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Probing the Stress Effect on the Electronic Structure of Graphite by Resonant Raman Spectroscopy Miriam Peña-Alvarez, Elena del Corro, Valentín García Baonza, and Mercedes Taravillo J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/jp505730v • Publication Date (Web): 08 Oct 2014 Downloaded from http://pubs.acs.org on October 14, 2014

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The Journal of Physical Chemistry C 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.

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The Journal of Physical Chemistry

Probing the Stress Effect on the Electronic Structure of Graphite by Resonant Raman Spectroscopy

Miriam Peña-Álvarez, Elena del Corro, Valentín G. Baonza, and Mercedes Taravillo* MALTA CONSOLIDER Team, Departamento de Química Física I, Facultad de Ciencias Químicas, Universidad Complutense de Madrid, 28040-Madrid, Spain ABSTRACT In this work we report the dispersive behavior of the most characteristic Raman contributions of highly oriented pyrolytic graphite at biaxial stresses up to 10 GPa, using a moissanite anvil cell as pressure device. The stress coefficients and the relative Grüneisen parameters are obtained for two different excitation wavelengths, 488.0 and 532.0 nm. We observe for some of the Raman contributions different stress slopes depending on the excitation energy (2.54 and 2.33 eV). Specifically, the stress coefficients vary with the excitation wavelength for those contributions originated by resonant processes. Additionally, we have carried out selected experiments at lower excitation energies of 2.18 and 1.96 eV. Finally, the analysis of the dispersive behavior of strained graphite allows us to qualitatively estimate the influence of the stress on the electronic structure of graphite, associating the changes in the dispersion with stress to an energy gap closure. Keywords: High Pressure, dispersion, Grüneisen parameters

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*[email protected]; MALTA CONSOLIDER Team, Departamento de Química Física I, Facultad de Ciencias Químicas, Universidad Complutense de Madrid, 28040-Madrid, Spain; Phone: 34 91 394 4139


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1. INTRODUCTION It has been demonstrated that Raman spectroscopy with different excitation laser energies combined with theory can be used to provide valuable information about the electronic structure and phonon dispersion relations of carbon materials such as graphite,1,2 carbon nanotubes (CNTs),3,4 and graphene.5,6 On the other hand, analysis of the induced changes by strain in the behavior of materials is commonly used as a probe of their properties, for instance it has been undertaken by subjecting graphene to both compressive and tensile stress under uniaxial,7 biaxial,8 and hydrostatic conditions.9-11 These studies reflect how the substrate affects the strain behavior of graphene; it has been suggested that the pure mechanical response of graphene and graphite is essentially the same and, in the absence of additional perturbations, the measured vibrational frequencies provide a correct estimation of the strain.10,12 However, it is clear that due to the resonant nature of the Raman spectrum of graphene,13 to obtain reliable conclusions based on Raman measurements is convenient to carry out this analysis by using different excitation energies.14 Thus, because graphite possesses the same resonant nature than graphene does,15,16 analyzing the strain effect on graphite with different excitation energies seems not only interesting, but desirable. To the best of our knowledge, this work may be the first attempt. So, by analyzing the dispersive behavior of the Raman signatures of graphite at different stresses we have been able to estimate qualitatively the effect of the stress on its electronic structure. High-pressure studies on graphite are largely focused on the phase transition to a new super-hard phase around 17 GPa;17,18 whose exact nature is still under debate.19-23 Consequently, few studies exist about the pressure-induced changes in the Raman spectrum of graphite at moderate pressures.24 This is partly due to the employment of diamond anvil cells that prevent, at moderate pressures, the observation of one of the most ACS Paragon Plus Environment

