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Probing Young’s modulus and Poisson’s ratio in graphene/metal interfaces and graphite: a comparative study Antonio Politano 1 () and Gennaro Chiarello 1,2 Nano Res., Just Accepted Manuscript • DOI: 10.1007/s12274-014-0691-9 http://www.thenanoresearch.com on December 16 2014 © Tsinghua University Press 2014 Just Accepted This is a “Just Accepted” manuscript, which has been examined by the peer-review process and has been accepted for publication. A “Just Accepted” manuscript is published online shortly after its acceptance, which is prior to technical editing and formatting and author proofing. Tsinghua University Press (TUP) provides “Just Accepted” as an optional and free service which allows authors to make their results available to the research community as soon as possible after acceptance. After a manuscript has been technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Please note that technical editing may introduce minor changes to the manuscript text and/or graphics which may affect the content, and all legal disclaimers that apply to the journal pertain. In no event shall TUP be held responsible for errors or consequences arising from the use of any information contained in these “Just Accepted” manuscripts. To cite this manuscript please use its Digital Object Identifier (DOI®), which is identical for all formats of publication. Nano Research DOI 10.1007/s12274-014-0691-9

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  • Nano Res

    1

    Probing Youngs modulus and Poissons ratio in

    graphene/metal interfaces and graphite: a comparative

    study

    Antonio Politano1 () and Gennaro Chiarello1,2

    Nano Res., Just Accepted Manuscript DOI: 10.1007/s12274-014-0691-9

    http://www.thenanoresearch.com on December 16 2014

    Tsinghua University Press 2014

    Just Accepted

    This is a Just Accepted manuscript, which has been examined by the peer-review process and has been

    accepted for publication. A Just Accepted manuscript is published online shortly after its acceptance,

    which is prior to technical editing and formatting and author proofing. Tsinghua University Press (TUP)

    provides Just Accepted as an optional and free service which allows authors to make their results available

    to the research community as soon as possible after acceptance. After a manuscript has been technically

    edited and formatted, it will be removed from the Just Accepted Web site and published as an ASAP

    article. Please note that technical editing may introduce minor changes to the manuscript text and/or

    graphics which may affect the content, and all legal disclaimers that apply to the journal pertain. In no event

    shall TUP be held responsible for errors or consequences arising from the use of any information contained

    in these Just Accepted manuscripts. To cite this manuscript please use its Digital Object Identifier (DOI),

    which is identical for all formats of publication.

    Nano Research DOI 10.1007/s12274-014-0691-9

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    Probing Youngs modulus and Poissons ratio in

    graphene/metal interfaces and graphite: a comparative

    study

    The Youngs modulus and the Poissons ratio in various

    graphene/metal interfaces and in graphite has been studied by

    phonon-dispersion experiments.

    Provide the authors webside if possible.

    Antonio Politano, https://www.researchgate.net/profile/Antonio_Politano?ev=hdr_xprf

    https://www.researchgate.net/profile/Antonio_Politano?ev=hdr_xprf

  • Probing Youngs modulus and Poissons ratio in

    graphene/metal interfaces and graphite: a comparative

    study

    Antonio Politano1 () and Gennaro Chiarello1,2

    Received: day month year

    Revised: day month year

    Accepted: day month year

    (automatically inserted by

    the publisher)

    Tsinghua University Press

    and Springer-Verlag Berlin

    Heidelberg 2014

    KEYWORDS

    Youngs modulus,

    Poissons ration, elastic

    properties, graphene

    ABSTRACT

    By analyzing phonon dispersion, we have evaluated the average Youngs

    modulus and Poissons ratio in graphene grown on Ru(0001), Pt(111), Ir(111),

    Ni(111), BC3/NbB2(0001) and, moreover, in graphite. In both flat and

    corrugated graphene sheets and graphite, we find a Poissons ratio of 0.19

    and a Youngs modulus of 342 N/m. The unique exception is graphene/Ni(111),

    for which we find different values (0.36 and 310 N/m, respectively) due to the

    stretching of C-C bonds occurring in this commensurate overstructure. Such

    findings are in excellent agreement with calculations performed for a

    free-standing graphene membrane. The high crystalline quality of graphene

    grown on metal substrates leads to macroscopic samples of high tensile

    strength and bending flexibility to be used for technological applications such

    as electromechanical devices and carbon-fiber reinforcements.

