Dispersive soft X-ray absorption fine-structure
1
Dispersive soft X-ray absorption fine-structure spectroscopy in graphite with an attosecond pulse: supplementary material BÁRBARA BUADES1, DOOSHAYE MOONSHIRAM2, THEMISTOKLIS P. H. SIDIROPOULOS 1, IKER LEÓN1, PETER SCHMIDT1, IRINA PI1, NICOLA DI PALO1, SETH L. COUSIN1, ANTONIO PICÓN1,3, FRANK KOPPENS1,4, JENS BIEGERT1,4,* 1ICFO-Institut 2Max
de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain Planck Institute for Chemical Energy Conversion, Stiftstr. 34-36, D-45470, Mülheim an der Ruhr, Germany
3Grupo
de Investigación en Aplicaciones del Láser y Fotónica, Departamento de Física Aplicada, University of Salamanca, E-37008 Salamanca, Spain 4ICREA,
Pg. Lluis Companys 23, 08010 Barcelona, Spain * Corresponding author: [email protected] Published 25 April 2018
This document contains supplementary information to “Dispersive soft X-ray absorption finestructure spectroscopy in graphite with an attosecond pulse,” https://doi.org/10.1364/OPTICA.5.000502. It contains details of the experimental methods, the sample preparation and the simulations with a brief description of the software used for the data analysis and a detailed extraction of the results.
1. EXPERIMENTAL METHODS Soft X-ray attosecond pulses are produced by high harmonic generation (HHG) driven by CEP stable 12 fs (1.8-cycle), 1850 nm pulses at a repetition rate of 1 kHz [1]. These pulses are derived from the 7 mJ, 40 fs output of a Ti:Sapphire system which is frequency converted to 1850 nm in a high-energy TOPAS (Light Conversion). Afterwards, the pulses nonlinearly propagate in a hollow core fibre filled with 1.5 bar of argon, and are chirp compensated with bulk material [1–3]. The resulting sub-2-cycle pulses at 1850 nm are focused using a 100-mm focal length mirror to a peak intensity of 0.5 PW/cm2 to generate high harmonic radiation. The exact setup and conditions for HHG are described in [4,5]. The emerging soft X-ray attosecond pulse [6] is focused using an ellipsoid mirror at 2 degree grazing incidence onto the 95nm graphite sample. A 100-nm thin aluminium foil is placed along the beam propagation to remove any remaining fundamental radiation. The transmitted radiation is spectrally resolved with a homebuilt spectrograph consisting of a flat-field imaging grating (Hitachi, 2400 lines/mm) and a Peltier-cooled, back-illuminated charge-coupled device camera (PIXIS-XO-2048B, Princeton Instruments).
A. Soft X-ray attosecond pulse graphite response Figure Fig. S1 shows the transmitted signal, S, measured through the 95-nm graphite sample that rests on a 50 nm Si3N4 membrane together with the reference signal, S 0, measured through a 50 nm Si3N4 membrane.
Fig. S1. CEP-controlled soft X-ray attosecond pulses generated in helium (8.25 bar). The blue curve indicates the detected spectral photon counts/s of the reference signal, S0, after propagating the SXR beam through a Si3N4 50 nm membrane. The red curve
2
accounts for the transmitted signal, S, through a 95-nm graphite flake resting on a 50-nm Si3N4 membrane. This signal shows XANES features at 284 eV and EXAFS oscillations up to 200 eV above the absorption edge. Both plots are the average over 6 spectra taken with 10 second integration time. The strong S0 spectral depletion at the carbon K-shell edge arises from the absorption of hydrocarbons on the surface of the Si 3N4 membrane.
Here, XANES measurements shown in the main manuscript in Fig. 2 as function of the incident angle are compared with published data. Table S1 show excellent agreement with published values. Table S1. Relative peak intensity of (1𝑠 → 𝜋*)/(1𝑠 → 𝜎∗ ) transition as a function of the incidence angle compared with values in the literature. Incidence Total Scanning XANES angle Electric Transmission shown in Yield [7] Microscopy [8] Fig.1 00 0.03 0.01 0.02 0.02 200 0.25 0.19 0.32 0.02 350 0.70 0.62 0.55 0.02 The energy separation between both transitions 1𝑠 → 𝜋* and 1𝑠 → 𝜎∗ is constant and equal to 6.6 eV with is in agreement with Ref. [8].
