Graphene Strained by Defects Jeremy T. Robinson,*,†,# Maxim K. Zalalutdinov,‡,# Cory D. Cress,† James C. Culbertson,† Adam L. Friedman,§ Andrew Merrill,∥ and Brian J. Landi∥,⊥ Electronics Science and Technology Division, ‡Acoustics Division, and §Materials Science Division, U.S. Naval Research Laboratory, Washington, D.C. 20375, United States ∥ NanoPower Research Laboratory and ⊥Department of Chemical Engineering, Rochester Institute of Technology, Rochester, New York 14623, United States ACS Nano 2017.11:4745-4752. Downloaded from pubs.acs.org by UNIV OF NEW ENGLAND on 09/29/18. For personal use only.
†
S Supporting Information *
ABSTRACT: Using graphene nanomechanical resonators we demonstrate the extent to which the mechanical properties of multilayer graphene films are controllable, in real time, through introduction and rearrangement of defects. We show both static and re-entrant (cyclical) changes in the tensile stress using a combination of ion implantation, chemical functionalization, and thermal treatment. While the dramatic increase in static tensile stress achievable through laser annealing can be of importance for various MEMS applications, we view the direct observation of a time-variable stress as even more significant. We find that defect-rich films exhibit a slow relaxation component of the tensile stress that remains in the resonator long after the laser exposure is finished (trelax ≈ 100 s ≫ tcooling), analogous to a wind-up toy. We attribute this persistent component of the time-variable stress to a set of metastable, multivacancy structures formed during the laser anneal. Our results indicate that significant stress fields generated by multivacancies, in combination with their finite lifetime, could make them a powerful and flexible tool in nanomechanics. KEYWORDS: graphene, defects, nanomechanics, resonator, strain, mechanical energy metastable multivacancy structures such as the tetravacancy.10 Such multivacancy complexes are expected to introduce lattice distortions and long-range mechanical stress within the film11 that can be intermittent with lifetimes on the order of minutes.10 In graphene systems composed of a few layers, the Wigner defect is capable of forging interlayer connectivity.12 Such localized bridging structures can introduce far-reaching inplane mechanical strains and, when relaxed, can lead to dramatic effects associated with energy release.13 Thus, the transitory nature of such defect complexes invites a consideration of the dynamic control of the defect-induced stresses within 2D materials. In this article, we report an in situ observation of the effects that defect evolution has on graphene’s mechanical properties. By measuring the resonant frequency of nanomechanical drumtype resonators, we monitor in real time the in-plane stress within the suspended multilayer graphene. We find that local laser annealing of defect-rich films can lead to a dramatic increase in the mechanical in-plane stress, which is in contrast
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nderstanding the connection between defects introduced in a material and the resultant mechanical properties is a long-standing goal in materials science. In the field of two-dimensional (2D) materials, the role of defects is exaggerated by the fact that the extension of a typical defect (e.g., vacancy) is commensurate with the total thickness of the structure. Graphene, a 2D material of great research interest,1 has strong sp2-carbon bonds that give it the highest measured strength of any material.2 While defects such as grain boundaries have little impact on overall material stiffness and strength,3 multiatom vacancies and sp3 functional groups do affect graphene’s mechanical properties.4,5 Defects implemented as chemisorbed atoms can change bond lengths within graphene’s basal plane and also introduce stress within the film. For example, chemical functionalization can be used to widely enhance the response of graphene-based mechanical resonators,6−8 improving their resonance quality factors (>20×) and frequency tuning (>500%).7 The ability of defects to diffuse and to rearrange into unique structures within 2D materials affords them with opportunities that are lacking in their bulk 3D counterparts. For example, the thermal treatment of graphene oxide leads to oxygen atom aggregation forming well-ordered edge ether groups.9 Alternatively, vacancies in graphene can diffuse and coalesce to form © 2017 American Chemical Society
Received: February 9, 2017 Accepted: May 2, 2017 Published: May 2, 2017 4745
DOI: 10.1021/acsnano.7b00923 ACS Nano 2017, 11, 4745−4752
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Figure 1. Exfoliated and CVD graphene resonators. (A) Optical image of graphene flakes on a SiO2 (285 nm)/Si substrate with circular wells (largest diameter = 4 um). (Inset) AFM height image after milling a hole in the resonator using a FIB. (B) Optical image showing a three-layer CVD graphene resonator sample. (C) Raman spectra (λ = 488 nm) of ML exfoliated resonators before and after Ar+ implantation. (D) Raman spectra from the fluorinated CVD graphene sample in B. (E, F) Raman mapping of the same region in A, after Ar+ implantation and local laser annealing, shows the (E) D/G ratio (color scale bar: 0 to 1.5) and (F) D peak full-width at half-maximum (fwhm) (color scale bar: 0 to 80 cm−1).