    1 Introduction

    The elastic moduli of single-layer graphene sheets

    have attracted considerable interest in recent years.

    In fact, the extraordinary intrinsic strength of

    graphene[1] makes graphene a suitable material for

    applications such as actuators[2] and

    nano-electromechanical devices[3, 4] and, moreover,

    as carbon-fiber reinforcement in polymeric

    nanocomposites[5].

    Graphene can be formed by graphite exfoliation [6],

    thermal decomposition of SiC [7] and by epitaxial

    growth on metal surfaces[8]. The preparation of

    highly ordered monolayer graphene could be

    extended up to the millimeter scale when graphene is

    Nano Research DOI (automatically inserted by the publisher)

    Address correspondence to Antonio Politano, [email protected]

    Research Article Please choose one

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    2 Nano Res.

    epitaxially grown on transition-metal substrates. [9]

    Furthermore, the possibility of transfer of the

    graphene sheet onto insulating substrates may be a

    promising route toward large scale production of

    graphene devices [10]. Thus, it is important to know

    the interaction strength between the graphene layer

    and the metallic substrate in order to discern

    between physisorption and chemisorption of

    graphene and, moreover, to appraise the quality of

    the contacts between metallic electrodes and

    graphene devices[11-13].

    Graphene has been grown on different transition

    metal substrates: Pt(111)[14], Ni(111)[15],

    Ru(0001)[16], Ir(111)[17], Rh(111)[18], Pd(111)[19],

    Re(0001)[20], Cu(111)[21], and Co(0001)[22]. Among

    the above-mentioned graphene systems, three

    general classes may be distinguished.

    Firstly, for the class of Ni and Co substrates, the

    mismatch in the lattice parameter is negligible, thus

    the graphene unit cell may be directly matched with

    the substrate unit cell by slightly quenching or

    stretching the bonds between carbon atoms of the

    graphene lattice. In this case, a strong hybridization

    between the substrate d bands and the bands of

    graphene occurs[11]. Thus, graphene is chemisorbed

    onto these substrates with a small graphene-substrate

    distance (2.1 for Ni [23] and 1.5-2.2 for Co [22]).

    Whenever the mismatch in the lattice parameter

    approaches 5-10%, a Moir pattern appears. In this

    case, the graphene sheet may be weakly (Pt, Ir) or

    strongly bonded (Ru, Re, Pd, Rh) to the substrate.

    The strong interaction occurring for graphene on

    Ru(0001) [24] and Re(0001) [20] causes a strong

    corrugation of the graphene sheet.

    To date, a comparative investigation of elastic moduli

    of graphene/metal interfaces is hitherto missing. Such

    a comparative analysis could clarify whether the

    elastic properties of periodically rippled graphene on

    Ru(0001)[8, 25, 26] are different with respect to

    systems in which the graphene overstructure is

    nearly flat. Moreover, it would be interesting to

    understand the influence of the stretching of C-C

    bonds occurring in graphene/Ni(111) on the elastic

    properties of the graphene sheet.

    Herein, we estimate the average elastic properties

    (Youngs modulus and the Poissons ratio) in

    graphene epitaxially grown on Ru(0001), Pt(111),

    Ir(111), Ni(111), BC3/NbB2(0001) and graphite, based

    on the investigation of the phonon dispersion.

    In most cases, we estimate the same values of the

    Poissons ratio (0.19) and the Youngs modulus

    (342 N/m) of the graphene sheet. The unique

    exception is represented by graphene/Ni(111), for

    which theirs values are 0.36 and 310 N/m,

    respectively. Despite the macroscopic size of our

    graphene sample which usually reduces the

    tensile strength for the presence of defects and

    grain boundaries, the above parameters well agree

    with results reported for suspended graphene

    membranes[27] with diameter of 1.0-1.5 m.

