**3. Friction anisotropy in MoS2**

The MoS2 has similar lamellar structure as graphene and has been considered promising in the field of nanotribology, despites its various applications due to its functional properties. The inherent crystallographic characteristics of h-MoS2 equips it with friction anisotropy pertaining to the effect of the lateral sliding direction on the friction behaviors or the commensurability/incommensurability conditions between two sliding planes. In the case of incommensurability where the two sliding surfaces have crystallographic nonmatching, ultralow friction is obtained and superlubricity occurs, which has been observed in 2D materials, such as MoS2, graphene and highly oriented pyrolytic graphite to name a few. The superlubricity is related to the structural anisotropy. **Figure 4** presents the debris of five-layer thick MoS2 after a wear test and the high resolution transition electron

#### **Figure 4.**

*High resolution TEM micrograph of a five-layer thick MoS2 specimen after a wear test and the slide led to different mosaic lattice domains with 15° and 30° relative rotations. Reprinted with permission from reference [21].*

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

direction were elastically deformed until their critical strength was reached and then they broke, forming the broken hanging chains. In the other hand, the deformation along the armchair direction in **Figure 3b** caused the four 120° bond angles with a � 30 ° relation with the applied force to decrease, transferring the hexagonal lattice into the quasi-rectangular shape, until any of the bonds except the two bonds normal to the testing direction broke. In the armchair mode, once triggered, the crack front would lead to a sequential instantaneous bond-breaking along the same direction and this left a 60° rupture along the armchair direction. Therefore, the two bonds parallel to the zigzag testing direction and the four bonds perpendicular to the armchair testing directions underwent the larger stress. As a result, the

of the zigzag direction. In reality, the 0.21 TPa of the armchair direction is approximately 1.2 times of the 0.18 TPa of the ziazag direction, which is attributed to the evolving geometrical changes of the hexagonal structures amid the elongation processes. In addition, the geometrical changes of the hexagonal units during the straining determined the critical fracture stains for two testing directions. In order to validate the observation, the simulated dimensions were investigated to verify if the mechanical anisotropy has a size effect and it was found that the size effect was

The MoS2 has similar lamellar structure as graphene and has been considered promising in the field of nanotribology, despites its various applications due to its functional properties. The inherent crystallographic characteristics of h-MoS2 equips it with friction anisotropy pertaining to the effect of the lateral sliding direction on the friction behaviors or the commensurability/incommensurability conditions between two sliding planes. In the case of incommensurability where the

two sliding surfaces have crystallographic nonmatching, ultralow friction is obtained and superlubricity occurs, which has been observed in 2D materials, such as MoS2, graphene and highly oriented pyrolytic graphite to name a few. The superlubricity is related to the structural anisotropy. **Figure 4** presents the debris of five-layer thick MoS2 after a wear test and the high resolution transition electron

*High resolution TEM micrograph of a five-layer thick MoS2 specimen after a wear test and the slide led to different mosaic lattice domains with 15° and 30° relative rotations. Reprinted with permission from*

<sup>3</sup> <sup>p</sup> *<sup>σ</sup>C*�*C*, 1.73 times of the *<sup>σ</sup>C*�*<sup>C</sup>*

critical stress along the armchair is calculated to be ffiffiffi

negligible.

*Material Flow Analysis*

**Figure 4.**

**60**

*reference [21].*

**3. Friction anisotropy in MoS2**

microscopic (HRTEM) image shows different mosaic lattice domains as a result of 15° and 30° relative rotations between MoS2 nanosheets [21]. Commonly, six-fold and two-fold symmetry of the friction behaviors have been captured on empirical and computational researches. Some two-fold symmetry of friction behaviors, namely 180° periodicity, have been attributed to the oriented linear wrinkles induced by the elastic deformation of the substrate and the testing conditions, one of which is the direction-dependent friction measured by an AFM tip with rotation. It was hypothesized that the tip rotation generated a variety of possible combination of the tip-specimen interfaces and the friction results might be able to reflect the genuine crystallographic pattern of the tested materials.

