Limits...
Inverse pseudo Hall-Petch relation in polycrystalline graphene.

Sha ZD, Quek SS, Pei QX, Liu ZS, Wang TJ, Shenoy VB, Zhang YW - Sci Rep (2014)

Bottom Line: We also show that its breaking strength and average grain size follow an inverse pseudo Hall-Petch relation, in agreement with experimental measurements.Further, we find that this inverse pseudo Hall-Petch relation can be naturally rationalized by the weakest-link model, which describes the failure behavior of brittle materials.Our present work reveals insights into controlling the mechanical properties of polycrystalline graphene and provides guidelines for the applications of polycrystalline graphene in flexible electronics and nano-electronic-mechanical devices.

View Article: PubMed Central - PubMed

Affiliation: International Center for Applied Mechanics, State Key Laboratory for Strength and Vibration of Mechanical Structures, Xi'an Jiaotong University, Xi'an 710049, China.

ABSTRACT
Understanding the grain size-dependent failure behavior of polycrystalline graphene is important for its applications both structurally and functionally. Here we perform molecular dynamics simulations to study the failure behavior of polycrystalline graphene by varying both grain size and distribution. We show that polycrystalline graphene fails in a brittle mode and grain boundary junctions serve as the crack nucleation sites. We also show that its breaking strength and average grain size follow an inverse pseudo Hall-Petch relation, in agreement with experimental measurements. Further, we find that this inverse pseudo Hall-Petch relation can be naturally rationalized by the weakest-link model, which describes the failure behavior of brittle materials. Our present work reveals insights into controlling the mechanical properties of polycrystalline graphene and provides guidelines for the applications of polycrystalline graphene in flexible electronics and nano-electronic-mechanical devices.

No MeSH data available.


The correlations among the grain size, the density of GB junctions, and the breaking strength of polycrystalline graphene.(a) The trend of the breaking strength as a function of the GB junction density (Number of GB junctions per nm2). Inset is the schematic of one GB triple junction configuration. The grain orientations (α1, α2, and α3) are randomly picked. Thus the misorientations between any of two grains are random and can take any value. In addition, the angles (β1, β2, and β3) between two GBs are also formed randomly. Furthermore, the triple junction can form any angle with respect to the loading direction. This also adds in more configurations for GB junctions. Overall, the number of different GB junctions (weak-links) is infinite. (b) The density of GB junctions as a function of the average grain size <d>.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC4125985&req=5

f3: The correlations among the grain size, the density of GB junctions, and the breaking strength of polycrystalline graphene.(a) The trend of the breaking strength as a function of the GB junction density (Number of GB junctions per nm2). Inset is the schematic of one GB triple junction configuration. The grain orientations (α1, α2, and α3) are randomly picked. Thus the misorientations between any of two grains are random and can take any value. In addition, the angles (β1, β2, and β3) between two GBs are also formed randomly. Furthermore, the triple junction can form any angle with respect to the loading direction. This also adds in more configurations for GB junctions. Overall, the number of different GB junctions (weak-links) is infinite. (b) The density of GB junctions as a function of the average grain size <d>.

Mentions: In order to further reveal the physical origin of this correlation between the average grain size and mechanical properties of polycrystalline graphene, we plot the breaking strength vs. GB junction density in Fig. 3(a). It is seen that the breaking strength decreases with increasing density of GB junctions following a power law with an exponent of −0.05. For a brittle material, it is well-known that defect structure and distribution govern its failure properties. As a result, its failure behavior can be described by the weakest-link model, which states that the failure strength of a brittle material follows a power-law relation with the number of weak links in the material2829. To apply the weakest-link model, it is necessary that the distribution of weak-links is broad and unbounded. In the present context, GB junctions are the weak links. GB junctions are formed by N (N ≥ 3) GBs. The inset in Fig. 3(a) displays a representative GB triple junction. Each grain orientation (α1, α2, and α3) is chosen randomly, thus the grains can take any crystalline orientation. This means that the misorientation between any of the two grains can take any angle from 0 to 60 degrees. It is known that GBs with different misorientations will have different atomic structures, which in turn give rise to different GB energies and different failure strengths. In addition, the angles (β1, β2, and β3) between any of two GBs are also formed randomly. These imply that there are infinitely different configurations of GBs, which give rise to infinitely different configurations of GB junctions. Furthermore, the orientation of the GBs with respect to the loading direction also influences the failure. Since the GBs in our polycrystalline graphene are formed randomly, the formed GBs can take any angle with respect to the loading direction. Also since GB junctions with different angles with respect to the loading direction may have different failure strengths, therefore, they basically are different weak-links, and the number of such configurations is also infinite. Consequently, the distribution of weak-link defects (GB junctions) is broad and unbounded in terms of the number of GB, the grain orientations, the angles between two GBs, and the orientation of the GBs with respect to the loading direction. Hence it is expected that the failure of polycrystalline graphene can be described by the weakest-link model and its failure strength σs should follow a power-law relation with the number of GB junctions or the GB junctions density ρGB, that is, σs ∝ ρGBμ, which is exactly the relation that we have observed in our MD results. The density of GB junctions is scaled with the grain size in an inverse quadratic relation, which is confirmed by our plot shown in Fig. 3(b). As a result, the breaking strength will also follow a power law with the grain size with an exponent of 0.1, and this power law fits nicely with the present MD simulation results as shown in Fig. 2(d), supporting the inverse pseudo Hall-Petch relation. Hence the present work indicates that the breaking strength and the average grain size follow an inverse pseudo Hall-Petch relation.


