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Oct 1, 2018 - Chris Sturm,. §. Jan Griebel,. † ... Universität Leipzig, Felix-Bloch-Institut für Festkörperphysik, Linnéstr. 5, 04103 Leipzig, ...
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C: Physical Processes in Nanomaterials and Nanostructures

Photo-Induced-Heating of Graphitized Nanodiamonds Monitored by the Raman-Diamond-Peak Christian Laube, Jessica Hellweg, Chris Sturm, Jan Griebel, Marius Grundmann, Axel Kahnt, and Bernd Abel J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b09164 • Publication Date (Web): 01 Oct 2018 Downloaded from http://pubs.acs.org on October 16, 2018

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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

Photo-Induced-Heating of Graphitized Nanodiamonds Monitored by the Raman-DiamondPeak

Christian Laubea,b, Jessica Hellwega, Chris Sturmc, Jan Griebela, Marius Grundmannc, Axel Kahnta*, Bernd Abela,b*

a

Leibniz-Institute of Surface Engineering (IOM), Permoserstr. 15, 04318 Leipzig, Germany

b

Wilhelm-Ostwald-Institute for Physical and Theoretical Chemistry, University of Leipzig, Linnéstr. 2, 04103 Leipzig, Germany

c

Universität Leipzig, Felix-Bloch-Institut für Festkörperphysik, Linnéstr. 5, 04103 Leipzig, Germany

ABSTRACT

Raman Scattering investigations of the diamond peak properties of nanodiamonds with a size of 25 nm were performed in terms of temperature and laser power dependency. A similar trend of a bathochromic shift with increasing temperature and laser power was found, indicating the optical

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induced heating mechanism to be one of the main influencing factors on the Raman scattering behavior of nanodiamonds. As a direct consequence, nanodiamond particle impurities such as graphite have an indirect influence on the diamond peak properties by means of enhanced optical absorption of the particle, resulting in a higher rate of photo-induced heating. The results presented here are not only supplementing the list of influencing factors on the Raman scattering properties of nanodiamonds, they also demonstrate that even a low graphite content leads to local particle temperature differences in the range of hundreds °C already at low laser intensities 4

5

within the range of 10 -10 W/cm-2 with a substantial effect on the Raman spectrum of the nanodiamonds. This effect needs to be considered in numerous potential applications utilizing nanodiamonds as sensors.

Introduction Nanodiamonds (NDs) have recently received considerable attention in fundamental science and analytical applications within last the two decades.1-4 This is mostly based on the broad range of different properties of the ND such as the outstanding mechanical robustness,5 the biocompatibility,6 the high sensory potential of lattice inserted color centers7 and the versatile possibilities of surface modification.4 Another main characteristic of NDs is its surface graphite content that is an ubiquitous contamination of pristine NDs as it is formed as a by-product during the synthesis of the ND.8 Due to its properties, the surface graphite content has strong influences on the optical, electronic and chemical properties of the ND, and thus, on the suitability of the NDs for electronic, photocatalytic and medical applications.9-10 For example; the decrease of the biocompatibility of the NDs and increased oxidative stress in cells with increasing surface graphite coverage.11

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This in regard, the control of the surface graphite content of NDs and a deep understanding of the influence of the graphite on the NDs properties is of essential importance for the applicability of this highly promising nanomaterial. In the light of the latter, Raman spectroscopy became the method of choice for the determination of the diamond lattice quality and the surface graphite content.12-13 The Raman spectrum of graphitized nanodiamonds is characterized by the diamond peak (DP) located at 1332 cm-1, corresponding to the vibrations of the two interpenetrating cubic sub-lattices5, 14 and the graphite related D and G band.14-15 Herein, the G band is related to the doubly degenerate E2g symmetry phonon mode of the sp² network and the D peak is caused by disordered structures of graphite.15 To the best of our knowledge, even the Raman scattering effect of graphite was intensively studied under multiple conditions and for diverse carbon materials, a relation or influence of the graphite content on the Raman DP of NDs was only briefly suggested in literature but neither proven nor investigated in details so far.16 In addition to this, there is still an open discussion about the interpretation of the diamond peak shape and positon of NDs as it is dependent on several characteristics of the ND particle.17