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important signatures Raman of graphite, the defect-related D band. This band is observed for carbon materials (graphene, carbon nanotubes, etc) around 1350 cm−1, so the coincidence with the intense Raman signature of diamond used as anvil has prevented in high pressure studies its clear analysis under compressive stress. Regarding the stressinduced changes on the electronic structure of carbon materials, it is known that strain dramatically modifies it in CNTs.25-27 However, very little is known about the electronic properties of strained graphene. Because of all the experimental difficulties that these experiments involve, in this field most of the revealing results come from theoretical analysis,28 and few experimental studies have been described so far.29,30 In graphite, there are only few studies about how stress affect its electronic structure,31-33 remaining some issues still unsolved. Recently, we have carried out Raman spectroscopy measurements of graphite subjected to biaxial strain,12,34-36 using a moissanite anvil cell as pressure device, with the aim of examining the effect of the stress on the defect-related bands. Suitability of our device to research carbon materials at high pressures was demonstrated with these results. Here, we introduce a first approach to the understanding of the stress effect on the graphite electronic structure. We address this issue by Raman measurements of compressed graphite, using two different excitation wavelengths: 488.0 and 532.0 nm. We obtain for each Raman feature analyzed, different stress trends which vary depending on the used excitation line. These results provide us information about the stress-induced variations in the frequency dispersion of some Raman features allowing us to suggest a probable scenario to explain how the electronic bands involved in the resonant processes are affected by stress. In addition, because of the close electronic structures of graphene and graphite,37 our results may have significant implications in the researches of this challenging area.


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2. EXPERIMENTAL SECTION Our experimental setup is based on a Moissanite Anvil Cell (MAC) coupled to a microRaman spectrometer, which has already been described in the literature.38 Raman measurements were performed using an air-cooled argon ion laser, a Spectra-Physics solid state laser and a Helium–Neon laser, operating at 488.0, 532.0 and 632.8 nm, respectively. The device is equipped with a 10x Mitutoyo long working distance objective coupled to a 10x Navitar zoom system and focused onto the slit of an ISA HR460 monochromator with a grating of 600 grooves mm−1 and a liquid nitrogen cooled CCD detector (ISA CCD3000, 1024 – 256 pixels). Spectra were measured with a spectral resolution of about 2-3 cm−1 and calibrated with a standard neon emission lamp. The MAC is mounted on a xyz stage, which allows us to move the sample with an accuracy of 1 µm. The typical sampling area was about 1-2 µm in diameter. Some other measurements were performed with a triple monochromator spectrometer (DILOR) equipped with an Argon/Krypton laser operating at 568.2 nm. Highly oriented pyrolytic graphite (HOPG) discs (3 mm diameter, 60 µm thickness) were purchased from SPI, from which small flakes were cut to build our samples. Moissanite anvils with culets of about 380 µm of diameter were used. The samples are directly placed between the anvils, without any gasket and stress transmitting medium, as depicted in Figure 1, reaching maximum stresses around 8-10 GPa, in different experimental runs. As shown in this scheme, with this configuration we obtain a stress profile across the sample in which stress decreases as we move out from the center of the sample, approximately the nearest contact point between the anvils.34 Spectra were measured across the sample following two perpendicular directions each 20 µm steps. Several runs were performed at different values of the maximum stress with 488.0 and 532.0 nm excitation wavelengths, in order to check the reproducibility of our


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measurements and to confirm that the observed behavior does not depend on the maximum stress generated on the sample. Selected experiments were carried out in new specimens by using 568.2 and 632.8 nm excitation wavelengths. With the employed configuration no stress marker could be used, as it would cause bridging between the anvils, therefore the most intense feature of Raman spectrum of graphite (G band) is used as stress indicator,24,39 analogously to previous related works.34-36 This band appearing at around 1580 cm−1, it is conveniently used as reference due to the fact that it displays almost no dispersive behavior with the different excitation wavelengths.40-42 Regarding the analysis of the data, to get the spectra of the strained graphite without any anvil contribution, the coincident second order Raman features of the anvils were subtracted from all the spectra, following the methodology described elsewhere.34 A second derivative analysis of the spectra was used to obtain the Raman frequencies of the D, G, D´, D+D´´, D+D´ and 2D´ bands. It must to be mentioned that, with the spectra taken with the 568.2 and 632.8 nm excitation wavelengths, we have only obtained the frequencies of the G, D and 2D bands so, the weaker bands (D´, D+D´´, D+D´ and 2D´) have not been determined at these energies. Regarding on the spectral region of 2D band, we have carried out a combined analysis between second derivative followed by fits to two Lorentzian functions centered at the frequencies obtained from the analysis of the second derivative of the spectrum; this was performed to obtain more reliable values of their frequencies. 3. RESULTS AND DISCUSSION As mentioned before, when compressing graphite in our experimental device a stress profile is generated across the sample. In Figures 2a and 2b we show the Raman spectra of a compressed graphite sample measured along one of the radius, using the 532.0 and 488.0 nm excitation wavelengths; spectra at almost the same stress values, between 0 and 8 GPa, ACS Paragon Plus Environment