    Hence, our results demonstrate that high-quality

    and macroscopic samples of epitaxial graphene on

    metal substrates exhibit the tensile strength

    predicted by theory. Moreover, we have

    demonstrated that surface corrugation and the

    graphene-substrate interaction do not play any

    peculiar role on the elastic moduli of the graphene

    sheet.

    2 Experimental

    Experiments were carried out in an ultra-high

    vacuum (UHV) chamber operating at a base

    pressure of 510-9 Pa. The samples were single

    crystals delivered from MaTecK GmbH.

    Substrates have been cleaned by repeated cycles

    of ion sputtering and annealing at 1300 K.

    Surface cleanliness and order were checked using

    Auger electron spectroscopy (AES) and

    low-energy electron diffraction (LEED)

    measurements, respectively. Graphene was obtained by dosing ethylene onto the

    clean substrate held at 1150 K, with the exception of

    graphene on Ni(111), for which a lower sample

    temperature was used (800 K) [28]. The presence of a

    single sheet of graphene in the whole sample has

    been confirmed by ex-situ Raman spectroscopy[29].

    Similar conclusions have been reported in other

    works on the same systems in the same experimental

    conditions [14, 30].

    The inspection of the LEED pattern clearly shows the

    presence of well-resolved spots which are

    fingerprint of the order of the graphene

    overstructure.

    Graphene grows on Ru(0001) with a single

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    3 Nano Res.

    )sinE

    E1(sin

    mE2q S

    p

    lossi

    p

    macroscopic domain which extend up to millimeter

    scale [9]. Similar results have been obtained for

    graphene on Ni(111) [31]. By contrast, micrometric

    graphene domains grow on Ir(111) [32] and Pt(111)

    [33, 34] with two and three rotational orientations,

    respectively.

    High-resolution electron energy loss spectroscopy

    (HREELS) experiments were performed by using an

    electron energy loss spectrometer (Delta 0.5, SPECS).

    The energy resolution of the spectrometer was

    degraded to 4 meV so as to increase the

    signal-to-noise ratio of loss peaks. Dispersion of the

    loss peaks, i.e., Eloss(q||), was measured by moving

    the analyzer while keeping the sample and the

    monochromator in a fixed position. To measure the

    dispersion relation, values for the parameters Ep,

    impinging energy and i , the incident angle, were

    chosen so as to obtain the highest signal-to-noise

    ratio. The primary beam energy used for the

    dispersion, Ep=20 eV, provided, in fact, the best

    compromise among surface sensitivity, the highest

    cross-section for phonon excitation and q||

    resolution.

    As

    the parallel momentum transfer, q|| depends on Ep,

    Eloss, i and s according to:

    where Eloss is the energy loss and s is the electron

    scattering angle [35].

    Accordingly, the integration window in reciprocal

    space [36] is

    where is the angular acceptance of the apparatus

    (0.5 in our case). For the investigated range of q||,

    the indeterminacy has been found to range from

    0.005 (near ) to 0.022 -1 (for higher momenta). The phonon dispersion for all systems has been

    measured with the sample aligned along the

    M . To obtain the energies of loss peaks, a polynomial background was subtracted from each

    spectrum. The resulting spectra were fitted by a

    Gaussian line shape (not shown herein).

    All measurements were made at room temperature.

    3 Results and discussion

    HREEL spectra, recorded as a function of the

    scattering angle, show several dispersing features,

    all assigned to phonon excitations. As a selected

    case, we show in Figure 1 measurements of

    graphene/Ru(0001) recorded at Ep=20 eV as a

    function of the parallel momentum transfer q||.

    Phonon modes are excited in electron scattering by

    the impact mechanism[37]. Thus, the intensity of

    phonon modes notably increases with q|| (Figure 1),

    even if they are noticeable also at small momenta

    just by increasing the acquisition time for improving

    the signal-to-noise ratio (not shown).

