Scale effects for strength, ductility, and toughness in “brittle” materials

Abstract

Decreasing scales effectively increase nearly all important mechanical properties of at least some "brittle" materials below 100 nm. With an emphasis on silicon nanopillars, nanowires, and nanospheres, it is shown that strength, ductility, and toughness all increase roughly with the inverse radius of the appropriate dimension. This is shown experimentally as well as on a mechanistic basis using a proposed dislocation shielding model. Theoretically, this collects a reasonable array of semiconductors and ceramics onto the same field using fundamental physical parameters. This gives proportionality between fracture toughness and the other mechanical properties. Additionally, this leads to a fundamental concept of work per unit fracture area, which predicts the critical event for brittle fracture. In semibrittle materials such as silicon, this can occur at room temperature when the scale is sufficiently small. When the local stress associated with dislocation nucleation increases to that sufficient to break bonds, an instability occurs resulting in fracture.

Brittle‐to‐Ductile Transition in Uniaxial Compression of Silicon Pillars at Room Temperature

“…[19] In the present paper, it is proposed that the brittle-ductile transition is scale dependent, can be dropped hundreds of degrees centigrade and can be quantified in nanovolumes. Using single crystal silicon as a prototypical brittle material with a brittle-toductile transition temperature (BDT) of 550 8C in bulk form, [20] nanopillars as the small volume structures and finite element modeling of the experimentally developed cracks by in situ nanoindentation, the promise of ductile ceramics is explored.…”

Nanoscale effects on the thermal and mechanical properties of AlGaAs/GaAs quantum well laser diodes: influence on the catastrophic optical damage

“…We have already argued about their capital influence on the thermal conductivity, but now is the time to focus on the mechanical behaviour [47][48][49]. Whereas the stress-strain relationships on the microscale have been found to be very similar to those of the bulk, remarkably high sub-micron yield strengths have been reported for different materials [47,[50][51][52]. This has been rationalized in terms of different mechanisms, such as the Hall-Petch [50,53,54] or modified confined layer slip (CLS) models [51,55].…”

Linking Nanoscales and Dislocation Shielding to the Ductile–Brittle Transition of Silicon

“…From five different studies [1,10,[34][35][36] it can be seen that at the given length scale, five different relationships evolve. In the 20-100 nm scale regime, near-theoretical strengths are observed which then decrease as size increases.…”