkeley National Laboratory