    In graphene, two kinds of phonons exist: lattice vibrations in the plane of the sheet giving rise to transverse and

    longitudinal acoustic (TA and LA) and optical (TO and

    LO) branches, and lattice vibrations out of the plane

    of the layer which give rise to the so-called flexural phonons (ZA and ZO). Modes classified with T are

    shear in-plane phonon excitations; L modes are

    longitudinal in-plane vibrations; while Z indicates

    out-of-plane polarization. In graphite and graphene, the

    ZO mode is significantly softened with respect to the other

    two optical modes, i.e. TO and LO. This is due to the

    higher freedom for atom motion perpendicular to the plane

    with respect to the in-plane motion. Figure 2 shows a

    selected HREELS spectrum showing the above-mentioned

    six phonon modes of the graphene lattice. The sharpness

    of phonon modes observed in Figure 2 indicates an

    excellent crystalline order in the graphene sample.

    In principle, EELS planar scattering from an isolated

    graphene sheet does not allow the observation of the

    TA branch for selection rules inhibiting the

    observation of odd phonons under reflection

    symmetries[37]. However, the presence of an

    underlying substrate acts as a symmetry breaking

    and this allows to record a weak signal also from the

    TA mode. Such a reduced intensity implies that long

    acquisition time is required for detecting TA with a

    sufficient signal-to-noise ratio.

    Figures 3 and 4 report the dispersion of the TA and

    LA phonons, respectively, for different systems, that

    is graphene epitaxially grown on Ni(111), Pt(111),

    Ir(111), Ru(0001), BC3/NbB2(0001) and, moreover,

    graphite.

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    4 Nano Res.

    Sound velocities have been extracted from the

    experimental slope of the acoustic branches in the

    low-q|| limit, for which TA and LA phonons along

    the K and M directions coincide. In particular, we define vL, longitudinal sound velocity,

    and vT, transverse sound velocity, as

    and where and are the

    frequencies of longitudinal and transverse acoustic

    phonons, respectively.

    We obtain 14.0 and 22.0 km/s for the TA and the LA

    branches, respectively. The only exception is the

    transverse sound velocity for graphene/Ni(111),

    which is found to be lower by 11% (12.4 km/s).

    The difference for graphene/Ni(111) arises from the

    fact that the CC bonds of the graphene layer are

    stretched by 1.48% to form a 1 1 structure. The

    energetically most favorable configuration is that

    with one carbon atom is on top of a Ni atom and the

    other carbon atom on a hollow site[38].

    Data on the dispersion of acoustic phonons of a

    graphene can provide information on its elastic

    properties. According to the procedure illustrated in

    Ref. [39], the sound velocities of the TA and LA

    branches could be used for calculating the in-plane

    stiffness (the 2D analogous of the bulk modulus)

    and the shear modulus of the graphene sheet,

    respectively:

    D

    T

    D

    L

    v

    v

    2

    2

    Thus, we estimate and to be 211 and 144 N/m for

    all systems with the exception of graphene/Ni(111),

    for which their values are 244 and 114 N/m,

    respectively. It is worth noticing that graphene is a

    true 2D material, therefore its elastic behavior is

    properly described by 2D properties with units of

    force/length.

    On the other hand, the 2D shear and bulk moduli are

    also defined as a function of the Poissons ratio and

    the Youngs modulus for 2D samples E2D:

    )1(2

    )1(22

    2

    D

    D

    E

    E

    Hence, from and it is possible to estimate the

    Poissons ratio, i.e. the ratio of transverse contraction

    strain to longitudinal extension strain in the direction

    of the stretching force:

    19.0

    1

    1

    The obtained value for most systems, i.e. 0.19, agrees

    well with results for graphite in the basal plane (0.165)

    [40, 41] while it is 0.28 in carbon nanotubes [42]. It

    represents an intermediate value with respect to

    those reported by calculations for graphene, as

    shown in Table I. Instead, for graphene/Ni(111) its

    value is 0.36.

