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Materials science

Deformation of the ultra-strong

Nature volume 456, pages 716717 (11 December 2008) | Download Citation

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In situ electron microscopy observations of the extrusion of single nanocrystals from graphitic cages show that these crystals deform near their theoretical strength limits. The question is how this happens.

Many nanostructured materials can sustain specimen-wide stress up to more than a tenth of their ideal strength for a considerable time. For example, a test performed on a monolayer of graphene yielded a strength value very close to its ideal strength calculated by quantum mechanics1. But the way that these ultra-strong materials respond to deformation at high temperatures remains mysterious because performing temperature-controlled mechanical tests of nanostructures in situ is not easy.

Writing in Physical Review Letters2, Sun et al. report observations of plasticity — the permanent, irreversible deformation of a material, as opposed to elastic deformation in which atomic bonds are stretched but not broken — of nanometre-sized metallic crystals inside a transmission electron microscope (TEM). They ascribe the observed deformation to the activity of short-lived, string-like defects in the crystals, known as dislocations.

In 1926, Jacov Frenkel estimated3 the ideal (maximum attainable) shear strength of a perfect crystal to be about a tenth of its shear modulus (initial rigidity). But at that time, tests performed on real materials yielded strengths two to three orders of magnitude lower. This discrepancy was attributed to dislocations, which are boundaries of planar fault regions in the crystal structure where atoms slip out of position when the material is strained. But dislocations were directly observed in the TEM only 30 years later4. Once created, dislocations move and multiply easily on their own as the material is subjected to loading. Common metal objects — for example, a kitchen fork — contain many dislocations to start with, and thus deform at stresses much lower than their ideal shear strengths.

Relatively large characteristic structural dimensions, such as micrometre-sized grains in bulk materials, facilitate the continuous generation, entanglement and storage of dislocations during plastic deformation. However, as the characteristic scale (such as the crystal grain size or the smallest dimension of a thin film) shrinks below 100 nm, dislocations are 'fatally attracted' to internal interfaces (such as crystal grain boundaries) and surfaces of the specimen. Consequently, it becomes much more difficult to sustain a permanent population of mobile dislocations — which are the vehicles of plastic deformation during straining — inside the material5,6. In these cases, deformation can be achieved only if new dislocations are nucleated afresh, usually from the same internal interfaces and surfaces that also absorb and annihilate them7,8. The continual need to nucleate new dislocations in these tiny crystals results in a significant increase in the material's strength.

In their experiment, Sun and colleagues2 initially confined individual, three-dimensional crystals (as small as 10 nm in diameter) of materials, including gold and platinum, in spherical graphitic shells. Subsequent puncturing and irradiation of the shells by a focused electron beam at different temperatures led to the extrusion of the crystals from the capsules (Fig. 1a, b). From direct comparison of the lattice spacings in the gold nanocrystals inside and outside the capsules, the authors inferred a prevailing pressure of about 20 gigapascals (about 200,000 times the standard atmospheric pressure) in the capsule when this was irradiated at about 300 °C. This is an extremely high stress for gold, considering that its ideal shear strength is only about 1 gigapascal. There is thus no question that these systems are ultra-strong.

Figure 1: Crystal plasticity.
Figure 1

Sun et al.2 performed in situ transmission electron microscopy observations of the extrusion of single gold nanocrystals from graphitic capsules under electron irradiation at 300 °C. a, Before irradiation. b, After irradiation for 540 seconds. c, Deformation mechanisms. The black curve shows the typical dependence of the strengths of crystalline materials — expressed as a fraction of their shear modulus, µ — on temperature. As the temperature increases, one of three competing mechanisms operates: displacive, mixed or diffusional plasticity. Superimposed are illustrative simulations, which we carried out, of the plasticity of copper nanospheres at a temperature of 300 K (sphere at the top) and 900 K (sphere on the right), in which deformation is thought to be controlled by displacive and diffusional plasticity, respectively. The copper atoms are shown in two colours (red and cyan) to make it easier to track their motions from the undeformed crystal state (bottom left sphere) to the deformed state. At 900 K, the random mixing of red- and cyan-coloured atoms in the extrusion-neck region (where the stress gradient is largest) indicates that extensive surface diffusion is taking place. (a,b, Courtesy American Physical Society.)

More controversial, however, is the mechanism of deformation during extrusion. With a TEM, Sun et al. observed a highly perfect atomic structure with occasional grain boundaries and planar stacking faults. But dislocations were not visible. On the basis of molecular- dynamics simulations, Sun et al. conclude that deformation originates from individual, transient dislocations that are freshly nucleated and vanish so fast that they cannot be seen with a TEM. Although diffusive atomic processes could be active at 300 °C in gold, the authors argue that diffusion does not contribute to plastic strain, and that the observed strength and deformation can be accounted for solely by the nucleation and motion of short-lived dislocations.

One of three competing mechanisms, all dependent on temperature and mechanical strain rate, induces plastic deformation: displacive, diffusional or mixed plasticity. Displacive plasticity5,7,8 is produced by the collective shearing of atoms, that is, the glide of dislocations. Diffusional plasticity9 is governed by many, almost random, individual atom or vacancy hops. In conventional coarse-grained metals, typically below about TM/3, where TM is the absolute temperature at melting, deformation is dominated by displacive mechanisms, whereas above about 2TM/3 diffusional mechanisms control the process. A mixture of these two mechanisms occurs at in-between temperatures; in such cases the inelastic strain is still mainly produced by dislocation glide but its rate is controlled by diffusion (Fig. 1c).

Lack of understanding of the deformation mechanisms that can operate in ultra-strong materials severely limits our ability to create nanometre-scale systems with the desired mechanical properties. Information about deformation mechanisms is often gathered from molecular-dynamics simulations, but these are limited to unrealistically high strain rates. Recently, progress has been made through the use of computational methods that elucidate mechanisms of displacive plasticity at low temperatures through direct calculations of the activation volume, which characterizes the sensitivity of plastic-yield stress (the stress at which the material deforms permanently) to strain rate. Such computational studies reveal that low-temperature deformation of ultra-strong systems, such as the nanocrystals studied by Sun et al., become highly sensitive to strain rate and temperature7,8. The underlying mechanism involves the nucleation, absorption and desorption of dislocations from interfaces and free surfaces, with a resultant reduction in activation volume, typically 2–20 times the volume of a single atom (Ω0). This activation volume is much smaller than those observed for traditional displacive-plasticity mechanisms (about 103 Ω0) that operate in coarse-grained polycrystals. It is, however, still larger than those of typical vacancy processes, for which the activation volume is less than about Ω0.

But at higher temperatures, such as 300 °C in gold, the way deformation changes with strain rate and the scale of nanostructures is unknown. In particular, the temperature and stress boundaries that separate the displacive processes from the diffusional and mixed processes will shift from those of the corresponding coarse-grained materials. Further experiments and modelling at higher temperatures9,10,11 will inevitably be needed to understand deformation in nanostructured materials. Meanwhile, Sun et al.2 have developed an innovative in situ experimental method that could provide insight into the process.

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  1. Subra Suresh is in the School of Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.  ssuresh@mit.edu

    • Subra Suresh
  2. Ju Li is in the Department of Materials Science and Engineering, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA.  liju@seas.upenn.edu

    • Ju Li

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