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are depicted. In Figures 2c and 2d we also show spectra obtained with the 568.2 and 632.8 nm excitation wavelengths at selected stress values. The intensities of all the spectra have been normalized to the corresponding 2D band height. This feature (~2700 cm−1) is the second most prominent feature in graphite samples.43 It consists on a convolution of an infinite number of peaks in a narrow spectral range where only two features can be resolved, labeled here as 2D1 and 2D2 bands.15,43-45 As the intensity of this feature is not dependent on the excitation wavelength,46,47 such normalization seems convenient. Concerning the Raman shifts of the different contributions, in Figure 2 we observe how for a certain excitation line the whole spectrum redshifts as we move to larger radii where the stress decreases. A stress profile across the sample is presented as is depicted in Figure 3, where we have plotted the shifts of the G and D bands as a function of the radius for 488.0 and 532.0 nm wavelengths. This Gaussian like distribution of stress resembles the stress profile generated when the anvils are in direct contact in the absence of sample.48 It is interesting to notice how, when reaching the same stress value, the D band is more sensitive to stress than the G band. For instance, with the 532.0 line and for an effective stress of about 9 GPa, the D band upshifts about 60 cm−1 while the G band does around 40 cm−1. This larger shift of the D band is in agreement with the reported larger average Grüneisen parameter in the compressive regime.8 Moreover, this difference is more significant with the 488.0 nm line, since the spectra at about 10 GPa present an upshift of the D band around 80 cm−1, while the G band does 40 cm−1. These results also evidence the non-dispersive behavior of the G band, and the dispersion of the D band. Although they are not shown here, similar stress profiles are depicted by using the other contributions studied. In the following we are going to describe our experimental results regarding the changes induced by stress over the D and G band intensities, both referred to the 2D band


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intensity. D band is associated with the existence of defects,15,16 so consequently its intensity is directly related to its concentration. However, the D band intensity also depends on the excitation wavelength,49 and a barely variation with pressure in hydrostatic experiments has been observed.50 In our experiments this quantity increases in a no monotonically fashion when we move to higher radius values out from the center, even though the highest stress is achieved just right there. This enhancement of the D band is due to the apparition of shear stress components exerted by the anvils as we move away from the location where the gems are in closest contact and consequently where the stress is higher.48 Regarding the non-dispersive G band with different excitation lines, whose intensity is not related with defects but it depends on the square of excitation wavelength,51 we can observe in Figure 2 that for a given excitation line, the G band intensity (referred to that of the 2D band) increases with the stress, at least for the values achieved in this work, about 12 GPa. Because the coincidental frequency range between the G band and the also defects related D’ band, the intensity increase as the defect concentration grows is not so well appreciated as in the D band case. Here it is seen how, as expected,36 the intensity of this band grows parallel with the D band intensity. Similar intensity variations are observed in other resonant defect activated bands as the D+D’’ (~2450 cm−1) and the D+D’ (~2950 cm−1), regardless on the excitation line. In Figure 4 we show the stress evolution of the position of the main Raman contributions for the 488.0 and 532.0 nm excitation lines, i.e., 2.54 and 2.33 eV, respectively. From these results we have estimated the parameters summarized in Table I: the frequency shift with respect to that of the G band, dωi/dωG, the relative Grüneisen parameters, γi/γG, and the stress coefficients, dωi/dσeff. As it was described by Del Corro et al.35 and others,52-54 we observe that all those features in which the D band is involved exhibit larger Grüneisen parameter ratios. Moreover, for those contributions in which the D