2. SAMPLE PREPARATION A graphite flake with a homogenous thickness of 95 nm across an area larger than 50 µm in diameter is obtained using a dry-transfer technique similar to [9]. Graphite flakes are exfoliated and deposited on a transparent polymer (Gel-Pak gelfilms). Suitable flakes are identified under an optical microscope and transferred onto a 50-nm Si3N4 membrane using a micromanipulator stage. We note that the graphite samples are never in contact with any wet solvents, therefore minimizing their contamination while maintaining an atomically flat surface. After the transfer, we inspect the uniformity and thickness of the graphite flake by means of optical and atomic force microscopy (AFM). Finally, a pinhole with a diameter of 50 µm is placed onto the sample to define the area of interaction.
3. SIMULATIONS The structure of graphene and the material’s relevant wavefunctions were calculated with the density functional theory (DFT) code BAND [10–12] using a local density approximation (LDA) exchange correlation functional with triple zeta plus double polarization basis set [13]. The EXAFS data processing used the Athena and Artemis software packages [14]. The EXAFS data analysis proceeds along well-established steps [15–19], and included the extraction of the signal from the normalized spectrum by subtracting a spline polynomial, normalization of the signal to the edge jump, and conversion of energy to wave-vector scale. Then the Fourier transform magnitude is determined using a Hanning window function to minimize the effects of data truncation. Scattering amplitudes and phases are calculated with FEFF [20]. A. EXAFS analysis The Athena and Artemis software packages [14] were used for data processing. Data in energy space are pre-edge corrected, normalized, deglitched (if necessary), and background corrected. The processed data are next converted to the photoelectron wave vector (k) space. The electron wave number is defined 𝑘 =
[2𝑚(𝐸 − 𝐸0 )ℏ2 ]1/2 where E0 is the energy origin or the threshold energy. k-space data were truncated near the zero crossings (k = 1.180 to 6.9 Å-1) in EXAFS before Fourier transformation. The kspace data are transferred into the Artemis Software for curve fitting. In order to fit the data, the Fourier peaks are isolated separately, grouped together, or the entire (unfiltered) spectrum was used. The individual Fourier peaks were isolated by applying a Hanning window to the first and last 15% of the chosen range, leaving the middle 70% untouched. Curve fitting is performed using ab initio-calculated phases and amplitudes from the FEFF8 [20] program and ab initio-calculated phases and amplitudes are used in the EXAFS equation [21] −2𝑅
𝜒(𝑘) = 𝑆02 ∑ 𝑗
𝑗 𝑁𝑗 −2𝜎𝑗2 𝑘 2 𝜆𝑗 (𝑘) 𝑓 𝑘, 𝑅 𝑒 𝑒 (𝜋, 𝑗) 𝑘𝑅𝑗2 𝑒𝑓𝑓𝑗
× sin (2𝑘𝑅𝑗 + Φ𝑖𝑗 (𝑘)) ,
(𝑺𝟏)
where Nj is the number of atoms in the jth shell; Rj the mean distance between the absorbing atom and the atoms in the jth shell; 𝑓𝑒𝑓𝑓𝑗 (𝜋, 𝑘, 𝑅𝑗 ) is the ab initio amplitude function for shell j, and the Debye-Waller term exp(−2𝜎𝑗2 𝑘 2) accounts for damping due to static and thermal disorder in absorber-backscatterer distances. The mean free path term exp(2𝑅𝑗 /𝜆𝑗 (𝑘)) reflects losses due to inelastic scattering, where λj(k), is the electron mean free path. The oscillations in the EXAFS spectrum are reflected in the sinusoidal term sin (2𝑘𝑅𝑗 + Φ𝑖𝑗 (𝑘)), where Φ𝑖𝑗 (𝑘) is the ab initio phase function for shell j. This sinusoidal term shows the direct relation between the frequency of the EXAFS oscillations in k-space and the absorber-back scattered distance. 