A study involving experimental and MD simulation results on the friction property of MoS2 was present [22]. The direction-dependent friction behaviors were measured by changing the scanning direction and a 5 nm travel distance was applied to preclude the influence from the nanowrinkles. The atomic configuration and the scanning direction with respect to the lattice are illustrated in **Figure 5a**. **Figure 5b** presents the two friction loops consisting of forward and backward lateral scans, measured by AFM along zigzag and armchair directions, and it shows that the energy dissipated in each scan cycle of the tests along the armchair direction was 11 times higher than that of the tests along the zigzag direction. **Figure 5c** shows comparable simulation results and the quantitative discrepancy between the empirical and simulation results originates from the difference in tip conditions and the magnitude of the scanning speed and force. The Prandtl-Tomlinson model alleged that the friction at the atomic level relies on the height of the surface energy barrier and longer scanning length along the armchair direction would result in accumulated energy dissipation in comparison with the zigzag direction. Hence, the direction-dependent friction behaviors were examined using potential energy surface (PES). **Figure 6a** reveals a six-fold symmetry of the friction force in nN in comparison with the two-fold symmetry. To further comprehend the friction symmetry, PEC at various angular positions was observed with a 10° interval. **Figure 6b** reflects the cross-section energy profiles for the scans at 0°, 10° and 50°. **Figure 6c**-**j** show that PES possessed a 60° periodicity, e.g. the energy surfaces of the 0° and 60° being identical. Therefore, a friction anisotropy was explored at an atomic level, proving that the testing direction and tip-specimen contact quality greatly play significant roles in changing the energy landscape and affecting the friction behaviors. X. Cao et al. have exhibited that the friction behaviors of MoS2 had a thickness effect [13]. In brief, the decrease in MoS2 thickness down to a few nanometers could progressively weaken the anisotropy phenomenon and be more governed by the puckering effect.

#### **Figure 5.**

*(a) Atomic configuration of a MoS2 monolayer in the simulations, indicating the armchair (30°) and zigzag directions (60°). (b) the experimental friction loops consisting of the forward and backward scanning along the armchair and zigzag directions. (c) the friction traces, due to tip-specimen contacts, predicted by the MD simulations along the armchair and zigzag directions. Reprinted with permission from reference [22].*

columnar GBs that contributes to the structural anisotropy has been largely ignored. Li et al. selected Al-Fe alloys produced by magnetron sputtering to investigate the anisotropy and tension-compression asymmetry along both the film in-plane and out-of-plane directions by adopting comprehensive in-situ micro-compression and

**Figure 7a** shows the dark-field TEM image and HRTEM image, suggesting that the Al-Fe alloys have abundant vertical GBs, which were identified as incoherent twin boundaries (ITBs) with a diffused feature, and an average grain size of 5 nm. It is expected that the tiny grain size would greatly suppress the dislocation accumulation process that takes place in the plastic deformation of single crystals or polycrystalline materials with large grain size, making the deformation or fracture events more dominantly influenced by the directionality of the GBs. **Figure 7b**-**d** illustrate the micro-tension and compression experiments along in-plane and outof-plane directions and exhibit the microsized specimens awaiting the in-situ

The experiment results showed that the out-of-plane compression experiments gave rise to a 2 GPa strength and exhibited extensive deformability attributed to the grain coarsening, whereas in-plane compressions yielded a 1.6 GPa strength but an intergranular shear deformation along the GBs, leaving the formation of shear bands. This deformation mode was governed by the maximum resolved shear stress. In addition, out-of-plane tensile experiments gave a tensile strength of 1.8 GPa, comparable to the 2 GPa compressive strength, and a fracture mode governed by the intragranular shear propagation which were substantially deflected by vertical GBs. The apparent global engineering strain cannot be equated to the

*(a) Cross-section dark-field TEM image showing abundant vertical GBs in a (111)-textured Al-Fe thin film and the neighboring columnar nanograins having twin relation. (b) Schematics illustrating how to perform micro-tension and compression experiments along both in-plane and out-of-plane directions. (c) Schematics of the setups of the* in-situ *micro-tension and compression experiments along with the scanning electron microscope (SEM) images of the tensile gripper and the flat punch. (d) Micropillars and tensile micro-coupons awaiting the in-situ tension and compression experiments. Note that OPC, IPC, OPT and IPT denote out-of-plane compression, in-plane compression, out-of-plane tension, and in-plane tension, respectively. Reprinted with*

tension techniques [9].

