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Topic Name: Penn Engineers has Constructed a Theoretical Model to Predict the Strength of Metals at the Nanoscale, Surface Dislocation Nucleation

Category: Nanobiotechnology

Research persons: Penn Research Team

Location: School of Engineering and Applied Science, University of Pennsylvania, United States

Details

For centuries, engineers have bent and torn metals to test their strength and ductility. Now, materials scientists at the University of Pennsylvania School of Engineering and Applied Science are studying the same metals but at nanoscale sizes in the form of wires a thousand times thinner than a human hair. This work has enable Penn engineers to construct a theoretical model to predict the strength of metals at the nanoscale. Using this model, they have found that, while metals tend to be stronger at nanoscale volumes, their strengths saturate at around 10-50 nanometers diameter, at which point they also become more sensitive to temperature and strain rate. Such prediction of different strength regimes of nano-solids is important for future application and engineering design of  nanotechnology.

Such small-volume materials with relatively large surface areas are now routinely employed in microchips and nanoscience and technology, and their mechanical properties can differ vastly from their macroscale counterparts. Typically, smaller is stronger. A gold wire 200 nanometers in diameter can be 50 times stronger per area than centimeter-sized single-crystal gold. Engineers investigated the "smaller is stronger" trend.

Ju Li, an associate professor in the Department of Materials Science and Engineering at Penn, and his collaborators at the Georgia Institute of Technology have combined transition state theory, explicit atomistic energy landscape calculation and computer simulation to establish a theoretical framework to predict the strengths of small-volume materials. Unlike previous models, their prediction can be directly compared with experiments performed at realistic temperature and loading rates. This research appeared as a cover article in Volume 100 of Physical Review Letters.

Their study demonstrated that the free, exterior surface of nanosized materials can be fertile breeding grounds of dislocations at high stresses. Dislocations are string-like defects whose movements give rise to plastic flow, or shape change, of solids. In large-volume materials, it is easy for dislocations to multiply and entangle and to maintain a decent population inside; however, in small-volume materials, dislocations could show up and then exit the sample, one at a time. To initiate and sustain plastic flow in this case, dislocations need to be frequently nucleated fresh from the surface.

Since surface is itself a defect, researchers asked to what degree the measured strength of a small-volume material reflects surface properties and surface-mediated processes, particularly when the sample size is in the range of tens of nanometers. Li and his team modeled tiny bits of gold and copper to investigate the probabilistic nature of surface dislocation nucleation. The study showed that the activation volume associated with surface dislocation nucleation is characteristically in the range of 1–10 times the atomic volume, much smaller than that of many conventional dislocation processes. Small activation volumes will lead to sensitive temperature and strain-rate dependence of the critical stress, providing an upper bound to the size-strength relation.

From this, the team predicted that the "smaller is stronger" trend will saturate at wire diameters 10-50 nanometers for most metals. For comparison, computers now contain microchips with 45 nanometer strained silicon features. Associated with this saturation in strength is a transition in the rate-controlling mechanism, from collective dislocation dynamics to single dislocation nucleation.

Note for Dislocation
In materials science, a dislocation is a crystallographic defect, or irregularity, within a crystal structure. The presence of dislocations strongly influences many of the properties of materials. The theory was originally developed by Vito Volterra in 1905. Some types of dislocations can be visualised as being caused by the termination of a plane of atoms in the middle of a crystal. In such a case, the surrounding planes are not straight, but instead bend around the edge of the terminating plane so that the crystal structure is perfectly ordered on either side. The analogy with a stack of paper is apt: if a half a piece of paper is inserted in a stack of paper, the defect in the stack is only noticeable at the edge of the half sheet.
Mathematically, dislocations are a type of topological defect, sometimes called a soliton. The mathematical theory explains why dislocations behave as stable particles: they can be moved about, but maintain their identity as they move. Two dislocations of opposite orientation, when brought together, can cancel each other (this is the process of annihilation), but a single dislocation typically cannot "disappear" on its own.
There are two main types of dislocation, edge and screw. Dislocations found in real materials typically are mixed, meaning that they have characteristics of both.
A crystalline material consists of a regular array of atoms, arranged into e planes (imagine stacking oranges in a grocers, each of the trays of oranges are the lattice planes). One approach is to begin by considering a 3-d representation of a perfect crystal lattice, with the atoms represented by spheres. The viewer may then start to simplify the representation by visualising planes of atoms instead of the atoms themselves.
When a dislocation line intersects the surface of a metallic material, the associated strain field locally increases the relative susceptibility of the material to acidic etching and an etch pit of regular geometrical format results. If the material is strained (deformed) and repeatedly re-etched, a series of etch pits can be produced which effectively trace the movement of the dislocation in question.
Transmission electron microscopy can be used to observe dislocations within the microstructure of the material. Thin foils of metallic samples are prepared to render them transparent to the electron beam of the microscope. The electron beam suffers diffraction by the regular crystal lattice planes of the metal atoms and the differing relative angles between the beam and the lattice planes of each grain in the metal's microstructure result in image contrast (between grains of different crystallographic orientation). The less regular atomic structures of the grain boundaries and in the strain fields around dislocation lines have different diffractive properties than the regular lattice within the grains, and therefore present different contrast effects in the electron micrographs. (The dislocations are seen as dark lines in the lighter, central region of the micrographs on the right). Transmission electron micrographs of dislocations typically utilize magnifications of 50,000 to 300,000 times (though the equipment itself offers a wider range of magnifications than this).

