Letter pubs.acs.org/NanoLett
Confining Crack Propagation in Defective Graphene Guillermo López-Polín,† Julio Gómez-Herrero,†,‡ and Cristina Gómez-Navarro*,†,‡ †
Departamento de Física de la Materia Condensada, INC, and ‡Centro de Investigación de Física de la Materia Condensada, Universidad Autónoma de Madrid, 28049, Madrid, Spain S Supporting Information *
ABSTRACT: Crack propagation in graphene is essential to understand mechanical failure in 2D materials. We report a systematic study of crack propagation in graphene as a function of defect content. Nanoindentations and subsequent images of graphene membranes with controlled induced defects show that while tears in pristine graphene span microns length, crack propagation is strongly reduced in the presence of defects. Accordingly, graphene oxide exhibits minor crack propagation. Our work suggests controlled defect creation as an approach to avoid catastrophic failure in graphene. KEYWORDS: Graphene, defects, crack propagation, toughness, atomic force microscopy
P
scanning electron microscopy (SEM) images of the broken membranes after indentation allow us to study crack propagation in such samples showing that the presence of atomic scale defects limits tear propagation. Analogous experiments on monolayers of graphene oxide confirm this conclusion and reveal that, due to its partial amorphous character, crack propagation is also very restricted in these membranes. Pristine single graphene layers were obtained by cleavage of natural graphite on viscoelastic polymer stamps and then transferred to SiO2/Si substrates with predefined circular wells as described in ref 10. Graphene sheets tested here usually cover several circular wells, forming graphene drumheads (see section SI1 of the Supporting Information) and present absence of ripples and low pretensions. Raman spectroscopy confirmed their monolayered nature and the absence of defects in these samples.11 Indentation experiments were performed with an AFM tip at the center of the suspended graphene membrane. In order to avoid tip−apex breaking, these experiments required low wear tips with well-defined geometry (see section SI2 of the Supporting Information). Indentation curves were performed with a constant rate of 90 nm/s up to the failure point. Our force (F) vs indentation (δ) curves showed a cubic dependence, fitting the expression12
erfect graphene is believed to be the stiffest and strongest material in nature, with a Young’s modulus of 1 TPa and strength above 90 GPa (30 N/m in two dimensions), exceeding that of steel.1,2 The unique combination of stiffness, strength, and high flexibility postulates graphene as a good candidate in applications such as flexible electronics, electromechanical devices, and composite reinforcement.3 However, up to date the existing methods of large-scale production of graphene are known to yield layers with a certain defect content. Atomically perfect large area graphene samples are not currently available and might be too expensive in the near future for most proposed applications. Therefore, comprehensive studies on the role of defects in graphene’s properties are highly desirable. Much attention has been paid to the electronic properties in the presence of defects4,5 whereas their role in the mechanical properties remains largely unexplored. Atomic scale defects are known to lessen the strength of graphene;6 therefore, even in low defective samples mechanical properties are dominated by the presence of defects.7,8 Under this scenario, rather than its intrinsic strength, the engineering relevant magnitude turns out to be its fracture toughness, i.e., the ability of containing a crack to resist fracture. In 2D materials such as graphene, catastrophic failure is attained by tearing (i.e., crack propagation). Limiting crack propagation in graphene is therefore essential for all mentioned applications. In this work we focus on the ability of preventing macro crack formation from the evolution of atomic-sized cracks on pristine and defective graphene single layers. With this purpose we perform indentation experiments on suspended graphene membranes with a known density of randomly distributed carbon single defects created by argon ion irradiation. The breaking strength of the layers is observed to rapidly decrease with defect density from its pristine value of ∼90 GPa down to ∼50 GPa (18 N/m) where it seems to saturate. Our results suggest that the Griffith criterion of fracture9 no longer stands for such small defects. Atomic force microscopy (AFM) and © 2015 American Chemical Society