insulator (SOI) substrates using standard wet-chemical transfer techniques. To minimize interlayer debris during multiple stackings, we transferred a poly(methyl methacrylate) (PMMA)/graphene film directly onto a graphene-on-copper sample, then etched the copper substrate and repeated these steps to build up films of three layers. Irrigation holes (1−5 μm) were etched through the films to the top Si layer of the underlying SOI substrate, and the sample was then exposed to xenon difluoride (XeF2) gas to undercut the silicon support layer and form suspended graphene resonators (diameters: 5− 20 μm, Figure 1B). The XeF2 silicon-etch step is also used to introduce fluorine functionalization on graphene17 (we refer to these fluorinated graphene resonators as “F-GR”). The defect density associated with different states of the resonators was characterized using Raman spectroscopy. As deposited, the exfoliated samples have a low defect density (ID peak/IG peak = 0.03). After implantation the D/G ratio increases and is dependent on the number of layers, where a monolayer has a ratio of approximately 1.5 and a six-layer film has a ratio of approximately 0.6 (Figure 1C). For the XeF2 released resonators, we measured a D/G peak ratio of 0.2 (Figure 1D). After defluorination through laser annealing, the D/G peak ratio does not significantly change, which implies vacancy-type defects are formed as some fluorine is removed as CxFy species.18 In an attempt to deconvolute specific classes of defects (sp2 versus sp3), we analyzed the D/D′ peak-height ratios as outlined by Eckmann et al.19 (see Supporting Information). Due to the multilayer nature of the drum resonators studied here, there was no clear dependence on the type of defect with D/D′ ratio. We use well-established optical techniques to measure the fundamental frequencies (f 0) of the drum resonators.20 In addition to a low power drive (λ = 405 nm, P ≈ 0.5 mW) and read-out (λ = 632 nm, P < 2 mW) laser, we used a third laser (λ = 405 nm, P = 1−300 mW) as an “annealing” laser to locally
to the intuitively expected reduction in stress level due to thermal annealing. Even more importantly, the presence of defects also enables a cyclic control over the stress state within a graphene film. We show that in the presence of structural defects, such as vacancies, the tensile stress induced by laser annealing relaxes on the time scale of minutes and can be reactivated by sequential laser irradiation. Molecular dynamics simulations give insight into how the defect distributions evolve with external stimuli.
RESULTS To understand the role of a particular defect type (structural or chemical) on the response of graphene resonators, we use two systems. One includes graphene films mechanically exfoliated from bulk graphite and subsequently bombarded with 300 eV Ar+ ions in order to introduce vacancies, carbon interstitials, and cross-linking defects. The other is based on chemical vapor deposition (CVD)-grown graphene films with defects induced through fluorine functionalization. While quantitative comparisons are best suited for measurements using a single source material, we employ these two systems to show common qualitative trends related to defect states that appear to be a feature intrinsic to graphene. To measure mechanical properties, we made drum-type resonators from each of these systems. For exfoliated samples, circular wells (diameter: 1−4 μm) were etched into a SiO2/Si substrate, onto which graphene flakes were exfoliated (Figure 1A). A small hole was pierced in some of the fully clamped resonators6 using a focused ion beam (FIB) to release trapped gas (inset in Figure 1A).14 To introduce defects, we exposed these samples to 300 eV Ar+ at a dose of (2.3 ± 0.4) × 1014 Ar/cm2, which has enough energy to penetrate approximately six or seven graphene layers. To form CVD graphene resonators, we first grew graphene on Cu foils15,16 and then transferred the films to silicon-on4746
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LAMMPS.23,24 Each of the 500 simulations began with an identical graphene structure, and the Ar+ are randomly positioned within a region above the top surface. For the 300 eV incident ions used here, Ar+ penetrates approximately six or seven layers within the stack and generates several types of defects, discussed later. The experimentally observed response of the graphene resonators indicates that the type of defect introduced into the resonators determines the in-plane stress and, therefore, dictates how the resonant frequency f 0 evolves. After exposing resonators to Ar+ implantation, f 0 significantly increases. For example, 4 μm diameter exfoliated resonators typically have f 0 ≈ 60−75 MHz (thickness and pretension dependent). After implantation, f 0 increases to ∼100−125 MHz, corresponding to a stress increase of 600 MPa (e.g., Figure 3A, 0 mW). After
impart high temperatures within the suspended structures (Figure 2A). During laser annealing, we implemented a 2D
Figure 2. (A) Schematic showing a graphene drum resonator together with the three lasers used for resonance experiments (not to scale; laser colors do not represent energy). The spot size of each laser is approximately 1 μm. (B) Schematic of the MD simulation setup. (C) Perspective image showing AB-stacked graphene layers implemented in the MD simulations. Layers 5−9 have been left out for clarity.