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band is not involved, such as 2D’ band, the ratio γ2D’/ γG is smaller than the unity. This corroborates the already described behavior of the γLO, which monotonously decreases as moving away from Γ.53,55 At room conditions, our results of the Figure 4 and Table 1 show the known behavior for the modes under study: with 488 nm excitation wavelength the Raman shifts are higher, except in the D+D’’ band. Our results demonstrate that these trends remain at high stress values up to, at least, 10 GPa. In some modes slight differences in their stress slopes with each excitation line are observed, as it is clear in the D+D’’ band. These results indicate that the energy dispersion changes with stress. We observe that with the 488.0 nm line, such quantities are larger than those obtained with the 532.0 nm line for some bands: D (6%), D’ (4%), 2D1 (8%) and D+D’ (10%). However, for the 2D2 and 2D’ bands differences are almost negligible, while in the case of the D+D’’ band, the slope with 488.0 nm is about 30% lower than with 532.0 nm. The energy dispersion exhibited by a given resonant Raman feature is associated with the slope of the corresponding phonon dispersion curve; so that when different excitation lines are employed, we access to phonons with different wave vectors, q, and therefore different frequency.1,2 Thus, the observed changes in the dispersive behavior with stress must be attributed to changes in both the phonon dispersion35 and the electronic curves,32 which promote alterations in the resonance conditions. Unfortunately, so far there are few studies about how stress affects the dispersive behavior of the resonant Raman bands and our results are hard to be compared. In the following we will analyze our results in a wider energy range. In Figure 5a we show the Raman spectrum of graphite, in the spectral region of the 2D band, at three different pressures, measured with the four excitation lines: 488.0, 532.0, 568.2, and 632.8 nm. For this Raman feature, we can clearly appreciate how the frequency difference of the maxima between the red and blue spectra lengthens. As was mentioned, lorentzian fits


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were carried out to obtain the above labeled 2D1 and 2D2 features that form the 2D band. In Figures 5 we have plotted separately some of these results for each wavelength. Figure 5d shows the 2D1 band position values as a function of the excitation energy for increasing stress values. It is observed that its dispersion considerably increases with stress, ranging from 70 cm−1eV−1 at 0.4 GPa, to 104 cm−1eV−1 at 5.5 GPa. In Figure 6 we have depicted the energy dispersion, defined as [(ω488-ω532)/∆E], for several bands. To estimate such quantities, we first calculate the Raman shift of each band for 488 and 532 nm excitation lines, and then (ω488-ω532) is divided by the energy difference (∆E = 0.21 eV). Since experimental values with both excitation energies for exactly the same stress conditions are not available, our 488.0 nm experimental Raman shifts have been fitted to a linear function, which enables us to estimate ω488 at any stress value within our experimental stress range. With this analysis we are able to evaluate the effect of stress on the energy dispersion for each Raman contribution. On regards to the D band, we observe in Figure 6a that its dispersion increases from about (40 ± 10) cm−1eV−1,15,16,56 at room conditions to (70 ± 10) cm−1eV−1 at 10 GPa. To validate that with other excitation energies our prediction of the dispersion at high stress values works, we have interpolated, from data in Figure 6a, the dispersion for three selected stress values. We have plotted in Figure 7a our predictions as a function of the excitation energy. It is observed that the comparison between our predictions and the experimental results (measured with 488.0, 532.0, and 632.8 nm excitation energies) is excellent, at least in this stress range. Implications of these observations in the stressinduced changes in phonon branches and electronic curves are described next. The D band is originated by a resonant process involving one iTO phonon around the K point.35,57 According with previous works we can assume a homogeneous upshift of the phonon branches with stress, where the curvature of the branches remains unaltered.35,53 Therefore, ACS Paragon Plus Environment

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the changes observed in the dispersion behavior of the D band with stress can be directly related to a modification in the slope of the involved electronic bands in the vicinity of the K point (so that, in the Fermi velocity around the K point) as already anticipated in the literature for strained graphite and graphene.31,28 Then, the dispersion increase with stress must be due to a closing in the gap energy of the electronic states involved in the resonance. The suggested mechanism has been schematized in Figure 7b, where the electronic and phonon branches are plotted at ambient and high stress conditions (around 10 GPa). In the bottom part of this scheme, we plot exclusively the π and π* graphite electronic states. Curves at room conditions have been taken from Ref. [58], while the stressed ones have been qualitatively depicted based on our results and those of Refs. [28] and [32]. Our predictions at high stresses are referred to graphite, although an analogue effect would be expected in graphene.37 In the upper part of this scheme, for simplicity, we represent just the iTO phonon branch, which is analogous for graphite and graphene.53 Again, the branch at the room conditions is based on data from Refs. [2] and [59], while the stressed one was taken from Ref. [35]. Red and blue arrows represent the excitation laser lines of 488.0 and 632.8 nm, respectively (light and dark colors stand for room and stress conditions, respectively). As schematized, stress induces the approach between the π and π* electronic states, so that the resonance takes place at larger q values and therefore, since the iTO phonon branch has a positive slope as moving from K to Γ points, the dispersion of the D band increases with stress. We assume that the energy gap remains closed under our biaxial stress conditions, since previous studies state that the band gap opening is only feasible under non-uniform uniaxial strain above 12-17%;60 while we generate lower compressive biaxial strain.12 Considering the behavior of the 2D band at room conditions, in the literature a dispersion of about 95-100 cm−1eV−1 for the maximum of this peak is found.15,56 It is seen