18-19

So for the

Diamond-Peak-Position (DPP) of NDs a bathochromic shift is often observed compared to bulk diamonds.14,

17-18, 20

Osswald et al. discussed the bathochromic shift as a phonon confinement

effect due to the finite prolongation of the excited phonons with reduced particle size.17 Li et al. regarded lattice stress due to higher contents of dangling bonds as origin of the effect.18 Mochalin et al. also suggested surface effects as an origin for observed bathochromic shift.20 Alternatively, laser-induced heating resulting in the bathochromic shift of the DPP, was considered in literature16,

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referring to earlier investigation of the temperature effect on bulk

diamonds.21-24 Thus, the temperature dependence of Raman peaks is caused by anharmonic effects of lattice vibrations. In particular, the changes of the normal mode frequency can be

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explained by an implicit term related thermal lattice expansion effect and an explicit term corresponding to the population of higher vibration levels resulting in phonon-phonon interactions deriving from the cubic and quartic terms of the self-energy.25-27 The temperature influence on the DPP needs to be recognized with special emphasis since it offers a great potential for noncontact, nanoscale resolution, temperature sensory applications. The possibility to examine local temperatures of NDs could be of great importance, especially for the growing field of diamond-based electronic devices,28 since the lattice properties29 and the local temperature30-32 directly affects the performance of electronic devices. Also it is easily comprehensible that graphite layers, which exhibit a higher optical absorption than pure NDs, at the surface of the ND may result in an enhanced local optical heating of the ND, which could influence the DPP of the ND due to the increased temperature. Therefore, surface graphite should have an effect on the DPP or in other words the DPP offers a new potential approach to investigate and monitor surface graphite formation. Another appearing potential application for graphitized NDs is its use in nanoscale laser intensity sensory applications utilizing the graphite enhance optical heating effect in combination with a DPP read out. Furthermore, the control of the photo-induced heating of individual NDs could open a wide field for applications such as nano-structuring, new ablation approaches, laser-induced chemical reaction control as well as medical applications by means of photo-thermal-therapy. Regarding the relevance and the multiple fields of potential application, we report on a comprehensive but compact study investigating the temperature and excitation intensity response of the Raman DDP in relation to the surface graphite content. Herein, we benefit from our previous works where we already demonstrate the controlled removal33 and formation34 of graphite layers on the surface of NDs, and thus, offer an essential foundation for this work.

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Experimental Section Materials and Graphitization The commercial nanodiamonds (GND) (MSY 0.0 - 0.05) were purchased from the Microdiamant AG (Lengwil, Switzerland). These diamonds were produced by a HighTemperature- High- Pressure- Process (HTHP). The size distribution of the achieved nanodiamonds was determined using dynamic light scattering (Malvern Zetasizer), giving an averaged size distribution of D (n = 0.5) = 50 nm. The pristine GND consist of a high graphite content and were treated at 590°C under air atmosphere for different duration times. After 17 hours, a full oxidation removal of the graphite content was achieved (OND) D(n = 0.5) = 30 nm. The controlled graphitization of the OND samples (BND) was performed in argon atmosphere at different temperatures 650 - 1000°C for 5 hours. Raman spectroscopy The Raman spectra were recorded using the second harmonic of a Nd:YAG (532 nm, beam diameter: 2.25 mm), coupled into an inverted microscope (IX71, Olympus). The light was focused and collected in a backscattering geometry by a 40x objective (Olympus, LucPlanFLN) with a numerical aperture (NA) of 0.6. The focused laser spot diameter was determined by d(laserspot) = 1.22·λex/NA to be 1.08 µm. The spectra were recorded using a iHR320 spectrometer (Horiba), equipped with a 1800 g grating and a Synapse CCD device (Horiba). The spectral resolution was chosen to be 1 cm-1. The heating experiments were carried out using a 10x objective (Olympus, UPlanFlN) with NA of 0.3, spot diameter: 2.16 µm to ensure a working distance of about 1 cm. The temperature was established via a resistance heated ceramic element equipped with a PT100 element for temperature control. For the Raman scattering experiments using λex = 325 nm, a HeCd laser (Kimmon) was utilized. The light was focused and collected in