F(δ) = πTδ +
E 3 δ a2
(1)
where T is the pretension accumulated in the sheet during the cleavage procedure, E is the elastic modulus of the membrane, and a is its radius. Detailed analysis of the elastic part of the curves has been published elsewhere.6 Figure 1b displays two representative F(δ) curves for pristine and defective memReceived: December 23, 2014 Revised: February 3, 2015 Published: February 24, 2015 2050
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Nano Letters
dimensions. While detailed studies have shown that this expression overestimates the strength in about 20%,1 it has been widely used in the literature and allows comparative studies. Our strength values are in agreement with previous literature.1,13 After initial characterization of defect-free membranes, we proceeded to irradiate the samples with a controlled dose of argon ions with 140 eV incoming energy (see section SI4 of the Supporting Information). Under these conditions we created a random distribution of carbon vacancies, mainly monoatomic vacancies.14,15 Defect density was tuned by in situ measuring the ionic current. Defect nature and density were later confirmed by Raman spectroscopy16,17 and scanning tunneling microscopy (see section SI5 of the Supporting Information). Indentation experiments were performed in ambient conditions after each irradiation dose with the same experimental parameters and with the same AFM probe as described above. F(δ) curves in defective membranes displayed also excellent fitting to eq 1, as for pristine membranes. Membranes with low defect content (below 0.25%) exhibited a higher elastic modulus than pristine ones, in agreement with previous work.6 Consecutive low dose irradiation of the samples allowed us plotting the dependence of strength with defect density. Figure 1c gathers our results: While pristine samples yield strengths values of 30 N/m, the introduction of vacancies decreases this figure down to 18 N/m at a mean defect distance of 10−15 nm, where the strength shows a saturation tendency. Similar behavior as the one observed here has been predicted theoretically;18 the strength of graphene drops substantially once a single defect is introduced but is almost independent of defect density until the mean distance between defects reaches 2−3 nm. Below this distance stress fields superpose, and the strength is further reduced. Please note that the higher defect density in our case corresponds to a mean distance between defects of ∼3 nm. Experimentally introducing higher defect contents leads to larger multivacancies impeding “clean” sampling of higher single vacancy densities. An interesting question to address is whether our results stand for the Griffith criterion of brittle fracture.9 According to this century-old thermodynamic rule, the product of the square root of the flaw length (b) and the stress at fracture (σf) is nearly constant, σf·b1/2 = C. While this law is valid for most materials down to microscopic flaws, some nanostructured materials have been observed to break this rule below a characteristic length.19 This behavior is usually known as nanoscale flaw tolerance, since the mechanical properties of these materials become insensitive to the size of nanoscale voids. Whether this concept applies to graphene or not has been theoretically studied in the literature,20,21 but very few
Figure 1. Strength of defective graphene. (a) Scheme of sample and experimental setup: AFM probe pushing a graphene membrane with drumhead geometry with diameter 2a. (b) Representative force vs indentation curves for pristine graphene (red) and defective graphene (blue) where the breaking point is marked as a circle. The diameter of both drumheads was 1.2 μm. (c) Strength as a function of defect density. Right axis is expressed in 3D units for easier comparison with conventional 3D materials. The σ3D is obtained as the σ2D divided by the interspacing of atomic layers in graphite, i.e.. σ2D/0.34 nm.