    It is worth noticing that, according to molecular

    dynamics calculations[43], the Poissons ratio

    increases with the size of the graphene sample up to

    reach a saturation value and it also depends on

    temperature. This opens the possibility to tailor the

    mechanical properties of graphene for engineering

    applications.

    The Poissons ratio could be used as a powerful test

    among the various existing calculations on phonon

    dispersion in graphene. As an example, the

    calculated LA and TA modes in Ref. [44] would lead

    to a clearly underestimated value of the Poissons

    ratio (0.05).

    It is also possible to estimate the Youngs modulus

    E2D, which is a measure of the stiffness of

    an isotropic elastic material. It is defined as the ratio

    of the uniaxial stress over the uniaxial strain.

    Table I. Poissons ratio , as reported in different

    experimental and theoretical works. Poissons

    ratio

    Experimental (HREELS), graphene on Pt(111),

    Ru(0001), Ir(111), BC3/NbB2(0001), graphite

    0.19

    Experimental, basal plane of graphite, Refs. [40, 41] 0.165

    Experimental (HREELS), graphene/Ni(111) 0.36

    Atomistic Monte Carlo, Ref. [45] 0.12

    Tersoff-Brenner potential, Ref. [46] 0.149

    Continuum plate theory, Ref. [47] 0.16

    http://en.wikipedia.org/wiki/Stiffnesshttp://en.wikipedia.org/wiki/Isotropichttp://en.wikipedia.org/wiki/Stress_(physics)http://en.wikipedia.org/wiki/Strain_(materials_science)

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    5 Nano Res.

    Density functional theory, Ref. [48] 0.162

    First-principles total-energy calculations, combined

    to continuum elasticity, Ref. [49]

    0.169

    Ab initio, Ref. [50] 0.173

    Ab initio, Ref. [51] 0.178

    DFT, Ref. [52] 0.18

    Ab initio, Ref. [53] 0.186

    Ab initio, Ref. [54] 0.19

    Valence force model, Ref. [55] 0.20

    LDA, Ref. [56] 0.20

    Cellular material mechanics theory, Ref. [57] 0.21

    Molecular dynamics, Ref. [43] 0.22

    Molecular dynamics, Ref. [58] 0.22

    Empirical force-constant calculations, Ref. [59] 0.227

    Brenners potential, Ref. [52] 0.27

    continuum elasticity theory and tight-binding

    atomistic simulations, Ref. [60]

    0.31

    Ab initio, Ref. [61] 0.32

    Molecular dynamics, Ref. [62] 0.32

    Brenners potential, Ref. [63] 0.397

    Multiple component correlation model, Ref. [64] 0.4

    Molecular dynamics, Ref. [65] 0.45

    As reported in Table II, many theoretical works

    found Youngs moduli ranging from 307 to 356 N/m.

    The obtained value of E2D for most graphene/metal

    interfaces, i.e. 342 N/m, agrees well with most

    theoretical results (Table II), a part from calculations

    in Ref. [66] (underestimated E2D). In particular, a

    good agreement exists between present results and

    first-principles total-energy calculations, combined to

    continuum elasticity, reported in Ref. [49].

    It will be helpful to compare present results with the

    case of three-dimensional (3D) materials and, in

    particular, with bulk graphite. To obtain the

    corresponding 3D parameter for the selected case of

    graphene/Pt(111), the value of E2D should be divided

    by the distance between the graphene and the

    underlying Pt(111) substrate (3.31 )[67, 68]. Thus,

    E2D as obtained by vibrational measurements

    corresponds to a 3D Youngs modulus E=1.03 TPa.

    This is in fair agreement with experiments on bulk

    graphite yielding 1.02 TPa for the in-plane Youngs

    modulus[40]. For the sake of completeness, the

    Youngs modulus obtained for single-walled carbon

    nanotubes ranges from 0.45 and 1.47 TPa [69], while

    for multi-walled carbon nanotubes it was found to

    range from 0.27 to 0.95 TPa [70]. In graphene/Ni(111)

    E2D is instead 310 N/m.