Note for Nanotechnology
Nanotechnology refers broadly to a field of applied science and technology whose unifying theme is the control of matter on the atomic and molecular scale, normally 1 to 100 nanometers, and the fabrication of devices with critical dimensions that lie within that size range.
It is a highly multidisciplinary field, drawing from fields such as applied physics, materials science, interface and colloid science, device physics, supramolecular chemistry (which refers to the area of chemistry that focuses on the noncovalent bonding interactions of molecules), self-replicating machines and robotics, chemical engineering, mechanical engineering, biological engineering, and electrical engineering. Much speculation exists as to what may result from these lines of research. Nanotechnology can be seen as an extension of existing sciences into the nanoscale, or as a recasting of existing sciences using a newer, more modern term.
Two main approaches are used in nanotechnology. In the "bottom-up" approach, materials and devices are built from molecular components which assemble themselves chemically by principles of molecular recognition. In the "top-down" approach, nano-objects are constructed from larger entities without atomic-level control. The impetus for nanotechnology comes from a renewed interest in Interface and Colloid Science, coupled with a new generation of analytical tools such as the atomic force microscope (AFM), and the scanning tunneling microscope (STM). Combined with refined processes such as electron beam lithography and molecular beam epitaxy, these instruments allow the deliberate manipulation of nanostructures, and led to the observation of novel phenomena.
Examples of nanotechnology in modern use are the manufacture of polymers based on molecular structure, and the design of computer chip layouts based on surface science. Despite the great promise of numerous nanotechnologies such as quantum dots and nanotubes, real commercial applications have mainly used the advantages of colloidal nanoparticles in bulk form, such as suntan lotion, cosmetics, protective coatings, drug delivery, and stain resistant clothing.
One nanometer (nm) is one billionth, or 10-9 of a meter. For comparison, typical carbon-carbon bond lengths, or the spacing between these atoms in a molecule, are in the range .12-.15 nm, and a DNA double-helix has a diameter around 2 nm. On the other hand, the smallest cellular lifeforms, the bacteria of the genus Mycoplasma, are around 200 nm in length. To put that scale in to context the comparative size of a nanometer to a meter is the same as that of a marble to the size of the earth. Or another way of putting it: a nanometer is the amount a man's beard grows in the time it takes him to raise the razor to his face.
Molecular nanotechnology, sometimes called molecular manufacturing, is a term given to the concept of engineered nanosystems (nanoscale machines) operating on the molecular scale. It is especially associated with the concept of a molecular assembler, a machine that can produce a desired structure or device atom-by-atom using the principles of mechanosynthesis. Manufacturing in the context of productive nanosystems is not related to, and should be clearly distinguished from, the conventional technologies used to manufacture nanomaterials such as carbon nanotubes and nanoparticles.
When the term "nanotechnology" was independently coined and popularized by Eric Drexler (who at the time was unaware of an earlier usage by Norio Taniguchi) it referred to a future manufacturing technology based on molecular machine systems. The premise was that molecular-scale biological analogies of traditional machine components demonstrated molecular machines were possible: by the countless examples found in biology, it is known that sophisticated, stochastically optimised biological machines can be produced.
It is hoped that developments in nanotechnology will make possible their construction by some other means, perhaps using biomimetic principles. However, Drexler and other researchers have proposed that advanced nanotechnology, although perhaps initially implemented by biomimetic means, ultimately could be based on mechanical engineering principles, namely, a manufacturing technology based on the mechanical functionality of these components (such as gears, bearings, motors, and structural members) that would enable programmable, positional assembly to atomic specification (PNAS-1981). The physics and engineering performance of exemplar designs were analyzed in Drexler's book Nanosystems.

The National Science Foundation-funded study was performed by Li and Amit Samanta of Penn and, from Georgia Tech, Ting Zhu and Ken Gall of the Woodruff School of Mechanical Engineering and Austin Leach of the School of Materials Science and Engineering.

In figure, Atomic configuration of nucleation (blue atom group) in the surface layer of a square copper nanowire (yellow and green atoms) under uniaxial stress. Nucleation occurs at a partial dislocation in the surface layer. Colors refer to the breaking of local inversion symmetry.