raster of the beam (0.5 μm step, 0.5 s/step) over an area that fully covers the drum resonator.7 Some of the drums that have undergone the 2D raster anneal have been used later to study a dynamic response to laser irradiation. To carry out dynamic frequency measurements, the position of the annealing laser was fixed, and we subsequently turned the annealing beam ON and OFF while simultaneously taking spectra with the drive and read-out beams. Here, we collected spectra at a rate between 1.5 and 3 Hz (300 to 650 ms) and turned ON the annealing beam between 5 and 60 s. The laser powers used for dynamic measurements were always lower than the powers used for the previous “conditioning” 2D raster anneal on any given drum, so as not to impart irreversible changes during dynamic measurements. All resonators described in this work exhibit a higher f 0 than the value expected in the absence of in-plane stress (i.e., predicted by a plate model). Therefore, we attribute the restoring force governing the resonators to in-plane stress exclusively, as opposed to the flexural rigidity of the film. Notably, such “built-in” pretension is commonly observed for both CVD-type and exfoliated graphene resonators.2,20−22 For high-tension thin-film resonators the frequency response is only weakly affected by the elastic constants, such as Young’s modulus, and those effects are beyond the precision of our measurements. The resonators are therefore treated as membranes with the fundamental frequency proportional to the square-root of the tension (T) and drum diameter: 1 fo ∝ D T . Finally, for all resonators measured here the resonant quality factors, Q, typically ranged between 500 and 3000. While some increase in Q was observed during the laser exposure (attributed to increased tension), we did not observe significant variation in Q during the postanneal relaxation (see Supporting Information). We used classical molecular dynamics (MD) simulations to analyze the formation of defects in multilayer graphene arising from Ar+ irradiation and their subsequent evolution through annealing (Figure 2B,C; see Methods). MD simulations were performed using the open-source molecular dynamics code
Figure 3. (A) Plot of the fundamental frequency (f 0) vs laser annealing power for an exfoliated ML graphene resonator before Ar+ implantation (blue triangles) and a neighboring resonator after Ar+ implantation (red squares). (B) Plot of normalized frequency ( f/f 0) vs laser power for a fluorinated 3 L CVD graphene drum (FGR, CVD) and the same exfoliated resonators from A.
laser annealing these implanted resonators, f 0 monotonically decreases with increasing laser power and converges to a steadystate value (Figure 3A, red squares). Nominally defect-free resonators showed virtually no frequency shift after laser annealing (Figure 3A, blue triangles), despite high tensile stress generated during the anneal by the negative thermal expansion coefficient of graphene. This result allows us to exclude film slippage as a contributing factor to shifts in f 0. In contrast, the presence of the chemisorbed atoms within the fluorinated resonators (F-GR) leads to an opposite response to laser annealing. Fundamental frequency f 0 monotonically increases by over 2× with increasing power (Figure 3B, black squares). The 20 μm F-GR resonators (Figure 1B) typically have f 0 ≈ 3−4 MHz, which increases to f 0 ≈ 7−8 MHz after annealing (corresponding to a stress increase from 13.4 to 74 MPa). 4747
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here (1 × 10−7 Torr). The inset in Figure 4A overlays the Δf 2 decay data with the functional form for mass (m) adsorption for A a tensioned circular resonator ( f0 ∝ m ), where both have a similar curvature. We note this comparison assumes a constant flux and sticking coefficient of molecules on the resonator, which is likely changing throughout the experiment. The introduction of defects drastically alters the resonators’ frequency relaxation. Figure 4B shows the dynamic response of an Ar+ implanted drum, measured after reaching its laserannealed, steady-state base frequency, to three different laser pulses (5, 15, and 60 s at 15 mW). The implanted resonators have two salient features that are different from defect-free resonators: (i) the initial sharp frequency increase with heating is larger (30% compared to 4% for the same power) and (ii) the implanted resonators have a significantly longer Δf 2 relaxation time. Furthermore, we observe that the frequency decay is laser-dose dependent, where longer laser exposures result in slower decay rates (Figure 4B). Performing the same dynamic measurements on laser-annealed F-GR resonators shows a qualitatively similar response to that of the implanted resonators (Figure 4C). In the laser ON state, Δf1 for F-GR resonators increased more than for defect-free resonators, to a percentage close to that of implanted resonators. Similar to the dose dependence found for the implanted resonators, as the laser power is increased, the Δf 2 decay time increases for F-GR resonators and can be as long as 100−150 s for a 20 μm F-GR drum resonator.
