Valleys and Hills of Graphene on Ru(0001) - ACS Publications

Subscriber access provided by STEPHEN F AUSTIN STATE UNIV

C: Surfaces, Interfaces, Porous Materials, and Catalysis

Valleys and Hills of Graphene on Ru(0001) Caio C. Silva, Marcella Iannuzzi, David A. Duncan, Paul T. P. Ryan, Katherine T. Clarke, Johannes T. Küchle, Jiaqi Cai, Wouter Jolie, Christoph Schlueter, Tien-Lin Lee, and Carsten Busse J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b05671 • Publication Date (Web): 20 Jul 2018 Downloaded from http://pubs.acs.org on July 20, 2018

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 25 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

The Journal of Physical Chemistry

Valleys and Hills of Graphene on Ru(0001) Caio C. Silva,∗,† Marcella Iannuzzi,‡ David A. Duncan,¶ Paul T. P. Ryan,¶,§ Katherine T. Clarke,¶ Johannes T. Küchle,¶,k Jiaqi Cai,† Wouter Jolie,⊥ Christoph Schlueter,¶ Tien-Lin Lee,¶ and Carsten Busse#,†,⊥ †Institut f¨ ur Materialphysik, Westfälische Wilhelms-Universität M¨ unster, Wilhelm-Klemm-Straße 10, 48149 M¨ unster, Germany ‡Chemie-Institut, Universität Z¨ urich, Winterthurerstrasse 190, 8057 Z¨ urich, Switzerland ¶Diamond Light Source, Didcot OX11 0DE, U.K. §Department of Materials, Imperial College London, Exhibition Road, SW7 2AZ London, U. K. kPhysik Department E20, Technische Universität M¨ unchen, James Franck Str. 1, 85748 Garching, Germany ⊥II. Physikalisches Institut, Universität zu K¨ oln, Z¨ ulpicher Straße 77, 50937 Köln, Germany #Department Physik, Universität Siegen, Walter-Flex-Straße 3, 57068 Siegen, Germany E-mail: [email protected] Phone: +49 (0)251 8339014

Abstract The structure of graphene on Ru(0001) has been extensively studied over the last decade, yet with no general agreement. Here we analyse graphene’s valleys and hills using a combination of x-ray standing waves (XSW) and density functional theory (DFT). The chemical specificity of XSW allows an independent analysis of valleys

1

ACS Paragon Plus Environment

The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

and hills which, together with DFT model, results in the precise determination of the distance between the flat, strongly bonded valleys of graphene and the substrate, as well the corrugation presented in the weakly bounded hills. From the theoretical viewpoint, the good agreement with experiment validates the choices regarding the unit cell size and the non-local correlation functional.

Introduction A periodic corrugation on the nanometer scale is a characteristic feature of epitaxially grown two-dimensional (2D) materials, found in, for example, graphene (gr) on Ir(111), 1 a monolayer of hexagonal boron nitride (hBN) on Cu(111), 2 and a monolayer of MoS2 on Au(111). 3 All these systems are characterized by a small lattice misfit between the substrate and the 2D-overlayer. As a consequence, a moiré superstructure develops consisting of alternating areas of strongly and more weakly bound adsorbates. For gr/Ru(0001), the lattice misfit of 9% leads to a particularly strong spatial variation of both geometry and electronic structure. The corrugation of gr/Ru(0001) was noted already in earlier studies, 4,5 and it has been shown that its moiré structure can serve as a template for the growth of well-ordered lattices of metal nanoclusters 6 and organic molecules. 7 Furthermore, the electronic structure of graphene is strongly perturbed, as compared to free-standing graphene, 8–10 and the corrugation leads to special, localized phonon modes 11,12 and plasmon modes. 13,14 The moiré unit cell of gr/Ru(0001) features a periodic variation in the registry between the carbon and Ru atoms of the topmost surface layer. When one of the carbon atoms from the two-atom basis of the gr honeycomb structure is approximately on top of a Ru substrate atom, a covalent bond forms, pulling the graphene closer to the metal surface. This low-lying and flat region of the unit cell is referred to as a valley. When neither of the two C atoms is in an on-top position, no chemical bond can form, and the graphene layer relaxes outwards to accommodate the lattice mismatch, thereby forming a hill which interacts with the substrate through van der Waals (vdW) force only. This presence of these two different regions reflects 2


Page 2 of 25

Page 3 of 25 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


itself in the electronic structure as splittings of the Dirac cone, 9 the C 1s core level, 15 and the image potential states. 10 The strong binding in the valley region is exemplified by the fact that helium atom scattering detects the same Rayleigh surface wave for Ru(0001) and gr/Ru(0001). 16 Quantification of corrugation-induced effects requires the knowledge of the geometric structure of the gr/Ru(0001) interface. The most fundamental structural parameters characterizing the interaction with the substrate are the adsorption height of the strongly interacting valley hmin and the corrugation amplitude ∆h, which measures the difference between hmin and the top of the hill at hmax . However, up to now, no agreement has been reached on these parameters despite numerous studies where experimental values between 1.45 and 2.10 ˚ A for hmin and 0.15 and 1.5 ˚ A for ∆h have been reported (see Tab. 1 for an overview). This is a common problem for epitaxial 2D materials arising from the the convolution of topography and electronic or mechanical properties in scanning probe methods 4,8,17 and the difficulty in modelling large moire unit cells in scattering techniques. 5,18,19 In addition, for the case of helium atom scattering, the low apparent corrugation could be due to a modulation of the Deby-Waller factor within the moiré cell in combination with an anticorrugation effect due to different positions of the Fermi level in the hills and the valleys. 20 In summary, the ambiguity of the experimental findings is a disquieting situation for such a well-studied system. Table 1: Summary of experimental results concerning the structure of gr/Ru(0001). The average bond distance between the substrate and the flat graphene valley is denoted hmin , and ∆h is the height of the hill above this value. LEEM: low-energy electron microscopy, LEED: low-energy electron diffraction, SXRD: surface x-ray diffraction, HAS: helium atom scattering. Method LEEM 5 LEED 18 SXRD 21 HAS 19