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in Figures 5d and 6e that the dispersion of the 2D1 contribution increases with stress, ranging from (67 ± 15) cm−1eV−1 at room conditions (in agreement with Mafra et al.5) to about (122 ± 20) cm−1eV−1 at 10 GPa. In accordance with the above behavior described for the D band dispersion, this increase seems reliable. On the other hand, the 2D2 contribution depicts a markedly different trend. At ambient conditions, a dispersion of about (74 ± 30) cm−1eV−1 is observed, and it remains almost constant or even shows a slightly decrease with stress, as seen in Figure 6d, reaching (62 ± 30) cm−1eV−1 at 10 GPa. Such intricate behavior evidences once again the complex electronic structure of graphene, which give rise to a 2D band with an unclear origin. Cancado et al. concluded that the 2D2 band is mainly originated by resonance processes involving the π1-π1* bands, whereas the 2D1 accounts for miscellaneous resonant processes in between the π1-π1* and the π2-π2* bands.61 Our results seem to indicate that the effect of stress cannot be considered the same for all the split π-π* electronic bands of graphite. The D’ band is also a Raman feature defect mediated,58 while the 2D’ band, is mediated by two phonons and does not need the existence of defects to be Raman active.13 They are originated by an intra-valley process, involving LO phonons with a small q close to the Γ point of the first Brillouin zone.1,2,62 In Figure 6b we see that D’ band has a dispersive behavior at room conditions of about (18 ± 8) cm−1eV−1, in agreement with previous results.15,56,62 This low dispersion is justified by the small positive slope of the LO phonon branch along the Γ-Κ direction.57 We appreciate that the stress induces a slight increase in the dispersion of D’ band, up to (40 ± 15) cm−1eV−1 at 5 GPa. From that stress value it seems that the dispersion does not increases, but slightly decreases with stress to about (35 ± 15) cm−1eV−1 at 10 GPa. If we consider that the D’ band corresponds to LO phonons in the vicinity of the maximum exhibited by this branch, the observed stress trend can be expected, see Figure 7c. This result is confirmed by the behavior of the 2D’ band


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(see Figure 6f), for which such subtle slope change is easier observed. At room conditions its dispersion is about (32 ± 15) cm−1eV−1, increases to reach a maximum around 5 GPa of about (70 ± 20) cm−1eV−1, and then it slightly decrease to about (50 ± 20) cm−1eV−1 at 10 GPa. Our experiments can be additionally used to confirm the assignment of certain bands with still unclear origin; since, under any stress conditions, the dispersion shown by a combination band has to fit with the sum of the dispersions of the corresponding bands. For instance, the band centered at 2950 cm−1 had been assigned to the (D+G) combination band,63,64 however, Ferrari et al.43 attributed this band to the (D+D’) peak. Because of the G band is not dispersive, if the 2950 cm−1 peak were the (D+G) band, it should show the same dispersion than the D band. However, in Figure 6g it is seen that the increase with the stress of the dispersion -from (58 ± 15) to (120 ± 20) cm−1eV−1 at 10 GPa- is larger than the observed for the D band, while the trend is consistent with a sum of the dispersion rises shown by the D and D’ bands. This supports the correct assignment of this feature as the (D+D´) combination mode. Finally, another remarkable result is the effect of stress on the band centered at around 2450 cm−1. This band is the result of the combination of two defect activated contributions; the D band and the D’’ band around, 1083 cm−1.5,62,63 The D’’ band corresponds to the LA phonon branch along the K-Γ direction, which exhibits a strong negative slope as the wave vector moves away from the K point.5,65 The energy dispersion of the D’’ band has been previously studied and, as expected, it displays a negative value of about −97 cm−1eV−1.5,13,65 As mentioned before, the D band has a positive dispersion at room conditions of about 40 cm−1eV−1. Accordingly, the combination mode (D+D’’) presents also a negative dispersion of about −31 cm−1eV−1 at room conditions.5 Our results depicted in Figure 6c are in excellent agreement with this value. With increasing stress the ACS Paragon Plus Environment