Once we reached steady-state frequency values after laser annealing (≥20 mW, Figure 3B), we performed dynamic annealing experiments to learn how residual defect motion/ migration impacts the resonator response. Figure 4A shows an
DISCUSSION We consider multiple mechanisms that are responsible for changes in film stress (or resonance frequency) as a result of either “chemical defects” or “structural defects”. First, for fluorine-functionalized resonators (chemical defects) we expect two atom types (C and F) and a distribution of in-plane sp2carbon−carbon bonds and out-of-plane sp3 carbon−fluorine bonds. The transition of sp2 → sp3 (or sp3 → sp2) transition in graphene’s C−C bonds results in longer (or shorter) bond lengths and an overall net increase (decrease) in length of the graphene backbone. In the limit of complete functionalization (100% F coverage, CF), the calculated in-plane lattice constant increases by 6%.7 Therefore, removing fluorine through laser annealing induces significant in-plane contraction of the graphene as longer sp3 C−F bonds convert to shorter sp2 C−C bonds. Regarding other mechanisms that can lead to shifts in resonator frequency, we note that fluorine desorption itself would result in mass loss from the resonator. However, this alone cannot explain the typically observed f 0 increases of 2.0− 2.5× for F-GR resonators (Figure 3B). Since f 0 is inversely proportional to the square root of the mass ( f ∝ m−1/2), to increase f 0 by 2× would require a decrease in mass by 4×. Using basic material parameters (see Supporting Information), we estimate that after completely desorbing 10% of F coverage off the graphene surface one would expect a 13.6% mass decrease for the membrane (corresponding to a relative frequency change of only 7%). On the other hand, DFT calculations7 show that an approximate 10% F coverage leads to an absolute change in the lattice parameter by 0.5−1.0% (strain ε = 0.005−0.01), which corresponds to stresses of 5−10 GPa or frequency shifts up to 10×. Mechanical strains of ε = 0.01 for crystalline solids are very large, and it is this change in lattice parameter through F desorption that we assign as the dominant
Figure 4. Dynamic response of graphene resonators to an external heating laser. (A) Plot of normalized frequency (f/f 0) vs time for an as-fabricated exfoliated graphene drum. The dashed line indicates when the annealing laser was turn ON and OFF while taking frequency measurements. (Inset) Plot of the decay portion of the 40 mW curve overlaid with an f(x)= Ax−1/2 curve (best fit: A = 0.028). (B) Plot of frequency vs time for Ar-implanted exfoliated resonators using an annealing power of 15 mW. The beam was turned ON for three different durations as labeled. (C) Plot of frequency vs time for F-GR resonators using the same exposure time but varying the laser power as labeled.
example of such a dynamic heating experiment on a nominally defect-free ML exfoliated drum (control experiment). Here, the annealing laser is turned ON for 30 s while collecting frequency data. Depending on the laser power, f 0 increases between 4% and 10% while the laser is ON, and we attribute this frequency jump to resonator heating in conjunction with graphene’s negative thermal expansion coefficient (α ≈ −7 × 10−6 K−1).25 When the laser is turned OFF, the tension rapidly relaxes as the resonator cools (Δf1, Figure 4A) and then decays back to its initial frequency (Δf 2, Figure 4A). In these nominally defectfree resonators we attribute the small Δf 2 to gas absorption, which could be present even at the high vacuum levels used 4748
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Figure 5. (A) Cross-section screen shot taken from an MD simulation run of Ar+ implantation in few-layer graphene. (Lower insets) Examples of a vacancy, chain (purple atoms), and bridge (red atoms) defects. (B) Plot of average number of chains and bridges per graphene layer for the MD simulations shown in Figure 2, before and after simulated annealing at 500 K. (C) Plot of average number of rings per layer before and after simulated annealing at 500 K. (D) Calculated temperature under the annealing laser spot for graphene with two different drum diameters (thermal conductivity κ = 500 W/m·K).
