Compressive stress effects on nanoparticle modulus and fracture

Individual nanoparticles of silicon and titanium having diameters in the range of $40--140\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ have been repeatedly compressed by a nanoindenter. Even at low loads, the small tip-particle and particle-substrate contacts generate extreme pressures within the confined particle, influencing its stiffness and fracture toughness. The effect of these high pressures on the measured modulus is taken into account by invoking a Murnaghan equation-of-state-based analysis. Fracture toughness of the silicon particles is found to increase by a factor of 4 in compression for a $40\text{\ensuremath{-}}\mathrm{nm}$-diam particle when compared to bulk silicon. Additionally, strain energy release rates increase by more than an order of magnitude for particles of this size when compared to bulk Si.