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backscattering geometry by a 50× UV–corrected microscope objective with a numerical aperture of 0.4. The spectra were recorded using a JobinYvon U1000 double spectrometer equipped with two gratings with 2400 grooves per millimeter and a liquid-nitrogen-cooled charge coupled device. The spectral resolution was chosen to be less than 1 cm-1. Attenuated total reflectance Infrared spectroscopy (ATR) The infrared spectra were measured using a VECTOR 22 (Bruker) combined with an attenuated total reflectance module (“Golden Gate”, Graseby, Specac). For all samples 128 scans were averaged. X-ray Photoelectron Spectroscopy (XPS) XPS analysis was carried out on a Kratos Axis Ultra (KratosAnalytical, Ltd., Manchester, United Kingdom) with a monochromatized Al excitation source at 150 W (15 kV, 10 mA, with pass energy of 40 eV). Surface spectra were collected over a range of 0 - 1200 eV. The nominal resolutions were 1.0 eV for the survey (pass energy = 160 eV) and 0.1 eV for the high-resolution scans (pass energy = 40 eV), respectively. The binding energies were corrected for the static charging of the samples by reference to the C1s main peak fixed at a binding energy of 284.8 eV. Thermogravimetric analysis (TGA) For the TGA measurement a Pyris 1 (PerkinElmer) Thermo gravimeter was used. The heating rate was 10°C/min under air atmosphere for a temperature range from 50°C to 800°C. UV-Vis spectroscopy using integrating sphere The UV/Vis spectra in reflection mode were recorded on a CARY 5000 (AGILENT) with a DRA-2500 unit (DRA: diffuse reflection accessory) with 150 mm diameter and a polytetrafluoroethylene coating. Results and Discussions

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For the investigation of the influence of the graphite content, temperature and photo heating of NDs on the DPP, NDs with well-defined graphite content were prepared and characterized using recently established protocols.33-34 As reference material for ND without a surrounding graphite layer, oxygen functionalized NDs (OND) were employed.33 The NDs were pressed into pellets to ensure homogeneous heat distribution and lower convection causing a cooling of the NDs.‡ The observed changes of the diamond peak at different temperatures and laser powers are illustrated in figure 1a and 1b. Figure 1c and 1d illustrates the laser power and temperature dependence of the DPP of OND in the range up to 111 mW (2.9 MW/cm-2) and 300°C. For a temperature of 25°C and a laser power of 11 mW, chosen as starting point for both experiments, a DPP of about (1331.7 ± 0.3) cm-1 was determined. The maximum observed standard deviation over all investigated temperature points was determined to be 0.86 cm-1 (see figure 1c for the error bars for each data point). Only a small DPP shift was seen up to 50°C, followed by a quasilinear progression at higher temperatures.# This trend agrees with the temperature dependence of the DPP of bulk diamonds published by several groups, discussing a saturation trend towards lower temperatures.25, 27, 35-36 The trend can be understood by the less pronounced influence of the explicit term at lower temperatures. In order to describe the temperature behaviour, several fitting approaches were proposed in literature.22,

35-36

For this work, the empirical expression

published by Cui et al.35 

  =  − [ ( ⁄)] ,  

(1)

was used as they demonstrated superior accuracy for the fitting of the temperature dependence of the DPP in case of bulk diamonds. Herein, ωT is the DPP at temperature T, ω0 is the DPP at T = 0 K; h, c and k denote the Planck constant, the speed of light and the Boltzmann constant. C and D are fit parameters. In order to compare our results with the results of Cui et al., a fit of the

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data using equation 1 with and without a fixed ω0 value of 1333 cm-1 was performed. C = 26.8, D = 0.477 were obtained for the fit with fixed ω0 and C = 36.38, D = 0.561 and ω0 = 1332.64 cm-1 for the three parameter fit. These C- and D-values differ from the bulk value of C = 61.14, D = 0.787, obtained by Cui et al.35

Figure 1 Temperature dependence of the DPP and FWHM for λex = 532 nm, 10x objective, NA: 0.3: a) Raman spectra in the range between (1275–1400) cm-1 for different temperatures, b) Raman spectra in the range between (1275–1400) cm-1 for different laser power. c) Temperature (red) measured for 11 mW and laser power (black) dependence of the DPP. d) Temperature (red) and laser power (black) dependence of the FWHM, comparison of the DPP shift (∆DPP) with the FWHM.&