branes where the breaking load is marked with a circle; the fracture point is experimentally noted as a sudden decrease of the applied force. These curves did not show any detectable deviation from the cubic dependence in eq 1 even at the higher applied loads, indicative of brittle fracture of the samples (see section SI3 of the Supporting Information). During this indentation experiments the majority (more than ∼90%) of the drumhead exhibits a moderate strain, below 1%. Only the small portion of membrane in contact with the AFM tip is highly strained, and this region is where initial fracture takes place. The breaking strength (σ) at this point can be estimated using the approximate expression σ = (FbreakE2D/4πRtip)1/2 and yields 30 N/m, corresponding to ∼90 GPa if expressed in three
Figure 2. Representative SEM images of graphene drumheads acquired after tearing produced during indentation experiments. Scale bar is 500 nm for all images. (a) Pristine membrane. (b) Defect density 1012 defects/cm−2. (c) Defect density 1013 defects/cm−2. The double arrow in panel b illustrates the tearing length. 2051
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Figure 3. Crack propagation as a function of defect content. (a) Tearing length as a function of defect density. The shaded region corresponds to the diameter of the section of the AFM tips used for indentation that impose an upper threshold in the measurements. Error bars are the standard deviation from multiple measurements. (b) Tearing length as a function of breaking force for two different graphene sheets; red points correspond to the pristine one and blue dots to a sheet irradiated up to a mean defect distance of 5 nm. The breaking force is mainly dictated by the radius of the AFM tip. Lower breaking forces correspond to smaller diameter tips. Please note that the scattering in pristine graphene is due to tears in pristine samples being usually limited by the size of the drumheads.
process (∼170 nm; see section SI6 of the Supporting Information). So, the lower value of tearing length in Figure 3a is just an upper bound for crack propagation at defect contents above 3 × 1012 defects/cm2. Indeed, indentations performed with slender tips yield smaller tearing lengths (see Figure 3a). In view of the results exposed in Figures 1c and 3a, a key experimental issue to tackle is whether the observed differences in tearing lengths are governed by the higher tension applied in pristine membranes in order to reach the failure point or if they are really limited by the presence of single defects, as suggested above. With the aim of discriminating the origin of the observed crack propagation, we performed experiments in pristine and defective membranes with tips of very different nominal radius. We used hemispherical WC covered tips with tip radius of 60 nm and slender diamond tips with a tip apex radius below 20 nm. Since the strength (pressure) required to break the membrane is concentrated in a small area of the order of the tip radius, the breaking force (and therefore the applied tension) depends on the tip radius. In Figure 3b, we show the tearing length as a function of breaking force for a pristine membrane (red dots) and a membrane with defect content of ∼3 × 1012/cm2 (blue dots). The data for small breaking forces correspond to those obtained with sharper tips. As we can observe in this graph, the tearing length strongly depends on defect content but it is not influenced by changes in breaking tension. Therefore, we can safely conclude that the tearing length is determined by the presence of defects and not by the tensions introduced during indentation experiments. These results also suggest that the strain energy introduced during indentation is easily released when the crack is started and point toward other driving forces for crack propagation. The most significant stress remaining in the graphene sheet after indentation is the one corresponding to the in plane prestrain accumulated during sample preparation procedure. This would imply that while fracture is initiated in tearing mode, crack propagation mainly takes place in tensile opening mode. Our results can be understood in the framework of several molecular dynamics studies on crack propagation in defective samples. According to these studies,24,26 the distribution of defects (vacancies) near the initial flaw changes the crack propagation trajectory. While crack propagation in pristine samples tend to follow straight lines, in samples with a random
experimental reports can be found. Previous reports on graphene bilayers with initial cracks of tens of nanometers in length22 estimated the constant C to be about 2 MPa m1/2. Considering an atomic crack of length 0.13 nm (interatomic distance in graphene) for our induced carbon monovacancies, and taking into account that the strength is overestimated, our calculated constant is C < 0.5 MPa m1/2. Although direct comparison of the results reported here and those reported in ref 22 might not be straightforward, this lower value of C suggests a breakdown of Griffith criterion at this length scale, implying that at a certain length below tens of nanometers graphene becomes notch size insensitive and the critical strength no longer depends on the size of the preexisting crack. In order to study crack propagation in our samples tested drumheads were imaged by AFM and SEM after failure in indentation