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Register a new userA Review on Mechanics and Mechanical Properties of 2D Materials - Graphene and Beyond
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Since the first successful synthesis of graphene just over a decade ago, a variety of two-dimensional (2D) materials (e.g., transition metal-dichalcogenides, hexagonal boron-nitride, etc.) have been discovered. Among the many unique and attractive properties of 2D materials, mechanical properties play important roles in manufacturing, integration and performance for their potential applications. Mechanics is indispensable in the study of mechanical properties, both experimentally and theoretically. The coupling between the mechanical and other physical properties (thermal, electronic, optical) is also of great interest in exploring novel applications, where mechanics has to be combined with condensed matter physics to establish a scalable theoretical framework. Moreover, mechanical interactions between 2D materials and various substrate materials are essential for integrated device applications of 2D materials, for which the mechanics of interfaces (adhesion and friction) has to be developed for the 2D materials. Here we review recent theoretical and experimental works related to mechanics and mechanical properties of 2D materials. While graphene is the most studied 2D material to date, we expect continual growth of interest in the mechanics of other 2D materials beyond graphene.
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Low-symmetry 2D materials---such as ReS$_2$ and ReSe$_2$ monolayers, black phosphorus monolayers, group-IV monochalcogenide monolayers, borophene, among others---have more complex atomistic structures than the honeycomb lattices of graphene, hexagonal boron nitride, and transition metal dichalcogenides. The reduced symmetries of these emerging materials give rise to inhomogeneous electron, optical, valley, and spin responses, as well as entirely new properties such as ferroelasticity, ferroelectricity, magnetism, spin-wave phenomena, large nonlinear optical properties, photogalvanic effects, and superconductivity. Novel electronic topological properties, nonlinear elastic properties, and structural phase transformations can also take place due to low symmetry. The Beyond Graphene: Low-Symmetry and Anisotropic 2D Materials Special Topic was assembled to highlight recent experimental and theoretical research on these emerging materials.
The interest in two-dimensional and layered materials continues to expand, driven by the compelling properties of individual atomic layers that can be stacked and/or twisted into synthetic heterostructures. The plethora of electronic properties as well as the emergence of many different quasiparticles, including plasmons, polaritons, trions and excitons with large, tunable binding energies that all can be controlled and modulated through electrical means has given rise to many device applications. In addition, these materials exhibit both room-temperature spin and valley polarization, magnetism, superconductivity, piezoelectricity that are intricately dependent on the composition, crystal structure, stacking, twist angle, layer number and phases of these materials. Initial results on graphene exfoliated from single bulk crystals motivated the development of wide-area, high purity synthesis and heterojunctions with atomically clean interfaces. Now by opening this design space to new synthetic two-dimensional materials beyond graphene, it is possible to explore uncharted opportunities in designing novel heterostructures for electrical tunable devices. To fully reveal the emerging functionalities and opportunities of these atomically thin materials in practical applications, this review highlights several representative and noteworthy research directions in the use of electrical means to tune these aforementioned physical and structural properties, with an emphasis on discussing major applications of beyond graphene 2D materials in tunable devices in the past few years and an outlook of what is to come in the next decade.
In this work we have investigated the mechanical properties and fracture patterns of some graphene nanowiggles (GNWs). Graphene nanoribbons are finite graphene segments with a large aspect ratio, while GNWs are nonaligned periodic repetitions of graphene nanoribbons. We have carried out fully atomistic molecular dynamics simulations using a reactive force field (ReaxFF), as implemented in the LAMPPS (Large-scale Atomic/Molecular Massively Parallel Simulator) code. Our results showed that the GNW fracture patterns are strongly dependent on the nanoribbon topology and present an interesting behavior, since some narrow sheets have larger ultimate failure strain values. This can be explained by the fact that narrow nanoribbons have more angular freedom when compared to wider ones, which can create a more efficient way to accumulate and to dissipate strain/stress. We have also observed the formation of linear atomic chains (LACs) and some structural defect reconstructions during the material rupture. The reported graphene failure patterns, where zigzag/armchair edge terminated graphene structures are fractured along armchair/zigzag lines, were not observed in the GNW analyzed cases.
The MechElastic Python package evaluates the mechanical and elastic properties of bulk and 2D materials using the elastic coefficient matrix ($C_{ij}$) obtained from any ab-initio density-functional theory (DFT) code. The current version of this package reads the output of VASP, ABINIT, and Quantum Espresso codes (but it can be easily generalized to any other DFT code) and performs the appropriate post-processing of elastic constants as per the requirement of the user. This program can also detect the input structures crystal symmetry and test the mechanical stability of all crystal classes using the Born-Huang criteria. Various useful material-specific properties such as elastic moduli, longitudinal and transverse elastic wave velocities, Debye temperature, elastic anisotropy, 2D layer modulus, hardness, Pughs ratio, Cauchys pressure, Kleinman parameter, and Lames coefficients, can be estimated using this program. Another existing feature of this program is to employ the ELATE package [J. Phys.: Condens. Matter 28, 275201 (2016)] and plot the spatial variation of several elastic properties such as Poissons ratio, linear compressibility, shear modulus, and Youngs modulus in three dimensions. Further, the MechElastic package can plot the equation of state (EOS) curves for energy and pressure for a variety of EOS models such as Murnaghan, Birch, Birch-Murnaghan, and Vinet, by reading the inputted energy/pressure versus volume data obtained via numerical calculations or experiments. This package is particularly useful for the high-throughput analysis of elastic and mechanical properties of materials.
Nanometer-scale imaging of magnetization and current density is the key to deciphering the mechanisms behind a variety of new and poorly understood condensed matter phenomena. The recently discovered correlated states hosted in atomically layered materials such as twisted bilayer graphene or van der Waals heterostructures are noteworthy examples. Manifestations of these states range from superconductivity, to highly insulating states, to magnetism. Their fragility and susceptibility to spatial inhomogeneities limits their macroscopic manifestation and complicates conventional transport or magnetization measurements, which integrate over an entire sample. In contrast, techniques for imaging weak magnetic field patterns with high spatial resolution overcome inhomogeneity by measuring the local fields produced by magnetization and current density. Already, such imaging techniques have shown the vulnerability of correlated states in twisted bilayer graphene to twist-angle disorder and revealed the complex current flows in quantum Hall edge states. Here, we review the state-of-the-art techniques most amenable to the investigation of such systems, because they combine the highest magnetic field sensitivity with the highest spatial resolution and are minimally invasive: magnetic force microscopy, scanning superconducting quantum interference device microscopy, and scanning nitrogen-vacancy center microscopy. We compare the capabilities of these techniques, their required operating conditions, and assess their suitability to different types of source contrast, in particular magnetization and current density. Finally, we focus on the prospects for improving each technique and speculate on its potential impact, especially in the rapidly growing field of two-dimensional (2D) materials.
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