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dispersion strongly decays to about (−124 ± 30) cm−1eV−1 at 10 GPa, due to the higher negative slope of the LA phonon curve57 compared to the positive one of the D peak (see Figure 7b). Lastly, a value for the dispersion of the D’’ band at 10 GPa of −194 cm−1eV−1 can be inferred. 4. CONCLUSIONS The stress dependence of the most relevant graphite Raman features has been analyzed in detail under compressive biaxial stresses up to 10 GPa, This study has been carried out with different excitation wavelengths (from 488.0 to 632.8 nm), which has allowed us to examine the stress effect on the dispersion of the double and triple resonant Raman bands. We have provided a complete set of Grüneisen parameters for the Raman features of graphite obtained with the 488.0 and 532.0 nm excitation lines (2.3-2.5 eV). Some of the stress coefficients have been observed to be slightly different for each excitation wavelength, enabling us to evaluate the effect of stress on the energy dispersion of the main bands. Additionally, we have checked that these experimental differences can be used to extrapolate how stress would affect the frequency of the Raman features when other excitation wavelengths are used, in the energy range between 1.9 -2.3 eV. Our predictions are in excellent agreement with experimental results, at least for stresses up to 7-10 GPa. Future work could be intended to experimentally prove that our predictions are consistent in a larger energy range, 3-4 eV. To our knowledge, these results are the first ones which provide how stress affects the dispersive behavior of the resonant Raman bands in graphite. Even though it is obvious certain scatter of data, it is clear that the stress response is different depending on the excitation wavelength used. Although this issue can be expected, our results are the first experimental ones which support it. Finally, as it has been explained along the work, we associate the changes in the dispersion with stress to an energy gap closure; which moves the resonant processes to larger q values from the K


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point. Therefore, this study represents a new approach to study the graphene electronic properties by means of Raman spectroscopy.

ACKNOWLEDGMENTS We thank Prof. M. A. Pimenta for allowing us to use his DILOR XY Raman spectrometer to take the spectra with the 568.2 nm excitation wavelength. We also thank Prof. J. González for valuable comments. This work was supported by the MINECO through the MALTA Consolider Project CSD2007-00045 and CTQ2012-38599-C02-02. Further financial support was obtained from Comunidad de Madrid and EU through the program QUIMAPRES-S2009/PPQ-1551 program. MPA is grateful to the Spanish Ministerio de Educación, Cultura y Deporte for an FPU grant.


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Page 22 of 41

Table 1. Raman shifts at ambient conditions (ω0), frequency shift with respect to that of the G band (dωi/ dωG), relative Grüneisen parameters (γi/ γG), and stress coefficients (dωi/dσeff) for different bands of graphite measured with 488.0 and 532.0 nm excitation wavelengths. λexc = 532.0 nm Band D G D’ D + D’’ 2D1 2D2 D + D’ 2D’

ω0 (cm−1) dωi/dωG 1349.1 1580.3 1622.2 2455.2 2688.8 2719.2 2944.4 3243.2

1.6 1.0 1.1 1.7 2.3 3.0 2.7 1.9

γi/γG 1.8 1.0 1.1 1.1 1.4 1.7 1.4 0.9

λexc = 488.0 nm dωi/dσeff ω (cm−1) dωi/dωG (cm−1·GPa−1) 0 6.3 4.0 4.5 6.7 9.6 12.0 10.9 7.5

1357.7 1581.1 1625.5 2449.0 2706.6 2739.5 2954.5 3250.5


1.6 1.0 1.2 1.2 2.6 2.9 3.0 1.9

γi/γG 1.9 1.0 1.2 0.8 1.5 1.7 1.6 0.9

dωi/dσeff (cm−1·GPa−1) 6.7 4.0 4.7 4.7 10.4 11.6 12.0 7.5

22

Page 23 of 41

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


FIGURES

Figure 1. Scheme of Raman experiments in a moissanite anvil cell for compressed graphite specimens and stress distribution along a radial path.