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The most feasible explanation for the observed differences in fitting parameters are size-related effects like different heat conductivity37 and surface effects20 whereas lattice impurities are assumed to have a negligible impact on the temperature dependence of the DPP.38 Note, the lower investigated temperature range compared to literature35 also needs to be considered. As stated above, the fit of the shift of the DPP follows a linear trend in the temperature range between 50 - 300°C with a determined progression slope of -0.01945 cm-1/K. This value is within the range of literature values for the temperature effect of Raman peak shifts of other nanomaterial and graphite related materials, commonly ranging from 0.01 cm-1/K to 0.035 cm1

/K.39-42 The laser power dependence of the DPP shift follows a curve with a similar progression to the

temperature profile, indicating a correlation of the laser power and the local temperature. The maximum observed standard deviation over all investigated Laser power settings was determined to be 1.22 cm-1. For the laser power range from 16 mW to 111 mW, the laser power dependence of the DPP follows a linear trend with a slope of 0.11 cm-1/mW for a focus spot diameter of 2.16 µm. From the observed data of the temperature and laser intensity dependence, a laser-induced heating of the OND sample of 5.6 K/mW was derived under the chosen conditions, suggesting the laser induced heating being the only reason for the bathochromic shift of the DPP. For the interpretation of the results of the laser-induced heating at a laser power above 111 mW, the nonadiabatic conditions during the experiment need to be taken into account. In turn, the curve progression deviates from the linear trend into a saturation curve (SI-SI3) due to considerable heat exchange with the surroundings. Moreover, the offset of the saturation curve indicates the degradation temperature of the ND (SI-SI3). Figure 1b illustrates the FWHM to DPP relation for thermal heating and optical heating experiments. Both approaches exhibit a broadening of the

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diamond peak with increasing temperature up to 300°C and laser power up to 64 mW. The broadening can be explained by the decreased phonon lifetime, due to higher decay rates of the Brillouin- zone-center optical phonon decay into two acoustical phonons with increasing temperature as described in the Klemens model.43 The observed nearly linear relation between the FWHM and ∆DPP (Figure 1d) is well in line with the results of Liu et al. who took this as an indicator that only the cubic anharmonic decay channel contributes to the temperature dependence of linewidth and peak shift, whereas thermal expansion and the quadric anharmonic term can be excluded since they cancel each other out.25-26, 44 Interestingly, the laser induced heating exhibits a much more pronounced peak broadening up to FWHM of 12.4 cm-1 (∆FWHM = 7.3 cm-1) compared to the effect observed by thermal heating FWHM of 7.2 cm-1 (∆FWHM = 1.4 cm-1) for the same DPP value. The observed maximum standard deviations over all investigated data points were determined to be 0.65 cm-1 for the energy variation and 0.51 cm-1 for the temperature variation. A possible explanation for the broader peak in the case of laser-induced heating is the inhomogeneous heat distribution within the sample due to the Gaussian shape of the laser spot profile. The results of the OND clearly suggest that the laser induced heating is the main reason for DPP shift in ND down to the size of 20 - 30 nm, which is in good agreement with previous studies.16,

19

However, as the photo-induced heating effect strongly depends on the optical

absorption of the sample, common impurities of the ND like graphite, that increase the optical absorption of the ND, are expected to show a strong effect on the DPP. With the aim to investigate the effect of the graphite impurities a controlled graphitization of the OND was performed utilizing an annealing approach under argon atmosphere. The OND were annealed at different temperatures for 5 hours where the temperature regulates the