𝑆02 is an amplitude reduction factor. The EXAFS equation (Eq. (S1)) is used to fit the experimental Fourier transformed data (in R-space) as well as unfiltered data (in k-space) using N, 𝑆02 , E0, R, and 𝜎 2 as variable parameters. N refers to the number of coordination atoms surrounding C for each shell. The quality of fit is evaluated by R-factor and the reduced 2 value. The deviation in E0 was required to be less than or equal to 10 eV. An R-factor less than 2% denotes that the fit is good enough whereas an R-factor between 2 and 5% denotes that the fit is correct within a consistently broad model [21]. The reduced 2 value is used to compare the quality of the fit as more absorberbackscatter shells are included to fit the data. A smaller reduced 2 value indicates a better fit. Similar results were obtained from fits done in k, q, and R-spaces. Table S2 shows the chosen variable parameters to minimise the reduced 2for two different fits. One with the inclusion of the second and third neighbour atoms and a second one with all neighbouring shells taken individually. The second fit with taking individually each neighbour shell improves the EXAFS fit since it has a smaller reduced 2 parameter. The amplitude reduction factor, 𝑆02 is fixed to 1 and the fit is carried out between 0.75 Å and 4 Å. Table S2. EXAFS Fit parameters of Graphite. Fit Shell R (Å) E0(eV) 2 N 1 C-C1, 3 1.64(3) 1.47 0.0161 C-C2,3, 9 2.95(5) 0.0109 C-C4, 6 4.04(7) 0.0144 2 C-C1,3 1.66(4) 2.97 0.0219 C-C2,6 2.58(12) 0.0353 C-C3,3 2.92(3) 0.0289 C-C4,6 4.01(10) 0.0118
R-factor
2 Reduced
0.024
315
0.009
195
3
The amplitude reduction factor, 𝑆02 was fixed to 1. The fit was carried out between 0.75 - 4 Å. R error bars to 100th of Å.
REFERENCES 1. S. L. Cousin, F. Silva, S. Teichmann, M. Hemmer, B. Buades, and J. Biegert, "High-flux table-top soft x-ray source driven by sub-2-cycle, CEP stable, 185-μm 1-kHz pulses for carbon K-edge spectroscopy," Opt. Lett. 39, 5383–5386 (2014). 2. N. Ishii, K. Kaneshima, K. Kitano, T. Kanai, S. Watanabe, and J. Itatani, "Carrier-envelope phase-dependent high harmonic generation in the water window using few-cycle infrared pulses," Nat. Commun. 5, 3331 (2014). 3. B. E. Schmidt, P. Béjot, M. Giguère, A. D. Shiner, C. Trallero-Herrero, E. Bisson, J. Kasparian, J.-P. Wolf, D. M. Villeneuve, J.-C. Kieffer, P. B. Corkum, and F. Légaré, "Compression of 1.8 μm laser pulses to sub two optical cycles with bulk material," Appl. Phys. Lett. 96, 121109 (2010). 4. S. M. Teichmann, F. Silva, S. L. Cousin, M. Hemmer, and J. Biegert, "0.5-keV Soft X-ray attosecond continua," Nat. Commun. 7, 11493 (2016). 5. F. Silva, S. M. Teichmann, S. L. Cousin, M. Hemmer, and J. Biegert, "Spatiotemporal isolation of attosecond soft X-ray pulses in the water window," Nat. Commun. 6, 6611 (2015). 6. S. L. Cousin, N. Di Palo, B. Buades, S. M. Teichmann, M. Reduzzi, M. Devetta, A. Kheifets, G. Sansone, and J. Biegert, "Attosecond Streaking in the Water Window: A New Regime of Attosecond Pulse Characterization," Phys. Rev. X 7, 41030 (2017). 7. R. A. Rosenberg, P. J. Love, and V. Rehn, "Polarization-dependent C(K) near-edge x-ray-absorption fine structure of graphite," Phys. Rev. B 33, 4034 (1986). 8. J. A. Brandes, G. D. Cody, D. Rumble, P. Haberstroh, S. Wirick, and Y. Gelinas, "Carbon K-edge XANES spectromicroscopy of natural graphite," Carbon 46, 1424–1434 (2008). 9. A. Castellanos-Gomez, M. Buscema, R. Molenaar, V. Singh, L. Janssen, H. S. J. van der Zant, and G. a Steele, "Deterministic transfer of two-dimensional materials by all-dry viscoelastic stamping," 2D Mater. 1, 11002 (2014). 10. G. te Velde, F. M. Bickelhaupt, E. J. Baerends, C. Fonseca Guerra, S. J. A. van Gisbergen, J. G. Snijders, and T. Ziegler, "Chemistry with ADF," J. Comput. Chem. 22, 931–967 (2001). 11. C. F. Guerra, J. Snijders, G. te Velde, and E. J. Baerends, "Towards an order-N DFT method," Theor. Chem. Acc. 99:391, (1998). 12. T. N. Vrije Universiteit, Amsterdam, "ADF2017, SCM, Theoretical Chemistry," (2016). 13. E. Van Lenthe and E. J. Baerends, "Optimized Slater-Type Basis Sets for the Elements 1 – 118," J. Comput. Chem. 24, 1142–1156 (2003). 