    Table II. 2D Youngs modulus E2D, expressed in N/m, as

    reported in different experimental and theoretical works. Young's modulus E2D (N/m)

    Experimental (HREELS),

    graphene on Pt(111), Ru(0001),

    Ir(111), BC3/NbB2(0001),

    graphite

    342

    Experimental (HREELS),

    graphene/Ni(111)

    310

    Experimental (AFM) on

    graphene/copper foils, Ref. [71]

    33917

    Experimental (AFM) on graphene

    membranes, Ref. [27]

    34050

    Experimental (AFM) on graphene

    membranes, Ref. [72]

    35050

    Tersoff-Brenner potential, Ref.

    [66]

    235

    Energetic model, Ref. [73] 307

    continuum elasticity theory and

    tight-binding atomistic

    simulations, Ref. [60]

    312

    DFT, Ref. [52] 330

    Brenners potential, Ref. [63] 336

    First-principles total-energy

    calculations, combined to

    continuum elasticity, Ref. [49]

    344

    Tersoff-Brenner potential, Ref.

    [46]

    345

    Ab initio, Ref. [53] 350

    Atomistic Monte Carlo, Ref. [45] 353

    Density functional theory, Ref.

    [48]

    356

    Empirical force-constant

    calculations, Ref. [59]

    384

    Experimental (AFM) on

    graphene/copper foils, Ref. [74]

    55

    Recently, nanoindentation AFM measurements [74]

    have been performed on graphene grown by CVD on

    copper foils and successively transferred onto silicon

    nitride grids with arrays of pre-patterned holes.

    These experiments have revealed a notably reduced

    E2D (55 N/m) with respect to the present finding (342

    N/m). Such extremely low value of E2D could be a

    consequence of the modification of the membrane

    structure induced by the transfer process (see Ref. [74]

    for more details).

    In addition, in the linear elastic regime, it is possible

    to estimate the elastic constants C11 and C12 , from E2D

    and :

    11

    12

    11

    2

    12

    2

    112

    C

    C

    C

    CCE D

    This, C11=422 N/m and C12=80 N/m, which are in

    good agreement with values reported by Cadelano et

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    6 Nano Res.

    al.[49] (354 and 60 N/m).

    Their corresponding 3D values are 1.27 and 0.24,

    respectively, which agree well with experimental

    findings for graphite reported in Ref. [75] (1.11 and

    0.18 TPa).

    Conclusions

    We have demonstrated that the elastic properties in

    graphene/metal interfaces are the same recorded in

    graphite and free-standing graphene, with the

    exception of graphene/Ni(111), where C-C bonds are

    stretched by 1.48%. This implies a variation of the 2D

    Youngs modulus by 9% (310 N/m versus 342 N/m in

    the other systems).

    The excellent crystalline quality of graphene grown

    on metal substrates (with a reduced number of

    defects and grain boundaries) leads to macroscopic

    samples of high bending flexibility and tensile

    strength, which could be used for applications in

    advanced nanocomposites. Due to its thermal

    stability up to 1200 K, chemical stability and

    robustness, epitaxial graphene represents a

    promising candidate for application in

    nano-electromechanical devices.

    Acknowledgements

    We thank Davide Campi and Fernando de Juan for

    helpful discussions. References

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    Figure 1: HREELS spectra recorded as a function of the

    parallel momentum transfer q|| for monolayer graphene on

    Ru(0001). The green arrow indicates the weak TA mode.

    Figure 2: HREELS spectrum reporting the six phonon

    modes of graphene on Ru(0001) for a selected value of the

    parallel momentum transfer q|| (~0.95 -1). Measurements have

    been carried out with a primary electron beam energy of 20 eV,

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    10 Nano Res.

    Figure 3: Dispersion of the TA mode in graphene

    epitaxially grown on BC3/NbB2(0001) (data taken from Ref.

    [76]), Ir(111), Pt(111), Ru(0001), Ni(111) and, moreover, in

    graphite.

    Figure 4: Dispersion of the LA mode in graphene

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    [76]), Ni(111) Ir(111), Pt(111), Ru(0001), and, moreover, in

    graphite.

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