˚) hmin (A ∆h (˚ A) 1.5 ± 0.1 2.1 ± 0.2 1.5 ± 0.2 0.82 ± 0.15 0.17 ± 0.03

From a theoretical point of view, there are two difficulties in calculating the structure 3



Page 4 of 25

of gr/Ru(0001). First, the size of the unit cell used in the model: SXRD experiments show that gr/Ru(0001) has a large unit cell with 25 × 25 graphene units on top of 23 × 23 Ru units (25-on-23). 22 The theoretical analysis of such a large unit cell is computationally expensive and models based on density functional theory (DFT) employ, in general, smaller ones, namely 11-on-10, 23,24 12-on-11 23,25 and 13-on-12. 17,18 The exception is the work of Iannuzzi et al. which presents calculations on a 25-on-23 superstructure. 26 The second problem is the proper description of the vdW interaction within the DFT model, since a universal ab initio method is not available at this level of theory. For example, it has been demonstrated that the correction of a standard correlation functional even by means of empirically formulated dispersion forces induces a reduction of about 25% in ∆h. 24 Table 2 is a summary of previous DFT calculations concerning the structure of gr/Ru(0001), showing the unit cell size, vdW corrections, and the values of hmin and ∆h. Table 2: Summary of DFT results related to the structure of gr/Ru(0001). The authors choices concerning the unit cell size and the vdW corrections are indicated, as well the values of hmin and ∆h. Jiang et al

23

Moritz et al 18 Stradi et al 24 Iannuzzi et al 26 Voloshina et al 17

Unit Cell vdW Corrections 12-on-11 11-on-10 13-on-12 12-on-11 11-on-10 DFT-D2 27 25-on-23 rVV10 28 13-on-12 DFT-D2 27

˚) hmin (˚ A) ∆h (A 2.20 1.67 2.30 1.75 2.20 1.59 2.10 1.50 2.20 1.20 2.20 1.20 2.15 1.27

A combination of an experimental analysis with DFT in a single study was successfully employed in the work of Moritz et al . 18 The values of hmin and ∆h which resulted from the LEED I(V) analysis are in good agreement with the 12-on-11 DFT model. At the same time that this work was published, a structural analysis based on SXRD was also published but with a different outcome. 21 This discrepancy was explained by the use of a restricted p3m1-symmetry and a 12-on-11 unit cell for Moritz et al. However, a later, complementary study by Iannuzzi et al 26 using a 25-on-23 model is still in disagreement with the SXRD 4


Page 5 of 25 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


results. The DFT study by Voloshina et al 17 is corroborated by AFM force spectroscopy which yield similar results than the theoretical predictions. The disagreement among the published experimental and theoretical results reveals the need for a precise structural analysis of this system. In the present work, the interaction between graphene and Ru(0001), as characterized by the modulated distance between the carbon atoms and the substrate surface, is experimentally studied by means of the x-ray standing wave (XSW) technique, 29,30 which has been successfully employed to analyse the structure of various epitaxially grown two-dimensional materials. 31–37 The high chemical specificity of x-ray photoelectron spectroscopy (XPS) used in conjunction with XSW is advantageous here as it allows us to characterize hills and valleys separately, similar to the recent study of hBN on Ir(111). 35 In conjunction with DFT calculations using a realistically large unit cell and including non-local interactions, our study allows a robust determination of the structural parameters for gr/Ru(0001).

Experimental Methods The experiments were performed at the I09 beamline at Diamond Light Source. The sample preparation was accomplished in an ultra-high vacuum (UHV) chamber with a base pressure of 3.0 × 10−10 mbar. The Ru(0001) crystal was prepared by cycles of 1.5 keV Ar ion sputtering and flash annealing to 1400°C in vacuum until a sharp LEED-pattern with no indication of any superstructure was observed. Single-layer graphene was formed by thermal decomposition of ethylene (C2 H4 ) at a pressure of 2.0 × 10−8 mbar at 800°C during 30 minutes. Then, ethylene was turned off and the sample was held at 800°C for another minute in UHV. The quality of graphene was monitored by LEED. To generate an XSW the incident photon energy is tuned to excite a substrate Bragg reflection. The interference between the incident and the outgoing waves forms the XSW with a periodicity identical to the Bragg plane spacing (dhkl ). Varying the photon energy

5



through the reflection causes a phase shift of the XSW and thus a movement of the wave field by

dhkl 2

perpendicular to the Bragg planes, which modulates the photoelectron yields as

functions of photon energy in a way that is characteristic of the distribution of the emitters relative to the Bragg planes. XSW measurements were carried out in a backscattering geometry using the Ru(0002) reflection. The Ru(0002) reflectivity curve was recorded using a fluorescent screen prior to each XSW measurement to center the photon energy range with the Bragg energy (EBragg = 2.897 keV). The C and Ru core-level spectra were measured by a Scienta EW4000 HAXPES analyser oriented perpendicular to the incident beam. The CCD detector of the analyser was operated in a pulse counting mode, which is expected not to suffer from the nonlinearity issues that have been observed in the analogue mode of this detector in the past. 38 To avoid saturation of this measurement mode the flux was decreased by a factor of 60 by detuning the I09 hard X-ray undulator. We performed 30 separate XSW measurements, each on a different spot on the sample. Due to the use of pulse mode of the analyser, the count rate is low. Thus, the XSW data presented here are the summed spectra over all 30 measurements. The relative X-ray absorption of C and Ru atoms was monitored by the integrated intensities of the chemical components of the C 1s, Ru 3d3/2 and Ru 3d5/2 core-levels peaks.