14. B. Ravel and M. Newville, "ATHENA, ARTEMIS, HEPHAESTUS: data analysis for X-ray absorption spectroscopy using IFEFFIT," J. Synchrotron Rad. 12, 537–541 (2005). 15. T. Hemraj-Benny, S. Banerjee, S. Sambasivan, M. Balasubramanian, D. A. Fischer, G. Eres, A. A. Puretzky, D. B. Geohegan, D. H. Lowndes, W. Han, J. A. Misewich, and S. S. Wong, "Near-edge X-ray absorption fine structure spectroscopy as a tool for investigating nanomaterials," Small 2, 26–35 (2006). 16. B. Watts, L. Thomsen, and P. C. Dastoor, "Methods in carbon Kedge NEXAFS: Experiment and analysis," J. Electron Spectros. Relat. Phenomena 151, 105–120 (2006). 17. G. Comelli, J. Stöhr, W. Jark, and B. B. Pate, "Extended x-rayabsorption fine-structure studies of diamond and graphite," Phys. Rev. B 37, 4383 (1988). 18. A. Gaur, B. D. Shrivastava, and H. L. Nigam, "X-Ray Absorption Fine Structure (XAFS) Spectroscopy – A Review," Proc Indian Natn Sci Acad 79, 921–966 (2013). 19. S. Kelly, D. Hesterberg, and B. Ravel, "Analysis of soils and minerals using X-ray absorption spectroscopy.," Methods Soil Anal. Part 5 Mineral. Methods. SSSA 387–464 (2008). 20. J. J. Rehr, J. J. Kas, F. D. Vila, M. P. Prange, and K. Jorissen, "Parameter-free calculations of X-ray spectra with FEFF9," Phys.
Chem. Chem. Phys. 12, 5503–5513 (2010). 21. D. Koningsberger and C. Prins, X Ray Absorption: Principles, Applications, Techniques of EXAFS, SEXAFS and XANES (John Wiley & Sons, 1988).
Dispersive soft X-ray absorption fine-structure spectroscopy in graphite with an attosecond pulse: supplementary material BÁRBARA BUADES1, DOOSHAYE MOONSHIRAM2, THEMISTOKLIS P. H. SIDIROPOULOS 1, IKER LEÓN1, PETER SCHMIDT1, IRINA PI1, NICOLA DI PALO1, SETH L. COUSIN1, ANTONIO PICÓN1,3, FRANK KOPPENS1,4, JENS BIEGERT1,4,* 1ICFO-Institut 2Max
de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain Planck Institute for Chemical Energy Conversion, Stiftstr. 34-36, D-45470, Mülheim an der Ruhr, Germany
3Grupo
de Investigación en Aplicaciones del Láser y Fotónica, Departamento de Física Aplicada, University of Salamanca, E-37008 Salamanca, Spain 4ICREA,
Pg. Lluis Companys 23, 08010 Barcelona, Spain * Corresponding author: [email protected] Published 25 April 2018
This document contains supplementary information to “Dispersive soft X-ray absorption finestructure spectroscopy in graphite with an attosecond pulse,” https://doi.org/10.1364/OPTICA.5.000502. It contains details of the experimental methods, the sample preparation and the simulations with a brief description of the software used for the data analysis and a detailed extraction of the results.
1. EXPERIMENTAL METHODS Soft X-ray attosecond pulses are produced by high harmonic generation (HHG) driven by CEP stable 12 fs (1.8-cycle), 1850 nm pulses at a repetition rate of 1 kHz [1]. These pulses are derived from the 7 mJ, 40 fs output of a Ti:Sapphire system which is frequency converted to 1850 nm in a high-energy TOPAS (Light Conversion). Afterwards, the pulses nonlinearly propagate in a hollow core fibre filled with 1.5 bar of argon, and are chirp compensated with bulk material [1–3]. The resulting sub-2-cycle pulses at 1850 nm are focused using a 100-mm focal length mirror to a peak intensity of 0.5 PW/cm2 to generate high harmonic radiation. The exact setup and conditions for HHG are described in [4,5]. The emerging soft X-ray attosecond pulse [6] is focused using an ellipsoid mirror at 2 degree grazing incidence onto the 95nm graphite sample. A 100-nm thin aluminium foil is placed along the beam propagation to remove any remaining fundamental radiation. The transmitted radiation is spectrally resolved with a homebuilt spectrograph consisting of a flat-field imaging grating (Hitachi, 2400 lines/mm) and a Peltier-cooled, back-illuminated charge-coupled device camera (PIXIS-XO-2048B, Princeton Instruments).
