Deformation Studies of Tungsten-Gold Contacts at the Nanometer Scale.

The deformation behavior of atomically clean, nanometer sized tungsten / gold contacts was studied at room temperature in ultra-high vacuum. An instrument that combines atomic force microscopy (AFM), scanning tunneling microscopy (STM), and field ion microscopy (FIM) into a single experimental apparatus was designed, constructed, and calibrated. A cross-hair force sensor having a spring constant of - 442 N/m was developed and its motion was monitored during indentation experiments with a differential interferometer. Tungsten tips of controlled size (12.8 nm < tip radius < 2 1.6 nm) were first shaped and characterized using FIM and then indented into a Au (1 10) single crystal to depths ranging from 1.5 nrn to 18 nm using the force sensor. Continuum mechanics models were found to be valid in predicting elastic deformation during initial contact and plastic zone depths despite our small size regime. Multiple discrete yielding events lasting < 1.5 ms were observed during the plastic deformation regime; at the yield points a maximum value for the principal shear stress was measured to be 5 + 1 GPa. During tip withdrawal, "pop-out" events relating to material relaxation within the contact were observed. Adhesion between the tip and sample led to experimental signatures that suggest neck formation prior to the break of contact. STM images of indentation holes revealed various shapes that can be attributed to the (1 1 1 ) (1 10) crystallographic slip system in gold. FIM images of the tip after indentation showed no evidence of tip damage

Magma-Driven Multiple Dike Propagation and Fracture Toughness of Crustal Rocks

Dike swarms consisting of tens to thousands of subparallel dikes are commonly observed at Earth's surface, raising the possibility of simultaneous propagation of two or more dikes at various stages of a swarm's development. The behavior of multiple propagating dikes differs from that of a single dike owing to the interacting stress fields associated with each dike. We analyze an array of parallel, periodically spaced dikes that grow simultaneously from an overpressured source into a semi-infinite, linear elastic host rock. To simplify the analysis, we assume steady state (constant velocity) magma flow and dike propagation. We use a perturbation method to analyze the coupled, nonlinear problem of multiple dike propagation and magma transport. The stress intensity factor at the dike tips and the opening displacements of the dike surfaces are calculated. The numerical results show that dike spacing has a profound effect on the behavior of dike propagation. The stress intensity factors at the tips of parallel dikes decrease with a decrease in dike spacing and are significantly smaller than that for a single dike with the same length. The reduced stress intensity factor indicates that, compared to a single dike, propagation of parallel dikes is more likely to be arrested under otherwise the same conditions. It also implies that fracture toughness of the host rock in a high confining pressure environment may not be as high as inferred from the propagation of a single dike. Our numerical results suggest fracture toughness values on the order of 100 MPa root m. The opening displacements for parallel dikes are smaller than that for a single dike, which results in higher magma pressure gradients in parallel dikes and lower flux of magma transport.