Computational Details The gr/Ru(0001) interface was reproduced by an extended slab model of six 23 × 23 Ru layers, covered on one side by a 25 × 25 carbon layer (4424 atoms). The simulation box was 35 ˚ A in the perpendicular direction, which provides a vacuum region of more than 20 ˚ A. The whole structure was relaxed by means of DFT electronic structure calculations, keeping the bottom Ru layer at fixed bulk coordinates and applying laterally the periodic boundary conditions. The simulations were performed using the cp2k program package 39,40 and employing the Gaussian and plane waves formalism. 41,42 Only the valence electrons’ density was opti-

6


Page 6 of 25

Page 7 of 25 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


mized explicitly, considering 16 electrons for each Ru atom and 4 for each carbon atom, for a total of 55784 electrons, and expanding the orbitals in double-zeta-valence (DZV) molopt basis sets. 43 The plane waves expansion of the density used to efficiently solve the Poisson equation in reciprocal space was truncated to a cutoff energy of 500 Ry. The interaction between valence and core electrons was described by means of Goedeker-Teter-Hutter pseudopotentials. 44 As mentioned above, the choice of the exchange and correlation functionals combined with the correlation correction to properly include the dispersion terms is crucial for these interface systems, where, due to the characteristic topographical corrugation, the interactions between substrate and sp2 layer need to be accurately reproduced over a critical range of distances, from 1 to 6 ˚ A. Based on the experience acquired by the investigation of similar interfaces 45 and on the screening of several possible combinations of functionals for the present case, we resolved that the optimal choice is the Perdew-Burke-Ernzerhof (PBE) functional 46 augmented by the revised Vydrov–Voorhis 28 (rVV10) non-local correlation functional. We notice that for the present simulations a more accurate description of the electronic structure of Ru (16 valence electrons and DZV) has been used in comparison to the previously presented results. 26 Also our choice of the correlation functional corresponds to a higher level of theory and requires larger computational effort. Other models with different unit cell sizes and different functionals and vdW correction were tested. Such models give qualitatively the same structural pattern, i.e., a corrugated graphene layer consisting of hills with a roughly triangular base surrounded by a wider flat area (valleys). Deviations are to be found in structural details like the actual flatness of the valleys (±0.1 ˚ A), the proportion between the areas of valleys and the hills, the maximum height of the hills and the peak-to-peak corrugation (variations up to 0.5 ˚ A). Nonetheless, the model presented here is the only which was validated by the matching with our experimental data. The resulting structure is shown in Figure 1. The separation of the carbon layer into hills and valleys is clearly visible, details will be discussed below with the experimental results.

7



Figure 1: Side and top view of the optimized gr/Ru(0001) slab model. The color code used for the carbon atoms indicates their height over the substrate, measured as the minimum vertical distance (projection along the surface normal) from the virtual unrelaxed Ru surface used as reference (to simplify the comparison with experiments). C at more than 3.40 ˚ A are in red, between 3.40 ˚ A and 3.10 ˚ A orange, between 3.10 ˚ A and 2.70 ˚ A yellow, between 2.70 ˚ ˚ ˚ A and 2.40 A green, closer blue. The minimum C height is 2.06 A.

Results and Discussion LEED images of gr/Ru(0001) are shown in Figure 2a for different values of electron energy, exemplifying the high structural quality of the carbon layer. The satellite spots surrounding the intense spot from Ru(0001) are characteristics of the moiré superstructure. The XPS data of gr/Ru(0001) is shown in Figure 2b. The spectrum presented in Figure 2b is measured with an incident photon energy of 330 eV. This value was chosen to increase the surface sensitivity due to the low value of the resulting photoelectron kinetic energy (≈ 46 eV). Moreover, the surface sensitivity was also enhanced by setting the emission angle close to 90°. Although the Ru 3d3/2 signal partially overlaps with the C 1s peaks, the analysis of

8


Page 8 of 25

Page 9 of 25 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


the photoemission spectrum shows that the data resolution is good enough to identify five different components: two components related to Ru 3d5/2 (bulk and surface), Ru 3d3/2 , and two components for the C 1s signal, namely C1 at lower binding energy and C2 at higher binding energy. Due to a limitation in the resolution, the separation between surface and bulk components connected to the Ru 3d3/2 was not clear. Therefore this core-level was fitted with a single component which is broader in contrast to the components of Ru 3d5/2 . The high surface sensitivity is essential to identify the C 1s components as it increases the intensity of C 1s components in comparison to the Ru lines. For the evaluation of the individual components in Figure 2b we fitted five Doniach-Sunjic line shapes 47 convolved with a Gaussian function after a Shirley background subtraction. 48 Such a peak shape is defined by the asymmetry parameter α and a convolution width m. Table 3 shows the fitting parameters deduced from this analysis. The binding energies of the components and the binding energy difference between C1 and C2 of 620 meV are comparable with previous measurements, 15 as well as the asymmetry parameter α of the photoemission lineshape. 49 The splitting of the C 1s peak is caused by the corrugation of graphene: the different chemical environments felt by carbon atoms placed in the hills and the valleys result in two different binding energies of the C 1s state. Table 3: Fit parameters for the C 1s and Ru 3d3/2 spectra from Figure 2b fitted with Doniach-Sunjic profile convoluted with a Gaussian function. Eb is the binding energy of each component, FWHM is the full width at half maximum, α is the asymmetry parameter and m is the width of the convoluted Gaussian function (0 < m < 499). Component Eb (eV) FWHM (eV) C1 284.5 ± 0.1 0.3 ± 0.1 C2 285.1 ± 0.1 0.6 ± 0.1 Ru 3d3/2 284.1 ± 0.1 1.3 ± 0.1 Ru 3d5/2 Bulk 280.1 ± 0.1 0.4 ± 0.1 Ru 3d5/2 Surface 279.8 ± 0.1 0.4 ± 0.1