experiments. Figure 2 displays three representative SEM images with increasing density of defects from left (pristine) to right. Pristine membranes showed large (microns length) tears with straight and sharp edges. Torn edges displayed angles multiples of 30°, indicating that crack propagation takes place along crystallographic directions. This observation is in agreement with previous experiments and predictions.23−25 In contrast, highly defective membranes showed a marked different behavior. The maximum edge lengths exposed after indentation in these membranes are an order of magnitude smaller than those observed in perfect layers suggesting that the presence of vacancies substantially restrain crack propagation.26 To further corroborate the above-described observation, we performed a systematic study of the tearing of graphene membranes as a function of defect content. Figure 3 a displays our main experimental finding. The maximum tearing length (Ltear) in graphene (as determined by SEM images) strongly depends on the density of atomic scale defects. While tearing in pristine graphene expands over microns length (and is usually confined in the well diameter) this length decreases with vacancy content in such a way that at mean defect distance of 10 nm (i.e., density of 1012/cm2) the tearing length is reduced down to 500 nm. Decreasing the mean distance between defects further yields to smaller cracks that cannot be probed by our experimental technique because our measurements of tearing length are limited by the notch created by the section of the tip embedded in the graphene sheet during the fracture 2052
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single layer level remains elusive. Similar experiments as the one described above for graphene were carried out in drumheads of GO sheets. Figure 4 illustrates our results. The elastic modulus of GO single layers is estimated to be 0.15 ± 0.03 TPa, in agreement with previous reports.29 The strength of GO membranes yields 4.4 ± 0.6 GPa (3.1 ± 0.4 N/m in 2D, the thickness of GO has been considered to be 0.7 nm), much lower than that of graphene and lower than that of graphene with random distribution of single defects (up to the defect concentration considered herein), but yet higher than that of steel. This is most likely due to the presence of larger voids (multivacancies) in the structure of GO membranes.20 In agreement with our previous results on defective graphene membranes, crack propagation in GO layers is also very limited. SEM images, as the one depicted in Figure 4a, show that the flaw produced by indentation experiments conforms to the AFM tip embedded in the membrane even for slender tips. This observation confirms that crack propagation is strongly restrained by the presence of defects. In summary, we have presented a systematic study on the effects of atomic scale defects in the fracture properties of graphene. We find that while defects lessen the strength of graphene, at the same time they considerably limit crack propagation. Although lower when compared to pristine membranes, the strength of defective graphene is still higher than that of steel and more than that required for most applications. Therefore, introduction of random distribution of atomic scale defects could be exploited as an approach to avoid catastrophic failure of graphene in future devices.
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ASSOCIATED CONTENT
* Supporting Information S
Detailed description of sample preparation and STM and Raman spectroscopy characterization. This material is available free of charge via the Internet at http://pubs.acs.org.
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Figure 4. Graphene oxide membranes. (a) Representative SEM image of a graphene oxide drumhead after tearing produced during indentation experiments. (b) Force vs indentation curve for a GO membrane. The failure point is marked with a circle. (c) Raman spectra of GO sheets where the amorphous character of the layers is reflected on a high D/G peak ratio.
AUTHOR INFORMATION
Corresponding Author
*E-mail
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work was supported by MAT2013-46753-C2-2-P, S2013/ MIT-3007, and Consolider CSD2010-0024.
distribution of vacancies crack is deflected randomly and tends to follow directions with higher density of vacancies. These continuous deflections are energetically costly and do not favor crack propagation in the absence of large tensions. We now turn our discussion to graphene oxide (GO) membranes. GO and its chemically reduced counterpart are widely spread in applied studies because of their availability in large scale and easy dispersion in water. Indeed, it is the most used graphene derived material in composite reinforcement.27 GO sheets are carbon atomic thin layers decorated with oxygen-containing groups. Although they maintain the characteristic honeycomb lattice of graphene for regions of several nanometers in length, disordered and defective regions are interspersed within crystalline regions.28 Hence, GO can be considered as the limiting case of defective graphene. Most studies concerning mechanical properties at the single layer level have been focused on the elastic behavior29,30 of these membranes. Many studies have reported the strength of graphene oxide papers and derivatives, but its strength at the
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