A. Soft X-ray attosecond pulse graphite response Figure Fig. S1 shows the transmitted signal, S, measured through the 95-nm graphite sample that rests on a 50 nm Si3N4 membrane together with the reference signal, S 0, measured through a 50 nm Si3N4 membrane.
Fig. S1. CEP-controlled soft X-ray attosecond pulses generated in helium (8.25 bar). The blue curve indicates the detected spectral photon counts/s of the reference signal, S0, after propagating the SXR beam through a Si3N4 50 nm membrane. The red curve
2
accounts for the transmitted signal, S, through a 95-nm graphite flake resting on a 50-nm Si3N4 membrane. This signal shows XANES features at 284 eV and EXAFS oscillations up to 200 eV above the absorption edge. Both plots are the average over 6 spectra taken with 10 second integration time. The strong S0 spectral depletion at the carbon K-shell edge arises from the absorption of hydrocarbons on the surface of the Si 3N4 membrane.
Here, XANES measurements shown in the main manuscript in Fig. 2 as function of the incident angle are compared with published data. Table S1 show excellent agreement with published values. Table S1. Relative peak intensity of (1𝑠 → 𝜋*)/(1𝑠 → 𝜎∗ ) transition as a function of the incidence angle compared with values in the literature. Incidence Total Scanning XANES angle Electric Transmission shown in Yield [7] Microscopy [8] Fig.1 00 0.03 0.01 0.02 0.02 200 0.25 0.19 0.32 0.02 350 0.70 0.62 0.55 0.02 The energy separation between both transitions 1𝑠 → 𝜋* and 1𝑠 → 𝜎∗ is constant and equal to 6.6 eV with is in agreement with Ref. [8].
2. SAMPLE PREPARATION A graphite flake with a homogenous thickness of 95 nm across an area larger than 50 µm in diameter is obtained using a dry-transfer technique similar to [9]. Graphite flakes are exfoliated and deposited on a transparent polymer (Gel-Pak gelfilms). Suitable flakes are identified under an optical microscope and transferred onto a 50-nm Si3N4 membrane using a micromanipulator stage. We note that the graphite samples are never in contact with any wet solvents, therefore minimizing their contamination while maintaining an atomically flat surface. After the transfer, we inspect the uniformity and thickness of the graphite flake by means of optical and atomic force microscopy (AFM). Finally, a pinhole with a diameter of 50 µm is placed onto the sample to define the area of interaction.
3. SIMULATIONS The structure of graphene and the material’s relevant wavefunctions were calculated with the density functional theory (DFT) code BAND [10–12] using a local density approximation (LDA) exchange correlation functional with triple zeta plus double polarization basis set [13]. The EXAFS data processing used the Athena and Artemis software packages [14]. The EXAFS data analysis proceeds along well-established steps [15–19], and included the extraction of the signal from the normalized spectrum by subtracting a spline polynomial, normalization of the signal to the edge jump, and conversion of energy to wave-vector scale. Then the Fourier transform magnitude is determined using a Hanning window function to minimize the effects of data truncation. Scattering amplitudes and phases are calculated with FEFF [20]. A. EXAFS analysis The Athena and Artemis software packages [14] were used for data processing. Data in energy space are pre-edge corrected, normalized, deglitched (if necessary), and background corrected. The processed data are next converted to the photoelectron wave vector (k) space. The electron wave number is defined 𝑘 =
