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2D materials

2D materials

2D boron sheets show novel ‘half-auxetic’ effect

07 Apr 2021 Isabelle Dumé
Compression or strain
Regardless of whether it is strained or compressed, the new material always expands. Copyright: Thomas Heine et al.

Researchers have discovered a two-dimensional material that expands regardless of whether it is stretched or compressed. This hitherto unobserved “half-auxetic” effect, as it has been dubbed, could find use in future nanoelectronics applications.

Most materials become thinner when stretched. If you stretch a rubber band across its length, for example, it will shrink in the other two directions (perpendicular and in-plane), becoming narrower and thinner as you pull. Auxetic materials, however, do just the opposite, expanding in both the perpendicular and in-plane directions relative to the applied strain. They also shrink when they are compressed, unlike ordinary materials that expand. In mathematical terms, conventional materials are characterized by a positive Poisson’s ratio and auxetic ones by a negative Poisson’s ratio.

One of the oldest and best-known applications of a natural material that is borderline auxetic is cork, which has a Poisson’s ratio of near zero and can be pushed into the thinner neck of a wine bottle. Other naturally-occurring examples include human tendons and cat skin.

Researchers seeking to mimic such behaviour in artificially-engineered auxetic materials have previously succeeded in making structures that are robust to indentation and tearing (shear stress). Such materials are now increasingly employed in products such as bicycle helmets or safety jackets.

Palladium-decorated borophene

An international team led by Thomas Heine from TU Dresden in Germany has now discovered “half-auxetic” behaviour in an atomically-thin version of the element boron that they made more stable to strain and stress by adding palladium (Pd) to it. The Pd-decorated borophene, as it is called, has three stable phases, one of which exhibits half-auxetic behaviour along one of its crystal axes.

Using computational modelling, Heine and colleagues showed that the material behaves like an auxetic material when strained (a negative Poisson’s ratio) but expands like an ordinary material when compressed (a positive Poisson’s ratio). Simply put, regardless of whether it is strained or compressed, the material always expands.

Novel negative Poisson’s ratio material

The researchers chose palladium as a stabilizer for their borophene studies because it is a transition metal widely employed in electronics and in catalysis and an efficient donor of electrons to boron. It also has the lowest melting point of all platinum group metals, which makes it easier to handle in experiments.

Heine and colleagues studied their palladium borides (PdBn, where n=2,3,4) theoretically using first-principles calculations combined with a “particle swarm optimization” (PSO) algorithm that enabled them to check the materials’ properties. “Poisson’s numbers are typically calculated by the ratio of strain in two directions, but for compressive and tensile strain, we found that the numbers were different in one PdBn,” Heine explains. “We therefore used the more complex (but more accurate) definition that the Poisson’s number is the derivative of one strain direction with respect to the other.”

These calculations revealed a material with a novel negative Poisson’s ratio and intriguing mechanical and electronic properties. Of the three stable phases of the PdBn they discovered, the PdB4 monolayer – a semiconductor with an indirect band gap of 1.22 eV – was the one that showed the half-auxetic behaviour.

Avoiding energetically-costly bond stretching

Describing their work in Nano Letters, the researchers say that the half-auxeticity they unearthed in PdB4 stems from the material trying to avoid an energetically-costly stretching of the Pd-B bonds when strained along its length. To overcome the significant stress it experiences during this applied strain, the sheet in effect becomes corrugated. This process pushes the neighbouring in-plane atoms away from each other, causing it to expand in both the lateral and vertical directions, like an auxetic material.

When the material is compressed, the PdB4 accommodates this stress by, again, pushing the in-plane atoms away from each other so that the material slightly expands in-plane. This is what a conventional material does.

Designing new structures

Heine says that the mechanism he and his colleagues identified might be used to design new half-auxetic structures. “These novel materials could lead to innovative applications in nanotechnology, for example in sensing or magneto-optics,” he explains. “A transfer to macroscopic materials is equally conceivable.”

Spurred on by their findings, members of the team, which includes researchers from Hebei Normal University in China and Singapore University of Technology and Design, say they now plan to find out whether the effect occurs in other classes of nanomaterials, such as metal-organic frameworks or 2D polymers and macroscopic frames produced by 3D printing. “It will also be interesting to explore if the half-auxetic effect can be found in the out-of-plane direction, that is, if the thickness of a material always expands when subject to in-plane tension or compression,” Heine tells Physics World.

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