On the solution of some diffusion equations with concentration-dependent diffusion coefficients-II

On the basis of further analytical results an improved algorithm for the numerical solution of a non-linear differential system arising from some diffusion systems with concentration-dependent diffusion coefficients is presented. In comparison with the previously reported approach the present method does not require the solution of an approximate equation and is simpler and more effective in its iteration processes. An example of numerical solutions of a diffusion system from the investigation of protons diffusion is demonstrated

Role of Graphene in Reducing Fatigue Damage in Cu/Gr Nanolayered Composite

Nanoscale metal/graphene nanolayered composite is known to have ultrahigh strength as the graphene effectively blocks dislocations from penetrating through the metal/graphene interface. The same graphene interface, which has a strong sp2 bonding, can simultaneously serve as an effective interface for deflecting the fatigue cracks that are generated under cyclic bendings. In this study, Cu/Gr composite with repeat layer spacing of 100 nm was tested for bending fatigue at 1.6% and 3.1% strain up to 1,000,000 cycles that showed for the first time a 5–6 times enhancement in fatigue resistance compared to the conventional Cu thin film. Fatigue cracks that are generated within the Cu layer were stopped by the graphene interface, which are evidenced by cross-sectional scanning electron microscopy and transmission electron microscopy images. Molecular dynamics simulations for uniaxial tension of Cu/Gr showed limited accumulation of dislocations at the film/substrate interface, which makes the fatigue crack formation and propagation through thickness of the film difficult in this materials system