[2𝑚(𝐸 − 𝐸0 )ℏ2 ]1/2 where E0 is the energy origin or the threshold energy. k-space data were truncated near the zero crossings (k = 1.180 to 6.9 Å-1) in EXAFS before Fourier transformation. The kspace data are transferred into the Artemis Software for curve fitting. In order to fit the data, the Fourier peaks are isolated separately, grouped together, or the entire (unfiltered) spectrum was used. The individual Fourier peaks were isolated by applying a Hanning window to the first and last 15% of the chosen range, leaving the middle 70% untouched. Curve fitting is performed using ab initio-calculated phases and amplitudes from the FEFF8 [20] program and ab initio-calculated phases and amplitudes are used in the EXAFS equation [21] −2𝑅
𝜒(𝑘) = 𝑆02 ∑ 𝑗
𝑗 𝑁𝑗 −2𝜎𝑗2 𝑘 2 𝜆𝑗 (𝑘) 𝑓 𝑘, 𝑅 𝑒 𝑒 (𝜋, 𝑗) 𝑘𝑅𝑗2 𝑒𝑓𝑓𝑗
× sin (2𝑘𝑅𝑗 + Φ𝑖𝑗 (𝑘)) ,
(𝑺𝟏)
where Nj is the number of atoms in the jth shell; Rj the mean distance between the absorbing atom and the atoms in the jth shell; 𝑓𝑒𝑓𝑓𝑗 (𝜋, 𝑘, 𝑅𝑗 ) is the ab initio amplitude function for shell j, and the Debye-Waller term exp(−2𝜎𝑗2 𝑘 2) accounts for damping due to static and thermal disorder in absorber-backscatterer distances. The mean free path term exp(2𝑅𝑗 /𝜆𝑗 (𝑘)) reflects losses due to inelastic scattering, where λj(k), is the electron mean free path. The oscillations in the EXAFS spectrum are reflected in the sinusoidal term sin (2𝑘𝑅𝑗 + Φ𝑖𝑗 (𝑘)), where Φ𝑖𝑗 (𝑘) is the ab initio phase function for shell j. This sinusoidal term shows the direct relation between the frequency of the EXAFS oscillations in k-space and the absorber-back scattered distance. 𝑆02 is an amplitude reduction factor. The EXAFS equation (Eq. (S1)) is used to fit the experimental Fourier transformed data (in R-space) as well as unfiltered data (in k-space) using N, 𝑆02 , E0, R, and 𝜎 2 as variable parameters. N refers to the number of coordination atoms surrounding C for each shell. The quality of fit is evaluated by R-factor and the reduced 2 value. The deviation in E0 was required to be less than or equal to 10 eV. An R-factor less than 2% denotes that the fit is good enough whereas an R-factor between 2 and 5% denotes that the fit is correct within a consistently broad model [21]. The reduced 2 value is used to compare the quality of the fit as more absorberbackscatter shells are included to fit the data. A smaller reduced 2 value indicates a better fit. Similar results were obtained from fits done in k, q, and R-spaces. Table S2 shows the chosen variable parameters to minimise the reduced 2for two different fits. One with the inclusion of the second and third neighbour atoms and a second one with all neighbouring shells taken individually. The second fit with taking individually each neighbour shell improves the EXAFS fit since it has a smaller reduced 2 parameter. The amplitude reduction factor, 𝑆02 is fixed to 1 and the fit is carried out between 0.75 Å and 4 Å. Table S2. EXAFS Fit parameters of Graphite. Fit Shell R (Å) E0(eV) 2 N 1 C-C1, 3 1.64(3) 1.47 0.0161 C-C2,3, 9 2.95(5) 0.0109 C-C4, 6 4.04(7) 0.0144 2 C-C1,3 1.66(4) 2.97 0.0219 C-C2,6 2.58(12) 0.0353 C-C3,3 2.92(3) 0.0289 C-C4,6 4.01(10) 0.0118
R-factor
2 Reduced
0.024
315
0.009
195
3
The amplitude reduction factor, 𝑆02 was fixed to 1. The fit was carried out between 0.75 - 4 Å. R error bars to 100th of Å.