mechanism providing the increase in f 0 for the laser-annealed F-GR resonators. We view the ability to locally introduce mechanical stresses on this magnitude as a powerful tool in nanomechanics (e.g., “nano-shrink-wrap”), where strain patterning is enabled by a sharply focused laser or electron beam. Equally important, our results show that in the absence of chemisorbed atoms (like fluorine) structural defects within graphene26 can also lead to changes in film stress. For the Ar+ implanted resonators, we expect only carbon atoms distributed as sp2-bonded layers with sp2/sp3 type carbon defects within and/or between the layers. To help assess this defect distribution, we implement MD simulations (Figure 5 and Methods), and our findings here are consistent with previous MD simulations.27−29 As it relates to the resonator frequency response, it is well-known that large anisotropic tensile strains emerge in bulk irradiated graphite due to expansion in the c-axis (from interstitials) and a contraction within the basal planes.12 As such, details of the defect distribution can shed light on the frequency shifts in our structures. Previous measurements of irradiated bulk graphite12 are consistent with our experiments here, where we measure that Ar+ implantation leads to a significant increase in f 0 and, hence, increased tensile strain (Figure 3A). For 300 eV Ar+ ions at a dose of 2.3 × 1014 Ar/cm2, our MD simulations show that up to six or seven layers of AB-stacked graphene will have lattice and interstitial defects. This family of defects includes vacancies/nanopores, chains, and bridges (Figure 5A), where “chains” are defined as structures in which more than one carbon atom is bonded to a graphene basal plane and extends outward into the interstitial space, “bridges” are defined as chains that terminate with bonds on two adjacent layers, and vacancies/nanopores are defined as missing carbon atoms in a layer. In the case of single-atom vacancies, a 12-atom “ring” (Figure 5A) is generated in the
graphene lattice, while multiatom defects lead to a large set of defect types that become difficult to enumerate or uniquely define with automated defect analysis software. For analysis purposes, we therefore count the length of each unique “ring” surrounding a vacancy/nanopore, where greater ring length is correlated with more lattice vacancies. Figure 5B plots the average number of chains and bridges per layer, and Figure 5C plots the average number of rings per layer. We find the distribution for all defect types peaks around the third layer from the surface for this implantation energy. Building on these results, we perform simulated annealing at 773 K to gain insight into how the defect distribution evolves at moderate temperatures. Shown in Figure 5B, on average the number of chains slightly decreases, while the number of bridges remains approximately the same. Figure 5C shows that on average the number of rings per layer increases, while simultaneously the ring size decreases (not shown). We attribute the decreasing number of interstitial chains and increased population of smaller rings to interstitial carbon atoms migrating back into the basal plane and partially healing larger nanopores and/or vacancy structures, leaving behind a larger number of smaller rings. These results agree well with recent simulations of implanted graphene annealed at much higher temperatures (3000 K),29 which similarly shows a larger number of smaller ring structures after annealing, as well as the coalescence of vacancies into multivacancy complexes that have been experimentally observed.10,29 Qualitatively, our MD simulations agree well with observations of defect migration in graphite. Annealing of irradiated graphite is a well-studied topic, particularly after the 1957 Windscale nuclear fire,30 in which there was rapid energy release from the graphite neutron moderator. It has been shown that already at low temperatures (≥200 °C) carbon interstitials relax back into the basal plane,12,13,31 resulting in 4749
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dynamic frequency measurements, higher temperatures and/or prolonged exposures lead to an increase in the frequency decay time, which supports the hypothesis of formation of an increased population of metastable defects with increased laser power and/or exposure time. Quantitative differences in the relaxation dynamics between CVD and exfoliated drums likely reflect variations in the defect population. Despite differences in the defect population/distribution or even resonator size between the exfoliated and CVD drums, a unifying feature of our results is the ability to cyclically actuate these defects and generate measurable changes in the stress fields across the resonators.