α 0.02 0.02 0.04 0.04 0.04

m (meV) 100 100 100 100 100

The finding that the carbon atoms can be attributed to two different species is confirmed by the DFT calculations of the 25-on-23 supercell of the gr/Ru superstructure. After relaxation, the formation of four unbound hills is observed while the largest part of the overlayer 9



Figure 2: LEED pattern and C 1s, Ru 3d3/2 and Ru 3d5/2 core-level emission spectrum for gr/Ru(0001). a) LEED pattern for different values of electron energy (inverted contrast). b) Photoemission spectrum with hν = 330 eV and emission angle close to 90°. Circles: Data points after background subtraction. Colored areas: Fits of the indicated components. Solid black line: Sum of fits. c) DFT calculation of the local density of states (DOS) of C 1s energies, computed separately for atoms at different heights from the surface. The same color code as in Figure 1 has been used. These calculations have been performed using an all electron representation for the C atoms. The binding energy of free-standing graphene is shown as a dashed line. The computed energies have been rigidly shifted to align the first C 1s peak to the experimental one. is approximately flat and bound to Ru. The calculated energy-resolved local density of states (DOS) of C 1s (see Figure 2c) shows that the binding energies depend on the adsorption heights, which correlates well with the splitting observed in the XPS data. It predicts a higher 1s binding energy for a lower-lying carbon atom. The calculated value of binding energy for free-standing graphene is 283.80 eV and it is represented by the vertical dashed line in figure 2c. The measured C 1s binding energies can be therefore attributed to the

10


Page 10 of 25

Page 11 of 25 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


different heights of the carbon atoms over the Ru surface, with component C1 corresponding to the physisorbed hills and C2 the chemisorbed valleys. It is important to realize that this separation into just two species is somewhat arbitrary as in reality there is a continuum of carbon atoms in different chemical environments. However, the classification we choose here is well established and can describe the experimental findings in a meaningful way. Note that from the calculated distribution it becomes obvious that the extended part of the valleys (blue curves) and the boundaries between valleys and hills (green curve) can not be distinguished experimentally. In order to perform the XSW analysis, XPS with incident photon energy around the Bragg energy must be recorded. Figure 3 shows the photoemission spectrum measured with an incident photon energy 5.5 eV above the center of reflectivity curve (off-Bragg condition). The spectrum in the inset of figure 3 is obtained with the incident photon energy tuned to the center of the reflectivity (Bragg condition). The binding energy differences between the components are the same as the spectrum in figure 2b, except Ru 3d5/2 which is fitted with a single component. This can be explained by the lack of surface sensitivity due to the high value of incident photon energy. The area ratio between Ru 3d3/2 and Ru 3d5/2 is constrained to 0.58 and the full width at half maximum ratio to 1.72 eV. These values are based on the XPS analysis of clean Ru(0001). The resulting off-Bragg intensity ratio between the two components of the C 1s peak is C1/C2 = 0.22. The noticeable difference in the line shape between the Bragg and off-Bragg cases, which arises from the standing wave movement, confirms the presence of the central component (C1) in the peak and the height separation between the two C species. The mean adsorption heights of C1 and C2 can be directly probed by XSW. First evidence of the XSW effect is already found in the increased intensity of the C1 signal at the Bragg condition (see inset of figure 3), which proves that carbon atoms contributing to C1 are at a different distance from the substrate with respect to those contributing to C2. Furthermore, the intensity change of C1 ensures the correct assignment of this component, since the

11



Figure 3: C 1s, Ru 3d3/2 and Ru 3d5/2 core-level emission spectrum for gr/Ru(0001). Photoemission spectrum with hν = EBragg + 5.5 eV (hν = EBragg shown in the inset). Circles: Data points after background subtraction. Colored areas: Fits of the indicated components. Solid black line: Sum of fits. contrast between C1 and Ru 3d3/2 becomes evident. For a full analysis we measure spectra in a range of incident photon energy, around the Bragg condition. All spectra acquired during the photon energy scan are fitted with a fixed binding energy difference between the four components, as well as with fixed FWHM. The same line-shape and background as in figure 3 were used here. Figure 4 summarize the XSW analysis of the photoelectron yields for the C1, C2, Ru 3d3/2 and Ru 3d5/2 components. The curves are normalized to their individual off-Bragg intensities. The dependence of the photoelectron yield on incident photon energy is described by the dynamical theory of x-ray diffraction with two structural parameters, 29,30 namely the coherent position P H and coherent fraction f H . The parameter P H is the Fourier-averaged position of all atoms of the analysed species and f H describes the distribution of atoms around

12


Page 12 of 25

Page 13 of 25 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


the mean position given by the coherent position. In our fitting procedure, we took into account the non-dipolar effects in the angular distribution of photoelectron emission. 50–52 In the analysis of the photoelectron yield of C1, C2, Ru 3d3/2 and Ru 3d5/2 , the values of forward-backward asymmetry parameter are QC1,C2 = 0.12 and QRu

3d3/2,3d5/2

= 0.11. These

parameters are calculated assuming an angle of 19° between the photon polarization vector and the photoemission direction, and using the tabulated dipolar asymmetry parameters (β), and the asymmetry factors associated to the interference between the electric dipole and electric quadrupole (γ). 53

Figure 4: XSW results for gr/Ru(0001). The analysis is presented for each component (C1, C2, Ru 3d3/2 and Ru 3d5/2 ) showing the variation in total photoelectron yield as function of the photon energy scan along the Darwin reflectivity curve. The values of coherent position (P H ) and coherent fraction (f H ) are shown to each component analysis. Using the values of P H shown in Figure 4, the mean position of each species can be given ¯ = P H × dRu(0002) , where dRu(0002) = 2.14 ˚ by h A is the Bragg plane spacing of Ru(0002). 54 Note that P H can only be determined modulo 1 as the x-ray standing wave field has the 13



periodicity of dhkl , leading to a modulo-d ambiguity for the determination of heights using XSW. 55 In practice, however, taking complementary experimental or theoretical results or simply the atomic radii of the atoms into account, almost always allows one to pin down the value of P H . For better readability, we will always give P H as a number that allows a direct calculation of the corresponding height. As the XSW method uses the standing wave field stemming from diffraction in the bulk, the heights of adsorbates are obtained in reference to an ideal bulk-truncated surface. As for gr/Ru(0001), it was found by SXRD that the top Ru layer relaxes inwards by 0.06 ˚ A, 21 this value should be added to all heights in this paper, when one wants to know the distance between the carbon atoms and the average surface (note the values of hmin given in the following also refer to the relaxed surface).