REFERENCES 1. S. L. Cousin, F. Silva, S. Teichmann, M. Hemmer, B. Buades, and J. Biegert, "High-flux table-top soft x-ray source driven by sub-2-cycle, CEP stable, 185-μm 1-kHz pulses for carbon K-edge spectroscopy," Opt. Lett. 39, 5383–5386 (2014). 2. N. Ishii, K. Kaneshima, K. Kitano, T. Kanai, S. Watanabe, and J. Itatani, "Carrier-envelope phase-dependent high harmonic generation in the water window using few-cycle infrared pulses," Nat. Commun. 5, 3331 (2014). 3. B. E. Schmidt, P. Béjot, M. Giguère, A. D. Shiner, C. Trallero-Herrero, E. Bisson, J. Kasparian, J.-P. Wolf, D. M. Villeneuve, J.-C. Kieffer, P. B. Corkum, and F. Légaré, "Compression of 1.8 μm laser pulses to sub two optical cycles with bulk material," Appl. Phys. Lett. 96, 121109 (2010). 4. S. M. Teichmann, F. Silva, S. L. Cousin, M. Hemmer, and J. Biegert, "0.5-keV Soft X-ray attosecond continua," Nat. Commun. 7, 11493 (2016). 5. F. Silva, S. M. Teichmann, S. L. Cousin, M. Hemmer, and J. Biegert, "Spatiotemporal isolation of attosecond soft X-ray pulses in the water window," Nat. Commun. 6, 6611 (2015). 6. S. L. Cousin, N. Di Palo, B. Buades, S. M. Teichmann, M. Reduzzi, M. Devetta, A. Kheifets, G. Sansone, and J. Biegert, "Attosecond Streaking in the Water Window: A New Regime of Attosecond Pulse Characterization," Phys. Rev. X 7, 41030 (2017). 7. R. A. Rosenberg, P. J. Love, and V. Rehn, "Polarization-dependent C(K) near-edge x-ray-absorption fine structure of graphite," Phys. Rev. B 33, 4034 (1986). 8. J. A. Brandes, G. D. Cody, D. Rumble, P. Haberstroh, S. Wirick, and Y. Gelinas, "Carbon K-edge XANES spectromicroscopy of natural graphite," Carbon 46, 1424–1434 (2008). 9. A. Castellanos-Gomez, M. Buscema, R. Molenaar, V. Singh, L. Janssen, H. S. J. van der Zant, and G. a Steele, "Deterministic transfer of two-dimensional materials by all-dry viscoelastic stamping," 2D Mater. 1, 11002 (2014). 10. G. te Velde, F. M. Bickelhaupt, E. J. Baerends, C. Fonseca Guerra, S. J. A. van Gisbergen, J. G. Snijders, and T. Ziegler, "Chemistry with ADF," J. Comput. Chem. 22, 931–967 (2001). 11. C. F. Guerra, J. Snijders, G. te Velde, and E. J. Baerends, "Towards an order-N DFT method," Theor. Chem. Acc. 99:391, (1998). 12. T. N. Vrije Universiteit, Amsterdam, "ADF2017, SCM, Theoretical Chemistry," (2016). 13. E. Van Lenthe and E. J. Baerends, "Optimized Slater-Type Basis Sets for the Elements 1 – 118," J. Comput. Chem. 24, 1142–1156 (2003). 14. B. Ravel and M. Newville, "ATHENA, ARTEMIS, HEPHAESTUS: data analysis for X-ray absorption spectroscopy using IFEFFIT," J. Synchrotron Rad. 12, 537–541 (2005). 15. T. Hemraj-Benny, S. Banerjee, S. Sambasivan, M. Balasubramanian, D. A. Fischer, G. Eres, A. A. Puretzky, D. B. Geohegan, D. H. Lowndes, W. Han, J. A. Misewich, and S. S. Wong, "Near-edge X-ray absorption fine structure spectroscopy as a tool for investigating nanomaterials," Small 2, 26–35 (2006). 16. B. Watts, L. Thomsen, and P. C. Dastoor, "Methods in carbon Kedge NEXAFS: Experiment and analysis," J. Electron Spectros. Relat. Phenomena 151, 105–120 (2006). 17. G. Comelli, J. Stöhr, W. Jark, and B. B. Pate, "Extended x-rayabsorption fine-structure studies of diamond and graphite," Phys. Rev. B 37, 4383 (1988). 18. A. Gaur, B. D. Shrivastava, and H. L. Nigam, "X-Ray Absorption Fine Structure (XAFS) Spectroscopy – A Review," Proc Indian Natn Sci Acad 79, 921–966 (2013). 19. S. Kelly, D. Hesterberg, and B. Ravel, "Analysis of soils and minerals using X-ray absorption spectroscopy.," Methods Soil Anal. Part 5 Mineral. Methods. SSSA 387–464 (2008). 20. J. J. Rehr, J. J. Kas, F. D. Vila, M. P. Prange, and K. Jorissen, "Parameter-free calculations of X-ray spectra with FEFF9," Phys.
Chem. Chem. Phys. 12, 5503–5513 (2010). 21. D. Koningsberger and C. Prins, X Ray Absorption: Principles, Applications, Techniques of EXAFS, SEXAFS and XANES (John Wiley & Sons, 1988).