both energy release (heat production) and strain release. These past findings can be connected to our Ar-ion-implanted resonators, where we observe stress relaxation (i.e., f 0 decrease) upon laser annealing (Figure 3a). While the Raman D/G peak ratio (Figure 1E) does not significantly change after laser annealing, the D-peak fwhm does measurably decrease (Figure 1F), indicating that the net distribution of defects is narrowed. Extrapolating from our MD simulations and Raman measurements, we propose that interstitial carbon atoms/chains become mobile during laser annealing and fall back into the basal plane, releasing tension. At the highest annealing powers, we estimate that the resonator temperature can reach 1500 K or higher7 (Figure 5D), which provides sufficient thermal energy to induce interstitial carbon diffusion. After the highest temperature anneals, we anticipate the remaining defects will primarily consist of basal plane vacancy structures and complexes since mobile or higher energy bonding configurations will relax into lower energy configurations.29 It is from this starting point that we initiate the dynamic laser annealing process (Figure 4) that results in the “wind-up toy”-like response of the graphene resonators. The fact that the resonant frequency of defect-rich graphene drums does not drop to their preanneal value immediately after turning the anneal laser OFF (given the submicrosecond cool down time) but instead remains at elevated stress values implies that an intermediate state is formed in a system where only carbon atoms and carbon defects are present. From the varying shape and curvature of the frequency response in Figure 4B and C we can rule out gas adsorption in a vacuum as a first-order effect since f ∝ m−1/2, which would result in a monotonic negative curvature (Figure 4A). Instead, we attribute the cyclical mechanical stresses sustained after the dynamic laser annealing to the formation, migration, and annihilation of remnant defects. The intermittent nature of the stress relaxation provides a “fingerprint” to identify and assign contributors to the stress state from a list of defects that can be present in graphene crystals. The formation energy (EF) of defects in graphene/ graphite normally ranges between ∼5 and 10 eV,32 where the most common structures include “5−7 ring” defects (e.g., Stone−Wales). In our system, various defects throughout this energy range are formed during the 300 eV implantation step or through chemical functionalization/defunctionalization of CVD graphene. Once formed, the migration energy (Em) for these defects is lower than EF (e.g., monovacancies and interstitial carbons: Em ≈ 0.5−1.5 eV).12,26,32 Such defects can migrate and coalesce into reconstructed or metastable, multidefect complexes at energies that we pump into the system (thermal energy up to ∼1200 °C; photon energy ∼3 eV). For example, Robertson et al.10 describe the formation of metastable tetravacancies and a hierarchy of tetravacancy configurations that can form with less than 3 eV energy and involve various combinations of Stone−Wales and vacancy defects. We propose these multivacancy complexes as the most viable candidates for cyclical stress modification, as they have been shown to have lifetimes on the order of tens to hundreds of seconds before breaking up into smaller structures.10 These time scales match well with our frequency relaxation data (Figure 4b,c). The ability to reactivate the metastable stress state by laser irradiation (as well as electron beam)10 is an important observation that may have implications for designing nanomechanical resonators made from 2D materials. In all of our
CONCLUSIONS In summary, our experimental results reveal two ways for controlling the mechanical response of graphene-based mechanical systems that can be implemented in situ and in real time: (i) annealing chemically functionalized graphene produces a permanent state of increased stress (Figure 3A) and (ii) annealing graphene with vacancy-type defects produces metastable defect complexes that dynamically change the mechanical response (Figure 4). In both cases, mechanical energy is introduced via distortions of the graphene lattice. However, the relaxation mechanisms are different. In the case of added fluorine atoms, chemically induced distortions elongate the graphene basal plane, locking in the deformed state. The elastic energy is stored indefinitely (at least at room temperature) and can be released on demand, for example, through laser-induced fluorine desorption. We envision this type of irreversible stored energy being useful for nanomechanical systems requiring single-shot actuators, such as that used in erecting hinged mechanical elements that transform a set of in-plane parts into a standing 3D structure. Alternatively, lattice distortions produced by vacancy-type defects are intermittent due to the metastable nature of larger vacancy complexes. When a defect-rich graphene film (in its relaxed state) becomes part of a nanomechanical device, the energy can be gained through vacancy coalescence into highorder structures (e.g., tetravacancies), which results in a net tensile