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graphitization rate of the ND surface (BND).10, 45 A detailed discussion of the surface properties of the obtained BNDs can be found in the supporting information, utilizing attenuated total reflection infrared spectroscopy (ATR), photoelectron spectroscopy (XPS) and Raman spectroscopy (SI-SI5-9). The different transmittance of the annealed NDs was determined using a UV-Vis spectrometer, equipped with an integration sphere. The maximum standard deviation of the transmission values are within the range of 5 %. The recorded transmittance spectra displayed an increasingly broad band absorption in the range of 350 - 800 nm with proceeding graphitization (SI-SI10). The correlation between the transmittance at 532 nm and the DPP upon excitation at 532 nm with a laser power of 19 mW is illustrated in figure 2a. Both curves follow the same trend. For annealing up to 650°C, there is only a small decrease of transmittance and the DPP. However, at higher temperatures within the range of 650 - 850°C the transmittance decreases significantly by 35% and the DPP shifts by 9 cm-1. This is consistent with the onset temperature of the graphitization of the surface of the ND reported in literature occur in the range between 800 and 900°C.10 For annealing temperatures above 850°C, the curve turns into saturation, for both, transmittance and the DPP at 28% and 1319.8 cm-1 respectively. The similarity of the curve progressions of the transmittance and the DPP with increasing graphitization rate provides clear evidence for their correlation. This effect becomes even more significant when the laser power dependency of the DPP for BND annealed at different temperatures is investigated. Figure 2b illustrates the laser power dependency up to 36 mW. The observed maximum standard deviations over all investigated data points were determined to be 1.35 cm-1.

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Figure 2 Influence of graphite on the DPP for NDs treated at different annealing temperatures under argon atmosphere for 5 hours measured using λex = 532 nm, 40x objective, NA: 0.6: a) relation of the transmission at 532 nm with the Raman DPP (19 mW), b) laser power dependence of DPP for ND samples treated at different annealing temperatures: OND (black), 650°C (red), 700°C (blue), 800°C (green), 850°C (orange), 950°C (magenta) 1000°C (brown star). c) Raman

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DPP (19 mW) for different sample treatments (for GND different duration times t = 0 – 60 min at 590°C were investigated).& With increasing graphite content, the decrease of the DPP with increasing laser power becomes more pronounced. Comparing OND and BND samples, a small DDP change of about 3.5 cm-1 (at 187°C)§ occurs for OND, whereas for BND treated at 1000°C, a DDP shift of more than 15 cm-1 (at 665°C)§ can be observed. For the latter the laser heating equivalent of 665°C thermal heating is already within the degradation range of the ND. This difference of equivalent temperature of about 448°C§ illustrates the strong effect of the surface graphitization. The change of the curve progression from a linear to a saturated curve with increasing graphite content can be again interpreted by means of the non-adiabatic conditions of the experiment. Even though the temperature effect on the DPP becomes quite clear with the experiments, other influencing factors described in literature were not included in the discussion so far. On the one hand, annealing-based graphitization also leads to a decrease of the sp3-carbon volume inside the BND. This size effect needs to be considered. On the other hand, the change of the surface functionality and surface carbon hybridization may lead to internal lattice stress by means of bond deformation. As a consequence, the importance of the optically induced heating influence on the DPP compared to these other influencing factors needs to be tested. It should be noted that the importance of influencing factors will depend on the size of the ND, and thus, all conclusions made here are solely related for ND within the size (diameter) range of 20 - 30 nm. At first, the effects of small size changes due to sp³ to sp² carbon hybridization change were investigated. Transmission electron microscopic studies described in our previous work had pointed out that the formed graphite shell does not overcome a thickness of 1 - 2 nm for BND annealed at 1050°C.34 Furthermore, Osswald et al. pointed out that the size effect is marginal in case of

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particle diameter over 20 nm.17 This in regards, it can be assumed that the phonon confinement has a negligible effect on the DPP for the chosen particle size. Nevertheless, the effect can be evaluated easily by an extension of the investigations presented so far, including the graphitized pristine commercial starting material (GND) to OND. The DPP shift for a set of samples was measured, where GND were treated for different times at 590°C under air atmosphere. Under these conditions, a partial degraphitization, as well as a partial degradation of the sp³ carbon appears.46 As a consequence of this, the graphite content decreases for GND to OND and increases for OND to BND, whereas a decrease of the sp³ carbon content for GND to OND and OND to BND can be assumed. In case of a notable size effect of the ND a bathochromic shift of the diamond peak would occur in the same order. The Raman shift of the DPP for gradually converted material from GND to OND and from OND to BND under upon 532 nm excitation with laser power of about 19 mW, using a 40x objective, NA = 0.6 are shown in figure 2c. Analyzing figure 2c, it becomes obvious that the DPP follows the trend of a bathochromic peak shift towards lower wavenumbers with increasing graphite content. For GND to OND, a hypsochromic shift towards higher wavenumbers of more than 10 cm-1 occurs, whereas for the graphitization of OND to BND, the DPP follows the already described bathochromic shift. This confirms that the size reduction related confinement effect plays only a negligible role for the investigated 20 - 30 nm NDs, compared to the photo-induced heating effects due to the graphitized surface. Furthermore, to exclude lattice stress effects due to the surface graphitization as the origin of the signal shift, an experiment using a homogenous 1:1 mixture of BND treated at 1000°C and OND was performed for laser energies up to 68 mW. If an effect on the position of the diamond peak due to the local stress based on the surface graphitization was occurring, two diamond peaks would appear, due to the two species within the sample. But in fact, only one