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

experiments.

**Figure 7.**

**63**

*permission from reference [9].*

#### **Figure 6.**

*(a) MD simulation that monitored a 6-fold symmetry in the results of friction tests on MoS2 as a function of the rotational. (b) Cross-sectional barrier profiles along the scanning distance at a sample rotation angle of 0°, 10° and 50°. (c j) potential energy surface (PES) calculated for the specimen rotated from 0° to 70°. Reprinted with permission from reference [22].*

### **4. Mechanical anisotropy in Al-Fe thin films**

Since the early 1950's when Hall and Petch empirically demonstrated that the Yield strength of metallic materials is inversely proportional to the square root of the microstructural features, researchers have put enormous efforts in refining the microstructure and thus developed ultrafine grained materials and nanocrystalline materials in order to lift mechanical strength for both fundamental exploration and practical applications. Non-equilibrium routes have been commonly used to shrink the grain size of the metallic materials and most of techniques, such as ultrahigh vacuum techniques and electrodeposition, produce 2D metallic materials, i.e. coatings and thin films. Researchers have found that the tensile strength collected from the tensile tests on thin film metals, especially alloys, fell short of the predicted strength translated from nanoindentation measurements according to the Taylor relation, i.e. H = C*σ* where C is the proportionality constant. H/*σ* = 3 is often observed for materials with low strain hardening coefficient and low yield strength (fully plastic contact mode), whereas 1.1 < H/*σ* < 3 is applicable for materials with high strain hardening coefficient and high yield strength (elastic–plastic transition mode). Most of time, nanoindentation studies showed empirically that H/*σ*≈2*:*7 for thin film metals with high strength. The off-proportionality has been often attributed to the voids potentially residing at the columnar GBs in thin film materials. However, the void size is proportional to columnar grain size and when the grain size is at nanoscale, the shadowing effect that originates from the 3D cluster growth should be negligible to cause void formation. Therefore, the directionality of the

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

columnar GBs that contributes to the structural anisotropy has been largely ignored. Li et al. selected Al-Fe alloys produced by magnetron sputtering to investigate the anisotropy and tension-compression asymmetry along both the film in-plane and out-of-plane directions by adopting comprehensive in-situ micro-compression and tension techniques [9].

**Figure 7a** shows the dark-field TEM image and HRTEM image, suggesting that the Al-Fe alloys have abundant vertical GBs, which were identified as incoherent twin boundaries (ITBs) with a diffused feature, and an average grain size of 5 nm. It is expected that the tiny grain size would greatly suppress the dislocation accumulation process that takes place in the plastic deformation of single crystals or polycrystalline materials with large grain size, making the deformation or fracture events more dominantly influenced by the directionality of the GBs. **Figure 7b**-**d** illustrate the micro-tension and compression experiments along in-plane and outof-plane directions and exhibit the microsized specimens awaiting the in-situ experiments.

The experiment results showed that the out-of-plane compression experiments gave rise to a 2 GPa strength and exhibited extensive deformability attributed to the grain coarsening, whereas in-plane compressions yielded a 1.6 GPa strength but an intergranular shear deformation along the GBs, leaving the formation of shear bands. This deformation mode was governed by the maximum resolved shear stress. In addition, out-of-plane tensile experiments gave a tensile strength of 1.8 GPa, comparable to the 2 GPa compressive strength, and a fracture mode governed by the intragranular shear propagation which were substantially deflected by vertical GBs. The apparent global engineering strain cannot be equated to the