stress. Here we find that laser annealing is a tool that can drive vacancy coalescence, which we consider as the “wind-up” part of the process. The higher order vacancy complexes that are metastable will eventually break apart, along with the mechanical stress associated with them. The capacity to uphold tensile stress for a finite time (i.e., a “short-term mechanical memory”) and then relax could be enabling for applications where cyclic loading is required (e.g., “nanomuscle”). METHODS Molecular Dynamic Simulations. MD simulations employed here are in agreement with previous reports on MD simulations of irradiated graphite/graphene.27−29 Our MD simulations add analytical features to help assess and correlate the frequency response of nanomechanical resonators to the presence and movement of defects within graphene. MD simulations were performed using the opensource molecular dynamics code LAMMPS.23,24 We generated the structure data for a 10-layer, AB-stacked graphene structure, where each layer measured approximately 100 nm2 in area, consisting of 1008 atoms per layer. The minimized energy structure was thermostated with a temperature ramp from 0 to 300 K, for 10 000 time steps, with a time step of 0.5 fs. We used two argon ions per nm2 to match the simulation conditions with the experimental fluence of ∼2.3 × 1014 Ar+/cm2. For the structural analysis, we analyzed the atomic configurations at the end of the second ion irradiation simulations 4750
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ACS Nano and annealing simulations to quantify the number and ring size of each defect and to classify the interstitial atoms positioned between the layers as members of chain or bridge defects. Using the ring length analysis, along with atom coordination numbers, unique ID, and initial layer number, we counted only unique rings that were in-plane, and differentiated chains/bridges based on the fact that chains are terminated with an atom that has a coordination number of 1, while bridges are terminated with an atom that is coordinated with 2 or more atoms, one of which is a member of the adjacent layer. For the annealing simulations, the atomic configurations at the end of the second ion simulations were annealed to 773 K using the Berendsen thermostat procedure within LAMMPs. We used a hybrid Ziegler−Biersack−Littmark (ZBL) Tersoff potential function to model the various Ar−Ar, Ar−C, and C−C interactions; this is carried out using the LAMMPs hybrid pair_style command followed with individual definitions using the pair_coeff command. For the Ar−C (and Ar−Ar) interactions, we used a pure ZBL potential with a long-range cutoff of 1.8 Å and inner switching function cutoff of 1.0 Å. As a result, for interatomic distances r(i, j) > 1.8 Å the atoms do not interact; for 1.0 Å < r(i, j) ≤ 1.8 Å a switching function is applied that gradually ramps the interaction until r(i, j) < 1.0 Å, at which point the Ar−C interaction follows the ZBL screened nuclear repulsion function for high-energy collisions between atoms. In the case of C−C interactions, we employ the built-in Tersoff/ZBL pair_style definition along with optimized Tersoff parameters defined by Lindsay et al.33 with an inner switching cutoff distance of r(C−C, ZBL) = 0.95 Å. Near r(C−C, ZBL) a Fermi-function-like smoothing function enables a continuous transition between the ZBL and Tersoff interactions. The time step used for the 300 eV Ar ion collisions was 0.5 fs. A 300 eV Ar ion travels at 0.381 Å/fs, so the Ar ions travel a total of 0.19 Å/ time step. With long-range cutoff and inner switching cutoff values of 1.8 and 1.0 Å, respectively, the Ar ion interacts with the nearest C atom for at least 10 time steps (usually more due to the motion of the C atom away from the Ar) when the C atom is initially at rest. For vibrating C atoms, the Tersoff parametrization employed yields peak ZO mode phonons (out-of-plane) with a frequency of f = ω/2π = ∼300/2π THz. The corresponding period of this mode is 20.9 fs, so a full cycle would require about 42 time steps. Raman Spectroscopy. Raman measurements were performed using a confocal geometry. Dichroic beam splitters were used to reflect single-mode 488 nm laser light onto the excitation/detection optical axis. A 100× microscope objective (NA = 0.65) focused the laser (spot ≈ 0.4 μm) onto the sample and gathered Raman scattered light for detection. The Raman scattered photons were dispersed in a halfmeter Acton Sp-2500 spectrometer and were detected using a Princeton Instruments CCD array (Spec-10:400BR back-thinned, deep-depleted array).
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ASSOCIATED CONTENT S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsnano.7b00923. Information on mass calculations, Raman spectroscopy, and resonant quality factors (PDF)
AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected]. ORCID
Jeremy T. Robinson: 0000-0001-8702-2680 Author Contributions #
J. T. Robinson and M. K. Zalalutdinov contributed equally.
Notes
The authors declare no competing financial interest. 4751
DOI: 10.1021/acsnano.7b00923 ACS Nano 2017, 11, 4745−4752
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