Valleys H The high value of fC2 = 0.86 points to a very narrow height distribution of the carbon

atoms in the valleys. Hence, the graphene region closer to the substrate is very flat and H one can determine the average height of carbon atoms in the valley (hvalley ) from PC2 , as H × dRu(0002) = 2.12 ˚ A. Due to the narrow height distribution of the carbon atoms hvalley = PC2

in the valleys, hvalley ≈ hmin (a comparison with the DFT calculations in the discussion below will show that hvalley − hmin ≈ 0.1 ˚ A). The value of hvalley is very close to the interlayer spacing dRu(0001) , which can explain why the growth of graphene starts with the formation of islands attached to the lower step edges of the Ru(0001) surface. 4,56 The XSW-determined height hvalley is in good agreement with previous LEED I(V) measurement 18 and suggests that hmin is significanly underestimated by LEEM. 5 Further insight can be obtained by direct comparison to the corresponding DFT model. First, we note that, consistent with the SXRD study, 21 a mean inward relaxation of 0.07 ˚ A of the Ru surface layer in contact with graphene is present. In order to facilitate comparison with the XSW result, we will also reference all heights determined by DFT to the virtual, unrelaxed surface. 14


Page 14 of 25

Page 15 of 25 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


The foot-print of the corrugated graphene layer can be recognized in the height modulation of the topmost Ru layer, as shown in Figure 5, which corresponds to a buckling of 0.159 ˚ A. Moving deeper towards the bulk, the Ru corrugation decays rapidly (see Table 4).

Figure 5: Representation of the topmost Ru layer, beneath the corrugated graphene layer, as resulting after optimization. The color code used for the Ru atoms indicate their relative A from height with respect to the average position hRu . In black are the Ru atoms at -0.052 ˚ ˚ ˚ hRu , in violet between -0.052 and 0.0 A, in magenta between 0.0 and +0.048 A, and in cyan up to +0.098˚ A.

Table 4: Corrugation ∆hRu , average height hRu , and interlayer distance from the layer underneath dslab , as calculated from the relaxed gr/Ru(0001) slab model. Ru layer ∆hRu ˚ A 1 0.16 2 0.14 3 0.10 4 0.06 5 0.02 6 0.00

hRu ˚ A -0.07 -2.13 -4.28 -6.43 -8.56 -10.62

dlayer ˚ A 2.06 2.15 2.15 2.13 2.06

We assign the carbon atoms to hills and valleys according to the off-Bragg C1/C2 intensity. By defining the valley as the lowest 82% of the carbon atoms (based on the XPS data), we obtain a rather flat area with a mean height of hvalley = 2.17 ˚ A (above the virtual unrelaxed surface), in good agreement with the value measured by XSW. This might be expected as in the valleys a strong chemisorption is present, which is typically described very well in DFT. The border between hills and valleys is found to be at a height of ≈ 2.7 ˚ A 15



and corresponds to very few atoms (colored green in Fig. 1), which cannot be distinguished from the rest of the valley in the C1 spectrum (see below). The deepest point of the valley is found to be at a height of 2.06 ˚ A, resulting in a minimum binding distance between C and Ru of 2.13 ˚ A. A alternative way to compare XSW and DFT is to calculate the geometric parameters H H from the DFT model, yielding PC2 = 1.01 and fC2 = 0.94 (Table 5). The agreement between

theory and experiment regarding the valleys is evident.

Hills According to the intensity ratio in off-Bragg XPS measurements, the C1 region corresponds to approximately 18% of the carbon atoms. The structural parameters determined by XSW H H = 0.72) clearly indicate a non-uniform distribution of carbon atoms = 1.43 and fC1 (PC1

¯ C1 = 3.06 ˚ around the mean height of h A. Due to this non-uniformity, the geometry of carbon atoms forming the hills cannot be directly determined from the XSW results and, therefore, the interpretation of the experimental data is necessarily based on comparison with the DFT model. The DFT model shows hills which somewhat resemble domes (spherical caps), yet with ¯ C1 = 3.09 ˚ a more triangular base and flattened tops. The average height is h A. The topmost atoms are found to be at a height of hmax = 3.53 ˚ A. Combined with the finding of hmin = 2.06 ˚ A from above indicates that the corrugation from DFT is ∆hmax = hmax −hmin = 1.47 ˚ A. H The calculated XSW parameters, using the atoms coordinates from DFT, are PC1 = 1.43 H and fC1 = 0.73. These values match our experimental data almost perfectly. The meaning

of this good agreement goes beyond the determination of the corrugation, it confirms the height distribution of all carbon atoms at hills. Moreover, the good agreement found in our study validates the dispersion corrections used in the DFT to model the physisorbed graphene.