#### **Figure 7.**

**4. Mechanical anisotropy in Al-Fe thin films**

**Figure 6.**

**62**

*with permission from reference [22].*

*Material Flow Analysis*

Since the early 1950's when Hall and Petch empirically demonstrated that the Yield strength of metallic materials is inversely proportional to the square root of the microstructural features, researchers have put enormous efforts in refining the microstructure and thus developed ultrafine grained materials and nanocrystalline materials in order to lift mechanical strength for both fundamental exploration and practical applications. Non-equilibrium routes have been commonly used to shrink the grain size of the metallic materials and most of techniques, such as ultrahigh vacuum techniques and electrodeposition, produce 2D metallic materials, i.e. coatings and thin films. Researchers have found that the tensile strength collected from the tensile tests on thin film metals, especially alloys, fell short of the predicted strength translated from nanoindentation measurements according to the Taylor relation, i.e. H = C*σ* where C is the proportionality constant. H/*σ* = 3 is often observed for materials with low strain hardening coefficient and low yield strength (fully plastic contact mode), whereas 1.1 < H/*σ* < 3 is applicable for materials with high strain hardening coefficient and high yield strength (elastic–plastic transition mode). Most of time, nanoindentation studies showed empirically that H/*σ*≈2*:*7 for thin film metals with high strength. The off-proportionality has been often attributed to the voids potentially residing at the columnar GBs in thin film materials. However, the void size is proportional to columnar grain size and when the grain size is at nanoscale, the shadowing effect that originates from the 3D cluster growth should be negligible to cause void formation. Therefore, the directionality of the

*(a) MD simulation that monitored a 6-fold symmetry in the results of friction tests on MoS2 as a function of the rotational. (b) Cross-sectional barrier profiles along the scanning distance at a sample rotation angle of 0°, 10° and 50°. (c j) potential energy surface (PES) calculated for the specimen rotated from 0° to 70°. Reprinted*

*(a) Cross-section dark-field TEM image showing abundant vertical GBs in a (111)-textured Al-Fe thin film and the neighboring columnar nanograins having twin relation. (b) Schematics illustrating how to perform micro-tension and compression experiments along both in-plane and out-of-plane directions. (c) Schematics of the setups of the* in-situ *micro-tension and compression experiments along with the scanning electron microscope (SEM) images of the tensile gripper and the flat punch. (d) Micropillars and tensile micro-coupons awaiting the in-situ tension and compression experiments. Note that OPC, IPC, OPT and IPT denote out-of-plane compression, in-plane compression, out-of-plane tension, and in-plane tension, respectively. Reprinted with permission from reference [9].*

ductility of the common ductile materials with larger grain size and dislocationdominated deformation mechanisms. In contrast, the in-plane tension experiments exhibited a relatively low strength of 1.1 GPa and classic brittle behaviors governed by the nominal stress-induced fracture. The premature fracture propagated along GBs. It was found that the chemical combination of binary Al-Fe alloys did not satisfy the embrittlement criteria in the Gibson-Schuh model [23], meaning that the relation between applied tensile stress and the directionality of the vertical void-free GBs, i.e. vertical ITBs, mostly rendered the premature fracture phenomenon under in-plane tension mode rather than other factors including voids and GB embrittlement. **Figure 8** had summarized the major deformation or fracture mechanisms of the tension and compression tests along the in-plane and out-of-plane directions. It is noted that the anisotropy experienced in the Al-Fe thin films is different from the anisotropy in single crystals and polycrystals, governed by the Schmid factor and the Tylor factors. Moreover, the thin film alloys, including the Al-Fe, are also different from the isotropic nanocrystalline metals and alloys with textureless feature. However, dislocations were indeed captured in the differently deformed Al-Fe specimens. It was found that under compression, the ratio of the yield strength collected under out-of-plane compression mode and in-plane compression mode was 1.25, which was mostly governed by the Taylor factors of two testing directions. Since the Al-Fe alloys have a strong (111) out-of-plane texture, the out-of-plane Taylor factor is 3.67. Moreover, the in-plane direction has no obvious texture or a weak (112) texture and the two possibilities rendered similar Taylor factor of 3.06. This two Taylor factors led to a strength ratio of 1.2, coinciding with the 1.25 collected experimentally. This indicates that the anisotropy in the Al-Fe thin films was both influenced by the directionality of the GBs and the

conventional Taylor factor. **Figure 9** plots the collected strengths under tension and compression along the in-plane and out-of-plane directions as a function of extrinsic specimen dimension and intrinsic microstructural feature size and it clearly manifested the anisotropy under both tension and compression modes. The Al-Fe alloys underwent negligible extrinsic size effect and are highly competitive as to the