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The Journal of Physical Chemistry

peak was observed. This result suggests that the DPP is only related to environmental equilibrium temperature settled around the NDs. This further corroborates our assumption that the shift of the DPP relates predominantly to the local temperature of the ND for our chosen experimental conditions. Conclusion The dependence of the diamond peak position (DPP) on the photo-induced heating of NDs and particle surface graphite content was investigated. Our results also demonstrate that beyond a number of recent sensoric applications of diamond materials employing NV centres47-49 also the Raman diamond peak of nanodiamonds can be employed as a specific temperature sensor. The temperature dependence was described by a simple linear relationship as well as by the empirical model of Cui et al.35 The Photo-induced heating up to the degradation temperature of the particle was monitored via the DPP. The results clearly demonstrate that this effect is the dominating influencing factor for the DPP and peak shape for the chosen experimental conditions. Furthermore, the effect is strongly dependent on the graphite content of the ND surface based on an indirect correlation due to the increased absorption rates of the particles with proceeding graphitization. Effects like phonon confinement and lattice stress play only a minor role for the DPP for the investigated particle size. Beyond the general importance of these results for the interpretation of Raman spectra of ND and the possible application of NDs as temperature sensor in devices, the strong and controllable photo-induced heating effect of the NDs may be of relevance for multiple applications like photocatalysis,50 photo thermal therapy,51 as well as laser-induced-ablation 52 and micro/nano-structuring applications. ASSOCIATED CONTENT Supporting Information.

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Supporting information is available free of charge on the ACS Publication website. Description and figures of the heating chamber for temperature dependent Raman spectroscopy, Thermogravimetrical-analysis, OND stability and Diamond peak position reproducibility test, ATR-IR spectra, XPS spectra, Raman spectra, UV-vis spectra, TEM images. AUTHOR INFORMATION Corresponding Author *Prof. Dr. Bernd Abel, [email protected] *Dr. Axel Kahnt, [email protected] Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Funding Sources German Science Foundation (DFG) through funds from SFB-TR 102 and SFB 762. Notes ‡

An illustration of the ceramic heating chamber can be found in SI-SI1. Due to the setup

parameter and experimental condition an uncertainty of 5°C for the temperature adjustment of the heating chamber can be assumed. A 10x objective, NA = 0.3 was used to realize a working distance of about 1 cm, necessary to avoid any temperature related influences of the optics was used. Nevertheless, the setup only allows temperature settings up to 300°C. For the characterization of the measured diamond peak a Voigt fit was used to determine the DDP as well as the full width at half maximum (FWHM) of the diamond peak. 53

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# By cooling the pellets to room temperature, the starting point of DPP could be regained. Nevertheless, a color change of the pellet occurs after heating at temperatures higher than 200°C, indicating a change of the ND surface functionality in agreement to the TGA results (see SI-SI2). A beginning decarboxylation is assumed as the reason of the changes. This result, on the other hand, proves that a low rate of surface defunctionalization can be neglected for the DPP shift dependency. § Temperature value was estimated via equation 1 with C = 26.8 cm-1, D = 0.477 and ω0 = 1333 cm-1. & Error bars were not inserted in order to improve the clarity of the graph the observed maximum standard deviation are stated within the discussion of the graph.

The authors declare no competing financial interests. ACKNOWLEDGMENT We want to thank Robert Konieczny and Sören Pyczak for the construction and building of the heating controller as well as Dr. Klaus Zimmer and Dr. Wolfgang Knolle for the valuable discussions. Support from the German Science Foundation (DFG) through funds from SFB-TR 102 and SFB 762 is gratefully acknowledged. REFERENCES (1) (2) (3)

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