Key puzzle in brittle-to-ductile transition in silicon resolved
Why does silicon, which usually shatters catastrophically like glass when fractured,
suddenly change and show ductile fracture like metals when the temperature is
increased? Reporting in a recent issue of Physical Review Letters June 2010, large
atomistic models that incorporate quantum mechanical effects of how atoms interact in
the material, now unravelled the fundamental events that explain the sudden change
from brittle cleavage to ductile dislocation emission at a crack tip in silicon. The research
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 work 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. In the long-term, the findings 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 industry, where the material is used to create very complex functional
structures, such as in computer chips or Nano/Micro-Electro-Mechanical Systems
(N/MEMS). The past decades have seen a vast amount of research efforts to push the scales
and structures that 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 mechanical reliability of silicon technology is still a major issue and often
prevents widespread application, and in particular dealing with the extreme brittleness of
silicon (it shatters like glass) has remained challenging to accomplish. The mechanical
reliability of silicon is key to ensure a safe functioning of these components, which
fundamentally relies on a detailed understanding of the properties on the atomistic level, in
particular for mechanisms of how a material responds to mechanical deformation and
extreme conditions, such as fracture (Figure 1).
It has been known for many 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 many years. There have been many attempts to explain the transition and
gain insight in the detailed mechanisms, but most them started at much larger scales and
did not incorporate the intricacies related to the quantum mechanical phenomena that
control the breaking of chemical bonds at a material’s smallest scale.
The key to understand the transition from brittle to ductile behaviour is to consider what
happens at the most fundamental level, at the tip of a crack in silicon (Figure 1).
Experimental techniques can, however, not yet image the structure and dynamical
mechanisms at that scale, due to severe limitations not only with regards to length scale
resolution, but also time scale. On the other hand, the most correct atomistic description in
theoretical models can be obtained by quantum mechanics theories, but because of the very
restricted volume that can realistically be treated (only a few hundreds of atoms, far below
the thousands of atoms involved in the complex mechanisms at the crack tip), the three
dimensional mechanisms at the crack tip can not be examined.
A MIT/NTNU team of researchers involving Prof. Christian Thaulow of NTNU, Prof.
Markus 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 f
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 in general,” Thaulow says.
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).
Figure legends
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.
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.
Figures and legends
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.
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.