**1.3 Anisotropy in non-metallic 2D nanomaterials**

The 2D non-metallic materials display remarked structural anisotropy due to the large interlayer spacing and comparably low interlayer cohesion and interaction, which causes that a monolayer of graphene could be readily mechanically exfoliated and hexagonal MoS2 (h-MoS2) with lamellar structure can be used as a solid lubricant owing to its superlubricity causing the facile glide among MoS2 nanosheets. However, in the in-plane direction, the assumption of mechanical isotropy in 2D materials is premature just based on the six-fold symmetry in their hexagonal lattice when the isotropy has been assumed for some estimations of the elastic behaviors in carbon nanotubes. Prior researches unveiled that friction force exerted on both graphene and MoS2 along in-plane 'zigzag' and 'armchair' directions of the hexagonal lattice gave rise to different results and friction tests along armchair direction resulted in larger friction forces. M. Dienwiebel et al. found the angular interval between two friction peak force being approximate 60° upon friction tests on graphite [12]. This suggests that the 2D materials with hexagonal lattice manifest a sixfold anisotropy with a 60° periodicity. Meanwhile, studies showed that the anisotropy in both graphene and MoS2 has a thickness dependence [13]. 2D nonmetallic nanomaterials have been often used as building blocks or components for micro/nano-electromechanical systems (M/NEMSs) and nanoelectronics. The anisotropy of those 2D materials have great influence on not only mechanical properties but also functional properties.

## **1.4 Anisotropy in metallic 2D thin films**

Metallic coating and thin films have been largely fabricated adopting nonequilibrium ultrahigh vacuum techniques and electrodeposition. When the nuclei heterogeneously grow and then 3D clusters collide amid the coalescence process, forming intercrystalline interface. This process generally gives rise to nanocolumnar grains whose grain size is small, even in monolithic metals, in contrast to other equilibrium processes. **Figure 1** shows the structure zone diagram after energetic deposition of a thin film on a substrate, indicating that columnar grains preferentially being generated at different generalized temperature *T/Tm* and argon pressure [14]. The columnar structure could even exist in amorphous Al-Cr thin films prepared by the sputtering technique as a result of chemical segregation [15]. These 2D

#### **Figure 1.**

*Structure zone diagram after energetic deposition at different generalized temperature* T/Tm *and argon pressure. Reprinted with permission from reference [14].*

metal coatings or thin films have higher hardness and strength, abiding by the wellknown Hall–Petch relationship. However, the abundant columnar GBs with directionality are often the sites where the voids reside. The sluggish adatom kinetics and the shadowing effect from the surface e roughness lead to void formation residing at the columnar GBs and void-free GBs have lower cohesive energy when compared to the grain interiors. Z. S. You et al. found that nanotwinned (NT) Cu with columnar grains packed with horizontal coherent twin boundaries (TBs) experienced inhomogeneous deformation and columnar GBs were subjected to much larger plastic strain, compared to the grain interiors [16]. This caused one ambiguous puzzle, that is, the constant in the Tabor equation expressed as *H=Cσ* which translates the indentation hardness to the tensile strength often remarkably fails to fall in the proper proportionality range [9]. The proportionality constant, *C*, is dependent on the deformation mode under indentation and it had been empirically determined that H/*σ*≈2*:*7 for materials with high strain hardening coefficient and yield strength (elastic–plastic transition mode). This indicates the 2D metallic thin films with columnar GBs possess substantial structural anisotropy, despite the crystal anisotropy governed by either Schmid factor or Taylor factor [2, 8]. Metallic coatings or thin films have been used as protective, reflective, conductive components on apparatuses and devices. Comprehension toward the anisotropy of 2D metallic materials would substantially help improve their reliability and realize property optimization.

> topological defects, whereas a rather smooth fracture feature was monitored as the strain varied from 43.859% to 43.866% under the test along armchair direction and the process left limited topological defects. It should be noted the five significant digits might be trivial in the real experiments but it was non-trivial in the MD simulations to capture detailed fracture process. The fracture evolutions along two directions were captured using snapshots in **Figure 3**. Since the C-C bonds have a critical strength, i.e. *σ<sup>C</sup><sup>C</sup>*, it is anticipated that the direction of the applied force with respect to the hexagonal honeycomb lattice eventually governed the fracture mode and the analysis on the evolution of bond angles during the straining under two testing conditions is essential to decipher the different fracture mechanisms. Along the ziazag direction in **Figure 3a**, two 120° bond angles that evolved in a symmetrical pattern with the increase in the strain declined down to <90 ° and sustained substantial external strain, while the bonds in parallel to the tensile

*Tensile strain-induced fracture process (a) along the zigzag direction and (b) along the armchair direction at*

*various strain levels. Reprinted with permission from reference [20].*

*Molecular dynamics simulation of tensile tests on 4.15 4.15 nm<sup>2</sup> square-shaped graphene monolayer along (a) zigzag and (b) armchair directions and the relations between applied force and one unit cell are present.*

**Figure 2.**

**Figure 3.**

**59**

*Reprinted with permission from reference [20].*

*Anisotropic Mechanical Properties of 2-D Materials DOI: http://dx.doi.org/10.5772/intechopen.96598*