16


Page 16 of 25

Page 17 of 25 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 5: Summary of results, see text. The errors of XSW measurements are given by the same method presented by Mercurio et al. 57

XSW DFT

valleys H H PC2 fC2 hvalley (˚ A) hmin (˚ A) 0.99 ± 0.01 0.86 ± 0.02 2.12 ± 0.03 1.01 0.94 2.17 2.06

hills H H PC1 fC1 ∆h (˚ A) 1.43 ± 0.02 0.72 ± 0.02 1.43 0.73 1.47

Conclusions We have studied the morphology of gr/Ru(0001) by means of x-ray standing wave analysis and DFT calculations. The chemical specificity of XSW is crucial to determine the geometric structure of gr/Ru(0001) in its different regions. The good agreement between the DFT model and the experimental data shows that the chosen unit cell size, the augmented exchange and correlation functional are ideal for describing not only the chemisorbed graphene at valleys, but also the weakly interacting graphene at hills with high accuracy. We find that the mean height of the valley hvalley is 2.17 ˚ A. Regarding the hills, the combination of XSW and DFT is necessary to clarify important aspects of the geometry. The values of hmin and ∆h resulting from this combination are 2.06 ˚ A and 1.47 ˚ A, respectively. Our results are thus able to resolve the uncertainties in the literature and corroborate the LEED I(V) study by Moritz et al. 18 Our structural parameters can serve as input for further studies on gr/Ru(0001).

Acknowledgement This work was supported by the DFG through the project BU2197/4-1 (part of SPP 1459 ‘Graphene’ and Cologne University via the Advanced Postdoc Grant ‘2D materials beyond graphene’. We acknowledge the staff of the I09 beamline for the support. C. C. S. acknowledges funding via CAPES Foundation, Ministry of Education of Brazil, Brasilia DF, Zip Code 70.040-020. We thank T. Michely for continuous support. We also acknowledge the computing resources from the Swiss National Supercomputer Centre. 17



References (1) Coraux, J.; N’Diaye, A. T.; Engler, M.; Busse, C.; Wall, D.; Buckanie, N.; Meyer zu Heringdorf, F.-J.; van Gastel, R.; Poelsema, B.; Michely, T. Growth of Graphene on Ir(111). New J. Phys. 2009, 11, 023006. (2) Joshi, S.; Ecija, D.; Koitz, R.; Iannuzzi, M.; Seitsonen, A. P.; Hutter, J.; Sachdev, H.; Vijayaraghavan, S.; Bischoff, F.; Seufert, K.; Barth, J. V.; Auwärter, W. Boron Nitride on Cu(111): An Electronically Corrugated Monolayer. Nano Lett. 2012, 12, 5821–5828. ˇ (3) Miwa, J. A.; Ulstrup, S.; Sørensen, S. G.; Dendzik, M.; Cabo, A. G.; Bianchi, M.; Lauritsen, J. V.; Hofmann, P. Electronic Structure of Epitaxial Single-Layer MoS2 . Phys. Rev. Lett. 2015, 114, 046802. (4) Marchini, S.; G¨ unther, S.; Wintterlin, J. Scanning Tunneling Microscopy of Graphene on Ru(0001). Phys. Rev. B 2007, 76, 075429. (5) Sutter, P. W.; Flege, J.-I.; Sutter, E. A. Epitaxial Graphene on Ruthenium. Nat. Mater. 2008, 7, 406–411. (6) Donner, K.; Jakob, P. Structural Properties and Site Specific Interactions of Pt with the Graphene/Ru(0001) Moiré Overlayer. J. Chem. Phys. 2009, 131, 164701. (7) Mao, J.; Zhang, H.; Jiang, Y.; Pan, Y.; Gao, M.; Xiao, W.; Gao, H.-J. Tunability of Supramolecular Kagome Lattices of Magnetic Phthalocyanines Using Graphene-Based Moiré Patterns as Templates. J. Am. Chem. Soc. 2009, 131, 14136–14137. (8) Vázquez de Parga, A. L.; Calleja, F.; Borca, B.; Passeggi, M. C. G.; Hinarejos, J. J.; Guinea, F.; Miranda, R. Periodically Rippled Graphene: Growth and Spatially Resolved Electronic Structure. Phys. Rev. Lett. 2008, 100, 056807. (9) Katsiev, K.; Losovyj, Y.; Zhou, Z.; Vescovo, E.; Liu, L.; Dowben, P. A.; Good-

18


Page 18 of 25

Page 19 of 25 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


man, D. W. Graphene on Ru(0001): Evidence for Two Graphene Band Structures. Phys. Rev. B 2012, 85, 195405. (10) Armbrust, N.; G¨ udde, J.; Jakob, P.; Höfer, U. Time-Resolved Two-Photon Photoemission of Unoccupied Electronic States of Periodically Rippled Graphene on Ru(0001). Phys. Rev. Lett. 2012, 108, 056801. (11) Maccariello, D.; Al Taleb, A.; Calleja, F.; Vázquez de Parga, A. L.; Perna, P.; Camarero, J.; Gnecco, E.; Far´ıas, D.; Miranda, R. Observation of Localized Vibrational Modes of Graphene Nanodomes by Inelastic Atom Scattering. Nano Lett. 2016, 16, 2–7. (12) Politano, A.; Campi, D.; Stradi, D.; Chiarello, G. Site-dependent Lattice Dynamics in Periodically Rippled Graphene on Ru(0001). Europhys. Lett. 2017, 118, 27007. (13) Politano, A.; Campi, D.; Formoso, V.; Chiarello, G. Evidence of Confinement of the π Plasmon in Periodically Rippled Graphene on Ru(0001). Phys. Chem. Chem. Phys. 2013, 15, 11356–11361. (14) Politano, A.; Slotman, G. J.; Roldn, R.; Chiarello, G.; Campi, D.; Katsnelson, M. I.; Yuan, S. Effect of Moiré Superlattice Reconstruction in the Electronic Excitation Spectrum of Graphene-metal Heterostructures. 2D Mater. 2017, 4, 021001. (15) Preobrajenski, A. B.; Ng, M. L.; Vinogradov, A. S.; M˚ artensson, N. Controlling Graphene Corrugation on Lattice-mismatched Substrates. Phys. Rev. B 2008, 78, 073401. (16) Maccariello, D.; Campi, D.; Taleb, A. A.; Benedek, G.; Faras, D.; Bernasconi, M.; Miranda, R. Low-energy Excitations of Graphene on Ru(0001). Carbon 2015, 93, 1– 10.