23


G

2D1

2D2

Intensity (a.u.) D

σeff(GPa)

r(µm) 2D' 0

D+D'' 8.06

D'

G

(b)

*5 σeff(GPa)

6.80

40

5.83

80

3.17

120

7.31

Intensity (a. u.)

(a)

D+D'

0.02

200

D'

40 80 120 160 D+D'

0.20 −1

Raman Shift (cm ) σeff(GPa)

2D2

Intensity (a.u.)

2D1

5.51

3.33 1.40

3.40 G D D'

D' 0.50

1400 1600 1800

200

1400 1600 1800 2400 2600 2800 3000 3200 3400

(d)

D+D''

r(µm) 2D' 0

D+D''

1.49 D

*8 σeff(GPa)

2D2

3.23

Raman Shift (cm ) G

2D1

5.56

−1

(c)

*7

6.62

160

0.96

1400 1600 1800 2400 2600 2800 3000 3200 3400

Intensity (a.u.)

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

Page 24 of 41

2500 2600 2700 2800 2900 −1

Raman Shift (cm )

1200

1500

1800

0.60 2100

2D1 2D2 D+D'' 2400

2700

3000

−1

Raman Shift (cm )

Figure 2. Raman spectra registered along a radial path in the compressed samples. Color lines indicate the use of different excitation lines: (a) blue (488.0 nm), (b) green (532.0 nm), (c) orange (568.2 nm) and (d) red (632.8 nm). Black figures denote the value of the radius where the 488.0 and 532.0 nm spectra were measured. Stress values (σeff) are plotted in different colors according with the excitation energy used. All the spectra were normalized to the 2D band.


24

9

60

9

40

6

20

3

0

0

0 -3 150 300 Radius (µm)

−1

G band

9

9

40

6

20

3

0

0

0 -3 150 300 Radius (µm)

-300 -150

0

D band

60

3 0

(d)

80

6

20

σeff (GPa)

0

12

∆ωD (cm )

(c)

−1

40

-3 150 300 Radius (µm)

-20 -300 -150

0

σeff (GPa)

-300 -150

12

12

σeff (GPa)

3 0

D band

80

6

20

(b)

12

−1

G band

∆ωD (cm )

(a)

−1

∆ωG (cm )

40

∆ωG (cm )

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


σeff (GPa)

Page 25 of 41

-3 150 300 Radius (µm)

-20 -300 -150

0

Figure 3. Raman shifts (∆ω) of the D and G bands, as a function of the value of the radius where the spectrum was measured, registered with the 488.0 nm line (a, b) and, with the 532.0 nm line (c, d). ∆ω is calculated as ∆ω = ω(σeff) − ω(0), being ω(0) referred as the value at ambient conditions of a pristine sample. σeff represents the effective stress obtained through the G band displacements by using the slope taken from ref. [24].


25


1450

2550

D+D''

−1

−1

ωD'(cm )

1400

D'

ωD+D''(cm )

1700

−1

ωD(cm )

D

1650

1350

2500

2450 1600

3350

2D2

2850

2D'

D+D' ωD+D'(cm )

3300

2D1

2750

−1

−1

−1

2800

ω2D'(cm )

3050

ω2D(cm )

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

Page 26 of 41

3250

2700

3000

2950 3200

0

5

10

0

σeff(GPa)

5

10

σeff(GPa)

0

5

10

σeff(GPa)

Figure 4. Raman shift for the most intense features of the spectra of graphite as a function of the effective stress. Green and blue data correspond to the results obtained with 532.0 and 488.0 nm excitation lines, respectively. Solid green lines (dashed blue) are the linear fits to the 532.0 nm (488.0 nm) data.


26

Page 27 of 41

(a)

(b)

488 nm

532 nm

(c)

Intensity (a.u.)