*(a) The yield strength or fracture strength, collected from different testing conditions, of Al-Fe thin films in comparison to the ones of other Al alloys with extrinsic dimensions at similar magnitudes. (b) the comparison of the strengths* as a function of *intrinsic microstructural feature size effect between Al-Fe thin film and other pure*

*Al and Al alloys. Reprinted with permission from reference [9].*

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

Some thin films or coatings consisting of constituent elements with low stacking

The synthesis, microstructural controls and the functional applications of 2D materials have been top trending research topics in the past 2 decades. However, the anisotropy of the 2D materials has not been put equal but actually exerts potent influence on not only their mechanical behaviors but also the multifunctional performance of materials and devices with 2D materials as components or building blocks. The unique microstructural characteristics of 2D materials result in distinct

and intriguing structural and crystal anisotropy. As to the non-metallic 2D nanomaterials, such as graphene and MoS2, the orientation of the applied stress

fault energy might have columnar grains packed with high-density horizontal coherent TBs (CTBs). Q. H. Lu et al. found that the dislocations were confined within the twin/matrix lamellae and the testing direction, the slip systems and the horizontal CTBs of the NT Cu could result in different dislocation structures and dislocation-CTB interactions, which rendered different hardening and softening modes and thus the anisotropy in metallic thin films made of constituent elements with low stacking fault energy [24]. Furthermore, it should be noted that not all the metallic thin films prepared by non-equilibrium methods possessed the conventional columnar GBs. Li et al. recently exhibited that manipulation of electrolytic solution with certain organic additive could potentially transfer the 3D cluster growth to a flat 2D layer-by-layer growth mode to facilitate the formation of TBs and suppress the formation of the columnar GBs from the island coalescence process [8]. The anisotropy of the NT metals mainly constructed by horizontal CTBs needs further investigation. Furthermore, the mechanical anisotropy in metallic materials could be also displayed from the dynamic strain-induced phase transformation. In a Transformation induced plasticity (TRIP) steel, a strong texture after rolling was obtained in the austenite and the texture in austenite gave rise to a higher martensitic transformation rate along the rolling direction, which contributed to a more pronounced TRIP effect and a higher strain-hardening rate [25, 26].

high strength.

**Figure 9.**

**5. Conclusions**

**65**

#### **Figure 8.**

*Schematics that illustrate the deformation or fracture mechanisms for Al-Fe specimens tested at different modes along different directions. Reprinted with permission from reference [9].*

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

#### **Figure 9.**

ductility of the common ductile materials with larger grain size and dislocationdominated deformation mechanisms. In contrast, the in-plane tension experiments

*Schematics that illustrate the deformation or fracture mechanisms for Al-Fe specimens tested at different modes*

*along different directions. Reprinted with permission from reference [9].*

exhibited a relatively low strength of 1.1 GPa and classic brittle behaviors governed by the nominal stress-induced fracture. The premature fracture propagated along GBs. It was found that the chemical combination of binary Al-Fe alloys did not satisfy the embrittlement criteria in the Gibson-Schuh model [23], meaning that the relation between applied tensile stress and the directionality of the vertical void-free GBs, i.e. vertical ITBs, mostly rendered the premature fracture phenomenon under in-plane tension mode rather than other factors including voids and GB embrittlement. **Figure 8** had summarized the major deformation or fracture mechanisms of the tension and compression tests along the in-plane and out-of-plane directions. It is noted that the anisotropy experienced in the Al-Fe thin films is different from the anisotropy in single crystals and polycrystals, governed by the Schmid factor and the Tylor factors. Moreover, the thin film alloys, including the Al-Fe, are also different from the isotropic nanocrystalline metals and alloys with textureless feature. However, dislocations were indeed captured in the differently deformed Al-Fe specimens. It was found that under compression, the ratio of the yield strength collected under out-of-plane compression mode and in-plane compression mode was 1.25, which was mostly governed by the Taylor factors of two testing directions. Since the Al-Fe alloys have a strong (111) out-of-plane texture, the out-of-plane Taylor factor is 3.67. Moreover, the in-plane direction has no obvious texture or a weak (112) texture and the two possibilities rendered similar Taylor factor of 3.06. This two Taylor factors led to a strength ratio of 1.2, coinciding with the 1.25 collected experimentally. This indicates that the anisotropy in the Al-Fe thin films was both influenced by the directionality of the GBs and the