19



(17) Voloshina, E.; Dedkov, Y. Atomic Force Spectroscopy and Density-functional Study of Graphene Corrugation on Ru(0001). Phys. Rev. B 2016, 93, 235418. (18) Moritz, W.; Wang, B.; Bocquet, M.-L.; Brugger, T.; Greber, T.; Wintterlin, J.; G¨ unther, S. Structure Determination of the Coincidence Phase of Graphene on Ru(0001). Phys. Rev. Lett. 2010, 104, 136102. (19) Borca, B.; Barja, S.; Garnica, M.; Minniti, M.; Politano, A.; Rodriguez-Garc´ıa, J. M.; Hinarejos, J. J.; Far´ıas, D.; Vázquez de Parga, A. L.; Miranda, R. Electronic and Geometric Corrugation of Periodically Rippled, Self-nanostructured Graphene Epitaxially Grown on Ru(0001). New J. Phys. 2010, 12, 093018. (20) Taleb, A. A.; Anemone, G.; Miranda, R.; Far´ıas, D. Characterization of Interlayer Forces in 2D Heterostructures Using Neutral Atom Scattering. 2D Mater. 2018, 5, 045002. (21) Martoccia, D.; Björck, M.; Schlep¨ utz, C. M.; Brugger, T.; Pauli, S. A.; Patterson, B. D.; Greber, T.; Willmott, P. R. Graphene on Ru(0001): a Corrugated and Chiral Structure. New J. Phys. 2010, 12, 043028. (22) Martoccia, D.; Willmott, P. R.; Brugger, T.; Björck, M.; G¨ unther, S.; Schlep¨ utz, C. M.; Cervellino, A.; Pauli, S. A.; Patterson, B. D.; Marchini, S.; Wintterlin, J.; Moritz, W.; Greber, T. Graphene on Ru(0001): A 25 × 25 Supercell. Phys. Rev. Lett. 2008, 101, 126102. (23) Jiang, D.-E.; Du, M.-H.; Dai, S. First Principles Study of the Graphene/Ru(0001) Interface. J. Chem. Phys. 2009, 130, 074705. (24) Stradi, D.; Barja, S.; D´ıaz, C.; Garnica, M.; Borca, B.; Hinarejos, J. J.; SánchezPortal, D.; Alcam´ı, M.; Arnau, A.; Vázquez de Parga, A. L.; Miranda, R.; Mart´ın, F. Role of Dispersion Forces in the Structure of Graphene Monolayers on Ru Surfaces. Phys. Rev. Lett. 2011, 106, 186102. 20


Page 20 of 25

Page 21 of 25 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(25) Wang, B.; Bocquet, M.-L.; Marchini, S.; G¨ unther, S.; Wintterlin, J. Chemical Origin of a Graphene Moire Overlayer on Ru(0001). Phys. Chem. Chem. Phys. 2008, 10, 3530–3534. (26) Iannuzzi, M.; Kalichava, I.; Ma, H.; Leake, S. J.; Zhou, H.; Li, G.; Zhang, Y.; Bunk, O.; Gao, H.; Hutter, J.; Willmott, P. R.; Greber, T. Moiré Beatings in Graphene on Ru(0001). Phys. Rev. B 2013, 88, 125433. (27) Grimme, S. Semiempirical GGA Type Density Functional Constructed with a Long Range Dispersion Correction. J. Comput. Chem. 2006, 27, 1787–1799. (28) Vydrov, O. A.; Van Voorhis, T. Nonlocal van der Waals Density Functional Made Simple. Phys. Rev. Lett. 2009, 103, 63004–63007. (29) Zegenhagen, J. Surface Structure Determination with X-ray Standing Waves. Sur. Sci. Rep. 1993, 18, 202–271. (30) Woodruff, D. P. Surface Structure Determination Using X-ray Standing Waves. Rep. Prog. Phys. 2005, 68, 743. (31) Busse, C.; Lazić, P.; Djemour, R.; Coraux, J.; Gerber, T.; Atodiresei, N.; Caciuc, V.; Brako, R.; N’Diaye, A. T.; Bl¨ ugel, S.; Zegenhagen, J.; Michely, T. Graphene on Ir(111): Physisorption with Chemical Modulation. Phys. Rev. Lett. 2011, 107, 036101. (32) Runte, S.; Lazić, P.; Vo-Van, C.; Coraux, J.; Zegenhagen, J.; Busse, C. Graphene Buckles under Stress: An X-ray Standing Wave and Scanning Tunneling Microscopy Study. Phys. Rev. B 2014, 89, 155427. (33) Sforzini, J.; Nemec, L.; Denig, T.; Stadtm¨ uller, B.; Lee, T.-L.; Kumpf, C.; Soubatch, S.; Starke, U.; Rinke, P.; Blum, V.; Bocquet, F. C.; Tautz, F. S. Approaching Truly Freestanding Graphene: The Structure of Hydrogen-Intercalated Graphene on 6H−SiC(0001). Phys. Rev. Lett. 2015, 114, 106804. 21



