During World War I, a British aeronautical engineer named A.A. Griffith noticed something odd about glass. He found that the atomic bonds in glass needed 10,000 megapascals of stress to break apart – but a macroscopic mass of glass could be broken apart by a stress of 100 megapascals. Something about glass changed between the atomic level and the bulk, making it more brittle than its atomic properties suggested.
Griffith attributed this difference to small imperfections in the bulk, like cracks and notches. He also realised the need for a new way to explain how brittle materials like glass fracture, since the atomic properties alone can’t explain it. He drew on thermodynamics to figure an equation based on two forms of energy: elastic energy and surface energy. The elastic energy is energy stored in a material when it is deformed – like the potential energy of a stretched rubber-band. The surface energy is the energy of molecules at the surface, which is always greater than that of molecules in the bulk. The greater the surface area of an object, the more surface energy it has.
Griffith took a block of glass, subjected it to a tensile load (i.e. a load that stretches the material without breaking it) and then etched a small crack in it. He found that the introduction of this flaw reduced the material’s elastic energy but increased its surface energy. He also found that the free energy – which is surface energy minus elastic energy – increased up to a point as he increased the crack length, before falling back down even if the crack got longer. A material fractures, i.e. breaks, when the amount of stress it is under exceeds this peak value.
Through experiments, engineers have also been able to calculate the fracture toughness of materials – a number essentially denoting the ability of a material to resist the propagation of surface cracks. Brittle materials usually have higher strength but lower fracture toughness. That is, they can withstand high loads without breaking or deforming, but when they do fail, they fail in catastrophic fashion. No half-measures.
If a material’s fracture characteristics are in line with Griffith’s theory, it’s usually brittle. For example, glass has a strength of 7 megapascals (with a theoretical upper limit of 17,000 megapascals) – but a fracture toughness of 0.6-0.8 megapascals per square-root metre.
Graphene is a 2D material, composed of a sheet of carbon atoms arranged in a hexagonal pattern. And like glass, its strength: 130,000 megapascals; its fracture toughness: 4 megapascals per square-root metre – the difference arising similarly from small flaws in the bulk material. Many people have posited graphene as a material of the future for its wondrous properties. Recently, scientists have been excited about the weird behaviour of electrons in graphene and the so-called ‘magic angle’. However, the fact that it is brittle automatically limits graphene’s applications to environments in which material failure can’t be catastrophic.
Another up-and-coming material is hexagonal boron nitride (h-BN). As its name indicates, h-BN is a grid of boron and nitrogen atoms arranged in a hexagonal pattern. (Boron nitride has two other forms: sphalerite and wurtzite.) h-BN is already used as a lubricant because it is very soft. It can also withstand high temperatures before losing its structural integrity, making it useful in applications related to spaceflight. However, since monolayer h-BN’s atomic structure is similar to that of graphene, it was likely to be brittle as well – with small flaws in the bulk material compromising the strength arising from its atomic bonds.
But a new study, published on June 2, has found that h-BN is not brittle. Scientists from China, Singapore and the US have reported that cracks in “single-crystal monolayer h-BN” don’t propagate according to Griffith’s theory, but that they do so in a more stable way, making the material tougher.
Even though h-BN is sometimes called ‘white graphene’, many of its properties are different. Aside from being able to withstand up to 300º C more in air before oxidising, h-BN is an insulator (graphene is a semiconductor) and is more chemically inert. In 2017, scientists from Australia, China, Japan, South Korea, the UK and the US also reported that while graphene’s strength dropped by 30% as the number of stacked layers was increased from one to eight, that of h-BN was pretty much constant. This suggested, the scientists wrote, “that BN nanosheets are one of the strongest insulating materials, and more importantly, the strong interlayer interaction in BN nanosheets, along with their thermal stability, make them ideal for mechanical reinforcement applications.”
The new study further cements this reputation, and in fact lends itself to the conclusion that h-BN is one of the thermally, chemically and mechanically toughest insulators that we know.
Here, the scientists found that when a crack is introduced in monolayer h-BN, the resulting release of energy is dissipated more effectively than is observed in graphene. And as the crack grows, they found that unlike in graphene, it gets deflected instead of proceeding along a straight path, and also sprouts branches. This way, monolayer h-BN redistributes the elastic energy released in a way that allows the crack length to increase without fracturing the material (i.e. without causing catastrophic failure).
According to their paper, this behaviour is the result of h-BN being composed of two different types of atoms, of boron and nitrogen, whereas graphene is composed solely of carbon atoms. As a result, when a bond between boron and nitrogen breaks, two types of crack-edges are formed: those with boron at the edge (B-edge) and those with nitrogen at the edge (N-edge). The scientists write that based on their calculations, “the amplitude of edge stress [along N-edges] is more than twice of that [along B-edges]”. Every time a crack branches or is deflected, the direction in which it propagates is determined according to the relative position of B-edges and N-edges around the crack tip. And as the crack propagates, the asymmetric stress along these two edges causes the crack to turn and branch at different times.
The scientists summarise this in their paper as that h-BN dissipates more energy by introducing “more local damage” – as opposed to global damage, i.e. fracturing – “which in turn induces a toughening effect”. “If the crack is branched, that means it is turning,” Jun Lou, one of the paper’s authors and a materials scientist at Rice University, Texas, told Nanowerk. “If you have this turning crack, it basically costs additional energy to drive the crack further. So you’ve effectively toughened your material by making it much harder for the crack to propagate.” The paper continues:
[These two mechanisms] contribute significantly to the one-order of magnitude increase in effective energy release rate compared with its Griffith’s energy release rate. This finding that the asymmetric characteristic of 2D lattice structures can intrinsically generate more energy dissipation through repeated crack deflection and branching, demonstrates a very important new toughening mechanism for brittle materials at the 2D limit.
To quote from Physics World:
The discovery that h-BN is also surprisingly tough means that it could be used to add tear resistance to flexible electronics, which Lou observes is one of the niche application areas for 2D-based materials. For flexible devices, he explains, the material needs to mechanically robust before you can bend it around something. “That h-BN is so fracture-resistant is great news for the 2D electronics community,” he adds.
The team’s findings may also point to a new way of fabricating tough mechanical metamaterials through engineered structural asymmetry. “Under extreme loading, fracture may be inevitable, but its catastrophic effects can be mitigated through structural design,” [Huajian Gao, also at Rice University and another member of the study], says.
Featured image: A representation of hexagonal boron nitride. Credit: Benjah-bmm27/Wikimedia Commons, public domain.