*Material Flow Analysis*

**Figure 8.**

**64**

*(a) The yield strength or fracture strength, collected from different testing conditions, of Al-Fe thin films in comparison to the ones of other Al alloys with extrinsic dimensions at similar magnitudes. (b) the comparison of the strengths* as a function of *intrinsic microstructural feature size effect between Al-Fe thin film and other pure Al and Al alloys. Reprinted with permission from reference [9].*

conventional Taylor factor. **Figure 9** plots the collected strengths under tension and compression along the in-plane and out-of-plane directions as a function of extrinsic specimen dimension and intrinsic microstructural feature size and it clearly manifested the anisotropy under both tension and compression modes. The Al-Fe alloys underwent negligible extrinsic size effect and are highly competitive as to the high strength.

Some thin films or coatings consisting of constituent elements with low stacking fault energy might have columnar grains packed with high-density horizontal coherent TBs (CTBs). Q. H. Lu et al. found that the dislocations were confined within the twin/matrix lamellae and the testing direction, the slip systems and the horizontal CTBs of the NT Cu could result in different dislocation structures and dislocation-CTB interactions, which rendered different hardening and softening modes and thus the anisotropy in metallic thin films made of constituent elements with low stacking fault energy [24]. Furthermore, it should be noted that not all the metallic thin films prepared by non-equilibrium methods possessed the conventional columnar GBs. Li et al. recently exhibited that manipulation of electrolytic solution with certain organic additive could potentially transfer the 3D cluster growth to a flat 2D layer-by-layer growth mode to facilitate the formation of TBs and suppress the formation of the columnar GBs from the island coalescence process [8]. The anisotropy of the NT metals mainly constructed by horizontal CTBs needs further investigation. Furthermore, the mechanical anisotropy in metallic materials could be also displayed from the dynamic strain-induced phase transformation. In a Transformation induced plasticity (TRIP) steel, a strong texture after rolling was obtained in the austenite and the texture in austenite gave rise to a higher martensitic transformation rate along the rolling direction, which contributed to a more pronounced TRIP effect and a higher strain-hardening rate [25, 26].

#### **5. Conclusions**

The synthesis, microstructural controls and the functional applications of 2D materials have been top trending research topics in the past 2 decades. However, the anisotropy of the 2D materials has not been put equal but actually exerts potent influence on not only their mechanical behaviors but also the multifunctional performance of materials and devices with 2D materials as components or building blocks. The unique microstructural characteristics of 2D materials result in distinct and intriguing structural and crystal anisotropy. As to the non-metallic 2D nanomaterials, such as graphene and MoS2, the orientation of the applied stress

with respect to the lattice often cause different interlayer friction, even the superlubricity, and the monolayer with the inherent crystallographic symmetry of the hexagonal honeycomb lattice also exhibited anisotropy when subjected to fracture. For the metallic thin films with 2D extension and limited thickness, the directional and abundant grain boundaries could influence the anisotropy comparison with the bulk single crystals or polycrystals whose anisotropy is primarily dominated by the Schmid factor or Taylor factor. It is anticipated that the sustainability and reliability of the materials and devices constructed by various 2D materials rely on the prominent anisotropy inside 2D materials. The in-depth comprehension toward the anisotropy of 2D materials would be also instructive to realize the orientation-dependent properties and the property optimization.

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