(34) Sforzini, J.; Hapala, P.; Franke, M.; van Straaten, G.; Stöhr, A.; Link, S.; Soubatch, S.; ˇ Jel´ınek, P.; Lee, T.-L.; Starke, U.; Svec, M.; Bocquet, F. C.; Tautz, F. S. Structural and Electronic Properties of Nitrogen-Doped Graphene. Phys. Rev. Lett. 2016, 116, 126805. (35) Farwick zum Hagen, F. H. et al. Structure and Growth of Hexagonal Boron Nitride on Ir(111). ACS Nano 2016, 10, 11012–11026. (36) Schwarz, M.; Riss, A.; Garnica, M.; Ducke, J.; Deimel, P. S.; Duncan, D. A.; Thakur, P. K.; Lee, T.-L.; Seitsonen, A. P.; Barth, J. V.; Allegretti, F.; Auwärter, W. Corrugation in the Weakly Interacting Hexagonal-BN/Cu(111) System: Structure Determination by Combining Noncontact Atomic Force Microscopy and X-ray Standing Waves. ACS Nano 2017, 11, 9151–9161. (37) Br¨ ulke, C.; Heepenstrick, T.; Humberg, N.; Krieger, I.; Sokolowski, M.; Weiß, S.; Tautz, F. S.; Soubatch, S. Long Vertical Distance Bonding of the Hexagonal Boron Nitride Monolayer on the Cu(111) Surface. J. Phys. Chem. C 2017, 121, 23964–23973. (38) Blowey, P. J.; Rochford, L. A.; Duncan, D. A.; Warr, D. A.; Lee, T.-L.; Woodruff, D. P.; Costantini, G. Probing the Interplay Between Geometric and Electronic Structure in a Two-dimensional K-TCNQ Charge Transfer Network. Faraday Discuss. 2017, 204, 97–110. (39) CP2k Developers Group under the Terms of the GNU General Public Licence; see http://www.cp2k.org. 2017. (40) Hutter, J.; Iannuzzi, M.; Schiffmann, F.; VandeVondele, J. cp2k: Atomistic Simulations of Condensed Matter Systems. Wiley Interdiscip. Rev.: Comput. Mol. Sci. 2014, 4, 15– 25. (41) Lippert, G.; Hutter, J.; Parrinello, M. A Hybrid Gaussian and Plane Wave Density Functional Scheme. Mol. Phys. 1997, 92, 477–487. 22


Page 22 of 25

Page 23 of 25 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(42) VandeVondele, J.; Krack, M.; Mohamed, F.; Parrinello, M.; Chassaing, T.; Hutter, J. Quickstep: Fast and Accurate Density Functional Calculations Using a Mixed Gaussian and Plane Waves Approach . Comput. Phys. Commun. 2005, 167, 103–128. (43) VandeVondele, J.; Hutter, J. Gaussian Basis Sets for Accurate Calculations on Molecular Systems in Gas and Condensed Phases. J. Chem. Phys. 2007, 127, 114105. (44) Goedecker, S.; Teter, M.; Hutter, J. Separable Dual-Space Gaussian Pseudopotentials. Phys. Rev. B 1996, 54, 1703–1710. (45) Iannuzzi, M.; Tran, F.; Widmer, R.; Dienel, T.; Radican, K.; Ding, Y.; Hutter, J.; Groning, O. Site-selective Adsorption of Phthalocyanine on h-BN/Rh(111) Nanomesh. Physical Chemistry Chemical Physics 2014, 16, 12374–12384. (46) Perdew, J.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865–3868. (47) Doniach, S.; Sunjic, M. Many-electron Singularity in X-ray Photoemission and X-ray Line Spectra from Metals. J. Phys. C: Solid State Phys. 1970, 3, 285. (48) Shirley, D. A. High-Resolution X-Ray Photoemission Spectrum of the Valence Bands of Gold. Phys. Rev. B 1972, 5, 4709–4714. ˇ (49) Despoja, V.; Sunji´ c, M. Theory of Core-level Spectra in X-ray Photoemission of Pristine and Doped Graphene. Phys. Rev. B 2013, 88, 245416. (50) Woodruff, D. Non-dipole Effects in High-energy Photoelectron Emission; Identification and Quantification Using X-ray Standing Waves. Nucl. Instr. Meth. Phys. Res. A 2005, 547, 187–195. (51) Lee, J.; Fisher, C.; Woodruff, D.; Roper, M.; Jones, R.; Cowie, B. Non-dipole Effects in Photoelectron-monitored X-ray Standing Wave Experiments: Characterisation and Calibration. Surf. Sci. 2001, 494, 166–182. 23



(52) Schreiber, F.; Ritley, K.; Vartanyants, I.; Dosch, H.; Zegenhagen, J.; Cowie, B. Nondipolar Contributions in XPS Detection of X-ray Standing waves. Surf. Sci. 2001, 486, L519–L523. (53) Trzhaskovskaya, M.; Nefedov, V.; Yarzhemsky, V. Photoelectron Angular Distribution Parameters for Elements Z=1 to Z=54 in the Photoelectron Energy Range 100-5000 eV. Atomic Data and Nuclear Data Tables 2001, 77, 97–159. (54) Michalk, G.; Moritz, W.; Pfn¨ ur, H.; Menzel, D. A Leed Determination of the Structures √ √ of Ru(001) and of CORu(001) - 3 × 3 R30◦ . Surf. Sci. 1983, 129, 92–106. (55) Zegehagen, J.; Kaimirov, A. The X-Ray Standing Wave Technique; World Scientific, 2013; Chapter 1, pp 3–35. (56) Zhang, H.; Fu, Q.; Cui, Y.; Tan, D.; Bao, X. Growth Mechanism of Graphene on Ru(0001) and O2 Adsorption on the Graphene/Ru(0001) Surface. J. Phys. Chem. C 2009, 113, 8296?8301. (57) Mercurio, G.; Bauer, O.; Willenbockel, M.; Fairley, N.; Reckien, W.; Schmitz, C. H.; Fiedler, B.; Soubatch, S.; Bredow, T.; Sokolowski, M.; Tautz, F. S. Adsorption Height Determination of Nonequivalent C and O Species of PTCDA on Ag(110) Using X-ray Standing Waves. Phys. Rev. B 2013, 87, 045421.

24


Page 24 of 25

Page 25 of 25 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Graphical TOC Entry

25


Valleys and Hills of Graphene on Ru(0001) - ACS Publications

Recommend Documents