5.5 GPa

3.4 GPa

0.4 GPa

2600

2800

3000 −1

Raman Shift (cm ) 2800

(d)

2600

5.5 GPa

5.5 GPa

3.4 GPa

3.4 GPa

0.4 GPa

0.4 GPa

2800

3000

2600

−1

568.2 nm

3000 −1

Raman Shift (cm ) (e)

2800

Raman Shift (cm ) (f)

632.8 nm

5.5 GPa 5.5 GPa

2750

3.4 GPa

−1

ω2D1 (cm )

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


3.4 GPa 3.4 GPa

2700 0.4 GPa

2650 1.8

0.4 GPa

0.4 GPa

2.0

2.2

2.4

Eexc (eV)

2.6

2600

2800

3000 −1

Raman Shift (cm )

2600

2800

3000 −1

Raman Shift (cm )

Figure 5. (a) Raman spectra of graphite in the 2D band spectral range at different effective stresses with different excitation lines: 488.0, 532.0, 568.2 and 632.8 nm, represented in blue, green, orange and red, respectively. (b,c,e,f) Lorentzian functions representing 2D1 (light gray) and 2D2 (gray) features, obtained from the fits of this spectral region. (d) Raman shift of the 2D1 band as a function of the excitation energy at: 0.4 (squares), 3.4 (triangles), and 5.5 GPa (circles). Lines represent the linear fits to the data with slopes around 70, 86 and 104 cm−1eV−1, respectively.


27


0 (a)

D

80

80

(b)

D'

(c) -50

40

40 -100

−1

−1

(ω488−ω532 )/∆E (cm eV )

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

Page 28 of 41

0 150

-150

0 (d)

2D2

100

150

(f)

2D'

150

D+D´´

(g)

D+D'

50 0 150

100

100

50

50

(e)

100 50

2D1

0 0

5

σeff(GPa)

10

0

0 0

5

10

σeff(GPa)

0

5

10

σeff(GPa)

Figure 6. Energy dispersion [(ω488.0 − ω532.0)/ ∆Ε] for the most intense features of the spectra of graphite as a function of the effective stress. Values denoted as ω488 are obtained from the linear fits to our 488.0 nm data; ω532 are our experimental data for 532.0 nm. ∆E = E488 – E532 = 0.21 eV. Lines are only guides to the eye.


28

(b)

5.5 GPa

−1

1380

1600

(c)

D (iTO)

−1

−1

Frequency (cm )

(a)

D band

1410

ωD (cm )

−1

55 cm

1400

−1

28 cm

1600

D´ (LO)

1400

1200

1200

10

10

1350

0.4 GPa

1320

Energy (eV)

3.4 GPa Energy (eV)

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


Frequency (cm )

Page 29 of 41

5 0 -5

1.8

2.0

2.2

2.4

2.6

0 -5

-10

Eexc (eV)

5

-10 Μ (D2h)

Κ (D3h)

Γ (D6h)

Μ (D2h)

Κ (D3h)

Γ (D6h)

Figure 7. Raman shift of the D band as a function of the excitation energy at: 0.4 (squares), 3.4 (triangles), and 5.5 GPa (circles). Lines are calculated from the interpolated slope values from Fig 4a at the three selected stress values. (b), (c) Simplified scheme of the of graphite of D (iTO phonon branch) and D’ (LO phonon branch) bands, respectively; electronic states of graphite (π-π*) and phonon dispersion curves along the ΜΚΓ direction. Solid lines are at ambient conditions (Ref. [2], [60], and [61]) and dashed lines are at high stress conditions, around10 GPa (Refs. [35] and [32]). Red and blue arrows represent the excitation energy (488.0 and 632.8 nm). Analogously, color points indicate the involved phonons for each excitation.


29


−1

Frequency (cm )

TABLE OF CONTENTS (TOC) Graphic 1600

10 GPa 0 GPa

D (iTO)

−1

55 cm

1400 −1

28 cm

1200 12

10

Energy (eV)

10 σeff (GPa)

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

Page 30 of 41

8 6 4 2 0 -200 -100 0 100 radius (µm)

200

5 0 -5 -10

Μ (D2h) Κ (D3h)

Γ (D6h)


30

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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


107x141mm (600 x 600 DPI)



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

79x67mm (300 x 300 DPI)


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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


79x68mm (300 x 300 DPI)



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

79x59mm (300 x 300 DPI)


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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


79x63mm (300 x 300 DPI)



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

86x76mm (300 x 300 DPI)


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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


154x88mm (300 x 300 DPI)



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

139x118mm (300 x 300 DPI)


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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


154x93mm (300 x 300 DPI)



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

149x75mm (300 x 300 DPI)


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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


35x28mm (600 x 600 DPI)


Probing the Stress Effect on the Electronic ... - ACS Publications

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