The Mechanics and Physics of Defect Nucleation
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all Length Scale and High Strength It is well known to materials scientists that material behaviors, especially mechanical properties, are controlled by defects. Frenkel estimated the ideal strength of a crystal to be around one-tenth of its modulus. But most metallic materials we exploit today deform at around one-thousandth of their moduli, when dislocations start to move. For brittle materials, Griffith and Weibull delineated the sabotaging effect of cleavage defects in relation to their size and population. It turns out that conventional monolithic ceramics perform even much worse than metals in tension. The gap of 10–3 to 10–1 just described—a factor of 100 below the ideal strength—is actually good news: it means we still have plenty of room for improvement. The most effective way to potentially close the gap significantly is to change the length scale of the material. This is demonstrated by recent experiments1,2 (Figure 1a) on
focused-ion-beam-carved Au nanopillars. As the pillar diameter approached hundreds of nanometers, one measured a uniaxial compressive strength of 800 MPa (Figure 1b).2,3 This is extremely high for Au. Density functional theory4 (DFT) calculation predicts an ideal shear strength of 850 MPa to 1.4 GPa for Au, depending on the loading constraints.5 One needs to further consider the weakening effect of free surfaces. In this case, it appears the ideal surface strength,6,7 rather than the ideal bulk strength,5,8 should be used as the benchmark. Preliminary molecular dynamics (MD) calculations using embedded-atom potentials9 suggest the ideal surface strength of metals to be around half of its ideal bulk strength, as atoms on the surface are weakened due to the missing neighbors. The experimental value is thus near the ceiling of what theory expects it can be. The achievability of such high strength experimentally is
MRS BULLETIN • VOLUME 32 • FEBRUARY 2007 • www.mrs.org/bulletin
confirmed by independent measurements on nanoporous Au,10,11 where individual metal ligaments are tens to hundreds of nanometers in thickness. Experimental studies on high-strength materials systems and phenomena (defined as sustaining stress broadly and persistently at a significant fraction of the ideal strength) have blossomed in recent years. One reason is the refinement of nanoindentation12–16 and other nanoscale mechanical experiments, which allows one to study near-ideal strength behavior quantitatively in a controlled fashion. In the case of nanoindentation, the small length scale is not that of the tested material, but the extent of high stress under the indenter, characterized by the size of the contact zone. Since elasticity is governed by the same family of equations as electromagnetics, a spherical indenter tip works somewhat like a lens, “projecting” the applied force to “focus” the maximum shear stress to an internal point inside the sample, away from the surface. This gives one a chance to probe bulk properties17 near the high-stress spot, which otherwise could be dominated entirely by the surface.
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