Key puzzle in brittle-to-ductile transition in silicon resolved
(Nanowerk Spotlight) Why does silicon, which usually shatters catastrophically like glass when fractured, suddenly change and show ductile fracture like metals when the temperature is increased? As Markus J Buehler, the Esther and Harold E. Edgerton Associate Professor in MIT's Department of Civil and Environmental Engineering, explains to Nanowerk, "the development of atomistic-level understanding of crack-tip events in silicon with increasing temperature have been hindered partly due to the lack of atomistic models that enable the simulation of sufficiently large systems to accurately describe the fracture processes at a range of temperatures."
Large atomistic models that incorporate quantum mechanical effects of how atoms interact in the material have now unravelled the fundamental events that cause the sudden change from brittle cleavage to ductile dislocation emission at a crack tip in silicon.
This research, reported in the June 11, 2010 online issue of Physical Review Letters ("Atomistic Study of Crack-Tip Cleavage to Dislocation Emission Transition in Silicon Single Crystals"), has revealed that at low temperatures, silicon fails under spreading of cracks, where atomic bonds are broken continuously such that fractures spread easily in the material. For temperatures beyond a critical point, however, this changes dramatically and rather than breaking atomic bonds, stacked planes of atoms in the silicon lattice are sheared altogether, shutting down the spreading of cracks and giving rise to a much more graceful mode of failure that resembles that of metals.
This research has major implications for our understanding of materials in extreme conditions, such as very low temperatures as found in arctic areas, and could enable the design of silicon materials without an intrinsic brittleness. This could facilitate the utilization of abundant resources, such as silica, for the design of mechanically important structures.
The failure of components made of silicon is an important practical issue in the electronics and nanotechnology industries, where the material is used to create very complex functional structures. The past decades have seen a vast amount of research efforts to push the scales and structures we can design with silicon – reaching down to ultra-small feature scales of tens of nanometres and below, which has resulted in many product developments. However, the reliability of silicon technology is still an issue, and in particular dealing with the extreme brittleness of silicon (it shatters like glass) has remained challenging to accomplish.
Figure 1: Failure of materials and structures involves many length-scales, from the macroscopic scale to the level of Angstrom where chemical bonds are found (adapted from Buehler and Xu, Nature, 2010). A comprehensive analysis of failure must start at a fundamental level in order to represent key mechanisms of how materials fail. (Images: Buehler group, MIT)
The mechanical reliability of silicon is key to ensure a safe functioning of these components, which relies on a detailed understanding of the properties on the atomistic level, in particular for mechanisms of how a material responds to mechanical deformation such as fracture (Figure 1).
It has been known for decades that silicon is a brittle material at low temperatures that shatters catastrophically, whereas at elevated temperatures, the behavior of silicon changes drastically over an extremely narrow temperature range of just a few degrees and suddenly becomes ductile and soft like metals. This brittle-to-ductile transition has been observed in experimental studies, yet its fundamental mechanisms remain unknown, and has puzzled researchers for decades. There have been many attempts to explain the transition and gain insight in the detailed mechanisms. But in spite all these efforts, the interactions at the crack tip responsible for the generation of dislocations have not been understood.
The key to understand this phenomenon is to consider what happens at the most fundamental level, at the tip of a crack in silicon (Figure 2). Experimental techniques can, however, not yet image the structure and dynamical mechanisms at that scale. On the other hand, the most correct atomistic description is obtained by quantum mechanics, but because of the very restricted volume that can realistically be treated (only a few hundreds of atoms), the three dimensional mechanisms at the crack tip can not be examined.
Figure 2: Atomistic model of fracture of silicon. Brittle fracture, left (crack extends suddenly and rapidly with a speed of several km/sec), and ductile fracture, right (crack does not extend, but rather the lattice is sheared along the reddish region shown in the lower right half of the image). Each sphere represents a silicon atom. (Images: Buehler group, MIT)
A MIT/NTNU team of researchers involving Prof. Christian Thaulow of NTNU, Buehler of MIT, graduate student Dipanjan Sen, undergraduate students Stella Schieffer and Alan Cohen of MIT now used a new quantum mechanics informed model of interatomic interactions that is capable of examining material volumes of sufficient dimensions. With this new method they could for the first time apply a computational microscope to obtain insight into the key processes at the tip of the crack, at levels of detail never seen before.
The team found that by solely raising the temperature at which the material is being torn apart, an abrupt change from brittle cracking (uncontrollable growth of the crack) to dislocation emission from a crack (shearing of the material without crack growth) occurs within a very narrow temperature range.
The atomistic-scale investigations revealed that the emergence of very small geometric irregularities formed along the crack front is a prerequisite for the transition from brittle to ductile appearance. As the critical temperature is approached, crack tip blunting dominates and is accompanied by changes in the perfect structure at the crack tip. Bond rotations at the crack tip lead to the formation of new bond structures that differ from the hexagonal rings typically found in silicon.
"Atomistic modeling of this phenomenon is fundamental to our understanding of what distinguishes brittle from ductile materials, and the new method applied here provides transformative insight into the failure mechanisms of materials," says Thaulow.
In continuum mechanics approaches commonly used by engineers for the analysis of materials failure, a homogeneous material description is often assumed together with ideal geometric features. The natural structure of materials is, however, highly inhomogeneous and the incorporation of the discreteness of matter and the natural variations of atoms are key elements that a comprehensive model must incorporate. The energy is far from being distributed evenly per length or volume, as assumed in continuum approaches. The formation of small ledges at the crack front, stimulating ductile material response, is a good example of the elegant natural mechanisms that can be discovered with such methods.
"Although we use silicon as model with enormous practical interest, the in-depth understanding of this phenomenon will also be relevant for the materials failure in general and for the future development of atomistic mechanics models for many other materials that are of great importance for materials engineering," Buehler adds. "Key challenges for the future could include the development of methods to make silicon based materials ductile under low temperature conditions, perhaps based on the utilization of biologically inspired structures that involve a hierarchy of material levels."
The realization of such materials could facilitate the utilization of abundant resources, such as silica, for the design of mechanically important structures.
Thaulow says, "One example with enormous practical relevance is the use of arctic steels. These steels undergo a transition from ductile to brittle fracture as the temperature drops, and the low design temperatures in arctic regions represent a challenge. Atomistic and multiscale material modelling and testing is now applied in ongoing research to understand the transition in material properties. This will stimulate development of new alloys/materials and better acceptance criteria. We currently explore these aspects in a large industrial/Norwegian Research Council supported research project Arctic Materials, at SINTEF/NTNU."
This research was supported by the United States Army Research Office (W911NF-06-1-0291), NOTUR (Norwegian High Performance Computing), the MIT UROP program, and the Arctic Materials project (SINTEF).
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