Inverse pseudo Hall-Petch relation in polycrystalline graphene.

Sha ZD, Quek SS, Pei QX, Liu ZS, Wang TJ, Shenoy VB, Zhang YW - Sci Rep (2014)

The correlations among the grain size, the density of GB junctions, and the breaking strength of polycrystalline graphene.(a) The trend of the breaking strength as a function of the GB junction density (Number of GB junctions per nm2). Inset is the schematic of one GB triple junction configuration. The grain orientations (α1, α2, and α3) are randomly picked. Thus the misorientations between any of two grains are random and can take any value. In addition, the angles (β1, β2, and β3) between two GBs are also formed randomly. Furthermore, the triple junction can form any angle with respect to the loading direction. This also adds in more configurations for GB junctions. Overall, the number of different GB junctions (weak-links) is infinite. (b) The density of GB junctions as a function of the average grain size <d>.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4125985&req=5

f3: The correlations among the grain size, the density of GB junctions, and the breaking strength of polycrystalline graphene.(a) The trend of the breaking strength as a function of the GB junction density (Number of GB junctions per nm2). Inset is the schematic of one GB triple junction configuration. The grain orientations (α1, α2, and α3) are randomly picked. Thus the misorientations between any of two grains are random and can take any value. In addition, the angles (β1, β2, and β3) between two GBs are also formed randomly. Furthermore, the triple junction can form any angle with respect to the loading direction. This also adds in more configurations for GB junctions. Overall, the number of different GB junctions (weak-links) is infinite. (b) The density of GB junctions as a function of the average grain size <d>.
Mentions: In order to further reveal the physical origin of this correlation between the average grain size and mechanical properties of polycrystalline graphene, we plot the breaking strength vs. GB junction density in Fig. 3(a). It is seen that the breaking strength decreases with increasing density of GB junctions following a power law with an exponent of −0.05. For a brittle material, it is well-known that defect structure and distribution govern its failure properties. As a result, its failure behavior can be described by the weakest-link model, which states that the failure strength of a brittle material follows a power-law relation with the number of weak links in the material2829. To apply the weakest-link model, it is necessary that the distribution of weak-links is broad and unbounded. In the present context, GB junctions are the weak links. GB junctions are formed by N (N ≥ 3) GBs. The inset in Fig. 3(a) displays a representative GB triple junction. Each grain orientation (α1, α2, and α3) is chosen randomly, thus the grains can take any crystalline orientation. This means that the misorientation between any of the two grains can take any angle from 0 to 60 degrees. It is known that GBs with different misorientations will have different atomic structures, which in turn give rise to different GB energies and different failure strengths. In addition, the angles (β1, β2, and β3) between any of two GBs are also formed randomly. These imply that there are infinitely different configurations of GBs, which give rise to infinitely different configurations of GB junctions. Furthermore, the orientation of the GBs with respect to the loading direction also influences the failure. Since the GBs in our polycrystalline graphene are formed randomly, the formed GBs can take any angle with respect to the loading direction. Also since GB junctions with different angles with respect to the loading direction may have different failure strengths, therefore, they basically are different weak-links, and the number of such configurations is also infinite. Consequently, the distribution of weak-link defects (GB junctions) is broad and unbounded in terms of the number of GB, the grain orientations, the angles between two GBs, and the orientation of the GBs with respect to the loading direction. Hence it is expected that the failure of polycrystalline graphene can be described by the weakest-link model and its failure strength σs should follow a power-law relation with the number of GB junctions or the GB junctions density ρGB, that is, σs ∝ ρGBμ, which is exactly the relation that we have observed in our MD results. The density of GB junctions is scaled with the grain size in an inverse quadratic relation, which is confirmed by our plot shown in Fig. 3(b). As a result, the breaking strength will also follow a power law with the grain size with an exponent of 0.1, and this power law fits nicely with the present MD simulation results as shown in Fig. 2(d), supporting the inverse pseudo Hall-Petch relation. Hence the present work indicates that the breaking strength and the average grain size follow an inverse pseudo Hall-Petch relation.

Bottom Line: We also show that its breaking strength and average grain size follow an inverse pseudo Hall-Petch relation, in agreement with experimental measurements.Further, we find that this inverse pseudo Hall-Petch relation can be naturally rationalized by the weakest-link model, which describes the failure behavior of brittle materials.Our present work reveals insights into controlling the mechanical properties of polycrystalline graphene and provides guidelines for the applications of polycrystalline graphene in flexible electronics and nano-electronic-mechanical devices.

View Article: PubMed Central - PubMed

Affiliation: International Center for Applied Mechanics, State Key Laboratory for Strength and Vibration of Mechanical Structures, Xi'an Jiaotong University, Xi'an 710049, China.

ABSTRACT
Understanding the grain size-dependent failure behavior of polycrystalline graphene is important for its applications both structurally and functionally. Here we perform molecular dynamics simulations to study the failure behavior of polycrystalline graphene by varying both grain size and distribution. We show that polycrystalline graphene fails in a brittle mode and grain boundary junctions serve as the crack nucleation sites. We also show that its breaking strength and average grain size follow an inverse pseudo Hall-Petch relation, in agreement with experimental measurements. Further, we find that this inverse pseudo Hall-Petch relation can be naturally rationalized by the weakest-link model, which describes the failure behavior of brittle materials. Our present work reveals insights into controlling the mechanical properties of polycrystalline graphene and provides guidelines for the applications of polycrystalline graphene in flexible electronics and nano-electronic-mechanical devices.

No MeSH data available.