Researchers Measure Mechanical Properties of 2D Materials

The thinnest materials produced nowadays have the thickness of a single atom. These materials - known as two-dimensional (2D) materials - display properties that are very diverse compared with their bulk three-dimensional (3D) counterparts.

Until lately, 2D materials were produced and exploited as films on the surface of certain suitable 3D substrates. Working in partnership with a team from the Leibniz Institute for New Materials, a team of physicists at Saarland University, led by Professor Uwe Hartmann, have for the first time been successful in characterizing the mechanical properties of free-standing single-atom-thick membranes of graphene. The measurements were done using scanning tunneling microscopy (STM). The results of their research have been published in the specialist journal Nanoscale.

Two-dimensional materials are a recent creation. In 2010, the scientists André Geim and Konstantin Novoselov received the Nobel Prize in Physics for their work on the material graphene - a 2D allotrope of pure carbon. Following that discovery, a number of other 2D materials made from germanium or silicon were created and characterized. "The special feature of these materials is that they are only one atom thick - they are practically all surface," explains Professor Uwe Hartmann, an experimental physicist at Saarland University. Consequently, they possess physical properties that are solely different to their more conventional 3D counterparts.

"The electronic properties of some configurations of graphene are spectacular. The electrons in the interior of the material are relativistic, i.e. they obey the laws of relativity theory, which is certainly not the case for electrons in conventional materials. This suggests a number of interesting advantages for electronic components manufactured from two-dimensional materials," says Hartmann.

The mechanical properties of these 2D materials are also exclusive. According to Hartmann: "Some configurations of these two-dimensional materials exhibit a degree of mechanical stability that is - relative to the thickness of the material -far greater than that seen in the most stable three-dimensional materials." So as to manipulate this potential, the EU started its Graphene Flagship project in 2013. With a research budget of €1 billion, it is thus far the EU's largest research initiative.

However, information regarding the mechanical properties of these unique materials has thus far been derived from simulations. "Up until now, working with two-dimensional materials has meant working with ultrathin films on the surface of a suitable three-dimensional substrate. As a result, the properties of the overall system are inevitably determined by the three-dimensional material," explains Hartmann.

Working in partnership with the Leibniz Institute for New Materials (INM), which is also situated in the Saarbrücken campus, Hartmann's research team at the Department of Nanostructure Research and Nanotechnology has been successful in directly measuring the mechanical properties of a free-standing, single-atom layer membrane of the carbon allotrope graphene for the first time.

"We are now in a position to directly compare the data from model calculations with our experimental findings. In addition, we can now measure how different defects in the membrane's crystal lattice affect its mechanical properties," says Professor Hartmann. These 2D materials hold substantial promise of innovative developments in a range of technological sectors from actuators and sensors to fuel cells and filter systems. The results and techniques developed by the team in Saarbrücken are thus of key interest in various fields of research.

The researchers in Saarbrücken used a graphene monolayer that was supported on a substrate with a standard array of circular holes. Hartmann explains the arrangement as follows: "The holes had a diameter of about one micrometre. Using a scanning tunnelling microscope (STM) we were able to analyse the free-standing membrane above the holes with atomic precision."

"When an electrical voltage is applied between the tip of the STM and the single-atom-thick membrane of graphene, an electrical current flows," explains Hartmann. This current, which is referred to as the "tunneling current", is highly sensitive to the distance between the microscope tip and the membrane sample and to the electron distribution in the graphene film. "We use this effect to make the individual atoms visible. The tunnelling current varies while the STM tip is scanned over the material."

The researchers also utilize another effect. When a voltage is applied between the tip of the STM and the sample, a force acts on the free-standing graphene membrane and it starts to bulge towards the tip. "As the tip is withdrawn, the atomically thin monolayer bulges even more, as it is effectively being lifted up by atomically precise tweezers. Measuring the membrane deflection as a function of the electrostatic pulling force generated by the STM yields a stress-strain diagram that provides us with the key mechanical properties of the graphene membrane," explains Hartmann.

By recording these experimental stress-strain diagrams, we have been able to directly verify the extraordinary mechanical properties that have been presumed up until now for these materials. And we were able to do this using forces of the order of a billionth of a Newton - far, far smaller than any force used in a conventional mechanical measurement. The researchers were also able to show that when a force was applied to a free-standing membrane of graphene, the membrane did not behave like the smooth skin of a kettledrum but looked much more like the rippled surface of a lake. The membranes exhibit a range of wavelike motions and they respond to any external disturbance by generating new ripples in the membrane's surface.

Professor Uwe Hartmann