A joint team from Tsinghua University and Rice University revealed the topological and geometrical roles of defects in modulating the mechanical responses of graphene, a single-atom thick membrane or a two-dimensional (2D) material, which provides guidance for rational material design for both structural and functional applications.
The team, led by Dr. Xu Zhiping and Dr. Boris I. Yakobson, published their research,“Defect-Detriment to Graphene Strength is Concealed by Local Probe: the Topological and Geometrical Effects”, in the journal ACS Nano on December 18th, 2014.
Graphene has been considered for some time as a magic material that not only features unique mechanical and optoelectronic properties, but also acts as a test bed for research on fundamental physics in 2D. Although significant effort in synthesizing graphene through techniques has demonstrated the capability of making single-crystalline graphene, the quality of continuum film of graphene and other 2D materials is still limited at the polycrystalline level, where crystalline domains up to centimeters are patched into a monolayer material with single-atom thickness. At the interfaces joining neighboring domains, there are numerous defects created during the synthesis, which could degrade the performance of graphenebased materials and devices, within which the response of such a 2D material under mechanical perturbation becomes of key importance. In contrast to the transport properties, the mechanical strength is determined by the weakest point in the material that does not show apparent dependence on the density of defects.
Compared to those in the bulk phase of materials, lattice imperfections in low-dimensional solids such as vacancies, dopants and dislocations play more remarkable roles in modifying material behavior. Recent experimental evidence has demonstrated that grain boundary defects in graphene are mainly composed of pentagons, heptagons and their pairs that can be considered as positive, negative disclinations and dislocations respectively. These topological defects not only create stress build-up in the material, but also warp the planar geometry of perfect graphene membrane. In recent studies by Dr. Xu’s research group and their collaborators, it was found that the pile-ups of dislocations along the grain boundaries of polycrystalline graphene led to significant stress accumulation that was scaled logarithmically with the length of the grain boundary that consists of pentagon/heptagon pairs as polar dislocations. This phenomenon is reminiscent of the well-known grain boundary strengthening mechanism in polycrystalline metals, namely the Hall- Petch relation, but originates from a different branch of physics.
In addition to this pseudo Hall-Petch effect, the distorted geometry of graphene out of its basal plane due to the presence of topological defects also modifies its mechanical response. Due to the technical difficulties in carrying out in-plane mechanical tests of single-atom-thick membranes, such as graphene, quantitative characterization of their mechanical responses can only be made through nanoindentation. In nanoindentation, a nanosized tip is pressed onto suspended membranes to measure the relationship between force and tip displacement. This approach, however, is limited to measuring local mechanical response only, which could be very different from the global one, as experienced in practice. Specifically, the strength probed is defined predominantly by the material under the tip, rather than the weakest point within the whole material. This deficiency becomes even more significant once the membrane buckles out of the plane, as occurs with graphene consisting of topological defects. The study by Xu and Yakobson’s team demonstrates that by considering this effect, the mechanical stiffness, strength and resilience probed by the nanoindentation could be significantly under- or overestimated, depending on the detailed atomic structures and geometry under the probe. A conclusion from these studiesis that understanding of the roles of topological defects in 2D materials should thus be reassessed by considering both the topological and geometrical effects for a reliable mechanical design of their applications. On the other hand, the topological effects could also be used to engineer 2D materials by implanting intrinsic stress, strain field and curved geometry, which is feasible as every atom of the single-atom-thick materials is exposed to the environment and can be modified.
Dr. Xu Zhiping and Dr. Boris I.Yakobson are the corresponding authors of the ACS Nano paper. Song Zhigong, a PhD student at Tsinghua’s Center for Nano and Micro Mechanics, is the lead author. Co-authors include Dr.Wu Jian from Tsinghua’s School of Aerospace Engineering, and Dr. Vasilii I. Artyukhov from Rice University.
[update: 2015-04]
