The Mechanics and Physics of Defect Nucleation

The following ar ticle is based on the Outstanding Young Investigator Award presentation given by Ju Li on April 19, 2006, at the Materials Research Society Spring Meeting in San Francisco. Li received the award “for his innovative work on the atomistic and first principles modeling of nanoindentation and ideal strength in revealing the genesis of ma te rials deformation and fracture.” Defect nucleation plays a critical role in the mechanical behavior of ma te rials, espe cially if the system size is reduced to the submicron scale. At the most fundamental level, defect nucleation is controlled by bond breaking and reformation events, driven typically by mechanical strain and electronegativity differences. For these proc esses, atomistic and first principles calculations are uniquely suited to provide an unprecedented level of mechanistic detail. Several connecting threads incorporating notions in continuum me chanics and explicit knowledge of the interatomic energy landscape can be identified, such as homogeneous versus heterogeneous nucleation, cleavage versus shear faulting tendencies, chemomechanical coupling, and the fact that defects are singularities at the continuum level but regularized at the atomic scale. Examples are chosen from nanoin dentation, crack tip proc esses, and grain boundary proc esses. In addition to the capacity of simulations to identify candidate mechanisms, the computed athermal strength, acti vation energy, and activation volume can be compared quantitatively with experiments to define the fundamental properties of defects in solids. Now in general, d is some kind of length scale—for example, the average grain size—and this inverse correlation between strength and length scale happens frequently in ma te rials (the exponent22 may not be 1; it may be 1/2 or some other value). The Frank–Read source thus has a sensitive length scale de pend ence. Subsequent expansion of this loop against, for instance, solute drag, is clearly an issue of mobility. The distinction between nucleation and mobility is not always clear cut. For ex am ple, forest dislocation hardening,32 which has similar length scaling as operating the Frank–Read source, is probably better con sidered a problem of mobility only because we envision the advancing mobile disloca tion maintaining its identity as it overcomes obstacles (i.e., the “forest” of dis locations it encounters in other slip systems). It is perhaps useful then to acknowledge there is a continuum between nucleation and mo bil ity, depending on the degree of identity change as mobile defects carry out free energy relaxation. With that in mind, let us examine another high strength system, nanocrystals.33 Figure 1c shows high purity Cu with nanoscale growth twins synthesized by pulsed electrodeposition, with twin lamella thickness on the order of 10 nm.34 This ma te rial has a tensile strength approaching 1 GPa, again a respectable fraction of copper’s ideal strength,5,8 although a lesser fraction compared with previous ex amples. From strain rate sensitivity meas ure ments,35 the activation volume32 was determined to be 12b3 to 22b3, which suggests interface mediated slip transfer reactions to be the rate limiting proc ess.36,37 To carry out plastic deformation, dislocations are forced to execute the kind of zigzag motion illustrated in Figure 1c, because the active slip system has to change from one lamella to the next. One may alternatively say new dislocations (either interfacial dislocations or bulk dislocations37) must be nucleated at each twin interface in order to satisfy Burgers vector conservation, and these nu cleation barriers are the reason for the ma te rial’s extraordinary strength. In ciden tally, this and some other nanocrystalline systems also manifest reasonably good ten sile ductility (Figure 1d),38,39 bolster ing the hope that high strength nanocrys talline sys tems may be developed into structural ma te rials that are truly superior to conven tional coarse grained ma te rials. Other high strength systems include metallic glasses,40,41 ma te rials under shock loading,42 and carbon nanotubes. Understanding defect nucleation in stressed ma te rials is not just important for traditional structural applications. Strained 152 MRS BULLETIN • VOLUME 32 • FEBRUARY 2007 • www.mrs.org/bulletin The Mechanics and Physics of Defect Nucleation Figure 1. (a) Focused-ion-beam-carved single-crystal Au nanopillar (diameter, 660 nm), after compression by a flat punch (left, 15% strain; right, 30% strain). (b) Uniaxial compression stress–strain curve for a 350-nm-diameter pillar. (Adapted from Greer et al.2) (c) Nano-twinned Cu synthesized by pulsed electrodeposition. The red zigzag line (added by the author) indicates the necessary path for dislocation motion. (d) Tensile stress–strain curve of nano-twinned Cu compared with nanocrystalline (nc) Cu with only general grain boundaries and coarse-grained Cu, showing high strength and good ductility. Inset shows shape and size of sample used for tensile testing. (Adapted from Lu et al.34) Table I: Recent Experimental Results of Maximum Shear Stress max Sustained at a High-Stress Spot inside a Tested Sample during Nanoindentation.